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. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #define DEBUG_TYPE "scalar-evolution"
62 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/GlobalAlias.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/Operator.h"
70 #include "llvm/Analysis/ConstantFolding.h"
71 #include "llvm/Analysis/Dominators.h"
72 #include "llvm/Analysis/LoopInfo.h"
73 #include "llvm/Analysis/ValueTracking.h"
74 #include "llvm/Assembly/Writer.h"
75 #include "llvm/Target/TargetData.h"
76 #include "llvm/Support/CommandLine.h"
77 #include "llvm/Support/ConstantRange.h"
78 #include "llvm/Support/Debug.h"
79 #include "llvm/Support/ErrorHandling.h"
80 #include "llvm/Support/GetElementPtrTypeIterator.h"
81 #include "llvm/Support/InstIterator.h"
82 #include "llvm/Support/MathExtras.h"
83 #include "llvm/Support/raw_ostream.h"
84 #include "llvm/ADT/Statistic.h"
85 #include "llvm/ADT/STLExtras.h"
86 #include "llvm/ADT/SmallPtrSet.h"
90 STATISTIC(NumArrayLenItCounts,
91 "Number of trip counts computed with array length");
92 STATISTIC(NumTripCountsComputed,
93 "Number of loops with predictable loop counts");
94 STATISTIC(NumTripCountsNotComputed,
95 "Number of loops without predictable loop counts");
96 STATISTIC(NumBruteForceTripCountsComputed,
97 "Number of loops with trip counts computed by force");
99 static cl::opt<unsigned>
100 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
101 cl::desc("Maximum number of iterations SCEV will "
102 "symbolically execute a constant "
106 static RegisterPass<ScalarEvolution>
107 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
108 char ScalarEvolution::ID = 0;
110 //===----------------------------------------------------------------------===//
111 // SCEV class definitions
112 //===----------------------------------------------------------------------===//
114 //===----------------------------------------------------------------------===//
115 // Implementation of the SCEV class.
120 void SCEV::dump() const {
125 bool SCEV::isZero() const {
126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
127 return SC->getValue()->isZero();
131 bool SCEV::isOne() const {
132 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
133 return SC->getValue()->isOne();
137 bool SCEV::isAllOnesValue() const {
138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
139 return SC->getValue()->isAllOnesValue();
143 SCEVCouldNotCompute::SCEVCouldNotCompute() :
144 SCEV(FoldingSetNodeID(), scCouldNotCompute) {}
146 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
147 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
151 const Type *SCEVCouldNotCompute::getType() const {
152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
156 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
161 bool SCEVCouldNotCompute::hasOperand(const SCEV *) const {
162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
166 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
167 OS << "***COULDNOTCOMPUTE***";
170 bool SCEVCouldNotCompute::classof(const SCEV *S) {
171 return S->getSCEVType() == scCouldNotCompute;
174 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
176 ID.AddInteger(scConstant);
179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
180 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>();
181 new (S) SCEVConstant(ID, V);
182 UniqueSCEVs.InsertNode(S, IP);
186 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
187 return getConstant(ConstantInt::get(getContext(), Val));
191 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
193 ConstantInt::get(cast<IntegerType>(Ty), V, isSigned));
196 const Type *SCEVConstant::getType() const { return V->getType(); }
198 void SCEVConstant::print(raw_ostream &OS) const {
199 WriteAsOperand(OS, V, false);
202 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID,
203 unsigned SCEVTy, const SCEV *op, const Type *ty)
204 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
206 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
207 return Op->dominates(BB, DT);
210 bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
211 return Op->properlyDominates(BB, DT);
214 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID,
215 const SCEV *op, const Type *ty)
216 : SCEVCastExpr(ID, scTruncate, op, ty) {
217 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
218 (Ty->isInteger() || isa<PointerType>(Ty)) &&
219 "Cannot truncate non-integer value!");
222 void SCEVTruncateExpr::print(raw_ostream &OS) const {
223 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
226 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID,
227 const SCEV *op, const Type *ty)
228 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
229 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
230 (Ty->isInteger() || isa<PointerType>(Ty)) &&
231 "Cannot zero extend non-integer value!");
234 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
235 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
238 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID,
239 const SCEV *op, const Type *ty)
240 : SCEVCastExpr(ID, scSignExtend, op, ty) {
241 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
242 (Ty->isInteger() || isa<PointerType>(Ty)) &&
243 "Cannot sign extend non-integer value!");
246 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
247 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
250 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
251 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
252 const char *OpStr = getOperationStr();
253 OS << "(" << *Operands[0];
254 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
255 OS << OpStr << *Operands[i];
259 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
260 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
261 if (!getOperand(i)->dominates(BB, DT))
267 bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
268 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
269 if (!getOperand(i)->properlyDominates(BB, DT))
275 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
276 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
279 bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
280 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT);
283 void SCEVUDivExpr::print(raw_ostream &OS) const {
284 OS << "(" << *LHS << " /u " << *RHS << ")";
287 const Type *SCEVUDivExpr::getType() const {
288 // In most cases the types of LHS and RHS will be the same, but in some
289 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
290 // depend on the type for correctness, but handling types carefully can
291 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
292 // a pointer type than the RHS, so use the RHS' type here.
293 return RHS->getType();
296 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
297 // Add recurrences are never invariant in the function-body (null loop).
301 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
302 if (QueryLoop->contains(L))
305 // This recurrence is variant w.r.t. QueryLoop if any of its operands
307 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
308 if (!getOperand(i)->isLoopInvariant(QueryLoop))
311 // Otherwise it's loop-invariant.
315 void SCEVAddRecExpr::print(raw_ostream &OS) const {
316 OS << "{" << *Operands[0];
317 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
318 OS << ",+," << *Operands[i];
320 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
324 void SCEVFieldOffsetExpr::print(raw_ostream &OS) const {
325 // LLVM struct fields don't have names, so just print the field number.
326 OS << "offsetof(" << *STy << ", " << FieldNo << ")";
329 void SCEVAllocSizeExpr::print(raw_ostream &OS) const {
330 OS << "sizeof(" << *AllocTy << ")";
333 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
334 // All non-instruction values are loop invariant. All instructions are loop
335 // invariant if they are not contained in the specified loop.
336 // Instructions are never considered invariant in the function body
337 // (null loop) because they are defined within the "loop".
338 if (Instruction *I = dyn_cast<Instruction>(V))
339 return L && !L->contains(I);
343 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
344 if (Instruction *I = dyn_cast<Instruction>(getValue()))
345 return DT->dominates(I->getParent(), BB);
349 bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
350 if (Instruction *I = dyn_cast<Instruction>(getValue()))
351 return DT->properlyDominates(I->getParent(), BB);
355 const Type *SCEVUnknown::getType() const {
359 void SCEVUnknown::print(raw_ostream &OS) const {
360 WriteAsOperand(OS, V, false);
363 //===----------------------------------------------------------------------===//
365 //===----------------------------------------------------------------------===//
367 static bool CompareTypes(const Type *A, const Type *B) {
368 if (A->getTypeID() != B->getTypeID())
369 return A->getTypeID() < B->getTypeID();
370 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) {
371 const IntegerType *BI = cast<IntegerType>(B);
372 return AI->getBitWidth() < BI->getBitWidth();
374 if (const PointerType *AI = dyn_cast<PointerType>(A)) {
375 const PointerType *BI = cast<PointerType>(B);
376 return CompareTypes(AI->getElementType(), BI->getElementType());
378 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) {
379 const ArrayType *BI = cast<ArrayType>(B);
380 if (AI->getNumElements() != BI->getNumElements())
381 return AI->getNumElements() < BI->getNumElements();
382 return CompareTypes(AI->getElementType(), BI->getElementType());
384 if (const VectorType *AI = dyn_cast<VectorType>(A)) {
385 const VectorType *BI = cast<VectorType>(B);
386 if (AI->getNumElements() != BI->getNumElements())
387 return AI->getNumElements() < BI->getNumElements();
388 return CompareTypes(AI->getElementType(), BI->getElementType());
390 if (const StructType *AI = dyn_cast<StructType>(A)) {
391 const StructType *BI = cast<StructType>(B);
392 if (AI->getNumElements() != BI->getNumElements())
393 return AI->getNumElements() < BI->getNumElements();
394 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i)
395 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) ||
396 CompareTypes(BI->getElementType(i), AI->getElementType(i)))
397 return CompareTypes(AI->getElementType(i), BI->getElementType(i));
403 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
404 /// than the complexity of the RHS. This comparator is used to canonicalize
406 class SCEVComplexityCompare {
409 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
411 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
412 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
416 // Primarily, sort the SCEVs by their getSCEVType().
417 if (LHS->getSCEVType() != RHS->getSCEVType())
418 return LHS->getSCEVType() < RHS->getSCEVType();
420 // Aside from the getSCEVType() ordering, the particular ordering
421 // isn't very important except that it's beneficial to be consistent,
422 // so that (a + b) and (b + a) don't end up as different expressions.
424 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
425 // not as complete as it could be.
426 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
427 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
429 // Order pointer values after integer values. This helps SCEVExpander
431 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
433 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
436 // Compare getValueID values.
437 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
438 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
440 // Sort arguments by their position.
441 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
442 const Argument *RA = cast<Argument>(RU->getValue());
443 return LA->getArgNo() < RA->getArgNo();
446 // For instructions, compare their loop depth, and their opcode.
447 // This is pretty loose.
448 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
449 Instruction *RV = cast<Instruction>(RU->getValue());
451 // Compare loop depths.
452 if (LI->getLoopDepth(LV->getParent()) !=
453 LI->getLoopDepth(RV->getParent()))
454 return LI->getLoopDepth(LV->getParent()) <
455 LI->getLoopDepth(RV->getParent());
458 if (LV->getOpcode() != RV->getOpcode())
459 return LV->getOpcode() < RV->getOpcode();
461 // Compare the number of operands.
462 if (LV->getNumOperands() != RV->getNumOperands())
463 return LV->getNumOperands() < RV->getNumOperands();
469 // Compare constant values.
470 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
471 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
472 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
473 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
474 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
477 // Compare addrec loop depths.
478 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
479 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
480 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
481 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
484 // Lexicographically compare n-ary expressions.
485 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
486 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
487 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
488 if (i >= RC->getNumOperands())
490 if (operator()(LC->getOperand(i), RC->getOperand(i)))
492 if (operator()(RC->getOperand(i), LC->getOperand(i)))
495 return LC->getNumOperands() < RC->getNumOperands();
498 // Lexicographically compare udiv expressions.
499 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
500 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
501 if (operator()(LC->getLHS(), RC->getLHS()))
503 if (operator()(RC->getLHS(), LC->getLHS()))
505 if (operator()(LC->getRHS(), RC->getRHS()))
507 if (operator()(RC->getRHS(), LC->getRHS()))
512 // Compare cast expressions by operand.
513 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
514 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
515 return operator()(LC->getOperand(), RC->getOperand());
518 // Compare offsetof expressions.
519 if (const SCEVFieldOffsetExpr *LA = dyn_cast<SCEVFieldOffsetExpr>(LHS)) {
520 const SCEVFieldOffsetExpr *RA = cast<SCEVFieldOffsetExpr>(RHS);
521 if (CompareTypes(LA->getStructType(), RA->getStructType()) ||
522 CompareTypes(RA->getStructType(), LA->getStructType()))
523 return CompareTypes(LA->getStructType(), RA->getStructType());
524 return LA->getFieldNo() < RA->getFieldNo();
527 // Compare sizeof expressions by the allocation type.
528 if (const SCEVAllocSizeExpr *LA = dyn_cast<SCEVAllocSizeExpr>(LHS)) {
529 const SCEVAllocSizeExpr *RA = cast<SCEVAllocSizeExpr>(RHS);
530 return CompareTypes(LA->getAllocType(), RA->getAllocType());
533 llvm_unreachable("Unknown SCEV kind!");
539 /// GroupByComplexity - Given a list of SCEV objects, order them by their
540 /// complexity, and group objects of the same complexity together by value.
541 /// When this routine is finished, we know that any duplicates in the vector are
542 /// consecutive and that complexity is monotonically increasing.
544 /// Note that we go take special precautions to ensure that we get determinstic
545 /// results from this routine. In other words, we don't want the results of
546 /// this to depend on where the addresses of various SCEV objects happened to
549 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
551 if (Ops.size() < 2) return; // Noop
552 if (Ops.size() == 2) {
553 // This is the common case, which also happens to be trivially simple.
555 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
556 std::swap(Ops[0], Ops[1]);
560 // Do the rough sort by complexity.
561 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
563 // Now that we are sorted by complexity, group elements of the same
564 // complexity. Note that this is, at worst, N^2, but the vector is likely to
565 // be extremely short in practice. Note that we take this approach because we
566 // do not want to depend on the addresses of the objects we are grouping.
567 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
568 const SCEV *S = Ops[i];
569 unsigned Complexity = S->getSCEVType();
571 // If there are any objects of the same complexity and same value as this
573 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
574 if (Ops[j] == S) { // Found a duplicate.
575 // Move it to immediately after i'th element.
576 std::swap(Ops[i+1], Ops[j]);
577 ++i; // no need to rescan it.
578 if (i == e-2) return; // Done!
586 //===----------------------------------------------------------------------===//
587 // Simple SCEV method implementations
588 //===----------------------------------------------------------------------===//
590 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
592 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
594 const Type* ResultTy) {
595 // Handle the simplest case efficiently.
597 return SE.getTruncateOrZeroExtend(It, ResultTy);
599 // We are using the following formula for BC(It, K):
601 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
603 // Suppose, W is the bitwidth of the return value. We must be prepared for
604 // overflow. Hence, we must assure that the result of our computation is
605 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
606 // safe in modular arithmetic.
608 // However, this code doesn't use exactly that formula; the formula it uses
609 // is something like the following, where T is the number of factors of 2 in
610 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
613 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
615 // This formula is trivially equivalent to the previous formula. However,
616 // this formula can be implemented much more efficiently. The trick is that
617 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
618 // arithmetic. To do exact division in modular arithmetic, all we have
619 // to do is multiply by the inverse. Therefore, this step can be done at
622 // The next issue is how to safely do the division by 2^T. The way this
623 // is done is by doing the multiplication step at a width of at least W + T
624 // bits. This way, the bottom W+T bits of the product are accurate. Then,
625 // when we perform the division by 2^T (which is equivalent to a right shift
626 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
627 // truncated out after the division by 2^T.
629 // In comparison to just directly using the first formula, this technique
630 // is much more efficient; using the first formula requires W * K bits,
631 // but this formula less than W + K bits. Also, the first formula requires
632 // a division step, whereas this formula only requires multiplies and shifts.
634 // It doesn't matter whether the subtraction step is done in the calculation
635 // width or the input iteration count's width; if the subtraction overflows,
636 // the result must be zero anyway. We prefer here to do it in the width of
637 // the induction variable because it helps a lot for certain cases; CodeGen
638 // isn't smart enough to ignore the overflow, which leads to much less
639 // efficient code if the width of the subtraction is wider than the native
642 // (It's possible to not widen at all by pulling out factors of 2 before
643 // the multiplication; for example, K=2 can be calculated as
644 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
645 // extra arithmetic, so it's not an obvious win, and it gets
646 // much more complicated for K > 3.)
648 // Protection from insane SCEVs; this bound is conservative,
649 // but it probably doesn't matter.
651 return SE.getCouldNotCompute();
653 unsigned W = SE.getTypeSizeInBits(ResultTy);
655 // Calculate K! / 2^T and T; we divide out the factors of two before
656 // multiplying for calculating K! / 2^T to avoid overflow.
657 // Other overflow doesn't matter because we only care about the bottom
658 // W bits of the result.
659 APInt OddFactorial(W, 1);
661 for (unsigned i = 3; i <= K; ++i) {
663 unsigned TwoFactors = Mult.countTrailingZeros();
665 Mult = Mult.lshr(TwoFactors);
666 OddFactorial *= Mult;
669 // We need at least W + T bits for the multiplication step
670 unsigned CalculationBits = W + T;
672 // Calcuate 2^T, at width T+W.
673 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
675 // Calculate the multiplicative inverse of K! / 2^T;
676 // this multiplication factor will perform the exact division by
678 APInt Mod = APInt::getSignedMinValue(W+1);
679 APInt MultiplyFactor = OddFactorial.zext(W+1);
680 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
681 MultiplyFactor = MultiplyFactor.trunc(W);
683 // Calculate the product, at width T+W
684 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
686 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
687 for (unsigned i = 1; i != K; ++i) {
688 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
689 Dividend = SE.getMulExpr(Dividend,
690 SE.getTruncateOrZeroExtend(S, CalculationTy));
694 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
696 // Truncate the result, and divide by K! / 2^T.
698 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
699 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
702 /// evaluateAtIteration - Return the value of this chain of recurrences at
703 /// the specified iteration number. We can evaluate this recurrence by
704 /// multiplying each element in the chain by the binomial coefficient
705 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
707 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
709 /// where BC(It, k) stands for binomial coefficient.
711 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
712 ScalarEvolution &SE) const {
713 const SCEV *Result = getStart();
714 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
715 // The computation is correct in the face of overflow provided that the
716 // multiplication is performed _after_ the evaluation of the binomial
718 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
719 if (isa<SCEVCouldNotCompute>(Coeff))
722 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
727 //===----------------------------------------------------------------------===//
728 // SCEV Expression folder implementations
729 //===----------------------------------------------------------------------===//
731 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
733 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
734 "This is not a truncating conversion!");
735 assert(isSCEVable(Ty) &&
736 "This is not a conversion to a SCEVable type!");
737 Ty = getEffectiveSCEVType(Ty);
740 ID.AddInteger(scTruncate);
744 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
746 // Fold if the operand is constant.
747 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
749 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
751 // trunc(trunc(x)) --> trunc(x)
752 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
753 return getTruncateExpr(ST->getOperand(), Ty);
755 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
756 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
757 return getTruncateOrSignExtend(SS->getOperand(), Ty);
759 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
760 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
761 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
763 // If the input value is a chrec scev, truncate the chrec's operands.
764 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
765 SmallVector<const SCEV *, 4> Operands;
766 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
767 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
768 return getAddRecExpr(Operands, AddRec->getLoop());
771 // The cast wasn't folded; create an explicit cast node.
772 // Recompute the insert position, as it may have been invalidated.
773 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
774 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>();
775 new (S) SCEVTruncateExpr(ID, Op, Ty);
776 UniqueSCEVs.InsertNode(S, IP);
780 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
782 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
783 "This is not an extending conversion!");
784 assert(isSCEVable(Ty) &&
785 "This is not a conversion to a SCEVable type!");
786 Ty = getEffectiveSCEVType(Ty);
788 // Fold if the operand is constant.
789 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
790 const Type *IntTy = getEffectiveSCEVType(Ty);
791 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
792 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
793 return getConstant(cast<ConstantInt>(C));
796 // zext(zext(x)) --> zext(x)
797 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
798 return getZeroExtendExpr(SZ->getOperand(), Ty);
800 // Before doing any expensive analysis, check to see if we've already
801 // computed a SCEV for this Op and Ty.
803 ID.AddInteger(scZeroExtend);
807 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
809 // If the input value is a chrec scev, and we can prove that the value
810 // did not overflow the old, smaller, value, we can zero extend all of the
811 // operands (often constants). This allows analysis of something like
812 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
813 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
814 if (AR->isAffine()) {
815 const SCEV *Start = AR->getStart();
816 const SCEV *Step = AR->getStepRecurrence(*this);
817 unsigned BitWidth = getTypeSizeInBits(AR->getType());
818 const Loop *L = AR->getLoop();
820 // If we have special knowledge that this addrec won't overflow,
821 // we don't need to do any further analysis.
822 if (AR->hasNoUnsignedWrap())
823 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
824 getZeroExtendExpr(Step, Ty),
827 // Check whether the backedge-taken count is SCEVCouldNotCompute.
828 // Note that this serves two purposes: It filters out loops that are
829 // simply not analyzable, and it covers the case where this code is
830 // being called from within backedge-taken count analysis, such that
831 // attempting to ask for the backedge-taken count would likely result
832 // in infinite recursion. In the later case, the analysis code will
833 // cope with a conservative value, and it will take care to purge
834 // that value once it has finished.
835 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
836 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
837 // Manually compute the final value for AR, checking for
840 // Check whether the backedge-taken count can be losslessly casted to
841 // the addrec's type. The count is always unsigned.
842 const SCEV *CastedMaxBECount =
843 getTruncateOrZeroExtend(MaxBECount, Start->getType());
844 const SCEV *RecastedMaxBECount =
845 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
846 if (MaxBECount == RecastedMaxBECount) {
847 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
848 // Check whether Start+Step*MaxBECount has no unsigned overflow.
850 getMulExpr(CastedMaxBECount,
851 getTruncateOrZeroExtend(Step, Start->getType()));
852 const SCEV *Add = getAddExpr(Start, ZMul);
853 const SCEV *OperandExtendedAdd =
854 getAddExpr(getZeroExtendExpr(Start, WideTy),
855 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
856 getZeroExtendExpr(Step, WideTy)));
857 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
858 // Return the expression with the addrec on the outside.
859 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
860 getZeroExtendExpr(Step, Ty),
863 // Similar to above, only this time treat the step value as signed.
864 // This covers loops that count down.
866 getMulExpr(CastedMaxBECount,
867 getTruncateOrSignExtend(Step, Start->getType()));
868 Add = getAddExpr(Start, SMul);
870 getAddExpr(getZeroExtendExpr(Start, WideTy),
871 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
872 getSignExtendExpr(Step, WideTy)));
873 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
874 // Return the expression with the addrec on the outside.
875 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
876 getSignExtendExpr(Step, Ty),
880 // If the backedge is guarded by a comparison with the pre-inc value
881 // the addrec is safe. Also, if the entry is guarded by a comparison
882 // with the start value and the backedge is guarded by a comparison
883 // with the post-inc value, the addrec is safe.
884 if (isKnownPositive(Step)) {
885 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
886 getUnsignedRange(Step).getUnsignedMax());
887 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
888 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
889 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
890 AR->getPostIncExpr(*this), N)))
891 // Return the expression with the addrec on the outside.
892 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
893 getZeroExtendExpr(Step, Ty),
895 } else if (isKnownNegative(Step)) {
896 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
897 getSignedRange(Step).getSignedMin());
898 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) &&
899 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) ||
900 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
901 AR->getPostIncExpr(*this), N)))
902 // Return the expression with the addrec on the outside.
903 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
904 getSignExtendExpr(Step, Ty),
910 // The cast wasn't folded; create an explicit cast node.
911 // Recompute the insert position, as it may have been invalidated.
912 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
913 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>();
914 new (S) SCEVZeroExtendExpr(ID, Op, Ty);
915 UniqueSCEVs.InsertNode(S, IP);
919 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
921 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
922 "This is not an extending conversion!");
923 assert(isSCEVable(Ty) &&
924 "This is not a conversion to a SCEVable type!");
925 Ty = getEffectiveSCEVType(Ty);
927 // Fold if the operand is constant.
928 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
929 const Type *IntTy = getEffectiveSCEVType(Ty);
930 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
931 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
932 return getConstant(cast<ConstantInt>(C));
935 // sext(sext(x)) --> sext(x)
936 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
937 return getSignExtendExpr(SS->getOperand(), Ty);
939 // Before doing any expensive analysis, check to see if we've already
940 // computed a SCEV for this Op and Ty.
942 ID.AddInteger(scSignExtend);
946 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
948 // If the input value is a chrec scev, and we can prove that the value
949 // did not overflow the old, smaller, value, we can sign extend all of the
950 // operands (often constants). This allows analysis of something like
951 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
952 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
953 if (AR->isAffine()) {
954 const SCEV *Start = AR->getStart();
955 const SCEV *Step = AR->getStepRecurrence(*this);
956 unsigned BitWidth = getTypeSizeInBits(AR->getType());
957 const Loop *L = AR->getLoop();
959 // If we have special knowledge that this addrec won't overflow,
960 // we don't need to do any further analysis.
961 if (AR->hasNoSignedWrap())
962 return getAddRecExpr(getSignExtendExpr(Start, Ty),
963 getSignExtendExpr(Step, Ty),
966 // Check whether the backedge-taken count is SCEVCouldNotCompute.
967 // Note that this serves two purposes: It filters out loops that are
968 // simply not analyzable, and it covers the case where this code is
969 // being called from within backedge-taken count analysis, such that
970 // attempting to ask for the backedge-taken count would likely result
971 // in infinite recursion. In the later case, the analysis code will
972 // cope with a conservative value, and it will take care to purge
973 // that value once it has finished.
974 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
975 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
976 // Manually compute the final value for AR, checking for
979 // Check whether the backedge-taken count can be losslessly casted to
980 // the addrec's type. The count is always unsigned.
981 const SCEV *CastedMaxBECount =
982 getTruncateOrZeroExtend(MaxBECount, Start->getType());
983 const SCEV *RecastedMaxBECount =
984 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
985 if (MaxBECount == RecastedMaxBECount) {
986 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
987 // Check whether Start+Step*MaxBECount has no signed overflow.
989 getMulExpr(CastedMaxBECount,
990 getTruncateOrSignExtend(Step, Start->getType()));
991 const SCEV *Add = getAddExpr(Start, SMul);
992 const SCEV *OperandExtendedAdd =
993 getAddExpr(getSignExtendExpr(Start, WideTy),
994 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
995 getSignExtendExpr(Step, WideTy)));
996 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
997 // Return the expression with the addrec on the outside.
998 return getAddRecExpr(getSignExtendExpr(Start, Ty),
999 getSignExtendExpr(Step, Ty),
1002 // Similar to above, only this time treat the step value as unsigned.
1003 // This covers loops that count up with an unsigned step.
1005 getMulExpr(CastedMaxBECount,
1006 getTruncateOrZeroExtend(Step, Start->getType()));
1007 Add = getAddExpr(Start, UMul);
1008 OperandExtendedAdd =
1009 getAddExpr(getSignExtendExpr(Start, WideTy),
1010 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1011 getZeroExtendExpr(Step, WideTy)));
1012 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1013 // Return the expression with the addrec on the outside.
1014 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1015 getZeroExtendExpr(Step, Ty),
1019 // If the backedge is guarded by a comparison with the pre-inc value
1020 // the addrec is safe. Also, if the entry is guarded by a comparison
1021 // with the start value and the backedge is guarded by a comparison
1022 // with the post-inc value, the addrec is safe.
1023 if (isKnownPositive(Step)) {
1024 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1025 getSignedRange(Step).getSignedMax());
1026 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1027 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1028 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1029 AR->getPostIncExpr(*this), N)))
1030 // Return the expression with the addrec on the outside.
1031 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1032 getSignExtendExpr(Step, Ty),
1034 } else if (isKnownNegative(Step)) {
1035 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1036 getSignedRange(Step).getSignedMin());
1037 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1038 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1039 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1040 AR->getPostIncExpr(*this), N)))
1041 // Return the expression with the addrec on the outside.
1042 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1043 getSignExtendExpr(Step, Ty),
1049 // The cast wasn't folded; create an explicit cast node.
1050 // Recompute the insert position, as it may have been invalidated.
1051 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1052 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>();
1053 new (S) SCEVSignExtendExpr(ID, Op, Ty);
1054 UniqueSCEVs.InsertNode(S, IP);
1058 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1059 /// unspecified bits out to the given type.
1061 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1063 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1064 "This is not an extending conversion!");
1065 assert(isSCEVable(Ty) &&
1066 "This is not a conversion to a SCEVable type!");
1067 Ty = getEffectiveSCEVType(Ty);
1069 // Sign-extend negative constants.
1070 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1071 if (SC->getValue()->getValue().isNegative())
1072 return getSignExtendExpr(Op, Ty);
1074 // Peel off a truncate cast.
1075 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1076 const SCEV *NewOp = T->getOperand();
1077 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1078 return getAnyExtendExpr(NewOp, Ty);
1079 return getTruncateOrNoop(NewOp, Ty);
1082 // Next try a zext cast. If the cast is folded, use it.
1083 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1084 if (!isa<SCEVZeroExtendExpr>(ZExt))
1087 // Next try a sext cast. If the cast is folded, use it.
1088 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1089 if (!isa<SCEVSignExtendExpr>(SExt))
1092 // Force the cast to be folded into the operands of an addrec.
1093 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1094 SmallVector<const SCEV *, 4> Ops;
1095 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1097 Ops.push_back(getAnyExtendExpr(*I, Ty));
1098 return getAddRecExpr(Ops, AR->getLoop());
1101 // If the expression is obviously signed, use the sext cast value.
1102 if (isa<SCEVSMaxExpr>(Op))
1105 // Absent any other information, use the zext cast value.
1109 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1110 /// a list of operands to be added under the given scale, update the given
1111 /// map. This is a helper function for getAddRecExpr. As an example of
1112 /// what it does, given a sequence of operands that would form an add
1113 /// expression like this:
1115 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1117 /// where A and B are constants, update the map with these values:
1119 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1121 /// and add 13 + A*B*29 to AccumulatedConstant.
1122 /// This will allow getAddRecExpr to produce this:
1124 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1126 /// This form often exposes folding opportunities that are hidden in
1127 /// the original operand list.
1129 /// Return true iff it appears that any interesting folding opportunities
1130 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1131 /// the common case where no interesting opportunities are present, and
1132 /// is also used as a check to avoid infinite recursion.
1135 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1136 SmallVector<const SCEV *, 8> &NewOps,
1137 APInt &AccumulatedConstant,
1138 const SmallVectorImpl<const SCEV *> &Ops,
1140 ScalarEvolution &SE) {
1141 bool Interesting = false;
1143 // Iterate over the add operands.
1144 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1145 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1146 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1148 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1149 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1150 // A multiplication of a constant with another add; recurse.
1152 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1153 cast<SCEVAddExpr>(Mul->getOperand(1))
1157 // A multiplication of a constant with some other value. Update
1159 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1160 const SCEV *Key = SE.getMulExpr(MulOps);
1161 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1162 M.insert(std::make_pair(Key, NewScale));
1164 NewOps.push_back(Pair.first->first);
1166 Pair.first->second += NewScale;
1167 // The map already had an entry for this value, which may indicate
1168 // a folding opportunity.
1172 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1173 // Pull a buried constant out to the outside.
1174 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
1176 AccumulatedConstant += Scale * C->getValue()->getValue();
1178 // An ordinary operand. Update the map.
1179 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1180 M.insert(std::make_pair(Ops[i], Scale));
1182 NewOps.push_back(Pair.first->first);
1184 Pair.first->second += Scale;
1185 // The map already had an entry for this value, which may indicate
1186 // a folding opportunity.
1196 struct APIntCompare {
1197 bool operator()(const APInt &LHS, const APInt &RHS) const {
1198 return LHS.ult(RHS);
1203 /// getAddExpr - Get a canonical add expression, or something simpler if
1205 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1206 bool HasNUW, bool HasNSW) {
1207 assert(!Ops.empty() && "Cannot get empty add!");
1208 if (Ops.size() == 1) return Ops[0];
1210 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1211 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1212 getEffectiveSCEVType(Ops[0]->getType()) &&
1213 "SCEVAddExpr operand types don't match!");
1216 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1217 if (!HasNUW && HasNSW) {
1219 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1220 if (!isKnownNonNegative(Ops[i])) {
1224 if (All) HasNUW = true;
1227 // Sort by complexity, this groups all similar expression types together.
1228 GroupByComplexity(Ops, LI);
1230 // If there are any constants, fold them together.
1232 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1234 assert(Idx < Ops.size());
1235 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1236 // We found two constants, fold them together!
1237 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1238 RHSC->getValue()->getValue());
1239 if (Ops.size() == 2) return Ops[0];
1240 Ops.erase(Ops.begin()+1); // Erase the folded element
1241 LHSC = cast<SCEVConstant>(Ops[0]);
1244 // If we are left with a constant zero being added, strip it off.
1245 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1246 Ops.erase(Ops.begin());
1251 if (Ops.size() == 1) return Ops[0];
1253 // Okay, check to see if the same value occurs in the operand list twice. If
1254 // so, merge them together into an multiply expression. Since we sorted the
1255 // list, these values are required to be adjacent.
1256 const Type *Ty = Ops[0]->getType();
1257 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1258 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1259 // Found a match, merge the two values into a multiply, and add any
1260 // remaining values to the result.
1261 const SCEV *Two = getIntegerSCEV(2, Ty);
1262 const SCEV *Mul = getMulExpr(Ops[i], Two);
1263 if (Ops.size() == 2)
1265 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1267 return getAddExpr(Ops, HasNUW, HasNSW);
1270 // Check for truncates. If all the operands are truncated from the same
1271 // type, see if factoring out the truncate would permit the result to be
1272 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1273 // if the contents of the resulting outer trunc fold to something simple.
1274 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1275 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1276 const Type *DstType = Trunc->getType();
1277 const Type *SrcType = Trunc->getOperand()->getType();
1278 SmallVector<const SCEV *, 8> LargeOps;
1280 // Check all the operands to see if they can be represented in the
1281 // source type of the truncate.
1282 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1283 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1284 if (T->getOperand()->getType() != SrcType) {
1288 LargeOps.push_back(T->getOperand());
1289 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1290 // This could be either sign or zero extension, but sign extension
1291 // is much more likely to be foldable here.
1292 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1293 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1294 SmallVector<const SCEV *, 8> LargeMulOps;
1295 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1296 if (const SCEVTruncateExpr *T =
1297 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1298 if (T->getOperand()->getType() != SrcType) {
1302 LargeMulOps.push_back(T->getOperand());
1303 } else if (const SCEVConstant *C =
1304 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1305 // This could be either sign or zero extension, but sign extension
1306 // is much more likely to be foldable here.
1307 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1314 LargeOps.push_back(getMulExpr(LargeMulOps));
1321 // Evaluate the expression in the larger type.
1322 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1323 // If it folds to something simple, use it. Otherwise, don't.
1324 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1325 return getTruncateExpr(Fold, DstType);
1329 // Skip past any other cast SCEVs.
1330 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1333 // If there are add operands they would be next.
1334 if (Idx < Ops.size()) {
1335 bool DeletedAdd = false;
1336 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1337 // If we have an add, expand the add operands onto the end of the operands
1339 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1340 Ops.erase(Ops.begin()+Idx);
1344 // If we deleted at least one add, we added operands to the end of the list,
1345 // and they are not necessarily sorted. Recurse to resort and resimplify
1346 // any operands we just aquired.
1348 return getAddExpr(Ops);
1351 // Skip over the add expression until we get to a multiply.
1352 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1355 // Check to see if there are any folding opportunities present with
1356 // operands multiplied by constant values.
1357 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1358 uint64_t BitWidth = getTypeSizeInBits(Ty);
1359 DenseMap<const SCEV *, APInt> M;
1360 SmallVector<const SCEV *, 8> NewOps;
1361 APInt AccumulatedConstant(BitWidth, 0);
1362 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1363 Ops, APInt(BitWidth, 1), *this)) {
1364 // Some interesting folding opportunity is present, so its worthwhile to
1365 // re-generate the operands list. Group the operands by constant scale,
1366 // to avoid multiplying by the same constant scale multiple times.
1367 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1368 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1369 E = NewOps.end(); I != E; ++I)
1370 MulOpLists[M.find(*I)->second].push_back(*I);
1371 // Re-generate the operands list.
1373 if (AccumulatedConstant != 0)
1374 Ops.push_back(getConstant(AccumulatedConstant));
1375 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1376 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1378 Ops.push_back(getMulExpr(getConstant(I->first),
1379 getAddExpr(I->second)));
1381 return getIntegerSCEV(0, Ty);
1382 if (Ops.size() == 1)
1384 return getAddExpr(Ops);
1388 // If we are adding something to a multiply expression, make sure the
1389 // something is not already an operand of the multiply. If so, merge it into
1391 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1392 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1393 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1394 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1395 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1396 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1397 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1398 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1399 if (Mul->getNumOperands() != 2) {
1400 // If the multiply has more than two operands, we must get the
1402 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1403 MulOps.erase(MulOps.begin()+MulOp);
1404 InnerMul = getMulExpr(MulOps);
1406 const SCEV *One = getIntegerSCEV(1, Ty);
1407 const SCEV *AddOne = getAddExpr(InnerMul, One);
1408 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1409 if (Ops.size() == 2) return OuterMul;
1411 Ops.erase(Ops.begin()+AddOp);
1412 Ops.erase(Ops.begin()+Idx-1);
1414 Ops.erase(Ops.begin()+Idx);
1415 Ops.erase(Ops.begin()+AddOp-1);
1417 Ops.push_back(OuterMul);
1418 return getAddExpr(Ops);
1421 // Check this multiply against other multiplies being added together.
1422 for (unsigned OtherMulIdx = Idx+1;
1423 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1425 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1426 // If MulOp occurs in OtherMul, we can fold the two multiplies
1428 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1429 OMulOp != e; ++OMulOp)
1430 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1431 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1432 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1433 if (Mul->getNumOperands() != 2) {
1434 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1436 MulOps.erase(MulOps.begin()+MulOp);
1437 InnerMul1 = getMulExpr(MulOps);
1439 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1440 if (OtherMul->getNumOperands() != 2) {
1441 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1442 OtherMul->op_end());
1443 MulOps.erase(MulOps.begin()+OMulOp);
1444 InnerMul2 = getMulExpr(MulOps);
1446 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1447 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1448 if (Ops.size() == 2) return OuterMul;
1449 Ops.erase(Ops.begin()+Idx);
1450 Ops.erase(Ops.begin()+OtherMulIdx-1);
1451 Ops.push_back(OuterMul);
1452 return getAddExpr(Ops);
1458 // If there are any add recurrences in the operands list, see if any other
1459 // added values are loop invariant. If so, we can fold them into the
1461 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1464 // Scan over all recurrences, trying to fold loop invariants into them.
1465 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1466 // Scan all of the other operands to this add and add them to the vector if
1467 // they are loop invariant w.r.t. the recurrence.
1468 SmallVector<const SCEV *, 8> LIOps;
1469 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1470 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1471 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1472 LIOps.push_back(Ops[i]);
1473 Ops.erase(Ops.begin()+i);
1477 // If we found some loop invariants, fold them into the recurrence.
1478 if (!LIOps.empty()) {
1479 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1480 LIOps.push_back(AddRec->getStart());
1482 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1484 AddRecOps[0] = getAddExpr(LIOps);
1486 // It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition
1487 // is not associative so this isn't necessarily safe.
1488 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1490 // If all of the other operands were loop invariant, we are done.
1491 if (Ops.size() == 1) return NewRec;
1493 // Otherwise, add the folded AddRec by the non-liv parts.
1494 for (unsigned i = 0;; ++i)
1495 if (Ops[i] == AddRec) {
1499 return getAddExpr(Ops);
1502 // Okay, if there weren't any loop invariants to be folded, check to see if
1503 // there are multiple AddRec's with the same loop induction variable being
1504 // added together. If so, we can fold them.
1505 for (unsigned OtherIdx = Idx+1;
1506 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1507 if (OtherIdx != Idx) {
1508 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1509 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1510 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1511 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1513 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1514 if (i >= NewOps.size()) {
1515 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1516 OtherAddRec->op_end());
1519 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1521 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1523 if (Ops.size() == 2) return NewAddRec;
1525 Ops.erase(Ops.begin()+Idx);
1526 Ops.erase(Ops.begin()+OtherIdx-1);
1527 Ops.push_back(NewAddRec);
1528 return getAddExpr(Ops);
1532 // Otherwise couldn't fold anything into this recurrence. Move onto the
1536 // Okay, it looks like we really DO need an add expr. Check to see if we
1537 // already have one, otherwise create a new one.
1538 FoldingSetNodeID ID;
1539 ID.AddInteger(scAddExpr);
1540 ID.AddInteger(Ops.size());
1541 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1542 ID.AddPointer(Ops[i]);
1545 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1547 S = SCEVAllocator.Allocate<SCEVAddExpr>();
1548 new (S) SCEVAddExpr(ID, Ops);
1549 UniqueSCEVs.InsertNode(S, IP);
1551 if (HasNUW) S->setHasNoUnsignedWrap(true);
1552 if (HasNSW) S->setHasNoSignedWrap(true);
1556 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1558 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1559 bool HasNUW, bool HasNSW) {
1560 assert(!Ops.empty() && "Cannot get empty mul!");
1561 if (Ops.size() == 1) return Ops[0];
1563 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1564 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1565 getEffectiveSCEVType(Ops[0]->getType()) &&
1566 "SCEVMulExpr operand types don't match!");
1569 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1570 if (!HasNUW && HasNSW) {
1572 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1573 if (!isKnownNonNegative(Ops[i])) {
1577 if (All) HasNUW = true;
1580 // Sort by complexity, this groups all similar expression types together.
1581 GroupByComplexity(Ops, LI);
1583 // If there are any constants, fold them together.
1585 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1587 // C1*(C2+V) -> C1*C2 + C1*V
1588 if (Ops.size() == 2)
1589 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1590 if (Add->getNumOperands() == 2 &&
1591 isa<SCEVConstant>(Add->getOperand(0)))
1592 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1593 getMulExpr(LHSC, Add->getOperand(1)));
1596 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1597 // We found two constants, fold them together!
1598 ConstantInt *Fold = ConstantInt::get(getContext(),
1599 LHSC->getValue()->getValue() *
1600 RHSC->getValue()->getValue());
1601 Ops[0] = getConstant(Fold);
1602 Ops.erase(Ops.begin()+1); // Erase the folded element
1603 if (Ops.size() == 1) return Ops[0];
1604 LHSC = cast<SCEVConstant>(Ops[0]);
1607 // If we are left with a constant one being multiplied, strip it off.
1608 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1609 Ops.erase(Ops.begin());
1611 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1612 // If we have a multiply of zero, it will always be zero.
1614 } else if (Ops[0]->isAllOnesValue()) {
1615 // If we have a mul by -1 of an add, try distributing the -1 among the
1617 if (Ops.size() == 2)
1618 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1619 SmallVector<const SCEV *, 4> NewOps;
1620 bool AnyFolded = false;
1621 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1623 const SCEV *Mul = getMulExpr(Ops[0], *I);
1624 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1625 NewOps.push_back(Mul);
1628 return getAddExpr(NewOps);
1633 // Skip over the add expression until we get to a multiply.
1634 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1637 if (Ops.size() == 1)
1640 // If there are mul operands inline them all into this expression.
1641 if (Idx < Ops.size()) {
1642 bool DeletedMul = false;
1643 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1644 // If we have an mul, expand the mul operands onto the end of the operands
1646 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1647 Ops.erase(Ops.begin()+Idx);
1651 // If we deleted at least one mul, we added operands to the end of the list,
1652 // and they are not necessarily sorted. Recurse to resort and resimplify
1653 // any operands we just aquired.
1655 return getMulExpr(Ops);
1658 // If there are any add recurrences in the operands list, see if any other
1659 // added values are loop invariant. If so, we can fold them into the
1661 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1664 // Scan over all recurrences, trying to fold loop invariants into them.
1665 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1666 // Scan all of the other operands to this mul and add them to the vector if
1667 // they are loop invariant w.r.t. the recurrence.
1668 SmallVector<const SCEV *, 8> LIOps;
1669 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1670 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1671 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1672 LIOps.push_back(Ops[i]);
1673 Ops.erase(Ops.begin()+i);
1677 // If we found some loop invariants, fold them into the recurrence.
1678 if (!LIOps.empty()) {
1679 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1680 SmallVector<const SCEV *, 4> NewOps;
1681 NewOps.reserve(AddRec->getNumOperands());
1682 if (LIOps.size() == 1) {
1683 const SCEV *Scale = LIOps[0];
1684 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1685 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1687 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1688 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
1689 MulOps.push_back(AddRec->getOperand(i));
1690 NewOps.push_back(getMulExpr(MulOps));
1694 // It's tempting to propagate the NSW flag here, but nsw multiplication
1695 // is not associative so this isn't necessarily safe.
1696 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
1697 HasNUW && AddRec->hasNoUnsignedWrap(),
1700 // If all of the other operands were loop invariant, we are done.
1701 if (Ops.size() == 1) return NewRec;
1703 // Otherwise, multiply the folded AddRec by the non-liv parts.
1704 for (unsigned i = 0;; ++i)
1705 if (Ops[i] == AddRec) {
1709 return getMulExpr(Ops);
1712 // Okay, if there weren't any loop invariants to be folded, check to see if
1713 // there are multiple AddRec's with the same loop induction variable being
1714 // multiplied together. If so, we can fold them.
1715 for (unsigned OtherIdx = Idx+1;
1716 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1717 if (OtherIdx != Idx) {
1718 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1719 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1720 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1721 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1722 const SCEV *NewStart = getMulExpr(F->getStart(),
1724 const SCEV *B = F->getStepRecurrence(*this);
1725 const SCEV *D = G->getStepRecurrence(*this);
1726 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1729 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1731 if (Ops.size() == 2) return NewAddRec;
1733 Ops.erase(Ops.begin()+Idx);
1734 Ops.erase(Ops.begin()+OtherIdx-1);
1735 Ops.push_back(NewAddRec);
1736 return getMulExpr(Ops);
1740 // Otherwise couldn't fold anything into this recurrence. Move onto the
1744 // Okay, it looks like we really DO need an mul expr. Check to see if we
1745 // already have one, otherwise create a new one.
1746 FoldingSetNodeID ID;
1747 ID.AddInteger(scMulExpr);
1748 ID.AddInteger(Ops.size());
1749 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1750 ID.AddPointer(Ops[i]);
1753 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1755 S = SCEVAllocator.Allocate<SCEVMulExpr>();
1756 new (S) SCEVMulExpr(ID, Ops);
1757 UniqueSCEVs.InsertNode(S, IP);
1759 if (HasNUW) S->setHasNoUnsignedWrap(true);
1760 if (HasNSW) S->setHasNoSignedWrap(true);
1764 /// getUDivExpr - Get a canonical unsigned division expression, or something
1765 /// simpler if possible.
1766 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1768 assert(getEffectiveSCEVType(LHS->getType()) ==
1769 getEffectiveSCEVType(RHS->getType()) &&
1770 "SCEVUDivExpr operand types don't match!");
1772 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1773 if (RHSC->getValue()->equalsInt(1))
1774 return LHS; // X udiv 1 --> x
1776 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1778 // Determine if the division can be folded into the operands of
1780 // TODO: Generalize this to non-constants by using known-bits information.
1781 const Type *Ty = LHS->getType();
1782 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1783 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1784 // For non-power-of-two values, effectively round the value up to the
1785 // nearest power of two.
1786 if (!RHSC->getValue()->getValue().isPowerOf2())
1788 const IntegerType *ExtTy =
1789 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1790 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1791 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1792 if (const SCEVConstant *Step =
1793 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1794 if (!Step->getValue()->getValue()
1795 .urem(RHSC->getValue()->getValue()) &&
1796 getZeroExtendExpr(AR, ExtTy) ==
1797 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1798 getZeroExtendExpr(Step, ExtTy),
1800 SmallVector<const SCEV *, 4> Operands;
1801 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1802 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1803 return getAddRecExpr(Operands, AR->getLoop());
1805 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1806 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1807 SmallVector<const SCEV *, 4> Operands;
1808 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1809 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1810 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1811 // Find an operand that's safely divisible.
1812 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1813 const SCEV *Op = M->getOperand(i);
1814 const SCEV *Div = getUDivExpr(Op, RHSC);
1815 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1816 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands();
1817 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(),
1820 return getMulExpr(Operands);
1824 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1825 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1826 SmallVector<const SCEV *, 4> Operands;
1827 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1828 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1829 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1831 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1832 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1833 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1835 Operands.push_back(Op);
1837 if (Operands.size() == A->getNumOperands())
1838 return getAddExpr(Operands);
1842 // Fold if both operands are constant.
1843 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1844 Constant *LHSCV = LHSC->getValue();
1845 Constant *RHSCV = RHSC->getValue();
1846 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1851 FoldingSetNodeID ID;
1852 ID.AddInteger(scUDivExpr);
1856 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1857 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>();
1858 new (S) SCEVUDivExpr(ID, LHS, RHS);
1859 UniqueSCEVs.InsertNode(S, IP);
1864 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1865 /// Simplify the expression as much as possible.
1866 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1867 const SCEV *Step, const Loop *L,
1868 bool HasNUW, bool HasNSW) {
1869 SmallVector<const SCEV *, 4> Operands;
1870 Operands.push_back(Start);
1871 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1872 if (StepChrec->getLoop() == L) {
1873 Operands.insert(Operands.end(), StepChrec->op_begin(),
1874 StepChrec->op_end());
1875 return getAddRecExpr(Operands, L);
1878 Operands.push_back(Step);
1879 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
1882 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1883 /// Simplify the expression as much as possible.
1885 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1887 bool HasNUW, bool HasNSW) {
1888 if (Operands.size() == 1) return Operands[0];
1890 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1891 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1892 getEffectiveSCEVType(Operands[0]->getType()) &&
1893 "SCEVAddRecExpr operand types don't match!");
1896 if (Operands.back()->isZero()) {
1897 Operands.pop_back();
1898 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
1901 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1902 if (!HasNUW && HasNSW) {
1904 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1905 if (!isKnownNonNegative(Operands[i])) {
1909 if (All) HasNUW = true;
1912 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1913 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1914 const Loop *NestedLoop = NestedAR->getLoop();
1915 if (L->contains(NestedLoop->getHeader()) ?
1916 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
1917 (!NestedLoop->contains(L->getHeader()) &&
1918 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
1919 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
1920 NestedAR->op_end());
1921 Operands[0] = NestedAR->getStart();
1922 // AddRecs require their operands be loop-invariant with respect to their
1923 // loops. Don't perform this transformation if it would break this
1925 bool AllInvariant = true;
1926 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1927 if (!Operands[i]->isLoopInvariant(L)) {
1928 AllInvariant = false;
1932 NestedOperands[0] = getAddRecExpr(Operands, L);
1933 AllInvariant = true;
1934 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
1935 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
1936 AllInvariant = false;
1940 // Ok, both add recurrences are valid after the transformation.
1941 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
1943 // Reset Operands to its original state.
1944 Operands[0] = NestedAR;
1948 // Okay, it looks like we really DO need an addrec expr. Check to see if we
1949 // already have one, otherwise create a new one.
1950 FoldingSetNodeID ID;
1951 ID.AddInteger(scAddRecExpr);
1952 ID.AddInteger(Operands.size());
1953 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1954 ID.AddPointer(Operands[i]);
1958 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1960 S = SCEVAllocator.Allocate<SCEVAddRecExpr>();
1961 new (S) SCEVAddRecExpr(ID, Operands, L);
1962 UniqueSCEVs.InsertNode(S, IP);
1964 if (HasNUW) S->setHasNoUnsignedWrap(true);
1965 if (HasNSW) S->setHasNoSignedWrap(true);
1969 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
1971 SmallVector<const SCEV *, 2> Ops;
1974 return getSMaxExpr(Ops);
1978 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1979 assert(!Ops.empty() && "Cannot get empty smax!");
1980 if (Ops.size() == 1) return Ops[0];
1982 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1983 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1984 getEffectiveSCEVType(Ops[0]->getType()) &&
1985 "SCEVSMaxExpr operand types don't match!");
1988 // Sort by complexity, this groups all similar expression types together.
1989 GroupByComplexity(Ops, LI);
1991 // If there are any constants, fold them together.
1993 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1995 assert(Idx < Ops.size());
1996 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1997 // We found two constants, fold them together!
1998 ConstantInt *Fold = ConstantInt::get(getContext(),
1999 APIntOps::smax(LHSC->getValue()->getValue(),
2000 RHSC->getValue()->getValue()));
2001 Ops[0] = getConstant(Fold);
2002 Ops.erase(Ops.begin()+1); // Erase the folded element
2003 if (Ops.size() == 1) return Ops[0];
2004 LHSC = cast<SCEVConstant>(Ops[0]);
2007 // If we are left with a constant minimum-int, strip it off.
2008 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2009 Ops.erase(Ops.begin());
2011 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2012 // If we have an smax with a constant maximum-int, it will always be
2018 if (Ops.size() == 1) return Ops[0];
2020 // Find the first SMax
2021 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2024 // Check to see if one of the operands is an SMax. If so, expand its operands
2025 // onto our operand list, and recurse to simplify.
2026 if (Idx < Ops.size()) {
2027 bool DeletedSMax = false;
2028 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2029 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
2030 Ops.erase(Ops.begin()+Idx);
2035 return getSMaxExpr(Ops);
2038 // Okay, check to see if the same value occurs in the operand list twice. If
2039 // so, delete one. Since we sorted the list, these values are required to
2041 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2042 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
2043 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2047 if (Ops.size() == 1) return Ops[0];
2049 assert(!Ops.empty() && "Reduced smax down to nothing!");
2051 // Okay, it looks like we really DO need an smax expr. Check to see if we
2052 // already have one, otherwise create a new one.
2053 FoldingSetNodeID ID;
2054 ID.AddInteger(scSMaxExpr);
2055 ID.AddInteger(Ops.size());
2056 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2057 ID.AddPointer(Ops[i]);
2059 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2060 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>();
2061 new (S) SCEVSMaxExpr(ID, Ops);
2062 UniqueSCEVs.InsertNode(S, IP);
2066 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2068 SmallVector<const SCEV *, 2> Ops;
2071 return getUMaxExpr(Ops);
2075 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2076 assert(!Ops.empty() && "Cannot get empty umax!");
2077 if (Ops.size() == 1) return Ops[0];
2079 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2080 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2081 getEffectiveSCEVType(Ops[0]->getType()) &&
2082 "SCEVUMaxExpr operand types don't match!");
2085 // Sort by complexity, this groups all similar expression types together.
2086 GroupByComplexity(Ops, LI);
2088 // If there are any constants, fold them together.
2090 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2092 assert(Idx < Ops.size());
2093 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2094 // We found two constants, fold them together!
2095 ConstantInt *Fold = ConstantInt::get(getContext(),
2096 APIntOps::umax(LHSC->getValue()->getValue(),
2097 RHSC->getValue()->getValue()));
2098 Ops[0] = getConstant(Fold);
2099 Ops.erase(Ops.begin()+1); // Erase the folded element
2100 if (Ops.size() == 1) return Ops[0];
2101 LHSC = cast<SCEVConstant>(Ops[0]);
2104 // If we are left with a constant minimum-int, strip it off.
2105 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2106 Ops.erase(Ops.begin());
2108 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2109 // If we have an umax with a constant maximum-int, it will always be
2115 if (Ops.size() == 1) return Ops[0];
2117 // Find the first UMax
2118 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2121 // Check to see if one of the operands is a UMax. If so, expand its operands
2122 // onto our operand list, and recurse to simplify.
2123 if (Idx < Ops.size()) {
2124 bool DeletedUMax = false;
2125 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2126 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
2127 Ops.erase(Ops.begin()+Idx);
2132 return getUMaxExpr(Ops);
2135 // Okay, check to see if the same value occurs in the operand list twice. If
2136 // so, delete one. Since we sorted the list, these values are required to
2138 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2139 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
2140 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2144 if (Ops.size() == 1) return Ops[0];
2146 assert(!Ops.empty() && "Reduced umax down to nothing!");
2148 // Okay, it looks like we really DO need a umax expr. Check to see if we
2149 // already have one, otherwise create a new one.
2150 FoldingSetNodeID ID;
2151 ID.AddInteger(scUMaxExpr);
2152 ID.AddInteger(Ops.size());
2153 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2154 ID.AddPointer(Ops[i]);
2156 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2157 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>();
2158 new (S) SCEVUMaxExpr(ID, Ops);
2159 UniqueSCEVs.InsertNode(S, IP);
2163 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2165 // ~smax(~x, ~y) == smin(x, y).
2166 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2169 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2171 // ~umax(~x, ~y) == umin(x, y)
2172 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2175 const SCEV *ScalarEvolution::getFieldOffsetExpr(const StructType *STy,
2177 // If we have TargetData we can determine the constant offset.
2179 const Type *IntPtrTy = TD->getIntPtrType(getContext());
2180 const StructLayout &SL = *TD->getStructLayout(STy);
2181 uint64_t Offset = SL.getElementOffset(FieldNo);
2182 return getIntegerSCEV(Offset, IntPtrTy);
2185 // Field 0 is always at offset 0.
2187 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2188 return getIntegerSCEV(0, Ty);
2191 // Okay, it looks like we really DO need an offsetof expr. Check to see if we
2192 // already have one, otherwise create a new one.
2193 FoldingSetNodeID ID;
2194 ID.AddInteger(scFieldOffset);
2196 ID.AddInteger(FieldNo);
2198 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2199 SCEV *S = SCEVAllocator.Allocate<SCEVFieldOffsetExpr>();
2200 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2201 new (S) SCEVFieldOffsetExpr(ID, Ty, STy, FieldNo);
2202 UniqueSCEVs.InsertNode(S, IP);
2206 const SCEV *ScalarEvolution::getAllocSizeExpr(const Type *AllocTy) {
2207 // If we have TargetData we can determine the constant size.
2208 if (TD && AllocTy->isSized()) {
2209 const Type *IntPtrTy = TD->getIntPtrType(getContext());
2210 return getIntegerSCEV(TD->getTypeAllocSize(AllocTy), IntPtrTy);
2213 // Expand an array size into the element size times the number
2215 if (const ArrayType *ATy = dyn_cast<ArrayType>(AllocTy)) {
2216 const SCEV *E = getAllocSizeExpr(ATy->getElementType());
2218 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()),
2219 ATy->getNumElements())));
2222 // Expand a vector size into the element size times the number
2224 if (const VectorType *VTy = dyn_cast<VectorType>(AllocTy)) {
2225 const SCEV *E = getAllocSizeExpr(VTy->getElementType());
2227 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()),
2228 VTy->getNumElements())));
2231 // Okay, it looks like we really DO need a sizeof expr. Check to see if we
2232 // already have one, otherwise create a new one.
2233 FoldingSetNodeID ID;
2234 ID.AddInteger(scAllocSize);
2235 ID.AddPointer(AllocTy);
2237 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2238 SCEV *S = SCEVAllocator.Allocate<SCEVAllocSizeExpr>();
2239 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2240 new (S) SCEVAllocSizeExpr(ID, Ty, AllocTy);
2241 UniqueSCEVs.InsertNode(S, IP);
2245 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2246 // Don't attempt to do anything other than create a SCEVUnknown object
2247 // here. createSCEV only calls getUnknown after checking for all other
2248 // interesting possibilities, and any other code that calls getUnknown
2249 // is doing so in order to hide a value from SCEV canonicalization.
2251 FoldingSetNodeID ID;
2252 ID.AddInteger(scUnknown);
2255 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2256 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>();
2257 new (S) SCEVUnknown(ID, V);
2258 UniqueSCEVs.InsertNode(S, IP);
2262 //===----------------------------------------------------------------------===//
2263 // Basic SCEV Analysis and PHI Idiom Recognition Code
2266 /// isSCEVable - Test if values of the given type are analyzable within
2267 /// the SCEV framework. This primarily includes integer types, and it
2268 /// can optionally include pointer types if the ScalarEvolution class
2269 /// has access to target-specific information.
2270 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2271 // Integers and pointers are always SCEVable.
2272 return Ty->isInteger() || isa<PointerType>(Ty);
2275 /// getTypeSizeInBits - Return the size in bits of the specified type,
2276 /// for which isSCEVable must return true.
2277 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2278 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2280 // If we have a TargetData, use it!
2282 return TD->getTypeSizeInBits(Ty);
2284 // Integer types have fixed sizes.
2285 if (Ty->isInteger())
2286 return Ty->getPrimitiveSizeInBits();
2288 // The only other support type is pointer. Without TargetData, conservatively
2289 // assume pointers are 64-bit.
2290 assert(isa<PointerType>(Ty) && "isSCEVable permitted a non-SCEVable type!");
2294 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2295 /// the given type and which represents how SCEV will treat the given
2296 /// type, for which isSCEVable must return true. For pointer types,
2297 /// this is the pointer-sized integer type.
2298 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2299 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2301 if (Ty->isInteger())
2304 // The only other support type is pointer.
2305 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
2306 if (TD) return TD->getIntPtrType(getContext());
2308 // Without TargetData, conservatively assume pointers are 64-bit.
2309 return Type::getInt64Ty(getContext());
2312 const SCEV *ScalarEvolution::getCouldNotCompute() {
2313 return &CouldNotCompute;
2316 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2317 /// expression and create a new one.
2318 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2319 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2321 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2322 if (I != Scalars.end()) return I->second;
2323 const SCEV *S = createSCEV(V);
2324 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2328 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
2329 /// specified signed integer value and return a SCEV for the constant.
2330 const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
2331 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2332 return getConstant(ConstantInt::get(ITy, Val));
2335 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2337 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2338 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2340 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2342 const Type *Ty = V->getType();
2343 Ty = getEffectiveSCEVType(Ty);
2344 return getMulExpr(V,
2345 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2348 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2349 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2350 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2352 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2354 const Type *Ty = V->getType();
2355 Ty = getEffectiveSCEVType(Ty);
2356 const SCEV *AllOnes =
2357 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2358 return getMinusSCEV(AllOnes, V);
2361 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2363 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2366 return getAddExpr(LHS, getNegativeSCEV(RHS));
2369 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2370 /// input value to the specified type. If the type must be extended, it is zero
2373 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2375 const Type *SrcTy = V->getType();
2376 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2377 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2378 "Cannot truncate or zero extend with non-integer arguments!");
2379 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2380 return V; // No conversion
2381 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2382 return getTruncateExpr(V, Ty);
2383 return getZeroExtendExpr(V, Ty);
2386 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2387 /// input value to the specified type. If the type must be extended, it is sign
2390 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2392 const Type *SrcTy = V->getType();
2393 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2394 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2395 "Cannot truncate or zero extend with non-integer arguments!");
2396 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2397 return V; // No conversion
2398 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2399 return getTruncateExpr(V, Ty);
2400 return getSignExtendExpr(V, Ty);
2403 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2404 /// input value to the specified type. If the type must be extended, it is zero
2405 /// extended. The conversion must not be narrowing.
2407 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2408 const Type *SrcTy = V->getType();
2409 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2410 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2411 "Cannot noop or zero extend with non-integer arguments!");
2412 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2413 "getNoopOrZeroExtend cannot truncate!");
2414 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2415 return V; // No conversion
2416 return getZeroExtendExpr(V, Ty);
2419 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2420 /// input value to the specified type. If the type must be extended, it is sign
2421 /// extended. The conversion must not be narrowing.
2423 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2424 const Type *SrcTy = V->getType();
2425 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2426 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2427 "Cannot noop or sign extend with non-integer arguments!");
2428 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2429 "getNoopOrSignExtend cannot truncate!");
2430 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2431 return V; // No conversion
2432 return getSignExtendExpr(V, Ty);
2435 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2436 /// the input value to the specified type. If the type must be extended,
2437 /// it is extended with unspecified bits. The conversion must not be
2440 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2441 const Type *SrcTy = V->getType();
2442 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2443 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2444 "Cannot noop or any extend with non-integer arguments!");
2445 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2446 "getNoopOrAnyExtend cannot truncate!");
2447 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2448 return V; // No conversion
2449 return getAnyExtendExpr(V, Ty);
2452 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2453 /// input value to the specified type. The conversion must not be widening.
2455 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2456 const Type *SrcTy = V->getType();
2457 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2458 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2459 "Cannot truncate or noop with non-integer arguments!");
2460 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2461 "getTruncateOrNoop cannot extend!");
2462 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2463 return V; // No conversion
2464 return getTruncateExpr(V, Ty);
2467 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2468 /// the types using zero-extension, and then perform a umax operation
2470 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2472 const SCEV *PromotedLHS = LHS;
2473 const SCEV *PromotedRHS = RHS;
2475 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2476 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2478 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2480 return getUMaxExpr(PromotedLHS, PromotedRHS);
2483 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2484 /// the types using zero-extension, and then perform a umin operation
2486 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2488 const SCEV *PromotedLHS = LHS;
2489 const SCEV *PromotedRHS = RHS;
2491 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2492 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2494 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2496 return getUMinExpr(PromotedLHS, PromotedRHS);
2499 /// PushDefUseChildren - Push users of the given Instruction
2500 /// onto the given Worklist.
2502 PushDefUseChildren(Instruction *I,
2503 SmallVectorImpl<Instruction *> &Worklist) {
2504 // Push the def-use children onto the Worklist stack.
2505 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2507 Worklist.push_back(cast<Instruction>(UI));
2510 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2511 /// instructions that depend on the given instruction and removes them from
2512 /// the Scalars map if they reference SymName. This is used during PHI
2515 ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) {
2516 SmallVector<Instruction *, 16> Worklist;
2517 PushDefUseChildren(I, Worklist);
2519 SmallPtrSet<Instruction *, 8> Visited;
2521 while (!Worklist.empty()) {
2522 Instruction *I = Worklist.pop_back_val();
2523 if (!Visited.insert(I)) continue;
2525 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
2526 Scalars.find(static_cast<Value *>(I));
2527 if (It != Scalars.end()) {
2528 // Short-circuit the def-use traversal if the symbolic name
2529 // ceases to appear in expressions.
2530 if (!It->second->hasOperand(SymName))
2533 // SCEVUnknown for a PHI either means that it has an unrecognized
2534 // structure, or it's a PHI that's in the progress of being computed
2535 // by createNodeForPHI. In the former case, additional loop trip
2536 // count information isn't going to change anything. In the later
2537 // case, createNodeForPHI will perform the necessary updates on its
2538 // own when it gets to that point.
2539 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
2540 ValuesAtScopes.erase(It->second);
2545 PushDefUseChildren(I, Worklist);
2549 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2550 /// a loop header, making it a potential recurrence, or it doesn't.
2552 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2553 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2554 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2555 if (L->getHeader() == PN->getParent()) {
2556 // If it lives in the loop header, it has two incoming values, one
2557 // from outside the loop, and one from inside.
2558 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2559 unsigned BackEdge = IncomingEdge^1;
2561 // While we are analyzing this PHI node, handle its value symbolically.
2562 const SCEV *SymbolicName = getUnknown(PN);
2563 assert(Scalars.find(PN) == Scalars.end() &&
2564 "PHI node already processed?");
2565 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2567 // Using this symbolic name for the PHI, analyze the value coming around
2569 Value *BEValueV = PN->getIncomingValue(BackEdge);
2570 const SCEV *BEValue = getSCEV(BEValueV);
2572 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2573 // has a special value for the first iteration of the loop.
2575 // If the value coming around the backedge is an add with the symbolic
2576 // value we just inserted, then we found a simple induction variable!
2577 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2578 // If there is a single occurrence of the symbolic value, replace it
2579 // with a recurrence.
2580 unsigned FoundIndex = Add->getNumOperands();
2581 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2582 if (Add->getOperand(i) == SymbolicName)
2583 if (FoundIndex == e) {
2588 if (FoundIndex != Add->getNumOperands()) {
2589 // Create an add with everything but the specified operand.
2590 SmallVector<const SCEV *, 8> Ops;
2591 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2592 if (i != FoundIndex)
2593 Ops.push_back(Add->getOperand(i));
2594 const SCEV *Accum = getAddExpr(Ops);
2596 // This is not a valid addrec if the step amount is varying each
2597 // loop iteration, but is not itself an addrec in this loop.
2598 if (Accum->isLoopInvariant(L) ||
2599 (isa<SCEVAddRecExpr>(Accum) &&
2600 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2601 bool HasNUW = false;
2602 bool HasNSW = false;
2604 // If the increment doesn't overflow, then neither the addrec nor
2605 // the post-increment will overflow.
2606 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2607 if (OBO->hasNoUnsignedWrap())
2609 if (OBO->hasNoSignedWrap())
2613 const SCEV *StartVal =
2614 getSCEV(PN->getIncomingValue(IncomingEdge));
2615 const SCEV *PHISCEV =
2616 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2618 // Since the no-wrap flags are on the increment, they apply to the
2619 // post-incremented value as well.
2620 if (Accum->isLoopInvariant(L))
2621 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2622 Accum, L, HasNUW, HasNSW);
2624 // Okay, for the entire analysis of this edge we assumed the PHI
2625 // to be symbolic. We now need to go back and purge all of the
2626 // entries for the scalars that use the symbolic expression.
2627 ForgetSymbolicName(PN, SymbolicName);
2628 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2632 } else if (const SCEVAddRecExpr *AddRec =
2633 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2634 // Otherwise, this could be a loop like this:
2635 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2636 // In this case, j = {1,+,1} and BEValue is j.
2637 // Because the other in-value of i (0) fits the evolution of BEValue
2638 // i really is an addrec evolution.
2639 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2640 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2642 // If StartVal = j.start - j.stride, we can use StartVal as the
2643 // initial step of the addrec evolution.
2644 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2645 AddRec->getOperand(1))) {
2646 const SCEV *PHISCEV =
2647 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2649 // Okay, for the entire analysis of this edge we assumed the PHI
2650 // to be symbolic. We now need to go back and purge all of the
2651 // entries for the scalars that use the symbolic expression.
2652 ForgetSymbolicName(PN, SymbolicName);
2653 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2659 return SymbolicName;
2662 // It's tempting to recognize PHIs with a unique incoming value, however
2663 // this leads passes like indvars to break LCSSA form. Fortunately, such
2664 // PHIs are rare, as instcombine zaps them.
2666 // If it's not a loop phi, we can't handle it yet.
2667 return getUnknown(PN);
2670 /// createNodeForGEP - Expand GEP instructions into add and multiply
2671 /// operations. This allows them to be analyzed by regular SCEV code.
2673 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2675 bool InBounds = GEP->isInBounds();
2676 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2677 Value *Base = GEP->getOperand(0);
2678 // Don't attempt to analyze GEPs over unsized objects.
2679 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2680 return getUnknown(GEP);
2681 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
2682 gep_type_iterator GTI = gep_type_begin(GEP);
2683 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2687 // Compute the (potentially symbolic) offset in bytes for this index.
2688 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2689 // For a struct, add the member offset.
2690 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2691 TotalOffset = getAddExpr(TotalOffset,
2692 getFieldOffsetExpr(STy, FieldNo),
2693 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2695 // For an array, add the element offset, explicitly scaled.
2696 const SCEV *LocalOffset = getSCEV(Index);
2697 if (!isa<PointerType>(LocalOffset->getType()))
2698 // Getelementptr indicies are signed.
2699 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
2700 // Lower "inbounds" GEPs to NSW arithmetic.
2701 LocalOffset = getMulExpr(LocalOffset, getAllocSizeExpr(*GTI),
2702 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2703 TotalOffset = getAddExpr(TotalOffset, LocalOffset,
2704 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2707 return getAddExpr(getSCEV(Base), TotalOffset,
2708 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2711 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2712 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2713 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2714 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2716 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2717 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2718 return C->getValue()->getValue().countTrailingZeros();
2720 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2721 return std::min(GetMinTrailingZeros(T->getOperand()),
2722 (uint32_t)getTypeSizeInBits(T->getType()));
2724 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2725 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2726 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2727 getTypeSizeInBits(E->getType()) : OpRes;
2730 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2731 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2732 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2733 getTypeSizeInBits(E->getType()) : OpRes;
2736 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2737 // The result is the min of all operands results.
2738 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2739 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2740 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2744 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2745 // The result is the sum of all operands results.
2746 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2747 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2748 for (unsigned i = 1, e = M->getNumOperands();
2749 SumOpRes != BitWidth && i != e; ++i)
2750 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2755 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2756 // The result is the min of all operands results.
2757 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2758 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2759 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2763 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2764 // The result is the min of all operands results.
2765 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2766 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2767 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2771 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2772 // The result is the min of all operands results.
2773 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2774 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2775 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2779 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2780 // For a SCEVUnknown, ask ValueTracking.
2781 unsigned BitWidth = getTypeSizeInBits(U->getType());
2782 APInt Mask = APInt::getAllOnesValue(BitWidth);
2783 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2784 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2785 return Zeros.countTrailingOnes();
2792 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2795 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2797 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2798 return ConstantRange(C->getValue()->getValue());
2800 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2801 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2802 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2803 X = X.add(getUnsignedRange(Add->getOperand(i)));
2807 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2808 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2809 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2810 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2814 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2815 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2816 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2817 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2821 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2822 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2823 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2824 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2828 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2829 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2830 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2834 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2835 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2836 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
2839 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2840 ConstantRange X = getUnsignedRange(SExt->getOperand());
2841 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
2844 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2845 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2846 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
2849 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
2851 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2852 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
2853 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
2854 ConstantRange ConservativeResult = FullSet;
2856 // If there's no unsigned wrap, the value will never be less than its
2858 if (AddRec->hasNoUnsignedWrap())
2859 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
2860 ConservativeResult =
2861 ConstantRange(C->getValue()->getValue(),
2862 APInt(getTypeSizeInBits(C->getType()), 0));
2864 // TODO: non-affine addrec
2865 if (Trip && AddRec->isAffine()) {
2866 const Type *Ty = AddRec->getType();
2867 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2868 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
2869 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2871 const SCEV *Start = AddRec->getStart();
2872 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2874 // Check for overflow.
2875 if (!AddRec->hasNoUnsignedWrap())
2876 return ConservativeResult;
2878 ConstantRange StartRange = getUnsignedRange(Start);
2879 ConstantRange EndRange = getUnsignedRange(End);
2880 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
2881 EndRange.getUnsignedMin());
2882 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
2883 EndRange.getUnsignedMax());
2884 if (Min.isMinValue() && Max.isMaxValue())
2885 return ConservativeResult;
2886 return ConstantRange(Min, Max+1);
2890 return ConservativeResult;
2893 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2894 // For a SCEVUnknown, ask ValueTracking.
2895 unsigned BitWidth = getTypeSizeInBits(U->getType());
2896 APInt Mask = APInt::getAllOnesValue(BitWidth);
2897 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2898 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
2899 if (Ones == ~Zeros + 1)
2901 return ConstantRange(Ones, ~Zeros + 1);
2907 /// getSignedRange - Determine the signed range for a particular SCEV.
2910 ScalarEvolution::getSignedRange(const SCEV *S) {
2912 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2913 return ConstantRange(C->getValue()->getValue());
2915 unsigned BitWidth = getTypeSizeInBits(S->getType());
2916 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
2918 // If the value has known zeros, the maximum signed value will have those
2919 // known zeros as well.
2920 uint32_t TZ = GetMinTrailingZeros(S);
2922 ConservativeResult =
2923 ConstantRange(APInt::getSignedMinValue(BitWidth),
2924 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
2926 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2927 ConstantRange X = getSignedRange(Add->getOperand(0));
2928 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2929 X = X.add(getSignedRange(Add->getOperand(i)));
2930 return ConservativeResult.intersectWith(X);
2933 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2934 ConstantRange X = getSignedRange(Mul->getOperand(0));
2935 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2936 X = X.multiply(getSignedRange(Mul->getOperand(i)));
2937 return ConservativeResult.intersectWith(X);
2940 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2941 ConstantRange X = getSignedRange(SMax->getOperand(0));
2942 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2943 X = X.smax(getSignedRange(SMax->getOperand(i)));
2944 return ConservativeResult.intersectWith(X);
2947 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2948 ConstantRange X = getSignedRange(UMax->getOperand(0));
2949 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2950 X = X.umax(getSignedRange(UMax->getOperand(i)));
2951 return ConservativeResult.intersectWith(X);
2954 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2955 ConstantRange X = getSignedRange(UDiv->getLHS());
2956 ConstantRange Y = getSignedRange(UDiv->getRHS());
2957 return ConservativeResult.intersectWith(X.udiv(Y));
2960 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2961 ConstantRange X = getSignedRange(ZExt->getOperand());
2962 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
2965 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2966 ConstantRange X = getSignedRange(SExt->getOperand());
2967 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
2970 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2971 ConstantRange X = getSignedRange(Trunc->getOperand());
2972 return ConservativeResult.intersectWith(X.truncate(BitWidth));
2975 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2976 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
2977 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
2979 // If there's no signed wrap, and all the operands have the same sign or
2980 // zero, the value won't ever change sign.
2981 if (AddRec->hasNoSignedWrap()) {
2982 bool AllNonNeg = true;
2983 bool AllNonPos = true;
2984 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
2985 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
2986 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
2989 ConservativeResult = ConservativeResult.intersectWith(
2990 ConstantRange(APInt(BitWidth, 0),
2991 APInt::getSignedMinValue(BitWidth)));
2993 ConservativeResult = ConservativeResult.intersectWith(
2994 ConstantRange(APInt::getSignedMinValue(BitWidth),
2995 APInt(BitWidth, 1)));
2998 // TODO: non-affine addrec
2999 if (Trip && AddRec->isAffine()) {
3000 const Type *Ty = AddRec->getType();
3001 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3002 if (getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3003 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3005 const SCEV *Start = AddRec->getStart();
3006 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
3008 // Check for overflow.
3009 if (!AddRec->hasNoSignedWrap())
3010 return ConservativeResult;
3012 ConstantRange StartRange = getSignedRange(Start);
3013 ConstantRange EndRange = getSignedRange(End);
3014 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3015 EndRange.getSignedMin());
3016 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3017 EndRange.getSignedMax());
3018 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3019 return ConservativeResult;
3020 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3024 return ConservativeResult;
3027 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3028 // For a SCEVUnknown, ask ValueTracking.
3029 if (!U->getValue()->getType()->isInteger() && !TD)
3030 return ConservativeResult;
3031 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3033 return ConservativeResult;
3034 return ConservativeResult.intersectWith(
3035 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3036 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3039 return ConservativeResult;
3042 /// createSCEV - We know that there is no SCEV for the specified value.
3043 /// Analyze the expression.
3045 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3046 if (!isSCEVable(V->getType()))
3047 return getUnknown(V);
3049 unsigned Opcode = Instruction::UserOp1;
3050 if (Instruction *I = dyn_cast<Instruction>(V))
3051 Opcode = I->getOpcode();
3052 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3053 Opcode = CE->getOpcode();
3054 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3055 return getConstant(CI);
3056 else if (isa<ConstantPointerNull>(V))
3057 return getIntegerSCEV(0, V->getType());
3058 else if (isa<UndefValue>(V))
3059 return getIntegerSCEV(0, V->getType());
3060 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3061 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3063 return getUnknown(V);
3065 Operator *U = cast<Operator>(V);
3067 case Instruction::Add:
3068 // Don't transfer the NSW and NUW bits from the Add instruction to the
3069 // Add expression, because the Instruction may be guarded by control
3070 // flow and the no-overflow bits may not be valid for the expression in
3072 return getAddExpr(getSCEV(U->getOperand(0)),
3073 getSCEV(U->getOperand(1)));
3074 case Instruction::Mul:
3075 // Don't transfer the NSW and NUW bits from the Mul instruction to the
3076 // Mul expression, as with Add.
3077 return getMulExpr(getSCEV(U->getOperand(0)),
3078 getSCEV(U->getOperand(1)));
3079 case Instruction::UDiv:
3080 return getUDivExpr(getSCEV(U->getOperand(0)),
3081 getSCEV(U->getOperand(1)));
3082 case Instruction::Sub:
3083 return getMinusSCEV(getSCEV(U->getOperand(0)),
3084 getSCEV(U->getOperand(1)));
3085 case Instruction::And:
3086 // For an expression like x&255 that merely masks off the high bits,
3087 // use zext(trunc(x)) as the SCEV expression.
3088 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3089 if (CI->isNullValue())
3090 return getSCEV(U->getOperand(1));
3091 if (CI->isAllOnesValue())
3092 return getSCEV(U->getOperand(0));
3093 const APInt &A = CI->getValue();
3095 // Instcombine's ShrinkDemandedConstant may strip bits out of
3096 // constants, obscuring what would otherwise be a low-bits mask.
3097 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3098 // knew about to reconstruct a low-bits mask value.
3099 unsigned LZ = A.countLeadingZeros();
3100 unsigned BitWidth = A.getBitWidth();
3101 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3102 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3103 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3105 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3107 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3109 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3110 IntegerType::get(getContext(), BitWidth - LZ)),
3115 case Instruction::Or:
3116 // If the RHS of the Or is a constant, we may have something like:
3117 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3118 // optimizations will transparently handle this case.
3120 // In order for this transformation to be safe, the LHS must be of the
3121 // form X*(2^n) and the Or constant must be less than 2^n.
3122 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3123 const SCEV *LHS = getSCEV(U->getOperand(0));
3124 const APInt &CIVal = CI->getValue();
3125 if (GetMinTrailingZeros(LHS) >=
3126 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3127 // Build a plain add SCEV.
3128 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3129 // If the LHS of the add was an addrec and it has no-wrap flags,
3130 // transfer the no-wrap flags, since an or won't introduce a wrap.
3131 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3132 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3133 if (OldAR->hasNoUnsignedWrap())
3134 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3135 if (OldAR->hasNoSignedWrap())
3136 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3142 case Instruction::Xor:
3143 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3144 // If the RHS of the xor is a signbit, then this is just an add.
3145 // Instcombine turns add of signbit into xor as a strength reduction step.
3146 if (CI->getValue().isSignBit())
3147 return getAddExpr(getSCEV(U->getOperand(0)),
3148 getSCEV(U->getOperand(1)));
3150 // If the RHS of xor is -1, then this is a not operation.
3151 if (CI->isAllOnesValue())
3152 return getNotSCEV(getSCEV(U->getOperand(0)));
3154 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3155 // This is a variant of the check for xor with -1, and it handles
3156 // the case where instcombine has trimmed non-demanded bits out
3157 // of an xor with -1.
3158 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3159 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3160 if (BO->getOpcode() == Instruction::And &&
3161 LCI->getValue() == CI->getValue())
3162 if (const SCEVZeroExtendExpr *Z =
3163 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3164 const Type *UTy = U->getType();
3165 const SCEV *Z0 = Z->getOperand();
3166 const Type *Z0Ty = Z0->getType();
3167 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3169 // If C is a low-bits mask, the zero extend is zerving to
3170 // mask off the high bits. Complement the operand and
3171 // re-apply the zext.
3172 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3173 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3175 // If C is a single bit, it may be in the sign-bit position
3176 // before the zero-extend. In this case, represent the xor
3177 // using an add, which is equivalent, and re-apply the zext.
3178 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3179 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3181 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3187 case Instruction::Shl:
3188 // Turn shift left of a constant amount into a multiply.
3189 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3190 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
3191 Constant *X = ConstantInt::get(getContext(),
3192 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3193 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3197 case Instruction::LShr:
3198 // Turn logical shift right of a constant into a unsigned divide.
3199 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3200 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
3201 Constant *X = ConstantInt::get(getContext(),
3202 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3203 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3207 case Instruction::AShr:
3208 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3209 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3210 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
3211 if (L->getOpcode() == Instruction::Shl &&
3212 L->getOperand(1) == U->getOperand(1)) {
3213 unsigned BitWidth = getTypeSizeInBits(U->getType());
3214 uint64_t Amt = BitWidth - CI->getZExtValue();
3215 if (Amt == BitWidth)
3216 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3218 return getIntegerSCEV(0, U->getType()); // value is undefined
3220 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3221 IntegerType::get(getContext(), Amt)),
3226 case Instruction::Trunc:
3227 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3229 case Instruction::ZExt:
3230 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3232 case Instruction::SExt:
3233 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3235 case Instruction::BitCast:
3236 // BitCasts are no-op casts so we just eliminate the cast.
3237 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3238 return getSCEV(U->getOperand(0));
3241 // It's tempting to handle inttoptr and ptrtoint, however this can
3242 // lead to pointer expressions which cannot be expanded to GEPs
3243 // (because they may overflow). For now, the only pointer-typed
3244 // expressions we handle are GEPs and address literals.
3246 case Instruction::GetElementPtr:
3247 return createNodeForGEP(cast<GEPOperator>(U));
3249 case Instruction::PHI:
3250 return createNodeForPHI(cast<PHINode>(U));
3252 case Instruction::Select:
3253 // This could be a smax or umax that was lowered earlier.
3254 // Try to recover it.
3255 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3256 Value *LHS = ICI->getOperand(0);
3257 Value *RHS = ICI->getOperand(1);
3258 switch (ICI->getPredicate()) {
3259 case ICmpInst::ICMP_SLT:
3260 case ICmpInst::ICMP_SLE:
3261 std::swap(LHS, RHS);
3263 case ICmpInst::ICMP_SGT:
3264 case ICmpInst::ICMP_SGE:
3265 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3266 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
3267 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3268 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
3270 case ICmpInst::ICMP_ULT:
3271 case ICmpInst::ICMP_ULE:
3272 std::swap(LHS, RHS);
3274 case ICmpInst::ICMP_UGT:
3275 case ICmpInst::ICMP_UGE:
3276 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3277 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
3278 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3279 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
3281 case ICmpInst::ICMP_NE:
3282 // n != 0 ? n : 1 -> umax(n, 1)
3283 if (LHS == U->getOperand(1) &&
3284 isa<ConstantInt>(U->getOperand(2)) &&
3285 cast<ConstantInt>(U->getOperand(2))->isOne() &&
3286 isa<ConstantInt>(RHS) &&
3287 cast<ConstantInt>(RHS)->isZero())
3288 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
3290 case ICmpInst::ICMP_EQ:
3291 // n == 0 ? 1 : n -> umax(n, 1)
3292 if (LHS == U->getOperand(2) &&
3293 isa<ConstantInt>(U->getOperand(1)) &&
3294 cast<ConstantInt>(U->getOperand(1))->isOne() &&
3295 isa<ConstantInt>(RHS) &&
3296 cast<ConstantInt>(RHS)->isZero())
3297 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
3304 default: // We cannot analyze this expression.
3308 return getUnknown(V);
3313 //===----------------------------------------------------------------------===//
3314 // Iteration Count Computation Code
3317 /// getBackedgeTakenCount - If the specified loop has a predictable
3318 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3319 /// object. The backedge-taken count is the number of times the loop header
3320 /// will be branched to from within the loop. This is one less than the
3321 /// trip count of the loop, since it doesn't count the first iteration,
3322 /// when the header is branched to from outside the loop.
3324 /// Note that it is not valid to call this method on a loop without a
3325 /// loop-invariant backedge-taken count (see
3326 /// hasLoopInvariantBackedgeTakenCount).
3328 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3329 return getBackedgeTakenInfo(L).Exact;
3332 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3333 /// return the least SCEV value that is known never to be less than the
3334 /// actual backedge taken count.
3335 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3336 return getBackedgeTakenInfo(L).Max;
3339 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3340 /// onto the given Worklist.
3342 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3343 BasicBlock *Header = L->getHeader();
3345 // Push all Loop-header PHIs onto the Worklist stack.
3346 for (BasicBlock::iterator I = Header->begin();
3347 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3348 Worklist.push_back(PN);
3351 const ScalarEvolution::BackedgeTakenInfo &
3352 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3353 // Initially insert a CouldNotCompute for this loop. If the insertion
3354 // succeeds, procede to actually compute a backedge-taken count and
3355 // update the value. The temporary CouldNotCompute value tells SCEV
3356 // code elsewhere that it shouldn't attempt to request a new
3357 // backedge-taken count, which could result in infinite recursion.
3358 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3359 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3361 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3362 if (BECount.Exact != getCouldNotCompute()) {
3363 assert(BECount.Exact->isLoopInvariant(L) &&
3364 BECount.Max->isLoopInvariant(L) &&
3365 "Computed backedge-taken count isn't loop invariant for loop!");
3366 ++NumTripCountsComputed;
3368 // Update the value in the map.
3369 Pair.first->second = BECount;
3371 if (BECount.Max != getCouldNotCompute())
3372 // Update the value in the map.
3373 Pair.first->second = BECount;
3374 if (isa<PHINode>(L->getHeader()->begin()))
3375 // Only count loops that have phi nodes as not being computable.
3376 ++NumTripCountsNotComputed;
3379 // Now that we know more about the trip count for this loop, forget any
3380 // existing SCEV values for PHI nodes in this loop since they are only
3381 // conservative estimates made without the benefit of trip count
3382 // information. This is similar to the code in forgetLoop, except that
3383 // it handles SCEVUnknown PHI nodes specially.
3384 if (BECount.hasAnyInfo()) {
3385 SmallVector<Instruction *, 16> Worklist;
3386 PushLoopPHIs(L, Worklist);
3388 SmallPtrSet<Instruction *, 8> Visited;
3389 while (!Worklist.empty()) {
3390 Instruction *I = Worklist.pop_back_val();
3391 if (!Visited.insert(I)) continue;
3393 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3394 Scalars.find(static_cast<Value *>(I));
3395 if (It != Scalars.end()) {
3396 // SCEVUnknown for a PHI either means that it has an unrecognized
3397 // structure, or it's a PHI that's in the progress of being computed
3398 // by createNodeForPHI. In the former case, additional loop trip
3399 // count information isn't going to change anything. In the later
3400 // case, createNodeForPHI will perform the necessary updates on its
3401 // own when it gets to that point.
3402 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3403 ValuesAtScopes.erase(It->second);
3406 if (PHINode *PN = dyn_cast<PHINode>(I))
3407 ConstantEvolutionLoopExitValue.erase(PN);
3410 PushDefUseChildren(I, Worklist);
3414 return Pair.first->second;
3417 /// forgetLoop - This method should be called by the client when it has
3418 /// changed a loop in a way that may effect ScalarEvolution's ability to
3419 /// compute a trip count, or if the loop is deleted.
3420 void ScalarEvolution::forgetLoop(const Loop *L) {
3421 // Drop any stored trip count value.
3422 BackedgeTakenCounts.erase(L);
3424 // Drop information about expressions based on loop-header PHIs.
3425 SmallVector<Instruction *, 16> Worklist;
3426 PushLoopPHIs(L, Worklist);
3428 SmallPtrSet<Instruction *, 8> Visited;
3429 while (!Worklist.empty()) {
3430 Instruction *I = Worklist.pop_back_val();
3431 if (!Visited.insert(I)) continue;
3433 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3434 Scalars.find(static_cast<Value *>(I));
3435 if (It != Scalars.end()) {
3436 ValuesAtScopes.erase(It->second);
3438 if (PHINode *PN = dyn_cast<PHINode>(I))
3439 ConstantEvolutionLoopExitValue.erase(PN);
3442 PushDefUseChildren(I, Worklist);
3446 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3447 /// of the specified loop will execute.
3448 ScalarEvolution::BackedgeTakenInfo
3449 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3450 SmallVector<BasicBlock *, 8> ExitingBlocks;
3451 L->getExitingBlocks(ExitingBlocks);
3453 // Examine all exits and pick the most conservative values.
3454 const SCEV *BECount = getCouldNotCompute();
3455 const SCEV *MaxBECount = getCouldNotCompute();
3456 bool CouldNotComputeBECount = false;
3457 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3458 BackedgeTakenInfo NewBTI =
3459 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3461 if (NewBTI.Exact == getCouldNotCompute()) {
3462 // We couldn't compute an exact value for this exit, so
3463 // we won't be able to compute an exact value for the loop.
3464 CouldNotComputeBECount = true;
3465 BECount = getCouldNotCompute();
3466 } else if (!CouldNotComputeBECount) {
3467 if (BECount == getCouldNotCompute())
3468 BECount = NewBTI.Exact;
3470 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3472 if (MaxBECount == getCouldNotCompute())
3473 MaxBECount = NewBTI.Max;
3474 else if (NewBTI.Max != getCouldNotCompute())
3475 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3478 return BackedgeTakenInfo(BECount, MaxBECount);
3481 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3482 /// of the specified loop will execute if it exits via the specified block.
3483 ScalarEvolution::BackedgeTakenInfo
3484 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3485 BasicBlock *ExitingBlock) {
3487 // Okay, we've chosen an exiting block. See what condition causes us to
3488 // exit at this block.
3490 // FIXME: we should be able to handle switch instructions (with a single exit)
3491 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3492 if (ExitBr == 0) return getCouldNotCompute();
3493 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3495 // At this point, we know we have a conditional branch that determines whether
3496 // the loop is exited. However, we don't know if the branch is executed each
3497 // time through the loop. If not, then the execution count of the branch will
3498 // not be equal to the trip count of the loop.
3500 // Currently we check for this by checking to see if the Exit branch goes to
3501 // the loop header. If so, we know it will always execute the same number of
3502 // times as the loop. We also handle the case where the exit block *is* the
3503 // loop header. This is common for un-rotated loops.
3505 // If both of those tests fail, walk up the unique predecessor chain to the
3506 // header, stopping if there is an edge that doesn't exit the loop. If the
3507 // header is reached, the execution count of the branch will be equal to the
3508 // trip count of the loop.
3510 // More extensive analysis could be done to handle more cases here.
3512 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3513 ExitBr->getSuccessor(1) != L->getHeader() &&
3514 ExitBr->getParent() != L->getHeader()) {
3515 // The simple checks failed, try climbing the unique predecessor chain
3516 // up to the header.
3518 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3519 BasicBlock *Pred = BB->getUniquePredecessor();
3521 return getCouldNotCompute();
3522 TerminatorInst *PredTerm = Pred->getTerminator();
3523 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3524 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3527 // If the predecessor has a successor that isn't BB and isn't
3528 // outside the loop, assume the worst.
3529 if (L->contains(PredSucc))
3530 return getCouldNotCompute();
3532 if (Pred == L->getHeader()) {
3539 return getCouldNotCompute();
3542 // Procede to the next level to examine the exit condition expression.
3543 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3544 ExitBr->getSuccessor(0),
3545 ExitBr->getSuccessor(1));
3548 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3549 /// backedge of the specified loop will execute if its exit condition
3550 /// were a conditional branch of ExitCond, TBB, and FBB.
3551 ScalarEvolution::BackedgeTakenInfo
3552 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3556 // Check if the controlling expression for this loop is an And or Or.
3557 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3558 if (BO->getOpcode() == Instruction::And) {
3559 // Recurse on the operands of the and.
3560 BackedgeTakenInfo BTI0 =
3561 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3562 BackedgeTakenInfo BTI1 =
3563 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3564 const SCEV *BECount = getCouldNotCompute();
3565 const SCEV *MaxBECount = getCouldNotCompute();
3566 if (L->contains(TBB)) {
3567 // Both conditions must be true for the loop to continue executing.
3568 // Choose the less conservative count.
3569 if (BTI0.Exact == getCouldNotCompute() ||
3570 BTI1.Exact == getCouldNotCompute())
3571 BECount = getCouldNotCompute();
3573 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3574 if (BTI0.Max == getCouldNotCompute())
3575 MaxBECount = BTI1.Max;
3576 else if (BTI1.Max == getCouldNotCompute())
3577 MaxBECount = BTI0.Max;
3579 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3581 // Both conditions must be true for the loop to exit.
3582 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3583 if (BTI0.Exact != getCouldNotCompute() &&
3584 BTI1.Exact != getCouldNotCompute())
3585 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3586 if (BTI0.Max != getCouldNotCompute() &&
3587 BTI1.Max != getCouldNotCompute())
3588 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3591 return BackedgeTakenInfo(BECount, MaxBECount);
3593 if (BO->getOpcode() == Instruction::Or) {
3594 // Recurse on the operands of the or.
3595 BackedgeTakenInfo BTI0 =
3596 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3597 BackedgeTakenInfo BTI1 =
3598 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3599 const SCEV *BECount = getCouldNotCompute();
3600 const SCEV *MaxBECount = getCouldNotCompute();
3601 if (L->contains(FBB)) {
3602 // Both conditions must be false for the loop to continue executing.
3603 // Choose the less conservative count.
3604 if (BTI0.Exact == getCouldNotCompute() ||
3605 BTI1.Exact == getCouldNotCompute())
3606 BECount = getCouldNotCompute();
3608 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3609 if (BTI0.Max == getCouldNotCompute())
3610 MaxBECount = BTI1.Max;
3611 else if (BTI1.Max == getCouldNotCompute())
3612 MaxBECount = BTI0.Max;
3614 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3616 // Both conditions must be false for the loop to exit.
3617 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3618 if (BTI0.Exact != getCouldNotCompute() &&
3619 BTI1.Exact != getCouldNotCompute())
3620 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3621 if (BTI0.Max != getCouldNotCompute() &&
3622 BTI1.Max != getCouldNotCompute())
3623 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3626 return BackedgeTakenInfo(BECount, MaxBECount);
3630 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3631 // Procede to the next level to examine the icmp.
3632 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3633 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3635 // If it's not an integer or pointer comparison then compute it the hard way.
3636 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3639 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3640 /// backedge of the specified loop will execute if its exit condition
3641 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3642 ScalarEvolution::BackedgeTakenInfo
3643 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3648 // If the condition was exit on true, convert the condition to exit on false
3649 ICmpInst::Predicate Cond;
3650 if (!L->contains(FBB))
3651 Cond = ExitCond->getPredicate();
3653 Cond = ExitCond->getInversePredicate();
3655 // Handle common loops like: for (X = "string"; *X; ++X)
3656 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3657 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3659 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3660 if (!isa<SCEVCouldNotCompute>(ItCnt)) {
3661 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType());
3662 return BackedgeTakenInfo(ItCnt,
3663 isa<SCEVConstant>(ItCnt) ? ItCnt :
3664 getConstant(APInt::getMaxValue(BitWidth)-1));
3668 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3669 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3671 // Try to evaluate any dependencies out of the loop.
3672 LHS = getSCEVAtScope(LHS, L);
3673 RHS = getSCEVAtScope(RHS, L);
3675 // At this point, we would like to compute how many iterations of the
3676 // loop the predicate will return true for these inputs.
3677 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3678 // If there is a loop-invariant, force it into the RHS.
3679 std::swap(LHS, RHS);
3680 Cond = ICmpInst::getSwappedPredicate(Cond);
3683 // If we have a comparison of a chrec against a constant, try to use value
3684 // ranges to answer this query.
3685 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3686 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3687 if (AddRec->getLoop() == L) {
3688 // Form the constant range.
3689 ConstantRange CompRange(
3690 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3692 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3693 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3697 case ICmpInst::ICMP_NE: { // while (X != Y)
3698 // Convert to: while (X-Y != 0)
3699 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3700 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3703 case ICmpInst::ICMP_EQ: { // while (X == Y)
3704 // Convert to: while (X-Y == 0)
3705 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3706 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3709 case ICmpInst::ICMP_SLT: {
3710 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3711 if (BTI.hasAnyInfo()) return BTI;
3714 case ICmpInst::ICMP_SGT: {
3715 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3716 getNotSCEV(RHS), L, true);
3717 if (BTI.hasAnyInfo()) return BTI;
3720 case ICmpInst::ICMP_ULT: {
3721 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3722 if (BTI.hasAnyInfo()) return BTI;
3725 case ICmpInst::ICMP_UGT: {
3726 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3727 getNotSCEV(RHS), L, false);
3728 if (BTI.hasAnyInfo()) return BTI;
3733 dbgs() << "ComputeBackedgeTakenCount ";
3734 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3735 dbgs() << "[unsigned] ";
3736 dbgs() << *LHS << " "
3737 << Instruction::getOpcodeName(Instruction::ICmp)
3738 << " " << *RHS << "\n";
3743 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3746 static ConstantInt *
3747 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3748 ScalarEvolution &SE) {
3749 const SCEV *InVal = SE.getConstant(C);
3750 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3751 assert(isa<SCEVConstant>(Val) &&
3752 "Evaluation of SCEV at constant didn't fold correctly?");
3753 return cast<SCEVConstant>(Val)->getValue();
3756 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3757 /// and a GEP expression (missing the pointer index) indexing into it, return
3758 /// the addressed element of the initializer or null if the index expression is
3761 GetAddressedElementFromGlobal(GlobalVariable *GV,
3762 const std::vector<ConstantInt*> &Indices) {
3763 Constant *Init = GV->getInitializer();
3764 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3765 uint64_t Idx = Indices[i]->getZExtValue();
3766 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3767 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3768 Init = cast<Constant>(CS->getOperand(Idx));
3769 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3770 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3771 Init = cast<Constant>(CA->getOperand(Idx));
3772 } else if (isa<ConstantAggregateZero>(Init)) {
3773 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3774 assert(Idx < STy->getNumElements() && "Bad struct index!");
3775 Init = Constant::getNullValue(STy->getElementType(Idx));
3776 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3777 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3778 Init = Constant::getNullValue(ATy->getElementType());
3780 llvm_unreachable("Unknown constant aggregate type!");
3784 return 0; // Unknown initializer type
3790 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3791 /// 'icmp op load X, cst', try to see if we can compute the backedge
3792 /// execution count.
3794 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3798 ICmpInst::Predicate predicate) {
3799 if (LI->isVolatile()) return getCouldNotCompute();
3801 // Check to see if the loaded pointer is a getelementptr of a global.
3802 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3803 if (!GEP) return getCouldNotCompute();
3805 // Make sure that it is really a constant global we are gepping, with an
3806 // initializer, and make sure the first IDX is really 0.
3807 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3808 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
3809 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3810 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3811 return getCouldNotCompute();
3813 // Okay, we allow one non-constant index into the GEP instruction.
3815 std::vector<ConstantInt*> Indexes;
3816 unsigned VarIdxNum = 0;
3817 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3818 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3819 Indexes.push_back(CI);
3820 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3821 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3822 VarIdx = GEP->getOperand(i);
3824 Indexes.push_back(0);
3827 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3828 // Check to see if X is a loop variant variable value now.
3829 const SCEV *Idx = getSCEV(VarIdx);
3830 Idx = getSCEVAtScope(Idx, L);
3832 // We can only recognize very limited forms of loop index expressions, in
3833 // particular, only affine AddRec's like {C1,+,C2}.
3834 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3835 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3836 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3837 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
3838 return getCouldNotCompute();
3840 unsigned MaxSteps = MaxBruteForceIterations;
3841 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3842 ConstantInt *ItCst = ConstantInt::get(
3843 cast<IntegerType>(IdxExpr->getType()), IterationNum);
3844 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
3846 // Form the GEP offset.
3847 Indexes[VarIdxNum] = Val;
3849 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
3850 if (Result == 0) break; // Cannot compute!
3852 // Evaluate the condition for this iteration.
3853 Result = ConstantExpr::getICmp(predicate, Result, RHS);
3854 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
3855 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
3857 dbgs() << "\n***\n*** Computed loop count " << *ItCst
3858 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
3861 ++NumArrayLenItCounts;
3862 return getConstant(ItCst); // Found terminating iteration!
3865 return getCouldNotCompute();
3869 /// CanConstantFold - Return true if we can constant fold an instruction of the
3870 /// specified type, assuming that all operands were constants.
3871 static bool CanConstantFold(const Instruction *I) {
3872 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
3873 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
3876 if (const CallInst *CI = dyn_cast<CallInst>(I))
3877 if (const Function *F = CI->getCalledFunction())
3878 return canConstantFoldCallTo(F);
3882 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
3883 /// in the loop that V is derived from. We allow arbitrary operations along the
3884 /// way, but the operands of an operation must either be constants or a value
3885 /// derived from a constant PHI. If this expression does not fit with these
3886 /// constraints, return null.
3887 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
3888 // If this is not an instruction, or if this is an instruction outside of the
3889 // loop, it can't be derived from a loop PHI.
3890 Instruction *I = dyn_cast<Instruction>(V);
3891 if (I == 0 || !L->contains(I)) return 0;
3893 if (PHINode *PN = dyn_cast<PHINode>(I)) {
3894 if (L->getHeader() == I->getParent())
3897 // We don't currently keep track of the control flow needed to evaluate
3898 // PHIs, so we cannot handle PHIs inside of loops.
3902 // If we won't be able to constant fold this expression even if the operands
3903 // are constants, return early.
3904 if (!CanConstantFold(I)) return 0;
3906 // Otherwise, we can evaluate this instruction if all of its operands are
3907 // constant or derived from a PHI node themselves.
3909 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
3910 if (!(isa<Constant>(I->getOperand(Op)) ||
3911 isa<GlobalValue>(I->getOperand(Op)))) {
3912 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
3913 if (P == 0) return 0; // Not evolving from PHI
3917 return 0; // Evolving from multiple different PHIs.
3920 // This is a expression evolving from a constant PHI!
3924 /// EvaluateExpression - Given an expression that passes the
3925 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
3926 /// in the loop has the value PHIVal. If we can't fold this expression for some
3927 /// reason, return null.
3928 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
3929 const TargetData *TD) {
3930 if (isa<PHINode>(V)) return PHIVal;
3931 if (Constant *C = dyn_cast<Constant>(V)) return C;
3932 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
3933 Instruction *I = cast<Instruction>(V);
3935 std::vector<Constant*> Operands;
3936 Operands.resize(I->getNumOperands());
3938 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3939 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
3940 if (Operands[i] == 0) return 0;
3943 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3944 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
3946 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3947 &Operands[0], Operands.size(), TD);
3950 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
3951 /// in the header of its containing loop, we know the loop executes a
3952 /// constant number of times, and the PHI node is just a recurrence
3953 /// involving constants, fold it.
3955 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
3958 std::map<PHINode*, Constant*>::iterator I =
3959 ConstantEvolutionLoopExitValue.find(PN);
3960 if (I != ConstantEvolutionLoopExitValue.end())
3963 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
3964 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
3966 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
3968 // Since the loop is canonicalized, the PHI node must have two entries. One
3969 // entry must be a constant (coming in from outside of the loop), and the
3970 // second must be derived from the same PHI.
3971 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3972 Constant *StartCST =
3973 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3975 return RetVal = 0; // Must be a constant.
3977 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3978 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3980 return RetVal = 0; // Not derived from same PHI.
3982 // Execute the loop symbolically to determine the exit value.
3983 if (BEs.getActiveBits() >= 32)
3984 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
3986 unsigned NumIterations = BEs.getZExtValue(); // must be in range
3987 unsigned IterationNum = 0;
3988 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
3989 if (IterationNum == NumIterations)
3990 return RetVal = PHIVal; // Got exit value!
3992 // Compute the value of the PHI node for the next iteration.
3993 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
3994 if (NextPHI == PHIVal)
3995 return RetVal = NextPHI; // Stopped evolving!
3997 return 0; // Couldn't evaluate!
4002 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4003 /// constant number of times (the condition evolves only from constants),
4004 /// try to evaluate a few iterations of the loop until we get the exit
4005 /// condition gets a value of ExitWhen (true or false). If we cannot
4006 /// evaluate the trip count of the loop, return getCouldNotCompute().
4008 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4011 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4012 if (PN == 0) return getCouldNotCompute();
4014 // Since the loop is canonicalized, the PHI node must have two entries. One
4015 // entry must be a constant (coming in from outside of the loop), and the
4016 // second must be derived from the same PHI.
4017 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4018 Constant *StartCST =
4019 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4020 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4022 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4023 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
4024 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
4026 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4027 // the loop symbolically to determine when the condition gets a value of
4029 unsigned IterationNum = 0;
4030 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4031 for (Constant *PHIVal = StartCST;
4032 IterationNum != MaxIterations; ++IterationNum) {
4033 ConstantInt *CondVal =
4034 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4036 // Couldn't symbolically evaluate.
4037 if (!CondVal) return getCouldNotCompute();
4039 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4040 ++NumBruteForceTripCountsComputed;
4041 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4044 // Compute the value of the PHI node for the next iteration.
4045 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4046 if (NextPHI == 0 || NextPHI == PHIVal)
4047 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4051 // Too many iterations were needed to evaluate.
4052 return getCouldNotCompute();
4055 /// getSCEVAtScope - Return a SCEV expression for the specified value
4056 /// at the specified scope in the program. The L value specifies a loop
4057 /// nest to evaluate the expression at, where null is the top-level or a
4058 /// specified loop is immediately inside of the loop.
4060 /// This method can be used to compute the exit value for a variable defined
4061 /// in a loop by querying what the value will hold in the parent loop.
4063 /// In the case that a relevant loop exit value cannot be computed, the
4064 /// original value V is returned.
4065 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4066 // Check to see if we've folded this expression at this loop before.
4067 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4068 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4069 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4071 return Pair.first->second ? Pair.first->second : V;
4073 // Otherwise compute it.
4074 const SCEV *C = computeSCEVAtScope(V, L);
4075 ValuesAtScopes[V][L] = C;
4079 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4080 if (isa<SCEVConstant>(V)) return V;
4082 // If this instruction is evolved from a constant-evolving PHI, compute the
4083 // exit value from the loop without using SCEVs.
4084 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4085 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4086 const Loop *LI = (*this->LI)[I->getParent()];
4087 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4088 if (PHINode *PN = dyn_cast<PHINode>(I))
4089 if (PN->getParent() == LI->getHeader()) {
4090 // Okay, there is no closed form solution for the PHI node. Check
4091 // to see if the loop that contains it has a known backedge-taken
4092 // count. If so, we may be able to force computation of the exit
4094 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4095 if (const SCEVConstant *BTCC =
4096 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4097 // Okay, we know how many times the containing loop executes. If
4098 // this is a constant evolving PHI node, get the final value at
4099 // the specified iteration number.
4100 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4101 BTCC->getValue()->getValue(),
4103 if (RV) return getSCEV(RV);
4107 // Okay, this is an expression that we cannot symbolically evaluate
4108 // into a SCEV. Check to see if it's possible to symbolically evaluate
4109 // the arguments into constants, and if so, try to constant propagate the
4110 // result. This is particularly useful for computing loop exit values.
4111 if (CanConstantFold(I)) {
4112 std::vector<Constant*> Operands;
4113 Operands.reserve(I->getNumOperands());
4114 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4115 Value *Op = I->getOperand(i);
4116 if (Constant *C = dyn_cast<Constant>(Op)) {
4117 Operands.push_back(C);
4119 // If any of the operands is non-constant and if they are
4120 // non-integer and non-pointer, don't even try to analyze them
4121 // with scev techniques.
4122 if (!isSCEVable(Op->getType()))
4125 const SCEV *OpV = getSCEVAtScope(Op, L);
4126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
4127 Constant *C = SC->getValue();
4128 if (C->getType() != Op->getType())
4129 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4133 Operands.push_back(C);
4134 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
4135 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
4136 if (C->getType() != Op->getType())
4138 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4142 Operands.push_back(C);
4152 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4153 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4154 Operands[0], Operands[1], TD);
4156 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4157 &Operands[0], Operands.size(), TD);
4162 // This is some other type of SCEVUnknown, just return it.
4166 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4167 // Avoid performing the look-up in the common case where the specified
4168 // expression has no loop-variant portions.
4169 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4170 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4171 if (OpAtScope != Comm->getOperand(i)) {
4172 // Okay, at least one of these operands is loop variant but might be
4173 // foldable. Build a new instance of the folded commutative expression.
4174 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4175 Comm->op_begin()+i);
4176 NewOps.push_back(OpAtScope);
4178 for (++i; i != e; ++i) {
4179 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4180 NewOps.push_back(OpAtScope);
4182 if (isa<SCEVAddExpr>(Comm))
4183 return getAddExpr(NewOps);
4184 if (isa<SCEVMulExpr>(Comm))
4185 return getMulExpr(NewOps);
4186 if (isa<SCEVSMaxExpr>(Comm))
4187 return getSMaxExpr(NewOps);
4188 if (isa<SCEVUMaxExpr>(Comm))
4189 return getUMaxExpr(NewOps);
4190 llvm_unreachable("Unknown commutative SCEV type!");
4193 // If we got here, all operands are loop invariant.
4197 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4198 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4199 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4200 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4201 return Div; // must be loop invariant
4202 return getUDivExpr(LHS, RHS);
4205 // If this is a loop recurrence for a loop that does not contain L, then we
4206 // are dealing with the final value computed by the loop.
4207 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4208 if (!L || !AddRec->getLoop()->contains(L)) {
4209 // To evaluate this recurrence, we need to know how many times the AddRec
4210 // loop iterates. Compute this now.
4211 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4212 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4214 // Then, evaluate the AddRec.
4215 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4220 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4221 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4222 if (Op == Cast->getOperand())
4223 return Cast; // must be loop invariant
4224 return getZeroExtendExpr(Op, Cast->getType());
4227 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4228 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4229 if (Op == Cast->getOperand())
4230 return Cast; // must be loop invariant
4231 return getSignExtendExpr(Op, Cast->getType());
4234 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4235 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4236 if (Op == Cast->getOperand())
4237 return Cast; // must be loop invariant
4238 return getTruncateExpr(Op, Cast->getType());
4241 if (isa<SCEVTargetDataConstant>(V))
4244 llvm_unreachable("Unknown SCEV type!");
4248 /// getSCEVAtScope - This is a convenience function which does
4249 /// getSCEVAtScope(getSCEV(V), L).
4250 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4251 return getSCEVAtScope(getSCEV(V), L);
4254 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4255 /// following equation:
4257 /// A * X = B (mod N)
4259 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4260 /// A and B isn't important.
4262 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4263 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4264 ScalarEvolution &SE) {
4265 uint32_t BW = A.getBitWidth();
4266 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4267 assert(A != 0 && "A must be non-zero.");
4271 // The gcd of A and N may have only one prime factor: 2. The number of
4272 // trailing zeros in A is its multiplicity
4273 uint32_t Mult2 = A.countTrailingZeros();
4276 // 2. Check if B is divisible by D.
4278 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4279 // is not less than multiplicity of this prime factor for D.
4280 if (B.countTrailingZeros() < Mult2)
4281 return SE.getCouldNotCompute();
4283 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4286 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4287 // bit width during computations.
4288 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4289 APInt Mod(BW + 1, 0);
4290 Mod.set(BW - Mult2); // Mod = N / D
4291 APInt I = AD.multiplicativeInverse(Mod);
4293 // 4. Compute the minimum unsigned root of the equation:
4294 // I * (B / D) mod (N / D)
4295 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4297 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4299 return SE.getConstant(Result.trunc(BW));
4302 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4303 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4304 /// might be the same) or two SCEVCouldNotCompute objects.
4306 static std::pair<const SCEV *,const SCEV *>
4307 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4308 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4309 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4310 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4311 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4313 // We currently can only solve this if the coefficients are constants.
4314 if (!LC || !MC || !NC) {
4315 const SCEV *CNC = SE.getCouldNotCompute();
4316 return std::make_pair(CNC, CNC);
4319 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4320 const APInt &L = LC->getValue()->getValue();
4321 const APInt &M = MC->getValue()->getValue();
4322 const APInt &N = NC->getValue()->getValue();
4323 APInt Two(BitWidth, 2);
4324 APInt Four(BitWidth, 4);
4327 using namespace APIntOps;
4329 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4330 // The B coefficient is M-N/2
4334 // The A coefficient is N/2
4335 APInt A(N.sdiv(Two));
4337 // Compute the B^2-4ac term.
4340 SqrtTerm -= Four * (A * C);
4342 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4343 // integer value or else APInt::sqrt() will assert.
4344 APInt SqrtVal(SqrtTerm.sqrt());
4346 // Compute the two solutions for the quadratic formula.
4347 // The divisions must be performed as signed divisions.
4349 APInt TwoA( A << 1 );
4350 if (TwoA.isMinValue()) {
4351 const SCEV *CNC = SE.getCouldNotCompute();
4352 return std::make_pair(CNC, CNC);
4355 LLVMContext &Context = SE.getContext();
4357 ConstantInt *Solution1 =
4358 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4359 ConstantInt *Solution2 =
4360 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4362 return std::make_pair(SE.getConstant(Solution1),
4363 SE.getConstant(Solution2));
4364 } // end APIntOps namespace
4367 /// HowFarToZero - Return the number of times a backedge comparing the specified
4368 /// value to zero will execute. If not computable, return CouldNotCompute.
4369 const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4370 // If the value is a constant
4371 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4372 // If the value is already zero, the branch will execute zero times.
4373 if (C->getValue()->isZero()) return C;
4374 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4377 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4378 if (!AddRec || AddRec->getLoop() != L)
4379 return getCouldNotCompute();
4381 if (AddRec->isAffine()) {
4382 // If this is an affine expression, the execution count of this branch is
4383 // the minimum unsigned root of the following equation:
4385 // Start + Step*N = 0 (mod 2^BW)
4389 // Step*N = -Start (mod 2^BW)
4391 // where BW is the common bit width of Start and Step.
4393 // Get the initial value for the loop.
4394 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4395 L->getParentLoop());
4396 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4397 L->getParentLoop());
4399 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4400 // For now we handle only constant steps.
4402 // First, handle unitary steps.
4403 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4404 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4405 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4406 return Start; // N = Start (as unsigned)
4408 // Then, try to solve the above equation provided that Start is constant.
4409 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4410 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4411 -StartC->getValue()->getValue(),
4414 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
4415 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4416 // the quadratic equation to solve it.
4417 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4419 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4420 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4423 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4424 << " sol#2: " << *R2 << "\n";
4426 // Pick the smallest positive root value.
4427 if (ConstantInt *CB =
4428 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4429 R1->getValue(), R2->getValue()))) {
4430 if (CB->getZExtValue() == false)
4431 std::swap(R1, R2); // R1 is the minimum root now.
4433 // We can only use this value if the chrec ends up with an exact zero
4434 // value at this index. When solving for "X*X != 5", for example, we
4435 // should not accept a root of 2.
4436 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4438 return R1; // We found a quadratic root!
4443 return getCouldNotCompute();
4446 /// HowFarToNonZero - Return the number of times a backedge checking the
4447 /// specified value for nonzero will execute. If not computable, return
4449 const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4450 // Loops that look like: while (X == 0) are very strange indeed. We don't
4451 // handle them yet except for the trivial case. This could be expanded in the
4452 // future as needed.
4454 // If the value is a constant, check to see if it is known to be non-zero
4455 // already. If so, the backedge will execute zero times.
4456 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4457 if (!C->getValue()->isNullValue())
4458 return getIntegerSCEV(0, C->getType());
4459 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4462 // We could implement others, but I really doubt anyone writes loops like
4463 // this, and if they did, they would already be constant folded.
4464 return getCouldNotCompute();
4467 /// getLoopPredecessor - If the given loop's header has exactly one unique
4468 /// predecessor outside the loop, return it. Otherwise return null.
4470 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
4471 BasicBlock *Header = L->getHeader();
4472 BasicBlock *Pred = 0;
4473 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
4475 if (!L->contains(*PI)) {
4476 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
4482 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4483 /// (which may not be an immediate predecessor) which has exactly one
4484 /// successor from which BB is reachable, or null if no such block is
4488 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4489 // If the block has a unique predecessor, then there is no path from the
4490 // predecessor to the block that does not go through the direct edge
4491 // from the predecessor to the block.
4492 if (BasicBlock *Pred = BB->getSinglePredecessor())
4495 // A loop's header is defined to be a block that dominates the loop.
4496 // If the header has a unique predecessor outside the loop, it must be
4497 // a block that has exactly one successor that can reach the loop.
4498 if (Loop *L = LI->getLoopFor(BB))
4499 return getLoopPredecessor(L);
4504 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4505 /// testing whether two expressions are equal, however for the purposes of
4506 /// looking for a condition guarding a loop, it can be useful to be a little
4507 /// more general, since a front-end may have replicated the controlling
4510 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4511 // Quick check to see if they are the same SCEV.
4512 if (A == B) return true;
4514 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4515 // two different instructions with the same value. Check for this case.
4516 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4517 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4518 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4519 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4520 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4523 // Otherwise assume they may have a different value.
4527 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
4528 return getSignedRange(S).getSignedMax().isNegative();
4531 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
4532 return getSignedRange(S).getSignedMin().isStrictlyPositive();
4535 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
4536 return !getSignedRange(S).getSignedMin().isNegative();
4539 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
4540 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
4543 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
4544 return isKnownNegative(S) || isKnownPositive(S);
4547 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
4548 const SCEV *LHS, const SCEV *RHS) {
4550 if (HasSameValue(LHS, RHS))
4551 return ICmpInst::isTrueWhenEqual(Pred);
4555 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4557 case ICmpInst::ICMP_SGT:
4558 Pred = ICmpInst::ICMP_SLT;
4559 std::swap(LHS, RHS);
4560 case ICmpInst::ICMP_SLT: {
4561 ConstantRange LHSRange = getSignedRange(LHS);
4562 ConstantRange RHSRange = getSignedRange(RHS);
4563 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
4565 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
4569 case ICmpInst::ICMP_SGE:
4570 Pred = ICmpInst::ICMP_SLE;
4571 std::swap(LHS, RHS);
4572 case ICmpInst::ICMP_SLE: {
4573 ConstantRange LHSRange = getSignedRange(LHS);
4574 ConstantRange RHSRange = getSignedRange(RHS);
4575 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
4577 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
4581 case ICmpInst::ICMP_UGT:
4582 Pred = ICmpInst::ICMP_ULT;
4583 std::swap(LHS, RHS);
4584 case ICmpInst::ICMP_ULT: {
4585 ConstantRange LHSRange = getUnsignedRange(LHS);
4586 ConstantRange RHSRange = getUnsignedRange(RHS);
4587 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
4589 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
4593 case ICmpInst::ICMP_UGE:
4594 Pred = ICmpInst::ICMP_ULE;
4595 std::swap(LHS, RHS);
4596 case ICmpInst::ICMP_ULE: {
4597 ConstantRange LHSRange = getUnsignedRange(LHS);
4598 ConstantRange RHSRange = getUnsignedRange(RHS);
4599 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
4601 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
4605 case ICmpInst::ICMP_NE: {
4606 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
4608 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
4611 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4612 if (isKnownNonZero(Diff))
4616 case ICmpInst::ICMP_EQ:
4617 // The check at the top of the function catches the case where
4618 // the values are known to be equal.
4624 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
4625 /// protected by a conditional between LHS and RHS. This is used to
4626 /// to eliminate casts.
4628 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
4629 ICmpInst::Predicate Pred,
4630 const SCEV *LHS, const SCEV *RHS) {
4631 // Interpret a null as meaning no loop, where there is obviously no guard
4632 // (interprocedural conditions notwithstanding).
4633 if (!L) return true;
4635 BasicBlock *Latch = L->getLoopLatch();
4639 BranchInst *LoopContinuePredicate =
4640 dyn_cast<BranchInst>(Latch->getTerminator());
4641 if (!LoopContinuePredicate ||
4642 LoopContinuePredicate->isUnconditional())
4645 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
4646 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
4649 /// isLoopGuardedByCond - Test whether entry to the loop is protected
4650 /// by a conditional between LHS and RHS. This is used to help avoid max
4651 /// expressions in loop trip counts, and to eliminate casts.
4653 ScalarEvolution::isLoopGuardedByCond(const Loop *L,
4654 ICmpInst::Predicate Pred,
4655 const SCEV *LHS, const SCEV *RHS) {
4656 // Interpret a null as meaning no loop, where there is obviously no guard
4657 // (interprocedural conditions notwithstanding).
4658 if (!L) return false;
4660 BasicBlock *Predecessor = getLoopPredecessor(L);
4661 BasicBlock *PredecessorDest = L->getHeader();
4663 // Starting at the loop predecessor, climb up the predecessor chain, as long
4664 // as there are predecessors that can be found that have unique successors
4665 // leading to the original header.
4667 PredecessorDest = Predecessor,
4668 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4670 BranchInst *LoopEntryPredicate =
4671 dyn_cast<BranchInst>(Predecessor->getTerminator());
4672 if (!LoopEntryPredicate ||
4673 LoopEntryPredicate->isUnconditional())
4676 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4677 LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4684 /// isImpliedCond - Test whether the condition described by Pred, LHS,
4685 /// and RHS is true whenever the given Cond value evaluates to true.
4686 bool ScalarEvolution::isImpliedCond(Value *CondValue,
4687 ICmpInst::Predicate Pred,
4688 const SCEV *LHS, const SCEV *RHS,
4690 // Recursivly handle And and Or conditions.
4691 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4692 if (BO->getOpcode() == Instruction::And) {
4694 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4695 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4696 } else if (BO->getOpcode() == Instruction::Or) {
4698 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4699 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4703 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4704 if (!ICI) return false;
4706 // Bail if the ICmp's operands' types are wider than the needed type
4707 // before attempting to call getSCEV on them. This avoids infinite
4708 // recursion, since the analysis of widening casts can require loop
4709 // exit condition information for overflow checking, which would
4711 if (getTypeSizeInBits(LHS->getType()) <
4712 getTypeSizeInBits(ICI->getOperand(0)->getType()))
4715 // Now that we found a conditional branch that dominates the loop, check to
4716 // see if it is the comparison we are looking for.
4717 ICmpInst::Predicate FoundPred;
4719 FoundPred = ICI->getInversePredicate();
4721 FoundPred = ICI->getPredicate();
4723 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
4724 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
4726 // Balance the types. The case where FoundLHS' type is wider than
4727 // LHS' type is checked for above.
4728 if (getTypeSizeInBits(LHS->getType()) >
4729 getTypeSizeInBits(FoundLHS->getType())) {
4730 if (CmpInst::isSigned(Pred)) {
4731 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
4732 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
4734 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
4735 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
4739 // Canonicalize the query to match the way instcombine will have
4740 // canonicalized the comparison.
4741 // First, put a constant operand on the right.
4742 if (isa<SCEVConstant>(LHS)) {
4743 std::swap(LHS, RHS);
4744 Pred = ICmpInst::getSwappedPredicate(Pred);
4746 // Then, canonicalize comparisons with boundary cases.
4747 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4748 const APInt &RA = RC->getValue()->getValue();
4750 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4751 case ICmpInst::ICMP_EQ:
4752 case ICmpInst::ICMP_NE:
4754 case ICmpInst::ICMP_UGE:
4755 if ((RA - 1).isMinValue()) {
4756 Pred = ICmpInst::ICMP_NE;
4757 RHS = getConstant(RA - 1);
4760 if (RA.isMaxValue()) {
4761 Pred = ICmpInst::ICMP_EQ;
4764 if (RA.isMinValue()) return true;
4766 case ICmpInst::ICMP_ULE:
4767 if ((RA + 1).isMaxValue()) {
4768 Pred = ICmpInst::ICMP_NE;
4769 RHS = getConstant(RA + 1);
4772 if (RA.isMinValue()) {
4773 Pred = ICmpInst::ICMP_EQ;
4776 if (RA.isMaxValue()) return true;
4778 case ICmpInst::ICMP_SGE:
4779 if ((RA - 1).isMinSignedValue()) {
4780 Pred = ICmpInst::ICMP_NE;
4781 RHS = getConstant(RA - 1);
4784 if (RA.isMaxSignedValue()) {
4785 Pred = ICmpInst::ICMP_EQ;
4788 if (RA.isMinSignedValue()) return true;
4790 case ICmpInst::ICMP_SLE:
4791 if ((RA + 1).isMaxSignedValue()) {
4792 Pred = ICmpInst::ICMP_NE;
4793 RHS = getConstant(RA + 1);
4796 if (RA.isMinSignedValue()) {
4797 Pred = ICmpInst::ICMP_EQ;
4800 if (RA.isMaxSignedValue()) return true;
4802 case ICmpInst::ICMP_UGT:
4803 if (RA.isMinValue()) {
4804 Pred = ICmpInst::ICMP_NE;
4807 if ((RA + 1).isMaxValue()) {
4808 Pred = ICmpInst::ICMP_EQ;
4809 RHS = getConstant(RA + 1);
4812 if (RA.isMaxValue()) return false;
4814 case ICmpInst::ICMP_ULT:
4815 if (RA.isMaxValue()) {
4816 Pred = ICmpInst::ICMP_NE;
4819 if ((RA - 1).isMinValue()) {
4820 Pred = ICmpInst::ICMP_EQ;
4821 RHS = getConstant(RA - 1);
4824 if (RA.isMinValue()) return false;
4826 case ICmpInst::ICMP_SGT:
4827 if (RA.isMinSignedValue()) {
4828 Pred = ICmpInst::ICMP_NE;
4831 if ((RA + 1).isMaxSignedValue()) {
4832 Pred = ICmpInst::ICMP_EQ;
4833 RHS = getConstant(RA + 1);
4836 if (RA.isMaxSignedValue()) return false;
4838 case ICmpInst::ICMP_SLT:
4839 if (RA.isMaxSignedValue()) {
4840 Pred = ICmpInst::ICMP_NE;
4843 if ((RA - 1).isMinSignedValue()) {
4844 Pred = ICmpInst::ICMP_EQ;
4845 RHS = getConstant(RA - 1);
4848 if (RA.isMinSignedValue()) return false;
4853 // Check to see if we can make the LHS or RHS match.
4854 if (LHS == FoundRHS || RHS == FoundLHS) {
4855 if (isa<SCEVConstant>(RHS)) {
4856 std::swap(FoundLHS, FoundRHS);
4857 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
4859 std::swap(LHS, RHS);
4860 Pred = ICmpInst::getSwappedPredicate(Pred);
4864 // Check whether the found predicate is the same as the desired predicate.
4865 if (FoundPred == Pred)
4866 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
4868 // Check whether swapping the found predicate makes it the same as the
4869 // desired predicate.
4870 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
4871 if (isa<SCEVConstant>(RHS))
4872 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
4874 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
4875 RHS, LHS, FoundLHS, FoundRHS);
4878 // Check whether the actual condition is beyond sufficient.
4879 if (FoundPred == ICmpInst::ICMP_EQ)
4880 if (ICmpInst::isTrueWhenEqual(Pred))
4881 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
4883 if (Pred == ICmpInst::ICMP_NE)
4884 if (!ICmpInst::isTrueWhenEqual(FoundPred))
4885 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
4888 // Otherwise assume the worst.
4892 /// isImpliedCondOperands - Test whether the condition described by Pred,
4893 /// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS,
4894 /// and FoundRHS is true.
4895 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
4896 const SCEV *LHS, const SCEV *RHS,
4897 const SCEV *FoundLHS,
4898 const SCEV *FoundRHS) {
4899 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
4900 FoundLHS, FoundRHS) ||
4901 // ~x < ~y --> x > y
4902 isImpliedCondOperandsHelper(Pred, LHS, RHS,
4903 getNotSCEV(FoundRHS),
4904 getNotSCEV(FoundLHS));
4907 /// isImpliedCondOperandsHelper - Test whether the condition described by
4908 /// Pred, LHS, and RHS is true whenever the condition desribed by Pred,
4909 /// FoundLHS, and FoundRHS is true.
4911 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
4912 const SCEV *LHS, const SCEV *RHS,
4913 const SCEV *FoundLHS,
4914 const SCEV *FoundRHS) {
4916 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4917 case ICmpInst::ICMP_EQ:
4918 case ICmpInst::ICMP_NE:
4919 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
4922 case ICmpInst::ICMP_SLT:
4923 case ICmpInst::ICMP_SLE:
4924 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
4925 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS))
4928 case ICmpInst::ICMP_SGT:
4929 case ICmpInst::ICMP_SGE:
4930 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
4931 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS))
4934 case ICmpInst::ICMP_ULT:
4935 case ICmpInst::ICMP_ULE:
4936 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
4937 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS))
4940 case ICmpInst::ICMP_UGT:
4941 case ICmpInst::ICMP_UGE:
4942 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
4943 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS))
4951 /// getBECount - Subtract the end and start values and divide by the step,
4952 /// rounding up, to get the number of times the backedge is executed. Return
4953 /// CouldNotCompute if an intermediate computation overflows.
4954 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
4958 assert(!isKnownNegative(Step) &&
4959 "This code doesn't handle negative strides yet!");
4961 const Type *Ty = Start->getType();
4962 const SCEV *NegOne = getIntegerSCEV(-1, Ty);
4963 const SCEV *Diff = getMinusSCEV(End, Start);
4964 const SCEV *RoundUp = getAddExpr(Step, NegOne);
4966 // Add an adjustment to the difference between End and Start so that
4967 // the division will effectively round up.
4968 const SCEV *Add = getAddExpr(Diff, RoundUp);
4971 // Check Add for unsigned overflow.
4972 // TODO: More sophisticated things could be done here.
4973 const Type *WideTy = IntegerType::get(getContext(),
4974 getTypeSizeInBits(Ty) + 1);
4975 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
4976 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
4977 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
4978 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
4979 return getCouldNotCompute();
4982 return getUDivExpr(Add, Step);
4985 /// HowManyLessThans - Return the number of times a backedge containing the
4986 /// specified less-than comparison will execute. If not computable, return
4987 /// CouldNotCompute.
4988 ScalarEvolution::BackedgeTakenInfo
4989 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
4990 const Loop *L, bool isSigned) {
4991 // Only handle: "ADDREC < LoopInvariant".
4992 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
4994 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
4995 if (!AddRec || AddRec->getLoop() != L)
4996 return getCouldNotCompute();
4998 // Check to see if we have a flag which makes analysis easy.
4999 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5000 AddRec->hasNoUnsignedWrap();
5002 if (AddRec->isAffine()) {
5003 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5004 const SCEV *Step = AddRec->getStepRecurrence(*this);
5007 return getCouldNotCompute();
5008 if (Step->isOne()) {
5009 // With unit stride, the iteration never steps past the limit value.
5010 } else if (isKnownPositive(Step)) {
5011 // Test whether a positive iteration iteration can step past the limit
5012 // value and past the maximum value for its type in a single step.
5013 // Note that it's not sufficient to check NoWrap here, because even
5014 // though the value after a wrap is undefined, it's not undefined
5015 // behavior, so if wrap does occur, the loop could either terminate or
5016 // loop infinitely, but in either case, the loop is guaranteed to
5017 // iterate at least until the iteration where the wrapping occurs.
5018 const SCEV *One = getIntegerSCEV(1, Step->getType());
5020 APInt Max = APInt::getSignedMaxValue(BitWidth);
5021 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5022 .slt(getSignedRange(RHS).getSignedMax()))
5023 return getCouldNotCompute();
5025 APInt Max = APInt::getMaxValue(BitWidth);
5026 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5027 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5028 return getCouldNotCompute();
5031 // TODO: Handle negative strides here and below.
5032 return getCouldNotCompute();
5034 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5035 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5036 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5037 // treat m-n as signed nor unsigned due to overflow possibility.
5039 // First, we get the value of the LHS in the first iteration: n
5040 const SCEV *Start = AddRec->getOperand(0);
5042 // Determine the minimum constant start value.
5043 const SCEV *MinStart = getConstant(isSigned ?
5044 getSignedRange(Start).getSignedMin() :
5045 getUnsignedRange(Start).getUnsignedMin());
5047 // If we know that the condition is true in order to enter the loop,
5048 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5049 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5050 // the division must round up.
5051 const SCEV *End = RHS;
5052 if (!isLoopGuardedByCond(L,
5053 isSigned ? ICmpInst::ICMP_SLT :
5055 getMinusSCEV(Start, Step), RHS))
5056 End = isSigned ? getSMaxExpr(RHS, Start)
5057 : getUMaxExpr(RHS, Start);
5059 // Determine the maximum constant end value.
5060 const SCEV *MaxEnd = getConstant(isSigned ?
5061 getSignedRange(End).getSignedMax() :
5062 getUnsignedRange(End).getUnsignedMax());
5064 // If MaxEnd is within a step of the maximum integer value in its type,
5065 // adjust it down to the minimum value which would produce the same effect.
5066 // This allows the subsequent ceiling divison of (N+(step-1))/step to
5067 // compute the correct value.
5068 const SCEV *StepMinusOne = getMinusSCEV(Step,
5069 getIntegerSCEV(1, Step->getType()));
5072 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5075 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5078 // Finally, we subtract these two values and divide, rounding up, to get
5079 // the number of times the backedge is executed.
5080 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5082 // The maximum backedge count is similar, except using the minimum start
5083 // value and the maximum end value.
5084 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5086 return BackedgeTakenInfo(BECount, MaxBECount);
5089 return getCouldNotCompute();
5092 /// getNumIterationsInRange - Return the number of iterations of this loop that
5093 /// produce values in the specified constant range. Another way of looking at
5094 /// this is that it returns the first iteration number where the value is not in
5095 /// the condition, thus computing the exit count. If the iteration count can't
5096 /// be computed, an instance of SCEVCouldNotCompute is returned.
5097 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5098 ScalarEvolution &SE) const {
5099 if (Range.isFullSet()) // Infinite loop.
5100 return SE.getCouldNotCompute();
5102 // If the start is a non-zero constant, shift the range to simplify things.
5103 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5104 if (!SC->getValue()->isZero()) {
5105 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5106 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
5107 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5108 if (const SCEVAddRecExpr *ShiftedAddRec =
5109 dyn_cast<SCEVAddRecExpr>(Shifted))
5110 return ShiftedAddRec->getNumIterationsInRange(
5111 Range.subtract(SC->getValue()->getValue()), SE);
5112 // This is strange and shouldn't happen.
5113 return SE.getCouldNotCompute();
5116 // The only time we can solve this is when we have all constant indices.
5117 // Otherwise, we cannot determine the overflow conditions.
5118 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5119 if (!isa<SCEVConstant>(getOperand(i)))
5120 return SE.getCouldNotCompute();
5123 // Okay at this point we know that all elements of the chrec are constants and
5124 // that the start element is zero.
5126 // First check to see if the range contains zero. If not, the first
5128 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5129 if (!Range.contains(APInt(BitWidth, 0)))
5130 return SE.getIntegerSCEV(0, getType());
5133 // If this is an affine expression then we have this situation:
5134 // Solve {0,+,A} in Range === Ax in Range
5136 // We know that zero is in the range. If A is positive then we know that
5137 // the upper value of the range must be the first possible exit value.
5138 // If A is negative then the lower of the range is the last possible loop
5139 // value. Also note that we already checked for a full range.
5140 APInt One(BitWidth,1);
5141 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5142 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5144 // The exit value should be (End+A)/A.
5145 APInt ExitVal = (End + A).udiv(A);
5146 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5148 // Evaluate at the exit value. If we really did fall out of the valid
5149 // range, then we computed our trip count, otherwise wrap around or other
5150 // things must have happened.
5151 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5152 if (Range.contains(Val->getValue()))
5153 return SE.getCouldNotCompute(); // Something strange happened
5155 // Ensure that the previous value is in the range. This is a sanity check.
5156 assert(Range.contains(
5157 EvaluateConstantChrecAtConstant(this,
5158 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5159 "Linear scev computation is off in a bad way!");
5160 return SE.getConstant(ExitValue);
5161 } else if (isQuadratic()) {
5162 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5163 // quadratic equation to solve it. To do this, we must frame our problem in
5164 // terms of figuring out when zero is crossed, instead of when
5165 // Range.getUpper() is crossed.
5166 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5167 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5168 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5170 // Next, solve the constructed addrec
5171 std::pair<const SCEV *,const SCEV *> Roots =
5172 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5173 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5174 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5176 // Pick the smallest positive root value.
5177 if (ConstantInt *CB =
5178 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5179 R1->getValue(), R2->getValue()))) {
5180 if (CB->getZExtValue() == false)
5181 std::swap(R1, R2); // R1 is the minimum root now.
5183 // Make sure the root is not off by one. The returned iteration should
5184 // not be in the range, but the previous one should be. When solving
5185 // for "X*X < 5", for example, we should not return a root of 2.
5186 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5189 if (Range.contains(R1Val->getValue())) {
5190 // The next iteration must be out of the range...
5191 ConstantInt *NextVal =
5192 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5194 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5195 if (!Range.contains(R1Val->getValue()))
5196 return SE.getConstant(NextVal);
5197 return SE.getCouldNotCompute(); // Something strange happened
5200 // If R1 was not in the range, then it is a good return value. Make
5201 // sure that R1-1 WAS in the range though, just in case.
5202 ConstantInt *NextVal =
5203 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5204 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5205 if (Range.contains(R1Val->getValue()))
5207 return SE.getCouldNotCompute(); // Something strange happened
5212 return SE.getCouldNotCompute();
5217 //===----------------------------------------------------------------------===//
5218 // SCEVCallbackVH Class Implementation
5219 //===----------------------------------------------------------------------===//
5221 void ScalarEvolution::SCEVCallbackVH::deleted() {
5222 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5223 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5224 SE->ConstantEvolutionLoopExitValue.erase(PN);
5225 SE->Scalars.erase(getValPtr());
5226 // this now dangles!
5229 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
5230 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5232 // Forget all the expressions associated with users of the old value,
5233 // so that future queries will recompute the expressions using the new
5235 SmallVector<User *, 16> Worklist;
5236 SmallPtrSet<User *, 8> Visited;
5237 Value *Old = getValPtr();
5238 bool DeleteOld = false;
5239 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5241 Worklist.push_back(*UI);
5242 while (!Worklist.empty()) {
5243 User *U = Worklist.pop_back_val();
5244 // Deleting the Old value will cause this to dangle. Postpone
5245 // that until everything else is done.
5250 if (!Visited.insert(U))
5252 if (PHINode *PN = dyn_cast<PHINode>(U))
5253 SE->ConstantEvolutionLoopExitValue.erase(PN);
5254 SE->Scalars.erase(U);
5255 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5257 Worklist.push_back(*UI);
5259 // Delete the Old value if it (indirectly) references itself.
5261 if (PHINode *PN = dyn_cast<PHINode>(Old))
5262 SE->ConstantEvolutionLoopExitValue.erase(PN);
5263 SE->Scalars.erase(Old);
5264 // this now dangles!
5269 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5270 : CallbackVH(V), SE(se) {}
5272 //===----------------------------------------------------------------------===//
5273 // ScalarEvolution Class Implementation
5274 //===----------------------------------------------------------------------===//
5276 ScalarEvolution::ScalarEvolution()
5277 : FunctionPass(&ID) {
5280 bool ScalarEvolution::runOnFunction(Function &F) {
5282 LI = &getAnalysis<LoopInfo>();
5283 DT = &getAnalysis<DominatorTree>();
5284 TD = getAnalysisIfAvailable<TargetData>();
5288 void ScalarEvolution::releaseMemory() {
5290 BackedgeTakenCounts.clear();
5291 ConstantEvolutionLoopExitValue.clear();
5292 ValuesAtScopes.clear();
5293 UniqueSCEVs.clear();
5294 SCEVAllocator.Reset();
5297 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5298 AU.setPreservesAll();
5299 AU.addRequiredTransitive<LoopInfo>();
5300 AU.addRequiredTransitive<DominatorTree>();
5303 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5304 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5307 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5309 // Print all inner loops first
5310 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5311 PrintLoopInfo(OS, SE, *I);
5314 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5317 SmallVector<BasicBlock *, 8> ExitBlocks;
5318 L->getExitBlocks(ExitBlocks);
5319 if (ExitBlocks.size() != 1)
5320 OS << "<multiple exits> ";
5322 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5323 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5325 OS << "Unpredictable backedge-taken count. ";
5330 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5333 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5334 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5336 OS << "Unpredictable max backedge-taken count. ";
5342 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5343 // ScalarEvolution's implementaiton of the print method is to print
5344 // out SCEV values of all instructions that are interesting. Doing
5345 // this potentially causes it to create new SCEV objects though,
5346 // which technically conflicts with the const qualifier. This isn't
5347 // observable from outside the class though, so casting away the
5348 // const isn't dangerous.
5349 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5351 OS << "Classifying expressions for: ";
5352 WriteAsOperand(OS, F, /*PrintType=*/false);
5354 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5355 if (isSCEVable(I->getType())) {
5358 const SCEV *SV = SE.getSCEV(&*I);
5361 const Loop *L = LI->getLoopFor((*I).getParent());
5363 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5370 OS << "\t\t" "Exits: ";
5371 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5372 if (!ExitValue->isLoopInvariant(L)) {
5373 OS << "<<Unknown>>";
5382 OS << "Determining loop execution counts for: ";
5383 WriteAsOperand(OS, F, /*PrintType=*/false);
5385 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5386 PrintLoopInfo(OS, &SE, *I);