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/Compiler.h"
78 #include "llvm/Support/ConstantRange.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->getHeader()))
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];
319 OS << "}<" << L->getHeader()->getName() + ">";
322 void SCEVFieldOffsetExpr::print(raw_ostream &OS) const {
323 // LLVM struct fields don't have names, so just print the field number.
324 OS << "offsetof(" << *STy << ", " << FieldNo << ")";
327 void SCEVAllocSizeExpr::print(raw_ostream &OS) const {
328 OS << "sizeof(" << *AllocTy << ")";
331 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
332 // All non-instruction values are loop invariant. All instructions are loop
333 // invariant if they are not contained in the specified loop.
334 // Instructions are never considered invariant in the function body
335 // (null loop) because they are defined within the "loop".
336 if (Instruction *I = dyn_cast<Instruction>(V))
337 return L && !L->contains(I->getParent());
341 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
342 if (Instruction *I = dyn_cast<Instruction>(getValue()))
343 return DT->dominates(I->getParent(), BB);
347 bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
348 if (Instruction *I = dyn_cast<Instruction>(getValue()))
349 return DT->properlyDominates(I->getParent(), BB);
353 const Type *SCEVUnknown::getType() const {
357 void SCEVUnknown::print(raw_ostream &OS) const {
358 WriteAsOperand(OS, V, false);
361 //===----------------------------------------------------------------------===//
363 //===----------------------------------------------------------------------===//
365 static bool CompareTypes(const Type *A, const Type *B) {
366 if (A->getTypeID() != B->getTypeID())
367 return A->getTypeID() < B->getTypeID();
368 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) {
369 const IntegerType *BI = cast<IntegerType>(B);
370 return AI->getBitWidth() < BI->getBitWidth();
372 if (const PointerType *AI = dyn_cast<PointerType>(A)) {
373 const PointerType *BI = cast<PointerType>(B);
374 return CompareTypes(AI->getElementType(), BI->getElementType());
376 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) {
377 const ArrayType *BI = cast<ArrayType>(B);
378 if (AI->getNumElements() != BI->getNumElements())
379 return AI->getNumElements() < BI->getNumElements();
380 return CompareTypes(AI->getElementType(), BI->getElementType());
382 if (const VectorType *AI = dyn_cast<VectorType>(A)) {
383 const VectorType *BI = cast<VectorType>(B);
384 if (AI->getNumElements() != BI->getNumElements())
385 return AI->getNumElements() < BI->getNumElements();
386 return CompareTypes(AI->getElementType(), BI->getElementType());
388 if (const StructType *AI = dyn_cast<StructType>(A)) {
389 const StructType *BI = cast<StructType>(B);
390 if (AI->getNumElements() != BI->getNumElements())
391 return AI->getNumElements() < BI->getNumElements();
392 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i)
393 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) ||
394 CompareTypes(BI->getElementType(i), AI->getElementType(i)))
395 return CompareTypes(AI->getElementType(i), BI->getElementType(i));
401 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
402 /// than the complexity of the RHS. This comparator is used to canonicalize
404 class VISIBILITY_HIDDEN SCEVComplexityCompare {
407 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
409 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
410 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
414 // Primarily, sort the SCEVs by their getSCEVType().
415 if (LHS->getSCEVType() != RHS->getSCEVType())
416 return LHS->getSCEVType() < RHS->getSCEVType();
418 // Aside from the getSCEVType() ordering, the particular ordering
419 // isn't very important except that it's beneficial to be consistent,
420 // so that (a + b) and (b + a) don't end up as different expressions.
422 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
423 // not as complete as it could be.
424 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
425 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
427 // Order pointer values after integer values. This helps SCEVExpander
429 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
431 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
434 // Compare getValueID values.
435 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
436 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
438 // Sort arguments by their position.
439 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
440 const Argument *RA = cast<Argument>(RU->getValue());
441 return LA->getArgNo() < RA->getArgNo();
444 // For instructions, compare their loop depth, and their opcode.
445 // This is pretty loose.
446 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
447 Instruction *RV = cast<Instruction>(RU->getValue());
449 // Compare loop depths.
450 if (LI->getLoopDepth(LV->getParent()) !=
451 LI->getLoopDepth(RV->getParent()))
452 return LI->getLoopDepth(LV->getParent()) <
453 LI->getLoopDepth(RV->getParent());
456 if (LV->getOpcode() != RV->getOpcode())
457 return LV->getOpcode() < RV->getOpcode();
459 // Compare the number of operands.
460 if (LV->getNumOperands() != RV->getNumOperands())
461 return LV->getNumOperands() < RV->getNumOperands();
467 // Compare constant values.
468 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
469 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
470 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
471 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
472 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
475 // Compare addrec loop depths.
476 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
477 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
478 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
479 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
482 // Lexicographically compare n-ary expressions.
483 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
484 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
485 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
486 if (i >= RC->getNumOperands())
488 if (operator()(LC->getOperand(i), RC->getOperand(i)))
490 if (operator()(RC->getOperand(i), LC->getOperand(i)))
493 return LC->getNumOperands() < RC->getNumOperands();
496 // Lexicographically compare udiv expressions.
497 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
498 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
499 if (operator()(LC->getLHS(), RC->getLHS()))
501 if (operator()(RC->getLHS(), LC->getLHS()))
503 if (operator()(LC->getRHS(), RC->getRHS()))
505 if (operator()(RC->getRHS(), LC->getRHS()))
510 // Compare cast expressions by operand.
511 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
512 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
513 return operator()(LC->getOperand(), RC->getOperand());
516 // Compare offsetof expressions.
517 if (const SCEVFieldOffsetExpr *LA = dyn_cast<SCEVFieldOffsetExpr>(LHS)) {
518 const SCEVFieldOffsetExpr *RA = cast<SCEVFieldOffsetExpr>(RHS);
519 if (CompareTypes(LA->getStructType(), RA->getStructType()) ||
520 CompareTypes(RA->getStructType(), LA->getStructType()))
521 return CompareTypes(LA->getStructType(), RA->getStructType());
522 return LA->getFieldNo() < RA->getFieldNo();
525 // Compare sizeof expressions by the allocation type.
526 if (const SCEVAllocSizeExpr *LA = dyn_cast<SCEVAllocSizeExpr>(LHS)) {
527 const SCEVAllocSizeExpr *RA = cast<SCEVAllocSizeExpr>(RHS);
528 return CompareTypes(LA->getAllocType(), RA->getAllocType());
531 llvm_unreachable("Unknown SCEV kind!");
537 /// GroupByComplexity - Given a list of SCEV objects, order them by their
538 /// complexity, and group objects of the same complexity together by value.
539 /// When this routine is finished, we know that any duplicates in the vector are
540 /// consecutive and that complexity is monotonically increasing.
542 /// Note that we go take special precautions to ensure that we get determinstic
543 /// results from this routine. In other words, we don't want the results of
544 /// this to depend on where the addresses of various SCEV objects happened to
547 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
549 if (Ops.size() < 2) return; // Noop
550 if (Ops.size() == 2) {
551 // This is the common case, which also happens to be trivially simple.
553 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
554 std::swap(Ops[0], Ops[1]);
558 // Do the rough sort by complexity.
559 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
561 // Now that we are sorted by complexity, group elements of the same
562 // complexity. Note that this is, at worst, N^2, but the vector is likely to
563 // be extremely short in practice. Note that we take this approach because we
564 // do not want to depend on the addresses of the objects we are grouping.
565 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
566 const SCEV *S = Ops[i];
567 unsigned Complexity = S->getSCEVType();
569 // If there are any objects of the same complexity and same value as this
571 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
572 if (Ops[j] == S) { // Found a duplicate.
573 // Move it to immediately after i'th element.
574 std::swap(Ops[i+1], Ops[j]);
575 ++i; // no need to rescan it.
576 if (i == e-2) return; // Done!
584 //===----------------------------------------------------------------------===//
585 // Simple SCEV method implementations
586 //===----------------------------------------------------------------------===//
588 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
590 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
592 const Type* ResultTy) {
593 // Handle the simplest case efficiently.
595 return SE.getTruncateOrZeroExtend(It, ResultTy);
597 // We are using the following formula for BC(It, K):
599 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
601 // Suppose, W is the bitwidth of the return value. We must be prepared for
602 // overflow. Hence, we must assure that the result of our computation is
603 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
604 // safe in modular arithmetic.
606 // However, this code doesn't use exactly that formula; the formula it uses
607 // is something like the following, where T is the number of factors of 2 in
608 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
611 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
613 // This formula is trivially equivalent to the previous formula. However,
614 // this formula can be implemented much more efficiently. The trick is that
615 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
616 // arithmetic. To do exact division in modular arithmetic, all we have
617 // to do is multiply by the inverse. Therefore, this step can be done at
620 // The next issue is how to safely do the division by 2^T. The way this
621 // is done is by doing the multiplication step at a width of at least W + T
622 // bits. This way, the bottom W+T bits of the product are accurate. Then,
623 // when we perform the division by 2^T (which is equivalent to a right shift
624 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
625 // truncated out after the division by 2^T.
627 // In comparison to just directly using the first formula, this technique
628 // is much more efficient; using the first formula requires W * K bits,
629 // but this formula less than W + K bits. Also, the first formula requires
630 // a division step, whereas this formula only requires multiplies and shifts.
632 // It doesn't matter whether the subtraction step is done in the calculation
633 // width or the input iteration count's width; if the subtraction overflows,
634 // the result must be zero anyway. We prefer here to do it in the width of
635 // the induction variable because it helps a lot for certain cases; CodeGen
636 // isn't smart enough to ignore the overflow, which leads to much less
637 // efficient code if the width of the subtraction is wider than the native
640 // (It's possible to not widen at all by pulling out factors of 2 before
641 // the multiplication; for example, K=2 can be calculated as
642 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
643 // extra arithmetic, so it's not an obvious win, and it gets
644 // much more complicated for K > 3.)
646 // Protection from insane SCEVs; this bound is conservative,
647 // but it probably doesn't matter.
649 return SE.getCouldNotCompute();
651 unsigned W = SE.getTypeSizeInBits(ResultTy);
653 // Calculate K! / 2^T and T; we divide out the factors of two before
654 // multiplying for calculating K! / 2^T to avoid overflow.
655 // Other overflow doesn't matter because we only care about the bottom
656 // W bits of the result.
657 APInt OddFactorial(W, 1);
659 for (unsigned i = 3; i <= K; ++i) {
661 unsigned TwoFactors = Mult.countTrailingZeros();
663 Mult = Mult.lshr(TwoFactors);
664 OddFactorial *= Mult;
667 // We need at least W + T bits for the multiplication step
668 unsigned CalculationBits = W + T;
670 // Calcuate 2^T, at width T+W.
671 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
673 // Calculate the multiplicative inverse of K! / 2^T;
674 // this multiplication factor will perform the exact division by
676 APInt Mod = APInt::getSignedMinValue(W+1);
677 APInt MultiplyFactor = OddFactorial.zext(W+1);
678 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
679 MultiplyFactor = MultiplyFactor.trunc(W);
681 // Calculate the product, at width T+W
682 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
684 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
685 for (unsigned i = 1; i != K; ++i) {
686 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
687 Dividend = SE.getMulExpr(Dividend,
688 SE.getTruncateOrZeroExtend(S, CalculationTy));
692 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
694 // Truncate the result, and divide by K! / 2^T.
696 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
697 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
700 /// evaluateAtIteration - Return the value of this chain of recurrences at
701 /// the specified iteration number. We can evaluate this recurrence by
702 /// multiplying each element in the chain by the binomial coefficient
703 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
705 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
707 /// where BC(It, k) stands for binomial coefficient.
709 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
710 ScalarEvolution &SE) const {
711 const SCEV *Result = getStart();
712 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
713 // The computation is correct in the face of overflow provided that the
714 // multiplication is performed _after_ the evaluation of the binomial
716 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
717 if (isa<SCEVCouldNotCompute>(Coeff))
720 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
725 //===----------------------------------------------------------------------===//
726 // SCEV Expression folder implementations
727 //===----------------------------------------------------------------------===//
729 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
731 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
732 "This is not a truncating conversion!");
733 assert(isSCEVable(Ty) &&
734 "This is not a conversion to a SCEVable type!");
735 Ty = getEffectiveSCEVType(Ty);
738 ID.AddInteger(scTruncate);
742 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
744 // Fold if the operand is constant.
745 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
747 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
749 // trunc(trunc(x)) --> trunc(x)
750 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
751 return getTruncateExpr(ST->getOperand(), Ty);
753 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
754 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
755 return getTruncateOrSignExtend(SS->getOperand(), Ty);
757 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
758 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
759 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
761 // If the input value is a chrec scev, truncate the chrec's operands.
762 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
763 SmallVector<const SCEV *, 4> Operands;
764 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
765 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
766 return getAddRecExpr(Operands, AddRec->getLoop());
769 // The cast wasn't folded; create an explicit cast node.
770 // Recompute the insert position, as it may have been invalidated.
771 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
772 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>();
773 new (S) SCEVTruncateExpr(ID, Op, Ty);
774 UniqueSCEVs.InsertNode(S, IP);
778 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
780 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
781 "This is not an extending conversion!");
782 assert(isSCEVable(Ty) &&
783 "This is not a conversion to a SCEVable type!");
784 Ty = getEffectiveSCEVType(Ty);
786 // Fold if the operand is constant.
787 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
788 const Type *IntTy = getEffectiveSCEVType(Ty);
789 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
790 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
791 return getConstant(cast<ConstantInt>(C));
794 // zext(zext(x)) --> zext(x)
795 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
796 return getZeroExtendExpr(SZ->getOperand(), Ty);
798 // Before doing any expensive analysis, check to see if we've already
799 // computed a SCEV for this Op and Ty.
801 ID.AddInteger(scZeroExtend);
805 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
807 // If the input value is a chrec scev, and we can prove that the value
808 // did not overflow the old, smaller, value, we can zero extend all of the
809 // operands (often constants). This allows analysis of something like
810 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
811 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
812 if (AR->isAffine()) {
813 const SCEV *Start = AR->getStart();
814 const SCEV *Step = AR->getStepRecurrence(*this);
815 unsigned BitWidth = getTypeSizeInBits(AR->getType());
816 const Loop *L = AR->getLoop();
818 // If we have special knowledge that this addrec won't overflow,
819 // we don't need to do any further analysis.
820 if (AR->hasNoUnsignedWrap())
821 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
822 getZeroExtendExpr(Step, Ty),
825 // Check whether the backedge-taken count is SCEVCouldNotCompute.
826 // Note that this serves two purposes: It filters out loops that are
827 // simply not analyzable, and it covers the case where this code is
828 // being called from within backedge-taken count analysis, such that
829 // attempting to ask for the backedge-taken count would likely result
830 // in infinite recursion. In the later case, the analysis code will
831 // cope with a conservative value, and it will take care to purge
832 // that value once it has finished.
833 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
834 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
835 // Manually compute the final value for AR, checking for
838 // Check whether the backedge-taken count can be losslessly casted to
839 // the addrec's type. The count is always unsigned.
840 const SCEV *CastedMaxBECount =
841 getTruncateOrZeroExtend(MaxBECount, Start->getType());
842 const SCEV *RecastedMaxBECount =
843 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
844 if (MaxBECount == RecastedMaxBECount) {
845 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
846 // Check whether Start+Step*MaxBECount has no unsigned overflow.
848 getMulExpr(CastedMaxBECount,
849 getTruncateOrZeroExtend(Step, Start->getType()));
850 const SCEV *Add = getAddExpr(Start, ZMul);
851 const SCEV *OperandExtendedAdd =
852 getAddExpr(getZeroExtendExpr(Start, WideTy),
853 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
854 getZeroExtendExpr(Step, WideTy)));
855 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
856 // Return the expression with the addrec on the outside.
857 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
858 getZeroExtendExpr(Step, Ty),
861 // Similar to above, only this time treat the step value as signed.
862 // This covers loops that count down.
864 getMulExpr(CastedMaxBECount,
865 getTruncateOrSignExtend(Step, Start->getType()));
866 Add = getAddExpr(Start, SMul);
868 getAddExpr(getZeroExtendExpr(Start, WideTy),
869 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
870 getSignExtendExpr(Step, WideTy)));
871 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
872 // Return the expression with the addrec on the outside.
873 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
874 getSignExtendExpr(Step, Ty),
878 // If the backedge is guarded by a comparison with the pre-inc value
879 // the addrec is safe. Also, if the entry is guarded by a comparison
880 // with the start value and the backedge is guarded by a comparison
881 // with the post-inc value, the addrec is safe.
882 if (isKnownPositive(Step)) {
883 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
884 getUnsignedRange(Step).getUnsignedMax());
885 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
886 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
887 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
888 AR->getPostIncExpr(*this), N)))
889 // Return the expression with the addrec on the outside.
890 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
891 getZeroExtendExpr(Step, Ty),
893 } else if (isKnownNegative(Step)) {
894 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
895 getSignedRange(Step).getSignedMin());
896 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) &&
897 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) ||
898 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
899 AR->getPostIncExpr(*this), N)))
900 // Return the expression with the addrec on the outside.
901 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
902 getSignExtendExpr(Step, Ty),
908 // The cast wasn't folded; create an explicit cast node.
909 // Recompute the insert position, as it may have been invalidated.
910 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
911 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>();
912 new (S) SCEVZeroExtendExpr(ID, Op, Ty);
913 UniqueSCEVs.InsertNode(S, IP);
917 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
919 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
920 "This is not an extending conversion!");
921 assert(isSCEVable(Ty) &&
922 "This is not a conversion to a SCEVable type!");
923 Ty = getEffectiveSCEVType(Ty);
925 // Fold if the operand is constant.
926 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
927 const Type *IntTy = getEffectiveSCEVType(Ty);
928 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
929 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
930 return getConstant(cast<ConstantInt>(C));
933 // sext(sext(x)) --> sext(x)
934 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
935 return getSignExtendExpr(SS->getOperand(), Ty);
937 // Before doing any expensive analysis, check to see if we've already
938 // computed a SCEV for this Op and Ty.
940 ID.AddInteger(scSignExtend);
944 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
946 // If the input value is a chrec scev, and we can prove that the value
947 // did not overflow the old, smaller, value, we can sign extend all of the
948 // operands (often constants). This allows analysis of something like
949 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
950 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
951 if (AR->isAffine()) {
952 const SCEV *Start = AR->getStart();
953 const SCEV *Step = AR->getStepRecurrence(*this);
954 unsigned BitWidth = getTypeSizeInBits(AR->getType());
955 const Loop *L = AR->getLoop();
957 // If we have special knowledge that this addrec won't overflow,
958 // we don't need to do any further analysis.
959 if (AR->hasNoSignedWrap())
960 return getAddRecExpr(getSignExtendExpr(Start, Ty),
961 getSignExtendExpr(Step, Ty),
964 // Check whether the backedge-taken count is SCEVCouldNotCompute.
965 // Note that this serves two purposes: It filters out loops that are
966 // simply not analyzable, and it covers the case where this code is
967 // being called from within backedge-taken count analysis, such that
968 // attempting to ask for the backedge-taken count would likely result
969 // in infinite recursion. In the later case, the analysis code will
970 // cope with a conservative value, and it will take care to purge
971 // that value once it has finished.
972 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
973 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
974 // Manually compute the final value for AR, checking for
977 // Check whether the backedge-taken count can be losslessly casted to
978 // the addrec's type. The count is always unsigned.
979 const SCEV *CastedMaxBECount =
980 getTruncateOrZeroExtend(MaxBECount, Start->getType());
981 const SCEV *RecastedMaxBECount =
982 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
983 if (MaxBECount == RecastedMaxBECount) {
984 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
985 // Check whether Start+Step*MaxBECount has no signed overflow.
987 getMulExpr(CastedMaxBECount,
988 getTruncateOrSignExtend(Step, Start->getType()));
989 const SCEV *Add = getAddExpr(Start, SMul);
990 const SCEV *OperandExtendedAdd =
991 getAddExpr(getSignExtendExpr(Start, WideTy),
992 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
993 getSignExtendExpr(Step, WideTy)));
994 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
995 // Return the expression with the addrec on the outside.
996 return getAddRecExpr(getSignExtendExpr(Start, Ty),
997 getSignExtendExpr(Step, Ty),
1000 // Similar to above, only this time treat the step value as unsigned.
1001 // This covers loops that count up with an unsigned step.
1003 getMulExpr(CastedMaxBECount,
1004 getTruncateOrZeroExtend(Step, Start->getType()));
1005 Add = getAddExpr(Start, UMul);
1006 OperandExtendedAdd =
1007 getAddExpr(getSignExtendExpr(Start, WideTy),
1008 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1009 getZeroExtendExpr(Step, WideTy)));
1010 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1011 // Return the expression with the addrec on the outside.
1012 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1013 getZeroExtendExpr(Step, Ty),
1017 // If the backedge is guarded by a comparison with the pre-inc value
1018 // the addrec is safe. Also, if the entry is guarded by a comparison
1019 // with the start value and the backedge is guarded by a comparison
1020 // with the post-inc value, the addrec is safe.
1021 if (isKnownPositive(Step)) {
1022 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1023 getSignedRange(Step).getSignedMax());
1024 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1025 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1026 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1027 AR->getPostIncExpr(*this), N)))
1028 // Return the expression with the addrec on the outside.
1029 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1030 getSignExtendExpr(Step, Ty),
1032 } else if (isKnownNegative(Step)) {
1033 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1034 getSignedRange(Step).getSignedMin());
1035 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1036 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1037 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1038 AR->getPostIncExpr(*this), N)))
1039 // Return the expression with the addrec on the outside.
1040 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1041 getSignExtendExpr(Step, Ty),
1047 // The cast wasn't folded; create an explicit cast node.
1048 // Recompute the insert position, as it may have been invalidated.
1049 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1050 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>();
1051 new (S) SCEVSignExtendExpr(ID, Op, Ty);
1052 UniqueSCEVs.InsertNode(S, IP);
1056 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1057 /// unspecified bits out to the given type.
1059 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1061 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1062 "This is not an extending conversion!");
1063 assert(isSCEVable(Ty) &&
1064 "This is not a conversion to a SCEVable type!");
1065 Ty = getEffectiveSCEVType(Ty);
1067 // Sign-extend negative constants.
1068 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1069 if (SC->getValue()->getValue().isNegative())
1070 return getSignExtendExpr(Op, Ty);
1072 // Peel off a truncate cast.
1073 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1074 const SCEV *NewOp = T->getOperand();
1075 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1076 return getAnyExtendExpr(NewOp, Ty);
1077 return getTruncateOrNoop(NewOp, Ty);
1080 // Next try a zext cast. If the cast is folded, use it.
1081 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1082 if (!isa<SCEVZeroExtendExpr>(ZExt))
1085 // Next try a sext cast. If the cast is folded, use it.
1086 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1087 if (!isa<SCEVSignExtendExpr>(SExt))
1090 // If the expression is obviously signed, use the sext cast value.
1091 if (isa<SCEVSMaxExpr>(Op))
1094 // Absent any other information, use the zext cast value.
1098 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1099 /// a list of operands to be added under the given scale, update the given
1100 /// map. This is a helper function for getAddRecExpr. As an example of
1101 /// what it does, given a sequence of operands that would form an add
1102 /// expression like this:
1104 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1106 /// where A and B are constants, update the map with these values:
1108 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1110 /// and add 13 + A*B*29 to AccumulatedConstant.
1111 /// This will allow getAddRecExpr to produce this:
1113 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1115 /// This form often exposes folding opportunities that are hidden in
1116 /// the original operand list.
1118 /// Return true iff it appears that any interesting folding opportunities
1119 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1120 /// the common case where no interesting opportunities are present, and
1121 /// is also used as a check to avoid infinite recursion.
1124 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1125 SmallVector<const SCEV *, 8> &NewOps,
1126 APInt &AccumulatedConstant,
1127 const SmallVectorImpl<const SCEV *> &Ops,
1129 ScalarEvolution &SE) {
1130 bool Interesting = false;
1132 // Iterate over the add operands.
1133 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1134 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1135 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1137 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1138 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1139 // A multiplication of a constant with another add; recurse.
1141 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1142 cast<SCEVAddExpr>(Mul->getOperand(1))
1146 // A multiplication of a constant with some other value. Update
1148 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1149 const SCEV *Key = SE.getMulExpr(MulOps);
1150 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1151 M.insert(std::make_pair(Key, NewScale));
1153 NewOps.push_back(Pair.first->first);
1155 Pair.first->second += NewScale;
1156 // The map already had an entry for this value, which may indicate
1157 // a folding opportunity.
1161 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1162 // Pull a buried constant out to the outside.
1163 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
1165 AccumulatedConstant += Scale * C->getValue()->getValue();
1167 // An ordinary operand. Update the map.
1168 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1169 M.insert(std::make_pair(Ops[i], Scale));
1171 NewOps.push_back(Pair.first->first);
1173 Pair.first->second += Scale;
1174 // The map already had an entry for this value, which may indicate
1175 // a folding opportunity.
1185 struct APIntCompare {
1186 bool operator()(const APInt &LHS, const APInt &RHS) const {
1187 return LHS.ult(RHS);
1192 /// getAddExpr - Get a canonical add expression, or something simpler if
1194 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1195 bool HasNUW, bool HasNSW) {
1196 assert(!Ops.empty() && "Cannot get empty add!");
1197 if (Ops.size() == 1) return Ops[0];
1199 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1200 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1201 getEffectiveSCEVType(Ops[0]->getType()) &&
1202 "SCEVAddExpr operand types don't match!");
1205 // Sort by complexity, this groups all similar expression types together.
1206 GroupByComplexity(Ops, LI);
1208 // If there are any constants, fold them together.
1210 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1212 assert(Idx < Ops.size());
1213 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1214 // We found two constants, fold them together!
1215 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1216 RHSC->getValue()->getValue());
1217 if (Ops.size() == 2) return Ops[0];
1218 Ops.erase(Ops.begin()+1); // Erase the folded element
1219 LHSC = cast<SCEVConstant>(Ops[0]);
1222 // If we are left with a constant zero being added, strip it off.
1223 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1224 Ops.erase(Ops.begin());
1229 if (Ops.size() == 1) return Ops[0];
1231 // Okay, check to see if the same value occurs in the operand list twice. If
1232 // so, merge them together into an multiply expression. Since we sorted the
1233 // list, these values are required to be adjacent.
1234 const Type *Ty = Ops[0]->getType();
1235 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1236 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1237 // Found a match, merge the two values into a multiply, and add any
1238 // remaining values to the result.
1239 const SCEV *Two = getIntegerSCEV(2, Ty);
1240 const SCEV *Mul = getMulExpr(Ops[i], Two);
1241 if (Ops.size() == 2)
1243 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1245 return getAddExpr(Ops, HasNUW, HasNSW);
1248 // Check for truncates. If all the operands are truncated from the same
1249 // type, see if factoring out the truncate would permit the result to be
1250 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1251 // if the contents of the resulting outer trunc fold to something simple.
1252 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1253 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1254 const Type *DstType = Trunc->getType();
1255 const Type *SrcType = Trunc->getOperand()->getType();
1256 SmallVector<const SCEV *, 8> LargeOps;
1258 // Check all the operands to see if they can be represented in the
1259 // source type of the truncate.
1260 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1261 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1262 if (T->getOperand()->getType() != SrcType) {
1266 LargeOps.push_back(T->getOperand());
1267 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1268 // This could be either sign or zero extension, but sign extension
1269 // is much more likely to be foldable here.
1270 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1271 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1272 SmallVector<const SCEV *, 8> LargeMulOps;
1273 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1274 if (const SCEVTruncateExpr *T =
1275 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1276 if (T->getOperand()->getType() != SrcType) {
1280 LargeMulOps.push_back(T->getOperand());
1281 } else if (const SCEVConstant *C =
1282 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1283 // This could be either sign or zero extension, but sign extension
1284 // is much more likely to be foldable here.
1285 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1292 LargeOps.push_back(getMulExpr(LargeMulOps));
1299 // Evaluate the expression in the larger type.
1300 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1301 // If it folds to something simple, use it. Otherwise, don't.
1302 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1303 return getTruncateExpr(Fold, DstType);
1307 // Skip past any other cast SCEVs.
1308 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1311 // If there are add operands they would be next.
1312 if (Idx < Ops.size()) {
1313 bool DeletedAdd = false;
1314 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1315 // If we have an add, expand the add operands onto the end of the operands
1317 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1318 Ops.erase(Ops.begin()+Idx);
1322 // If we deleted at least one add, we added operands to the end of the list,
1323 // and they are not necessarily sorted. Recurse to resort and resimplify
1324 // any operands we just aquired.
1326 return getAddExpr(Ops);
1329 // Skip over the add expression until we get to a multiply.
1330 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1333 // Check to see if there are any folding opportunities present with
1334 // operands multiplied by constant values.
1335 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1336 uint64_t BitWidth = getTypeSizeInBits(Ty);
1337 DenseMap<const SCEV *, APInt> M;
1338 SmallVector<const SCEV *, 8> NewOps;
1339 APInt AccumulatedConstant(BitWidth, 0);
1340 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1341 Ops, APInt(BitWidth, 1), *this)) {
1342 // Some interesting folding opportunity is present, so its worthwhile to
1343 // re-generate the operands list. Group the operands by constant scale,
1344 // to avoid multiplying by the same constant scale multiple times.
1345 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1346 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1347 E = NewOps.end(); I != E; ++I)
1348 MulOpLists[M.find(*I)->second].push_back(*I);
1349 // Re-generate the operands list.
1351 if (AccumulatedConstant != 0)
1352 Ops.push_back(getConstant(AccumulatedConstant));
1353 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1354 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1356 Ops.push_back(getMulExpr(getConstant(I->first),
1357 getAddExpr(I->second)));
1359 return getIntegerSCEV(0, Ty);
1360 if (Ops.size() == 1)
1362 return getAddExpr(Ops);
1366 // If we are adding something to a multiply expression, make sure the
1367 // something is not already an operand of the multiply. If so, merge it into
1369 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1370 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1371 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1372 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1373 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1374 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1375 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1376 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1377 if (Mul->getNumOperands() != 2) {
1378 // If the multiply has more than two operands, we must get the
1380 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1381 MulOps.erase(MulOps.begin()+MulOp);
1382 InnerMul = getMulExpr(MulOps);
1384 const SCEV *One = getIntegerSCEV(1, Ty);
1385 const SCEV *AddOne = getAddExpr(InnerMul, One);
1386 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1387 if (Ops.size() == 2) return OuterMul;
1389 Ops.erase(Ops.begin()+AddOp);
1390 Ops.erase(Ops.begin()+Idx-1);
1392 Ops.erase(Ops.begin()+Idx);
1393 Ops.erase(Ops.begin()+AddOp-1);
1395 Ops.push_back(OuterMul);
1396 return getAddExpr(Ops);
1399 // Check this multiply against other multiplies being added together.
1400 for (unsigned OtherMulIdx = Idx+1;
1401 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1403 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1404 // If MulOp occurs in OtherMul, we can fold the two multiplies
1406 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1407 OMulOp != e; ++OMulOp)
1408 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1409 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1410 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1411 if (Mul->getNumOperands() != 2) {
1412 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1414 MulOps.erase(MulOps.begin()+MulOp);
1415 InnerMul1 = getMulExpr(MulOps);
1417 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1418 if (OtherMul->getNumOperands() != 2) {
1419 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1420 OtherMul->op_end());
1421 MulOps.erase(MulOps.begin()+OMulOp);
1422 InnerMul2 = getMulExpr(MulOps);
1424 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1425 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1426 if (Ops.size() == 2) return OuterMul;
1427 Ops.erase(Ops.begin()+Idx);
1428 Ops.erase(Ops.begin()+OtherMulIdx-1);
1429 Ops.push_back(OuterMul);
1430 return getAddExpr(Ops);
1436 // If there are any add recurrences in the operands list, see if any other
1437 // added values are loop invariant. If so, we can fold them into the
1439 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1442 // Scan over all recurrences, trying to fold loop invariants into them.
1443 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1444 // Scan all of the other operands to this add and add them to the vector if
1445 // they are loop invariant w.r.t. the recurrence.
1446 SmallVector<const SCEV *, 8> LIOps;
1447 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1448 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1449 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1450 LIOps.push_back(Ops[i]);
1451 Ops.erase(Ops.begin()+i);
1455 // If we found some loop invariants, fold them into the recurrence.
1456 if (!LIOps.empty()) {
1457 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1458 LIOps.push_back(AddRec->getStart());
1460 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1462 AddRecOps[0] = getAddExpr(LIOps);
1464 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1465 // If all of the other operands were loop invariant, we are done.
1466 if (Ops.size() == 1) return NewRec;
1468 // Otherwise, add the folded AddRec by the non-liv parts.
1469 for (unsigned i = 0;; ++i)
1470 if (Ops[i] == AddRec) {
1474 return getAddExpr(Ops);
1477 // Okay, if there weren't any loop invariants to be folded, check to see if
1478 // there are multiple AddRec's with the same loop induction variable being
1479 // added together. If so, we can fold them.
1480 for (unsigned OtherIdx = Idx+1;
1481 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1482 if (OtherIdx != Idx) {
1483 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1484 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1485 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1486 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1488 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1489 if (i >= NewOps.size()) {
1490 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1491 OtherAddRec->op_end());
1494 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1496 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1498 if (Ops.size() == 2) return NewAddRec;
1500 Ops.erase(Ops.begin()+Idx);
1501 Ops.erase(Ops.begin()+OtherIdx-1);
1502 Ops.push_back(NewAddRec);
1503 return getAddExpr(Ops);
1507 // Otherwise couldn't fold anything into this recurrence. Move onto the
1511 // Okay, it looks like we really DO need an add expr. Check to see if we
1512 // already have one, otherwise create a new one.
1513 FoldingSetNodeID ID;
1514 ID.AddInteger(scAddExpr);
1515 ID.AddInteger(Ops.size());
1516 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1517 ID.AddPointer(Ops[i]);
1519 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1520 SCEVAddExpr *S = SCEVAllocator.Allocate<SCEVAddExpr>();
1521 new (S) SCEVAddExpr(ID, Ops);
1522 UniqueSCEVs.InsertNode(S, IP);
1523 if (HasNUW) S->setHasNoUnsignedWrap(true);
1524 if (HasNSW) S->setHasNoSignedWrap(true);
1529 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1531 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1532 bool HasNUW, bool HasNSW) {
1533 assert(!Ops.empty() && "Cannot get empty mul!");
1535 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1536 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1537 getEffectiveSCEVType(Ops[0]->getType()) &&
1538 "SCEVMulExpr operand types don't match!");
1541 // Sort by complexity, this groups all similar expression types together.
1542 GroupByComplexity(Ops, LI);
1544 // If there are any constants, fold them together.
1546 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1548 // C1*(C2+V) -> C1*C2 + C1*V
1549 if (Ops.size() == 2)
1550 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1551 if (Add->getNumOperands() == 2 &&
1552 isa<SCEVConstant>(Add->getOperand(0)))
1553 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1554 getMulExpr(LHSC, Add->getOperand(1)));
1558 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1559 // We found two constants, fold them together!
1560 ConstantInt *Fold = ConstantInt::get(getContext(),
1561 LHSC->getValue()->getValue() *
1562 RHSC->getValue()->getValue());
1563 Ops[0] = getConstant(Fold);
1564 Ops.erase(Ops.begin()+1); // Erase the folded element
1565 if (Ops.size() == 1) return Ops[0];
1566 LHSC = cast<SCEVConstant>(Ops[0]);
1569 // If we are left with a constant one being multiplied, strip it off.
1570 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1571 Ops.erase(Ops.begin());
1573 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1574 // If we have a multiply of zero, it will always be zero.
1579 // Skip over the add expression until we get to a multiply.
1580 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1583 if (Ops.size() == 1)
1586 // If there are mul operands inline them all into this expression.
1587 if (Idx < Ops.size()) {
1588 bool DeletedMul = false;
1589 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1590 // If we have an mul, expand the mul operands onto the end of the operands
1592 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1593 Ops.erase(Ops.begin()+Idx);
1597 // If we deleted at least one mul, we added operands to the end of the list,
1598 // and they are not necessarily sorted. Recurse to resort and resimplify
1599 // any operands we just aquired.
1601 return getMulExpr(Ops);
1604 // If there are any add recurrences in the operands list, see if any other
1605 // added values are loop invariant. If so, we can fold them into the
1607 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1610 // Scan over all recurrences, trying to fold loop invariants into them.
1611 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1612 // Scan all of the other operands to this mul and add them to the vector if
1613 // they are loop invariant w.r.t. the recurrence.
1614 SmallVector<const SCEV *, 8> LIOps;
1615 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1616 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1617 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1618 LIOps.push_back(Ops[i]);
1619 Ops.erase(Ops.begin()+i);
1623 // If we found some loop invariants, fold them into the recurrence.
1624 if (!LIOps.empty()) {
1625 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1626 SmallVector<const SCEV *, 4> NewOps;
1627 NewOps.reserve(AddRec->getNumOperands());
1628 if (LIOps.size() == 1) {
1629 const SCEV *Scale = LIOps[0];
1630 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1631 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1633 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1634 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
1635 MulOps.push_back(AddRec->getOperand(i));
1636 NewOps.push_back(getMulExpr(MulOps));
1640 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1642 // If all of the other operands were loop invariant, we are done.
1643 if (Ops.size() == 1) return NewRec;
1645 // Otherwise, multiply the folded AddRec by the non-liv parts.
1646 for (unsigned i = 0;; ++i)
1647 if (Ops[i] == AddRec) {
1651 return getMulExpr(Ops);
1654 // Okay, if there weren't any loop invariants to be folded, check to see if
1655 // there are multiple AddRec's with the same loop induction variable being
1656 // multiplied together. If so, we can fold them.
1657 for (unsigned OtherIdx = Idx+1;
1658 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1659 if (OtherIdx != Idx) {
1660 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1661 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1662 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1663 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1664 const SCEV *NewStart = getMulExpr(F->getStart(),
1666 const SCEV *B = F->getStepRecurrence(*this);
1667 const SCEV *D = G->getStepRecurrence(*this);
1668 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1671 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1673 if (Ops.size() == 2) return NewAddRec;
1675 Ops.erase(Ops.begin()+Idx);
1676 Ops.erase(Ops.begin()+OtherIdx-1);
1677 Ops.push_back(NewAddRec);
1678 return getMulExpr(Ops);
1682 // Otherwise couldn't fold anything into this recurrence. Move onto the
1686 // Okay, it looks like we really DO need an mul expr. Check to see if we
1687 // already have one, otherwise create a new one.
1688 FoldingSetNodeID ID;
1689 ID.AddInteger(scMulExpr);
1690 ID.AddInteger(Ops.size());
1691 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1692 ID.AddPointer(Ops[i]);
1694 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1695 SCEVMulExpr *S = SCEVAllocator.Allocate<SCEVMulExpr>();
1696 new (S) SCEVMulExpr(ID, Ops);
1697 UniqueSCEVs.InsertNode(S, IP);
1698 if (HasNUW) S->setHasNoUnsignedWrap(true);
1699 if (HasNSW) S->setHasNoSignedWrap(true);
1703 /// getUDivExpr - Get a canonical unsigned division expression, or something
1704 /// simpler if possible.
1705 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1707 assert(getEffectiveSCEVType(LHS->getType()) ==
1708 getEffectiveSCEVType(RHS->getType()) &&
1709 "SCEVUDivExpr operand types don't match!");
1711 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1712 if (RHSC->getValue()->equalsInt(1))
1713 return LHS; // X udiv 1 --> x
1715 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1717 // Determine if the division can be folded into the operands of
1719 // TODO: Generalize this to non-constants by using known-bits information.
1720 const Type *Ty = LHS->getType();
1721 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1722 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1723 // For non-power-of-two values, effectively round the value up to the
1724 // nearest power of two.
1725 if (!RHSC->getValue()->getValue().isPowerOf2())
1727 const IntegerType *ExtTy =
1728 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1729 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1730 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1731 if (const SCEVConstant *Step =
1732 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1733 if (!Step->getValue()->getValue()
1734 .urem(RHSC->getValue()->getValue()) &&
1735 getZeroExtendExpr(AR, ExtTy) ==
1736 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1737 getZeroExtendExpr(Step, ExtTy),
1739 SmallVector<const SCEV *, 4> Operands;
1740 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1741 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1742 return getAddRecExpr(Operands, AR->getLoop());
1744 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1745 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1746 SmallVector<const SCEV *, 4> Operands;
1747 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1748 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1749 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1750 // Find an operand that's safely divisible.
1751 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1752 const SCEV *Op = M->getOperand(i);
1753 const SCEV *Div = getUDivExpr(Op, RHSC);
1754 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1755 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands();
1756 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(),
1759 return getMulExpr(Operands);
1763 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1764 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1765 SmallVector<const SCEV *, 4> Operands;
1766 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1767 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1768 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1770 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1771 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1772 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1774 Operands.push_back(Op);
1776 if (Operands.size() == A->getNumOperands())
1777 return getAddExpr(Operands);
1781 // Fold if both operands are constant.
1782 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1783 Constant *LHSCV = LHSC->getValue();
1784 Constant *RHSCV = RHSC->getValue();
1785 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1790 FoldingSetNodeID ID;
1791 ID.AddInteger(scUDivExpr);
1795 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1796 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>();
1797 new (S) SCEVUDivExpr(ID, LHS, RHS);
1798 UniqueSCEVs.InsertNode(S, IP);
1803 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1804 /// Simplify the expression as much as possible.
1805 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1806 const SCEV *Step, const Loop *L,
1807 bool HasNUW, bool HasNSW) {
1808 SmallVector<const SCEV *, 4> Operands;
1809 Operands.push_back(Start);
1810 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1811 if (StepChrec->getLoop() == L) {
1812 Operands.insert(Operands.end(), StepChrec->op_begin(),
1813 StepChrec->op_end());
1814 return getAddRecExpr(Operands, L);
1817 Operands.push_back(Step);
1818 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
1821 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1822 /// Simplify the expression as much as possible.
1824 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1826 bool HasNUW, bool HasNSW) {
1827 if (Operands.size() == 1) return Operands[0];
1829 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1830 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1831 getEffectiveSCEVType(Operands[0]->getType()) &&
1832 "SCEVAddRecExpr operand types don't match!");
1835 if (Operands.back()->isZero()) {
1836 Operands.pop_back();
1837 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
1840 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1841 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1842 const Loop* NestedLoop = NestedAR->getLoop();
1843 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1844 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
1845 NestedAR->op_end());
1846 Operands[0] = NestedAR->getStart();
1847 // AddRecs require their operands be loop-invariant with respect to their
1848 // loops. Don't perform this transformation if it would break this
1850 bool AllInvariant = true;
1851 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1852 if (!Operands[i]->isLoopInvariant(L)) {
1853 AllInvariant = false;
1857 NestedOperands[0] = getAddRecExpr(Operands, L);
1858 AllInvariant = true;
1859 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
1860 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
1861 AllInvariant = false;
1865 // Ok, both add recurrences are valid after the transformation.
1866 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
1868 // Reset Operands to its original state.
1869 Operands[0] = NestedAR;
1873 FoldingSetNodeID ID;
1874 ID.AddInteger(scAddRecExpr);
1875 ID.AddInteger(Operands.size());
1876 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1877 ID.AddPointer(Operands[i]);
1880 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1881 SCEVAddRecExpr *S = SCEVAllocator.Allocate<SCEVAddRecExpr>();
1882 new (S) SCEVAddRecExpr(ID, Operands, L);
1883 UniqueSCEVs.InsertNode(S, IP);
1884 if (HasNUW) S->setHasNoUnsignedWrap(true);
1885 if (HasNSW) S->setHasNoSignedWrap(true);
1889 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
1891 SmallVector<const SCEV *, 2> Ops;
1894 return getSMaxExpr(Ops);
1898 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1899 assert(!Ops.empty() && "Cannot get empty smax!");
1900 if (Ops.size() == 1) return Ops[0];
1902 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1903 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1904 getEffectiveSCEVType(Ops[0]->getType()) &&
1905 "SCEVSMaxExpr operand types don't match!");
1908 // Sort by complexity, this groups all similar expression types together.
1909 GroupByComplexity(Ops, LI);
1911 // If there are any constants, fold them together.
1913 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1915 assert(Idx < Ops.size());
1916 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1917 // We found two constants, fold them together!
1918 ConstantInt *Fold = ConstantInt::get(getContext(),
1919 APIntOps::smax(LHSC->getValue()->getValue(),
1920 RHSC->getValue()->getValue()));
1921 Ops[0] = getConstant(Fold);
1922 Ops.erase(Ops.begin()+1); // Erase the folded element
1923 if (Ops.size() == 1) return Ops[0];
1924 LHSC = cast<SCEVConstant>(Ops[0]);
1927 // If we are left with a constant minimum-int, strip it off.
1928 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1929 Ops.erase(Ops.begin());
1931 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
1932 // If we have an smax with a constant maximum-int, it will always be
1938 if (Ops.size() == 1) return Ops[0];
1940 // Find the first SMax
1941 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1944 // Check to see if one of the operands is an SMax. If so, expand its operands
1945 // onto our operand list, and recurse to simplify.
1946 if (Idx < Ops.size()) {
1947 bool DeletedSMax = false;
1948 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1949 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1950 Ops.erase(Ops.begin()+Idx);
1955 return getSMaxExpr(Ops);
1958 // Okay, check to see if the same value occurs in the operand list twice. If
1959 // so, delete one. Since we sorted the list, these values are required to
1961 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1962 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1963 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1967 if (Ops.size() == 1) return Ops[0];
1969 assert(!Ops.empty() && "Reduced smax down to nothing!");
1971 // Okay, it looks like we really DO need an smax expr. Check to see if we
1972 // already have one, otherwise create a new one.
1973 FoldingSetNodeID ID;
1974 ID.AddInteger(scSMaxExpr);
1975 ID.AddInteger(Ops.size());
1976 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1977 ID.AddPointer(Ops[i]);
1979 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1980 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>();
1981 new (S) SCEVSMaxExpr(ID, Ops);
1982 UniqueSCEVs.InsertNode(S, IP);
1986 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
1988 SmallVector<const SCEV *, 2> Ops;
1991 return getUMaxExpr(Ops);
1995 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1996 assert(!Ops.empty() && "Cannot get empty umax!");
1997 if (Ops.size() == 1) return Ops[0];
1999 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2000 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2001 getEffectiveSCEVType(Ops[0]->getType()) &&
2002 "SCEVUMaxExpr operand types don't match!");
2005 // Sort by complexity, this groups all similar expression types together.
2006 GroupByComplexity(Ops, LI);
2008 // If there are any constants, fold them together.
2010 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2012 assert(Idx < Ops.size());
2013 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2014 // We found two constants, fold them together!
2015 ConstantInt *Fold = ConstantInt::get(getContext(),
2016 APIntOps::umax(LHSC->getValue()->getValue(),
2017 RHSC->getValue()->getValue()));
2018 Ops[0] = getConstant(Fold);
2019 Ops.erase(Ops.begin()+1); // Erase the folded element
2020 if (Ops.size() == 1) return Ops[0];
2021 LHSC = cast<SCEVConstant>(Ops[0]);
2024 // If we are left with a constant minimum-int, strip it off.
2025 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2026 Ops.erase(Ops.begin());
2028 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2029 // If we have an umax with a constant maximum-int, it will always be
2035 if (Ops.size() == 1) return Ops[0];
2037 // Find the first UMax
2038 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2041 // Check to see if one of the operands is a UMax. If so, expand its operands
2042 // onto our operand list, and recurse to simplify.
2043 if (Idx < Ops.size()) {
2044 bool DeletedUMax = false;
2045 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2046 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
2047 Ops.erase(Ops.begin()+Idx);
2052 return getUMaxExpr(Ops);
2055 // Okay, check to see if the same value occurs in the operand list twice. If
2056 // so, delete one. Since we sorted the list, these values are required to
2058 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2059 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
2060 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2064 if (Ops.size() == 1) return Ops[0];
2066 assert(!Ops.empty() && "Reduced umax down to nothing!");
2068 // Okay, it looks like we really DO need a umax expr. Check to see if we
2069 // already have one, otherwise create a new one.
2070 FoldingSetNodeID ID;
2071 ID.AddInteger(scUMaxExpr);
2072 ID.AddInteger(Ops.size());
2073 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2074 ID.AddPointer(Ops[i]);
2076 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2077 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>();
2078 new (S) SCEVUMaxExpr(ID, Ops);
2079 UniqueSCEVs.InsertNode(S, IP);
2083 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2085 // ~smax(~x, ~y) == smin(x, y).
2086 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2089 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2091 // ~umax(~x, ~y) == umin(x, y)
2092 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2095 const SCEV *ScalarEvolution::getFieldOffsetExpr(const StructType *STy,
2097 // If we have TargetData we can determine the constant offset.
2099 const Type *IntPtrTy = TD->getIntPtrType(getContext());
2100 const StructLayout &SL = *TD->getStructLayout(STy);
2101 uint64_t Offset = SL.getElementOffset(FieldNo);
2102 return getIntegerSCEV(Offset, IntPtrTy);
2105 // Field 0 is always at offset 0.
2107 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2108 return getIntegerSCEV(0, Ty);
2111 // Okay, it looks like we really DO need an offsetof expr. Check to see if we
2112 // already have one, otherwise create a new one.
2113 FoldingSetNodeID ID;
2114 ID.AddInteger(scFieldOffset);
2116 ID.AddInteger(FieldNo);
2118 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2119 SCEV *S = SCEVAllocator.Allocate<SCEVFieldOffsetExpr>();
2120 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2121 new (S) SCEVFieldOffsetExpr(ID, Ty, STy, FieldNo);
2122 UniqueSCEVs.InsertNode(S, IP);
2126 const SCEV *ScalarEvolution::getAllocSizeExpr(const Type *AllocTy) {
2127 // If we have TargetData we can determine the constant size.
2128 if (TD && AllocTy->isSized()) {
2129 const Type *IntPtrTy = TD->getIntPtrType(getContext());
2130 return getIntegerSCEV(TD->getTypeAllocSize(AllocTy), IntPtrTy);
2133 // Expand an array size into the element size times the number
2135 if (const ArrayType *ATy = dyn_cast<ArrayType>(AllocTy)) {
2136 const SCEV *E = getAllocSizeExpr(ATy->getElementType());
2138 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()),
2139 ATy->getNumElements())));
2142 // Expand a vector size into the element size times the number
2144 if (const VectorType *VTy = dyn_cast<VectorType>(AllocTy)) {
2145 const SCEV *E = getAllocSizeExpr(VTy->getElementType());
2147 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()),
2148 VTy->getNumElements())));
2151 // Okay, it looks like we really DO need a sizeof expr. Check to see if we
2152 // already have one, otherwise create a new one.
2153 FoldingSetNodeID ID;
2154 ID.AddInteger(scAllocSize);
2155 ID.AddPointer(AllocTy);
2157 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2158 SCEV *S = SCEVAllocator.Allocate<SCEVAllocSizeExpr>();
2159 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2160 new (S) SCEVAllocSizeExpr(ID, Ty, AllocTy);
2161 UniqueSCEVs.InsertNode(S, IP);
2165 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2166 // Don't attempt to do anything other than create a SCEVUnknown object
2167 // here. createSCEV only calls getUnknown after checking for all other
2168 // interesting possibilities, and any other code that calls getUnknown
2169 // is doing so in order to hide a value from SCEV canonicalization.
2171 FoldingSetNodeID ID;
2172 ID.AddInteger(scUnknown);
2175 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2176 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>();
2177 new (S) SCEVUnknown(ID, V);
2178 UniqueSCEVs.InsertNode(S, IP);
2182 //===----------------------------------------------------------------------===//
2183 // Basic SCEV Analysis and PHI Idiom Recognition Code
2186 /// isSCEVable - Test if values of the given type are analyzable within
2187 /// the SCEV framework. This primarily includes integer types, and it
2188 /// can optionally include pointer types if the ScalarEvolution class
2189 /// has access to target-specific information.
2190 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2191 // Integers and pointers are always SCEVable.
2192 return Ty->isInteger() || isa<PointerType>(Ty);
2195 /// getTypeSizeInBits - Return the size in bits of the specified type,
2196 /// for which isSCEVable must return true.
2197 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2198 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2200 // If we have a TargetData, use it!
2202 return TD->getTypeSizeInBits(Ty);
2204 // Integer types have fixed sizes.
2205 if (Ty->isInteger())
2206 return Ty->getPrimitiveSizeInBits();
2208 // The only other support type is pointer. Without TargetData, conservatively
2209 // assume pointers are 64-bit.
2210 assert(isa<PointerType>(Ty) && "isSCEVable permitted a non-SCEVable type!");
2214 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2215 /// the given type and which represents how SCEV will treat the given
2216 /// type, for which isSCEVable must return true. For pointer types,
2217 /// this is the pointer-sized integer type.
2218 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2219 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2221 if (Ty->isInteger())
2224 // The only other support type is pointer.
2225 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
2226 if (TD) return TD->getIntPtrType(getContext());
2228 // Without TargetData, conservatively assume pointers are 64-bit.
2229 return Type::getInt64Ty(getContext());
2232 const SCEV *ScalarEvolution::getCouldNotCompute() {
2233 return &CouldNotCompute;
2236 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2237 /// expression and create a new one.
2238 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2239 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2241 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2242 if (I != Scalars.end()) return I->second;
2243 const SCEV *S = createSCEV(V);
2244 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2248 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
2249 /// specified signed integer value and return a SCEV for the constant.
2250 const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
2251 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2252 return getConstant(ConstantInt::get(ITy, Val));
2255 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2257 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2258 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2260 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2262 const Type *Ty = V->getType();
2263 Ty = getEffectiveSCEVType(Ty);
2264 return getMulExpr(V,
2265 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2268 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2269 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2270 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2272 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2274 const Type *Ty = V->getType();
2275 Ty = getEffectiveSCEVType(Ty);
2276 const SCEV *AllOnes =
2277 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2278 return getMinusSCEV(AllOnes, V);
2281 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2283 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2286 return getAddExpr(LHS, getNegativeSCEV(RHS));
2289 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2290 /// input value to the specified type. If the type must be extended, it is zero
2293 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2295 const Type *SrcTy = V->getType();
2296 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2297 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2298 "Cannot truncate or zero extend with non-integer arguments!");
2299 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2300 return V; // No conversion
2301 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2302 return getTruncateExpr(V, Ty);
2303 return getZeroExtendExpr(V, Ty);
2306 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2307 /// input value to the specified type. If the type must be extended, it is sign
2310 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2312 const Type *SrcTy = V->getType();
2313 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2314 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2315 "Cannot truncate or zero extend with non-integer arguments!");
2316 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2317 return V; // No conversion
2318 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2319 return getTruncateExpr(V, Ty);
2320 return getSignExtendExpr(V, Ty);
2323 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2324 /// input value to the specified type. If the type must be extended, it is zero
2325 /// extended. The conversion must not be narrowing.
2327 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2328 const Type *SrcTy = V->getType();
2329 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2330 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2331 "Cannot noop or zero extend with non-integer arguments!");
2332 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2333 "getNoopOrZeroExtend cannot truncate!");
2334 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2335 return V; // No conversion
2336 return getZeroExtendExpr(V, Ty);
2339 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2340 /// input value to the specified type. If the type must be extended, it is sign
2341 /// extended. The conversion must not be narrowing.
2343 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2344 const Type *SrcTy = V->getType();
2345 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2346 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2347 "Cannot noop or sign extend with non-integer arguments!");
2348 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2349 "getNoopOrSignExtend cannot truncate!");
2350 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2351 return V; // No conversion
2352 return getSignExtendExpr(V, Ty);
2355 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2356 /// the input value to the specified type. If the type must be extended,
2357 /// it is extended with unspecified bits. The conversion must not be
2360 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2361 const Type *SrcTy = V->getType();
2362 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2363 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2364 "Cannot noop or any extend with non-integer arguments!");
2365 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2366 "getNoopOrAnyExtend cannot truncate!");
2367 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2368 return V; // No conversion
2369 return getAnyExtendExpr(V, Ty);
2372 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2373 /// input value to the specified type. The conversion must not be widening.
2375 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2376 const Type *SrcTy = V->getType();
2377 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2378 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2379 "Cannot truncate or noop with non-integer arguments!");
2380 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2381 "getTruncateOrNoop cannot extend!");
2382 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2383 return V; // No conversion
2384 return getTruncateExpr(V, Ty);
2387 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2388 /// the types using zero-extension, and then perform a umax operation
2390 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2392 const SCEV *PromotedLHS = LHS;
2393 const SCEV *PromotedRHS = RHS;
2395 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2396 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2398 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2400 return getUMaxExpr(PromotedLHS, PromotedRHS);
2403 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2404 /// the types using zero-extension, and then perform a umin operation
2406 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2408 const SCEV *PromotedLHS = LHS;
2409 const SCEV *PromotedRHS = RHS;
2411 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2412 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2414 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2416 return getUMinExpr(PromotedLHS, PromotedRHS);
2419 /// PushDefUseChildren - Push users of the given Instruction
2420 /// onto the given Worklist.
2422 PushDefUseChildren(Instruction *I,
2423 SmallVectorImpl<Instruction *> &Worklist) {
2424 // Push the def-use children onto the Worklist stack.
2425 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2427 Worklist.push_back(cast<Instruction>(UI));
2430 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2431 /// instructions that depend on the given instruction and removes them from
2432 /// the Scalars map if they reference SymName. This is used during PHI
2435 ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) {
2436 SmallVector<Instruction *, 16> Worklist;
2437 PushDefUseChildren(I, Worklist);
2439 SmallPtrSet<Instruction *, 8> Visited;
2441 while (!Worklist.empty()) {
2442 Instruction *I = Worklist.pop_back_val();
2443 if (!Visited.insert(I)) continue;
2445 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
2446 Scalars.find(static_cast<Value *>(I));
2447 if (It != Scalars.end()) {
2448 // Short-circuit the def-use traversal if the symbolic name
2449 // ceases to appear in expressions.
2450 if (!It->second->hasOperand(SymName))
2453 // SCEVUnknown for a PHI either means that it has an unrecognized
2454 // structure, or it's a PHI that's in the progress of being computed
2455 // by createNodeForPHI. In the former case, additional loop trip
2456 // count information isn't going to change anything. In the later
2457 // case, createNodeForPHI will perform the necessary updates on its
2458 // own when it gets to that point.
2459 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
2460 ValuesAtScopes.erase(It->second);
2465 PushDefUseChildren(I, Worklist);
2469 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2470 /// a loop header, making it a potential recurrence, or it doesn't.
2472 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2473 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2474 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2475 if (L->getHeader() == PN->getParent()) {
2476 // If it lives in the loop header, it has two incoming values, one
2477 // from outside the loop, and one from inside.
2478 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2479 unsigned BackEdge = IncomingEdge^1;
2481 // While we are analyzing this PHI node, handle its value symbolically.
2482 const SCEV *SymbolicName = getUnknown(PN);
2483 assert(Scalars.find(PN) == Scalars.end() &&
2484 "PHI node already processed?");
2485 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2487 // Using this symbolic name for the PHI, analyze the value coming around
2489 Value *BEValueV = PN->getIncomingValue(BackEdge);
2490 const SCEV *BEValue = getSCEV(BEValueV);
2492 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2493 // has a special value for the first iteration of the loop.
2495 // If the value coming around the backedge is an add with the symbolic
2496 // value we just inserted, then we found a simple induction variable!
2497 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2498 // If there is a single occurrence of the symbolic value, replace it
2499 // with a recurrence.
2500 unsigned FoundIndex = Add->getNumOperands();
2501 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2502 if (Add->getOperand(i) == SymbolicName)
2503 if (FoundIndex == e) {
2508 if (FoundIndex != Add->getNumOperands()) {
2509 // Create an add with everything but the specified operand.
2510 SmallVector<const SCEV *, 8> Ops;
2511 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2512 if (i != FoundIndex)
2513 Ops.push_back(Add->getOperand(i));
2514 const SCEV *Accum = getAddExpr(Ops);
2516 // This is not a valid addrec if the step amount is varying each
2517 // loop iteration, but is not itself an addrec in this loop.
2518 if (Accum->isLoopInvariant(L) ||
2519 (isa<SCEVAddRecExpr>(Accum) &&
2520 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2521 const SCEV *StartVal =
2522 getSCEV(PN->getIncomingValue(IncomingEdge));
2523 const SCEVAddRecExpr *PHISCEV =
2524 cast<SCEVAddRecExpr>(getAddRecExpr(StartVal, Accum, L));
2526 // If the increment doesn't overflow, then neither the addrec nor the
2527 // post-increment will overflow.
2528 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV))
2529 if (OBO->getOperand(0) == PN &&
2530 getSCEV(OBO->getOperand(1)) ==
2531 PHISCEV->getStepRecurrence(*this)) {
2532 const SCEVAddRecExpr *PostInc = PHISCEV->getPostIncExpr(*this);
2533 if (OBO->hasNoUnsignedWrap()) {
2534 const_cast<SCEVAddRecExpr *>(PHISCEV)
2535 ->setHasNoUnsignedWrap(true);
2536 const_cast<SCEVAddRecExpr *>(PostInc)
2537 ->setHasNoUnsignedWrap(true);
2539 if (OBO->hasNoSignedWrap()) {
2540 const_cast<SCEVAddRecExpr *>(PHISCEV)
2541 ->setHasNoSignedWrap(true);
2542 const_cast<SCEVAddRecExpr *>(PostInc)
2543 ->setHasNoSignedWrap(true);
2547 // Okay, for the entire analysis of this edge we assumed the PHI
2548 // to be symbolic. We now need to go back and purge all of the
2549 // entries for the scalars that use the symbolic expression.
2550 ForgetSymbolicName(PN, SymbolicName);
2551 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2555 } else if (const SCEVAddRecExpr *AddRec =
2556 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2557 // Otherwise, this could be a loop like this:
2558 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2559 // In this case, j = {1,+,1} and BEValue is j.
2560 // Because the other in-value of i (0) fits the evolution of BEValue
2561 // i really is an addrec evolution.
2562 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2563 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2565 // If StartVal = j.start - j.stride, we can use StartVal as the
2566 // initial step of the addrec evolution.
2567 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2568 AddRec->getOperand(1))) {
2569 const SCEV *PHISCEV =
2570 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2572 // Okay, for the entire analysis of this edge we assumed the PHI
2573 // to be symbolic. We now need to go back and purge all of the
2574 // entries for the scalars that use the symbolic expression.
2575 ForgetSymbolicName(PN, SymbolicName);
2576 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2582 return SymbolicName;
2585 // It's tempting to recognize PHIs with a unique incoming value, however
2586 // this leads passes like indvars to break LCSSA form. Fortunately, such
2587 // PHIs are rare, as instcombine zaps them.
2589 // If it's not a loop phi, we can't handle it yet.
2590 return getUnknown(PN);
2593 /// createNodeForGEP - Expand GEP instructions into add and multiply
2594 /// operations. This allows them to be analyzed by regular SCEV code.
2596 const SCEV *ScalarEvolution::createNodeForGEP(Operator *GEP) {
2598 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2599 Value *Base = GEP->getOperand(0);
2600 // Don't attempt to analyze GEPs over unsized objects.
2601 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2602 return getUnknown(GEP);
2603 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
2604 gep_type_iterator GTI = gep_type_begin(GEP);
2605 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2609 // Compute the (potentially symbolic) offset in bytes for this index.
2610 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2611 // For a struct, add the member offset.
2612 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2613 TotalOffset = getAddExpr(TotalOffset,
2614 getFieldOffsetExpr(STy, FieldNo));
2616 // For an array, add the element offset, explicitly scaled.
2617 const SCEV *LocalOffset = getSCEV(Index);
2618 if (!isa<PointerType>(LocalOffset->getType()))
2619 // Getelementptr indicies are signed.
2620 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
2621 LocalOffset = getMulExpr(LocalOffset, getAllocSizeExpr(*GTI));
2622 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2625 return getAddExpr(getSCEV(Base), TotalOffset);
2628 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2629 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2630 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2631 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2633 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2634 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2635 return C->getValue()->getValue().countTrailingZeros();
2637 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2638 return std::min(GetMinTrailingZeros(T->getOperand()),
2639 (uint32_t)getTypeSizeInBits(T->getType()));
2641 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2642 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2643 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2644 getTypeSizeInBits(E->getType()) : OpRes;
2647 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2648 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2649 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2650 getTypeSizeInBits(E->getType()) : OpRes;
2653 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2654 // The result is the min of all operands results.
2655 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2656 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2657 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2661 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2662 // The result is the sum of all operands results.
2663 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2664 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2665 for (unsigned i = 1, e = M->getNumOperands();
2666 SumOpRes != BitWidth && i != e; ++i)
2667 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2672 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2673 // The result is the min of all operands results.
2674 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2675 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2676 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2680 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2681 // The result is the min of all operands results.
2682 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2683 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2684 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2688 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2689 // The result is the min of all operands results.
2690 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2691 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2692 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2696 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2697 // For a SCEVUnknown, ask ValueTracking.
2698 unsigned BitWidth = getTypeSizeInBits(U->getType());
2699 APInt Mask = APInt::getAllOnesValue(BitWidth);
2700 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2701 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2702 return Zeros.countTrailingOnes();
2709 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2712 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2714 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2715 return ConstantRange(C->getValue()->getValue());
2717 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2718 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2719 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2720 X = X.add(getUnsignedRange(Add->getOperand(i)));
2724 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2725 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2726 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2727 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2731 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2732 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2733 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2734 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2738 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2739 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2740 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2741 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2745 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2746 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2747 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2751 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2752 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2753 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
2756 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2757 ConstantRange X = getUnsignedRange(SExt->getOperand());
2758 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
2761 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2762 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2763 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
2766 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
2768 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2769 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
2770 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
2771 if (!Trip) return FullSet;
2773 // TODO: non-affine addrec
2774 if (AddRec->isAffine()) {
2775 const Type *Ty = AddRec->getType();
2776 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2777 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
2778 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2780 const SCEV *Start = AddRec->getStart();
2781 const SCEV *Step = AddRec->getStepRecurrence(*this);
2782 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2784 // Check for overflow.
2785 // TODO: This is very conservative.
2786 if (!(Step->isOne() &&
2787 isKnownPredicate(ICmpInst::ICMP_ULT, Start, End)) &&
2788 !(Step->isAllOnesValue() &&
2789 isKnownPredicate(ICmpInst::ICMP_UGT, Start, End)))
2792 ConstantRange StartRange = getUnsignedRange(Start);
2793 ConstantRange EndRange = getUnsignedRange(End);
2794 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
2795 EndRange.getUnsignedMin());
2796 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
2797 EndRange.getUnsignedMax());
2798 if (Min.isMinValue() && Max.isMaxValue())
2800 return ConstantRange(Min, Max+1);
2805 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2806 // For a SCEVUnknown, ask ValueTracking.
2807 unsigned BitWidth = getTypeSizeInBits(U->getType());
2808 APInt Mask = APInt::getAllOnesValue(BitWidth);
2809 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2810 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
2811 if (Ones == ~Zeros + 1)
2813 return ConstantRange(Ones, ~Zeros + 1);
2819 /// getSignedRange - Determine the signed range for a particular SCEV.
2822 ScalarEvolution::getSignedRange(const SCEV *S) {
2824 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2825 return ConstantRange(C->getValue()->getValue());
2827 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2828 ConstantRange X = getSignedRange(Add->getOperand(0));
2829 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2830 X = X.add(getSignedRange(Add->getOperand(i)));
2834 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2835 ConstantRange X = getSignedRange(Mul->getOperand(0));
2836 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2837 X = X.multiply(getSignedRange(Mul->getOperand(i)));
2841 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2842 ConstantRange X = getSignedRange(SMax->getOperand(0));
2843 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2844 X = X.smax(getSignedRange(SMax->getOperand(i)));
2848 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2849 ConstantRange X = getSignedRange(UMax->getOperand(0));
2850 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2851 X = X.umax(getSignedRange(UMax->getOperand(i)));
2855 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2856 ConstantRange X = getSignedRange(UDiv->getLHS());
2857 ConstantRange Y = getSignedRange(UDiv->getRHS());
2861 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2862 ConstantRange X = getSignedRange(ZExt->getOperand());
2863 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
2866 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2867 ConstantRange X = getSignedRange(SExt->getOperand());
2868 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
2871 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2872 ConstantRange X = getSignedRange(Trunc->getOperand());
2873 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
2876 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
2878 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2879 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
2880 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
2881 if (!Trip) return FullSet;
2883 // TODO: non-affine addrec
2884 if (AddRec->isAffine()) {
2885 const Type *Ty = AddRec->getType();
2886 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2887 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
2888 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2890 const SCEV *Start = AddRec->getStart();
2891 const SCEV *Step = AddRec->getStepRecurrence(*this);
2892 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2894 // Check for overflow.
2895 // TODO: This is very conservative.
2896 if (!(Step->isOne() &&
2897 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) &&
2898 !(Step->isAllOnesValue() &&
2899 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End)))
2902 ConstantRange StartRange = getSignedRange(Start);
2903 ConstantRange EndRange = getSignedRange(End);
2904 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
2905 EndRange.getSignedMin());
2906 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
2907 EndRange.getSignedMax());
2908 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
2910 return ConstantRange(Min, Max+1);
2915 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2916 // For a SCEVUnknown, ask ValueTracking.
2917 unsigned BitWidth = getTypeSizeInBits(U->getType());
2918 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
2922 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
2923 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1);
2929 /// createSCEV - We know that there is no SCEV for the specified value.
2930 /// Analyze the expression.
2932 const SCEV *ScalarEvolution::createSCEV(Value *V) {
2933 if (!isSCEVable(V->getType()))
2934 return getUnknown(V);
2936 unsigned Opcode = Instruction::UserOp1;
2937 if (Instruction *I = dyn_cast<Instruction>(V))
2938 Opcode = I->getOpcode();
2939 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2940 Opcode = CE->getOpcode();
2941 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
2942 return getConstant(CI);
2943 else if (isa<ConstantPointerNull>(V))
2944 return getIntegerSCEV(0, V->getType());
2945 else if (isa<UndefValue>(V))
2946 return getIntegerSCEV(0, V->getType());
2947 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
2948 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
2950 return getUnknown(V);
2952 Operator *U = cast<Operator>(V);
2954 case Instruction::Add:
2955 return getAddExpr(getSCEV(U->getOperand(0)),
2956 getSCEV(U->getOperand(1)));
2957 case Instruction::Mul:
2958 return getMulExpr(getSCEV(U->getOperand(0)),
2959 getSCEV(U->getOperand(1)));
2960 case Instruction::UDiv:
2961 return getUDivExpr(getSCEV(U->getOperand(0)),
2962 getSCEV(U->getOperand(1)));
2963 case Instruction::Sub:
2964 return getMinusSCEV(getSCEV(U->getOperand(0)),
2965 getSCEV(U->getOperand(1)));
2966 case Instruction::And:
2967 // For an expression like x&255 that merely masks off the high bits,
2968 // use zext(trunc(x)) as the SCEV expression.
2969 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2970 if (CI->isNullValue())
2971 return getSCEV(U->getOperand(1));
2972 if (CI->isAllOnesValue())
2973 return getSCEV(U->getOperand(0));
2974 const APInt &A = CI->getValue();
2976 // Instcombine's ShrinkDemandedConstant may strip bits out of
2977 // constants, obscuring what would otherwise be a low-bits mask.
2978 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
2979 // knew about to reconstruct a low-bits mask value.
2980 unsigned LZ = A.countLeadingZeros();
2981 unsigned BitWidth = A.getBitWidth();
2982 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
2983 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
2984 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
2986 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
2988 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
2990 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2991 IntegerType::get(getContext(), BitWidth - LZ)),
2996 case Instruction::Or:
2997 // If the RHS of the Or is a constant, we may have something like:
2998 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2999 // optimizations will transparently handle this case.
3001 // In order for this transformation to be safe, the LHS must be of the
3002 // form X*(2^n) and the Or constant must be less than 2^n.
3003 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3004 const SCEV *LHS = getSCEV(U->getOperand(0));
3005 const APInt &CIVal = CI->getValue();
3006 if (GetMinTrailingZeros(LHS) >=
3007 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3008 // Build a plain add SCEV.
3009 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3010 // If the LHS of the add was an addrec and it has no-wrap flags,
3011 // transfer the no-wrap flags, since an or won't introduce a wrap.
3012 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3013 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3014 if (OldAR->hasNoUnsignedWrap())
3015 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3016 if (OldAR->hasNoSignedWrap())
3017 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3023 case Instruction::Xor:
3024 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3025 // If the RHS of the xor is a signbit, then this is just an add.
3026 // Instcombine turns add of signbit into xor as a strength reduction step.
3027 if (CI->getValue().isSignBit())
3028 return getAddExpr(getSCEV(U->getOperand(0)),
3029 getSCEV(U->getOperand(1)));
3031 // If the RHS of xor is -1, then this is a not operation.
3032 if (CI->isAllOnesValue())
3033 return getNotSCEV(getSCEV(U->getOperand(0)));
3035 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3036 // This is a variant of the check for xor with -1, and it handles
3037 // the case where instcombine has trimmed non-demanded bits out
3038 // of an xor with -1.
3039 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3040 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3041 if (BO->getOpcode() == Instruction::And &&
3042 LCI->getValue() == CI->getValue())
3043 if (const SCEVZeroExtendExpr *Z =
3044 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3045 const Type *UTy = U->getType();
3046 const SCEV *Z0 = Z->getOperand();
3047 const Type *Z0Ty = Z0->getType();
3048 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3050 // If C is a low-bits mask, the zero extend is zerving to
3051 // mask off the high bits. Complement the operand and
3052 // re-apply the zext.
3053 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3054 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3056 // If C is a single bit, it may be in the sign-bit position
3057 // before the zero-extend. In this case, represent the xor
3058 // using an add, which is equivalent, and re-apply the zext.
3059 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3060 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3062 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3068 case Instruction::Shl:
3069 // Turn shift left of a constant amount into a multiply.
3070 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3071 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
3072 Constant *X = ConstantInt::get(getContext(),
3073 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3074 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3078 case Instruction::LShr:
3079 // Turn logical shift right of a constant into a unsigned divide.
3080 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3081 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
3082 Constant *X = ConstantInt::get(getContext(),
3083 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3084 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3088 case Instruction::AShr:
3089 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3090 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3091 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
3092 if (L->getOpcode() == Instruction::Shl &&
3093 L->getOperand(1) == U->getOperand(1)) {
3094 unsigned BitWidth = getTypeSizeInBits(U->getType());
3095 uint64_t Amt = BitWidth - CI->getZExtValue();
3096 if (Amt == BitWidth)
3097 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3099 return getIntegerSCEV(0, U->getType()); // value is undefined
3101 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3102 IntegerType::get(getContext(), Amt)),
3107 case Instruction::Trunc:
3108 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3110 case Instruction::ZExt:
3111 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3113 case Instruction::SExt:
3114 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3116 case Instruction::BitCast:
3117 // BitCasts are no-op casts so we just eliminate the cast.
3118 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3119 return getSCEV(U->getOperand(0));
3122 // It's tempting to handle inttoptr and ptrtoint, however this can
3123 // lead to pointer expressions which cannot be expanded to GEPs
3124 // (because they may overflow). For now, the only pointer-typed
3125 // expressions we handle are GEPs and address literals.
3127 case Instruction::GetElementPtr:
3128 return createNodeForGEP(U);
3130 case Instruction::PHI:
3131 return createNodeForPHI(cast<PHINode>(U));
3133 case Instruction::Select:
3134 // This could be a smax or umax that was lowered earlier.
3135 // Try to recover it.
3136 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3137 Value *LHS = ICI->getOperand(0);
3138 Value *RHS = ICI->getOperand(1);
3139 switch (ICI->getPredicate()) {
3140 case ICmpInst::ICMP_SLT:
3141 case ICmpInst::ICMP_SLE:
3142 std::swap(LHS, RHS);
3144 case ICmpInst::ICMP_SGT:
3145 case ICmpInst::ICMP_SGE:
3146 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3147 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
3148 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3149 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
3151 case ICmpInst::ICMP_ULT:
3152 case ICmpInst::ICMP_ULE:
3153 std::swap(LHS, RHS);
3155 case ICmpInst::ICMP_UGT:
3156 case ICmpInst::ICMP_UGE:
3157 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3158 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
3159 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3160 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
3162 case ICmpInst::ICMP_NE:
3163 // n != 0 ? n : 1 -> umax(n, 1)
3164 if (LHS == U->getOperand(1) &&
3165 isa<ConstantInt>(U->getOperand(2)) &&
3166 cast<ConstantInt>(U->getOperand(2))->isOne() &&
3167 isa<ConstantInt>(RHS) &&
3168 cast<ConstantInt>(RHS)->isZero())
3169 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
3171 case ICmpInst::ICMP_EQ:
3172 // n == 0 ? 1 : n -> umax(n, 1)
3173 if (LHS == U->getOperand(2) &&
3174 isa<ConstantInt>(U->getOperand(1)) &&
3175 cast<ConstantInt>(U->getOperand(1))->isOne() &&
3176 isa<ConstantInt>(RHS) &&
3177 cast<ConstantInt>(RHS)->isZero())
3178 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
3185 default: // We cannot analyze this expression.
3189 return getUnknown(V);
3194 //===----------------------------------------------------------------------===//
3195 // Iteration Count Computation Code
3198 /// getBackedgeTakenCount - If the specified loop has a predictable
3199 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3200 /// object. The backedge-taken count is the number of times the loop header
3201 /// will be branched to from within the loop. This is one less than the
3202 /// trip count of the loop, since it doesn't count the first iteration,
3203 /// when the header is branched to from outside the loop.
3205 /// Note that it is not valid to call this method on a loop without a
3206 /// loop-invariant backedge-taken count (see
3207 /// hasLoopInvariantBackedgeTakenCount).
3209 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3210 return getBackedgeTakenInfo(L).Exact;
3213 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3214 /// return the least SCEV value that is known never to be less than the
3215 /// actual backedge taken count.
3216 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3217 return getBackedgeTakenInfo(L).Max;
3220 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3221 /// onto the given Worklist.
3223 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3224 BasicBlock *Header = L->getHeader();
3226 // Push all Loop-header PHIs onto the Worklist stack.
3227 for (BasicBlock::iterator I = Header->begin();
3228 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3229 Worklist.push_back(PN);
3232 const ScalarEvolution::BackedgeTakenInfo &
3233 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3234 // Initially insert a CouldNotCompute for this loop. If the insertion
3235 // succeeds, procede to actually compute a backedge-taken count and
3236 // update the value. The temporary CouldNotCompute value tells SCEV
3237 // code elsewhere that it shouldn't attempt to request a new
3238 // backedge-taken count, which could result in infinite recursion.
3239 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
3240 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3242 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
3243 if (ItCount.Exact != getCouldNotCompute()) {
3244 assert(ItCount.Exact->isLoopInvariant(L) &&
3245 ItCount.Max->isLoopInvariant(L) &&
3246 "Computed trip count isn't loop invariant for loop!");
3247 ++NumTripCountsComputed;
3249 // Update the value in the map.
3250 Pair.first->second = ItCount;
3252 if (ItCount.Max != getCouldNotCompute())
3253 // Update the value in the map.
3254 Pair.first->second = ItCount;
3255 if (isa<PHINode>(L->getHeader()->begin()))
3256 // Only count loops that have phi nodes as not being computable.
3257 ++NumTripCountsNotComputed;
3260 // Now that we know more about the trip count for this loop, forget any
3261 // existing SCEV values for PHI nodes in this loop since they are only
3262 // conservative estimates made without the benefit of trip count
3263 // information. This is similar to the code in
3264 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI
3266 if (ItCount.hasAnyInfo()) {
3267 SmallVector<Instruction *, 16> Worklist;
3268 PushLoopPHIs(L, Worklist);
3270 SmallPtrSet<Instruction *, 8> Visited;
3271 while (!Worklist.empty()) {
3272 Instruction *I = Worklist.pop_back_val();
3273 if (!Visited.insert(I)) continue;
3275 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
3276 Scalars.find(static_cast<Value *>(I));
3277 if (It != Scalars.end()) {
3278 // SCEVUnknown for a PHI either means that it has an unrecognized
3279 // structure, or it's a PHI that's in the progress of being computed
3280 // by createNodeForPHI. In the former case, additional loop trip
3281 // count information isn't going to change anything. In the later
3282 // case, createNodeForPHI will perform the necessary updates on its
3283 // own when it gets to that point.
3284 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3285 ValuesAtScopes.erase(It->second);
3288 if (PHINode *PN = dyn_cast<PHINode>(I))
3289 ConstantEvolutionLoopExitValue.erase(PN);
3292 PushDefUseChildren(I, Worklist);
3296 return Pair.first->second;
3299 /// forgetLoopBackedgeTakenCount - This method should be called by the
3300 /// client when it has changed a loop in a way that may effect
3301 /// ScalarEvolution's ability to compute a trip count, or if the loop
3303 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
3304 BackedgeTakenCounts.erase(L);
3306 SmallVector<Instruction *, 16> Worklist;
3307 PushLoopPHIs(L, Worklist);
3309 SmallPtrSet<Instruction *, 8> Visited;
3310 while (!Worklist.empty()) {
3311 Instruction *I = Worklist.pop_back_val();
3312 if (!Visited.insert(I)) continue;
3314 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
3315 Scalars.find(static_cast<Value *>(I));
3316 if (It != Scalars.end()) {
3317 ValuesAtScopes.erase(It->second);
3319 if (PHINode *PN = dyn_cast<PHINode>(I))
3320 ConstantEvolutionLoopExitValue.erase(PN);
3323 PushDefUseChildren(I, Worklist);
3327 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3328 /// of the specified loop will execute.
3329 ScalarEvolution::BackedgeTakenInfo
3330 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3331 SmallVector<BasicBlock*, 8> ExitingBlocks;
3332 L->getExitingBlocks(ExitingBlocks);
3334 // Examine all exits and pick the most conservative values.
3335 const SCEV *BECount = getCouldNotCompute();
3336 const SCEV *MaxBECount = getCouldNotCompute();
3337 bool CouldNotComputeBECount = false;
3338 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3339 BackedgeTakenInfo NewBTI =
3340 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3342 if (NewBTI.Exact == getCouldNotCompute()) {
3343 // We couldn't compute an exact value for this exit, so
3344 // we won't be able to compute an exact value for the loop.
3345 CouldNotComputeBECount = true;
3346 BECount = getCouldNotCompute();
3347 } else if (!CouldNotComputeBECount) {
3348 if (BECount == getCouldNotCompute())
3349 BECount = NewBTI.Exact;
3351 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3353 if (MaxBECount == getCouldNotCompute())
3354 MaxBECount = NewBTI.Max;
3355 else if (NewBTI.Max != getCouldNotCompute())
3356 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3359 return BackedgeTakenInfo(BECount, MaxBECount);
3362 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3363 /// of the specified loop will execute if it exits via the specified block.
3364 ScalarEvolution::BackedgeTakenInfo
3365 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3366 BasicBlock *ExitingBlock) {
3368 // Okay, we've chosen an exiting block. See what condition causes us to
3369 // exit at this block.
3371 // FIXME: we should be able to handle switch instructions (with a single exit)
3372 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3373 if (ExitBr == 0) return getCouldNotCompute();
3374 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3376 // At this point, we know we have a conditional branch that determines whether
3377 // the loop is exited. However, we don't know if the branch is executed each
3378 // time through the loop. If not, then the execution count of the branch will
3379 // not be equal to the trip count of the loop.
3381 // Currently we check for this by checking to see if the Exit branch goes to
3382 // the loop header. If so, we know it will always execute the same number of
3383 // times as the loop. We also handle the case where the exit block *is* the
3384 // loop header. This is common for un-rotated loops.
3386 // If both of those tests fail, walk up the unique predecessor chain to the
3387 // header, stopping if there is an edge that doesn't exit the loop. If the
3388 // header is reached, the execution count of the branch will be equal to the
3389 // trip count of the loop.
3391 // More extensive analysis could be done to handle more cases here.
3393 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3394 ExitBr->getSuccessor(1) != L->getHeader() &&
3395 ExitBr->getParent() != L->getHeader()) {
3396 // The simple checks failed, try climbing the unique predecessor chain
3397 // up to the header.
3399 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3400 BasicBlock *Pred = BB->getUniquePredecessor();
3402 return getCouldNotCompute();
3403 TerminatorInst *PredTerm = Pred->getTerminator();
3404 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3405 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3408 // If the predecessor has a successor that isn't BB and isn't
3409 // outside the loop, assume the worst.
3410 if (L->contains(PredSucc))
3411 return getCouldNotCompute();
3413 if (Pred == L->getHeader()) {
3420 return getCouldNotCompute();
3423 // Procede to the next level to examine the exit condition expression.
3424 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3425 ExitBr->getSuccessor(0),
3426 ExitBr->getSuccessor(1));
3429 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3430 /// backedge of the specified loop will execute if its exit condition
3431 /// were a conditional branch of ExitCond, TBB, and FBB.
3432 ScalarEvolution::BackedgeTakenInfo
3433 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3437 // Check if the controlling expression for this loop is an And or Or.
3438 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3439 if (BO->getOpcode() == Instruction::And) {
3440 // Recurse on the operands of the and.
3441 BackedgeTakenInfo BTI0 =
3442 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3443 BackedgeTakenInfo BTI1 =
3444 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3445 const SCEV *BECount = getCouldNotCompute();
3446 const SCEV *MaxBECount = getCouldNotCompute();
3447 if (L->contains(TBB)) {
3448 // Both conditions must be true for the loop to continue executing.
3449 // Choose the less conservative count.
3450 if (BTI0.Exact == getCouldNotCompute() ||
3451 BTI1.Exact == getCouldNotCompute())
3452 BECount = getCouldNotCompute();
3454 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3455 if (BTI0.Max == getCouldNotCompute())
3456 MaxBECount = BTI1.Max;
3457 else if (BTI1.Max == getCouldNotCompute())
3458 MaxBECount = BTI0.Max;
3460 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3462 // Both conditions must be true for the loop to exit.
3463 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3464 if (BTI0.Exact != getCouldNotCompute() &&
3465 BTI1.Exact != getCouldNotCompute())
3466 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3467 if (BTI0.Max != getCouldNotCompute() &&
3468 BTI1.Max != getCouldNotCompute())
3469 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3472 return BackedgeTakenInfo(BECount, MaxBECount);
3474 if (BO->getOpcode() == Instruction::Or) {
3475 // Recurse on the operands of the or.
3476 BackedgeTakenInfo BTI0 =
3477 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3478 BackedgeTakenInfo BTI1 =
3479 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3480 const SCEV *BECount = getCouldNotCompute();
3481 const SCEV *MaxBECount = getCouldNotCompute();
3482 if (L->contains(FBB)) {
3483 // Both conditions must be false for the loop to continue executing.
3484 // Choose the less conservative count.
3485 if (BTI0.Exact == getCouldNotCompute() ||
3486 BTI1.Exact == getCouldNotCompute())
3487 BECount = getCouldNotCompute();
3489 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3490 if (BTI0.Max == getCouldNotCompute())
3491 MaxBECount = BTI1.Max;
3492 else if (BTI1.Max == getCouldNotCompute())
3493 MaxBECount = BTI0.Max;
3495 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3497 // Both conditions must be false for the loop to exit.
3498 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3499 if (BTI0.Exact != getCouldNotCompute() &&
3500 BTI1.Exact != getCouldNotCompute())
3501 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3502 if (BTI0.Max != getCouldNotCompute() &&
3503 BTI1.Max != getCouldNotCompute())
3504 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3507 return BackedgeTakenInfo(BECount, MaxBECount);
3511 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3512 // Procede to the next level to examine the icmp.
3513 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3514 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3516 // If it's not an integer or pointer comparison then compute it the hard way.
3517 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3520 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3521 /// backedge of the specified loop will execute if its exit condition
3522 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3523 ScalarEvolution::BackedgeTakenInfo
3524 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3529 // If the condition was exit on true, convert the condition to exit on false
3530 ICmpInst::Predicate Cond;
3531 if (!L->contains(FBB))
3532 Cond = ExitCond->getPredicate();
3534 Cond = ExitCond->getInversePredicate();
3536 // Handle common loops like: for (X = "string"; *X; ++X)
3537 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3538 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3540 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3541 if (!isa<SCEVCouldNotCompute>(ItCnt)) {
3542 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType());
3543 return BackedgeTakenInfo(ItCnt,
3544 isa<SCEVConstant>(ItCnt) ? ItCnt :
3545 getConstant(APInt::getMaxValue(BitWidth)-1));
3549 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3550 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3552 // Try to evaluate any dependencies out of the loop.
3553 LHS = getSCEVAtScope(LHS, L);
3554 RHS = getSCEVAtScope(RHS, L);
3556 // At this point, we would like to compute how many iterations of the
3557 // loop the predicate will return true for these inputs.
3558 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3559 // If there is a loop-invariant, force it into the RHS.
3560 std::swap(LHS, RHS);
3561 Cond = ICmpInst::getSwappedPredicate(Cond);
3564 // If we have a comparison of a chrec against a constant, try to use value
3565 // ranges to answer this query.
3566 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3567 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3568 if (AddRec->getLoop() == L) {
3569 // Form the constant range.
3570 ConstantRange CompRange(
3571 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3573 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3574 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3578 case ICmpInst::ICMP_NE: { // while (X != Y)
3579 // Convert to: while (X-Y != 0)
3580 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3581 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3584 case ICmpInst::ICMP_EQ: { // while (X == Y)
3585 // Convert to: while (X-Y == 0)
3586 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3587 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3590 case ICmpInst::ICMP_SLT: {
3591 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3592 if (BTI.hasAnyInfo()) return BTI;
3595 case ICmpInst::ICMP_SGT: {
3596 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3597 getNotSCEV(RHS), L, true);
3598 if (BTI.hasAnyInfo()) return BTI;
3601 case ICmpInst::ICMP_ULT: {
3602 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3603 if (BTI.hasAnyInfo()) return BTI;
3606 case ICmpInst::ICMP_UGT: {
3607 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3608 getNotSCEV(RHS), L, false);
3609 if (BTI.hasAnyInfo()) return BTI;
3614 errs() << "ComputeBackedgeTakenCount ";
3615 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3616 errs() << "[unsigned] ";
3617 errs() << *LHS << " "
3618 << Instruction::getOpcodeName(Instruction::ICmp)
3619 << " " << *RHS << "\n";
3624 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3627 static ConstantInt *
3628 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3629 ScalarEvolution &SE) {
3630 const SCEV *InVal = SE.getConstant(C);
3631 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3632 assert(isa<SCEVConstant>(Val) &&
3633 "Evaluation of SCEV at constant didn't fold correctly?");
3634 return cast<SCEVConstant>(Val)->getValue();
3637 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3638 /// and a GEP expression (missing the pointer index) indexing into it, return
3639 /// the addressed element of the initializer or null if the index expression is
3642 GetAddressedElementFromGlobal(LLVMContext &Context, GlobalVariable *GV,
3643 const std::vector<ConstantInt*> &Indices) {
3644 Constant *Init = GV->getInitializer();
3645 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3646 uint64_t Idx = Indices[i]->getZExtValue();
3647 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3648 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3649 Init = cast<Constant>(CS->getOperand(Idx));
3650 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3651 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3652 Init = cast<Constant>(CA->getOperand(Idx));
3653 } else if (isa<ConstantAggregateZero>(Init)) {
3654 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3655 assert(Idx < STy->getNumElements() && "Bad struct index!");
3656 Init = Constant::getNullValue(STy->getElementType(Idx));
3657 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3658 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3659 Init = Constant::getNullValue(ATy->getElementType());
3661 llvm_unreachable("Unknown constant aggregate type!");
3665 return 0; // Unknown initializer type
3671 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3672 /// 'icmp op load X, cst', try to see if we can compute the backedge
3673 /// execution count.
3675 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3679 ICmpInst::Predicate predicate) {
3680 if (LI->isVolatile()) return getCouldNotCompute();
3682 // Check to see if the loaded pointer is a getelementptr of a global.
3683 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3684 if (!GEP) return getCouldNotCompute();
3686 // Make sure that it is really a constant global we are gepping, with an
3687 // initializer, and make sure the first IDX is really 0.
3688 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3689 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
3690 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3691 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3692 return getCouldNotCompute();
3694 // Okay, we allow one non-constant index into the GEP instruction.
3696 std::vector<ConstantInt*> Indexes;
3697 unsigned VarIdxNum = 0;
3698 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3699 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3700 Indexes.push_back(CI);
3701 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3702 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3703 VarIdx = GEP->getOperand(i);
3705 Indexes.push_back(0);
3708 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3709 // Check to see if X is a loop variant variable value now.
3710 const SCEV *Idx = getSCEV(VarIdx);
3711 Idx = getSCEVAtScope(Idx, L);
3713 // We can only recognize very limited forms of loop index expressions, in
3714 // particular, only affine AddRec's like {C1,+,C2}.
3715 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3716 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3717 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3718 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
3719 return getCouldNotCompute();
3721 unsigned MaxSteps = MaxBruteForceIterations;
3722 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3723 ConstantInt *ItCst = ConstantInt::get(
3724 cast<IntegerType>(IdxExpr->getType()), IterationNum);
3725 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
3727 // Form the GEP offset.
3728 Indexes[VarIdxNum] = Val;
3730 Constant *Result = GetAddressedElementFromGlobal(getContext(), GV, Indexes);
3731 if (Result == 0) break; // Cannot compute!
3733 // Evaluate the condition for this iteration.
3734 Result = ConstantExpr::getICmp(predicate, Result, RHS);
3735 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
3736 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
3738 errs() << "\n***\n*** Computed loop count " << *ItCst
3739 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
3742 ++NumArrayLenItCounts;
3743 return getConstant(ItCst); // Found terminating iteration!
3746 return getCouldNotCompute();
3750 /// CanConstantFold - Return true if we can constant fold an instruction of the
3751 /// specified type, assuming that all operands were constants.
3752 static bool CanConstantFold(const Instruction *I) {
3753 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
3754 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
3757 if (const CallInst *CI = dyn_cast<CallInst>(I))
3758 if (const Function *F = CI->getCalledFunction())
3759 return canConstantFoldCallTo(F);
3763 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
3764 /// in the loop that V is derived from. We allow arbitrary operations along the
3765 /// way, but the operands of an operation must either be constants or a value
3766 /// derived from a constant PHI. If this expression does not fit with these
3767 /// constraints, return null.
3768 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
3769 // If this is not an instruction, or if this is an instruction outside of the
3770 // loop, it can't be derived from a loop PHI.
3771 Instruction *I = dyn_cast<Instruction>(V);
3772 if (I == 0 || !L->contains(I->getParent())) return 0;
3774 if (PHINode *PN = dyn_cast<PHINode>(I)) {
3775 if (L->getHeader() == I->getParent())
3778 // We don't currently keep track of the control flow needed to evaluate
3779 // PHIs, so we cannot handle PHIs inside of loops.
3783 // If we won't be able to constant fold this expression even if the operands
3784 // are constants, return early.
3785 if (!CanConstantFold(I)) return 0;
3787 // Otherwise, we can evaluate this instruction if all of its operands are
3788 // constant or derived from a PHI node themselves.
3790 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
3791 if (!(isa<Constant>(I->getOperand(Op)) ||
3792 isa<GlobalValue>(I->getOperand(Op)))) {
3793 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
3794 if (P == 0) return 0; // Not evolving from PHI
3798 return 0; // Evolving from multiple different PHIs.
3801 // This is a expression evolving from a constant PHI!
3805 /// EvaluateExpression - Given an expression that passes the
3806 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
3807 /// in the loop has the value PHIVal. If we can't fold this expression for some
3808 /// reason, return null.
3809 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
3810 if (isa<PHINode>(V)) return PHIVal;
3811 if (Constant *C = dyn_cast<Constant>(V)) return C;
3812 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
3813 Instruction *I = cast<Instruction>(V);
3814 LLVMContext &Context = I->getParent()->getContext();
3816 std::vector<Constant*> Operands;
3817 Operands.resize(I->getNumOperands());
3819 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3820 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
3821 if (Operands[i] == 0) return 0;
3824 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3825 return ConstantFoldCompareInstOperands(CI->getPredicate(),
3826 &Operands[0], Operands.size(),
3829 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3830 &Operands[0], Operands.size(),
3834 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
3835 /// in the header of its containing loop, we know the loop executes a
3836 /// constant number of times, and the PHI node is just a recurrence
3837 /// involving constants, fold it.
3839 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
3842 std::map<PHINode*, Constant*>::iterator I =
3843 ConstantEvolutionLoopExitValue.find(PN);
3844 if (I != ConstantEvolutionLoopExitValue.end())
3847 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
3848 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
3850 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
3852 // Since the loop is canonicalized, the PHI node must have two entries. One
3853 // entry must be a constant (coming in from outside of the loop), and the
3854 // second must be derived from the same PHI.
3855 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3856 Constant *StartCST =
3857 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3859 return RetVal = 0; // Must be a constant.
3861 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3862 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3864 return RetVal = 0; // Not derived from same PHI.
3866 // Execute the loop symbolically to determine the exit value.
3867 if (BEs.getActiveBits() >= 32)
3868 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
3870 unsigned NumIterations = BEs.getZExtValue(); // must be in range
3871 unsigned IterationNum = 0;
3872 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
3873 if (IterationNum == NumIterations)
3874 return RetVal = PHIVal; // Got exit value!
3876 // Compute the value of the PHI node for the next iteration.
3877 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3878 if (NextPHI == PHIVal)
3879 return RetVal = NextPHI; // Stopped evolving!
3881 return 0; // Couldn't evaluate!
3886 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
3887 /// constant number of times (the condition evolves only from constants),
3888 /// try to evaluate a few iterations of the loop until we get the exit
3889 /// condition gets a value of ExitWhen (true or false). If we cannot
3890 /// evaluate the trip count of the loop, return getCouldNotCompute().
3892 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
3895 PHINode *PN = getConstantEvolvingPHI(Cond, L);
3896 if (PN == 0) return getCouldNotCompute();
3898 // Since the loop is canonicalized, the PHI node must have two entries. One
3899 // entry must be a constant (coming in from outside of the loop), and the
3900 // second must be derived from the same PHI.
3901 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3902 Constant *StartCST =
3903 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3904 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
3906 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3907 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3908 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
3910 // Okay, we find a PHI node that defines the trip count of this loop. Execute
3911 // the loop symbolically to determine when the condition gets a value of
3913 unsigned IterationNum = 0;
3914 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
3915 for (Constant *PHIVal = StartCST;
3916 IterationNum != MaxIterations; ++IterationNum) {
3917 ConstantInt *CondVal =
3918 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
3920 // Couldn't symbolically evaluate.
3921 if (!CondVal) return getCouldNotCompute();
3923 if (CondVal->getValue() == uint64_t(ExitWhen)) {
3924 ++NumBruteForceTripCountsComputed;
3925 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
3928 // Compute the value of the PHI node for the next iteration.
3929 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3930 if (NextPHI == 0 || NextPHI == PHIVal)
3931 return getCouldNotCompute();// Couldn't evaluate or not making progress...
3935 // Too many iterations were needed to evaluate.
3936 return getCouldNotCompute();
3939 /// getSCEVAtScope - Return a SCEV expression for the specified value
3940 /// at the specified scope in the program. The L value specifies a loop
3941 /// nest to evaluate the expression at, where null is the top-level or a
3942 /// specified loop is immediately inside of the loop.
3944 /// This method can be used to compute the exit value for a variable defined
3945 /// in a loop by querying what the value will hold in the parent loop.
3947 /// In the case that a relevant loop exit value cannot be computed, the
3948 /// original value V is returned.
3949 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
3950 // Check to see if we've folded this expression at this loop before.
3951 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
3952 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
3953 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
3955 return Pair.first->second ? Pair.first->second : V;
3957 // Otherwise compute it.
3958 const SCEV *C = computeSCEVAtScope(V, L);
3959 ValuesAtScopes[V][L] = C;
3963 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
3964 if (isa<SCEVConstant>(V)) return V;
3966 // If this instruction is evolved from a constant-evolving PHI, compute the
3967 // exit value from the loop without using SCEVs.
3968 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
3969 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
3970 const Loop *LI = (*this->LI)[I->getParent()];
3971 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
3972 if (PHINode *PN = dyn_cast<PHINode>(I))
3973 if (PN->getParent() == LI->getHeader()) {
3974 // Okay, there is no closed form solution for the PHI node. Check
3975 // to see if the loop that contains it has a known backedge-taken
3976 // count. If so, we may be able to force computation of the exit
3978 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
3979 if (const SCEVConstant *BTCC =
3980 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
3981 // Okay, we know how many times the containing loop executes. If
3982 // this is a constant evolving PHI node, get the final value at
3983 // the specified iteration number.
3984 Constant *RV = getConstantEvolutionLoopExitValue(PN,
3985 BTCC->getValue()->getValue(),
3987 if (RV) return getSCEV(RV);
3991 // Okay, this is an expression that we cannot symbolically evaluate
3992 // into a SCEV. Check to see if it's possible to symbolically evaluate
3993 // the arguments into constants, and if so, try to constant propagate the
3994 // result. This is particularly useful for computing loop exit values.
3995 if (CanConstantFold(I)) {
3996 std::vector<Constant*> Operands;
3997 Operands.reserve(I->getNumOperands());
3998 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3999 Value *Op = I->getOperand(i);
4000 if (Constant *C = dyn_cast<Constant>(Op)) {
4001 Operands.push_back(C);
4003 // If any of the operands is non-constant and if they are
4004 // non-integer and non-pointer, don't even try to analyze them
4005 // with scev techniques.
4006 if (!isSCEVable(Op->getType()))
4009 const SCEV* OpV = getSCEVAtScope(Op, L);
4010 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
4011 Constant *C = SC->getValue();
4012 if (C->getType() != Op->getType())
4013 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4017 Operands.push_back(C);
4018 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
4019 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
4020 if (C->getType() != Op->getType())
4022 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4026 Operands.push_back(C);
4036 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4037 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4038 &Operands[0], Operands.size(),
4041 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4042 &Operands[0], Operands.size(),
4048 // This is some other type of SCEVUnknown, just return it.
4052 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4053 // Avoid performing the look-up in the common case where the specified
4054 // expression has no loop-variant portions.
4055 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4056 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4057 if (OpAtScope != Comm->getOperand(i)) {
4058 // Okay, at least one of these operands is loop variant but might be
4059 // foldable. Build a new instance of the folded commutative expression.
4060 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4061 Comm->op_begin()+i);
4062 NewOps.push_back(OpAtScope);
4064 for (++i; i != e; ++i) {
4065 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4066 NewOps.push_back(OpAtScope);
4068 if (isa<SCEVAddExpr>(Comm))
4069 return getAddExpr(NewOps);
4070 if (isa<SCEVMulExpr>(Comm))
4071 return getMulExpr(NewOps);
4072 if (isa<SCEVSMaxExpr>(Comm))
4073 return getSMaxExpr(NewOps);
4074 if (isa<SCEVUMaxExpr>(Comm))
4075 return getUMaxExpr(NewOps);
4076 llvm_unreachable("Unknown commutative SCEV type!");
4079 // If we got here, all operands are loop invariant.
4083 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4084 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4085 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4086 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4087 return Div; // must be loop invariant
4088 return getUDivExpr(LHS, RHS);
4091 // If this is a loop recurrence for a loop that does not contain L, then we
4092 // are dealing with the final value computed by the loop.
4093 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4094 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
4095 // To evaluate this recurrence, we need to know how many times the AddRec
4096 // loop iterates. Compute this now.
4097 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4098 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4100 // Then, evaluate the AddRec.
4101 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4106 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4107 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4108 if (Op == Cast->getOperand())
4109 return Cast; // must be loop invariant
4110 return getZeroExtendExpr(Op, Cast->getType());
4113 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4114 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4115 if (Op == Cast->getOperand())
4116 return Cast; // must be loop invariant
4117 return getSignExtendExpr(Op, Cast->getType());
4120 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4121 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4122 if (Op == Cast->getOperand())
4123 return Cast; // must be loop invariant
4124 return getTruncateExpr(Op, Cast->getType());
4127 if (isa<SCEVTargetDataConstant>(V))
4130 llvm_unreachable("Unknown SCEV type!");
4134 /// getSCEVAtScope - This is a convenience function which does
4135 /// getSCEVAtScope(getSCEV(V), L).
4136 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4137 return getSCEVAtScope(getSCEV(V), L);
4140 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4141 /// following equation:
4143 /// A * X = B (mod N)
4145 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4146 /// A and B isn't important.
4148 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4149 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4150 ScalarEvolution &SE) {
4151 uint32_t BW = A.getBitWidth();
4152 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4153 assert(A != 0 && "A must be non-zero.");
4157 // The gcd of A and N may have only one prime factor: 2. The number of
4158 // trailing zeros in A is its multiplicity
4159 uint32_t Mult2 = A.countTrailingZeros();
4162 // 2. Check if B is divisible by D.
4164 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4165 // is not less than multiplicity of this prime factor for D.
4166 if (B.countTrailingZeros() < Mult2)
4167 return SE.getCouldNotCompute();
4169 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4172 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4173 // bit width during computations.
4174 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4175 APInt Mod(BW + 1, 0);
4176 Mod.set(BW - Mult2); // Mod = N / D
4177 APInt I = AD.multiplicativeInverse(Mod);
4179 // 4. Compute the minimum unsigned root of the equation:
4180 // I * (B / D) mod (N / D)
4181 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4183 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4185 return SE.getConstant(Result.trunc(BW));
4188 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4189 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4190 /// might be the same) or two SCEVCouldNotCompute objects.
4192 static std::pair<const SCEV *,const SCEV *>
4193 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4194 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4195 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4196 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4197 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4199 // We currently can only solve this if the coefficients are constants.
4200 if (!LC || !MC || !NC) {
4201 const SCEV *CNC = SE.getCouldNotCompute();
4202 return std::make_pair(CNC, CNC);
4205 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4206 const APInt &L = LC->getValue()->getValue();
4207 const APInt &M = MC->getValue()->getValue();
4208 const APInt &N = NC->getValue()->getValue();
4209 APInt Two(BitWidth, 2);
4210 APInt Four(BitWidth, 4);
4213 using namespace APIntOps;
4215 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4216 // The B coefficient is M-N/2
4220 // The A coefficient is N/2
4221 APInt A(N.sdiv(Two));
4223 // Compute the B^2-4ac term.
4226 SqrtTerm -= Four * (A * C);
4228 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4229 // integer value or else APInt::sqrt() will assert.
4230 APInt SqrtVal(SqrtTerm.sqrt());
4232 // Compute the two solutions for the quadratic formula.
4233 // The divisions must be performed as signed divisions.
4235 APInt TwoA( A << 1 );
4236 if (TwoA.isMinValue()) {
4237 const SCEV *CNC = SE.getCouldNotCompute();
4238 return std::make_pair(CNC, CNC);
4241 LLVMContext &Context = SE.getContext();
4243 ConstantInt *Solution1 =
4244 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4245 ConstantInt *Solution2 =
4246 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4248 return std::make_pair(SE.getConstant(Solution1),
4249 SE.getConstant(Solution2));
4250 } // end APIntOps namespace
4253 /// HowFarToZero - Return the number of times a backedge comparing the specified
4254 /// value to zero will execute. If not computable, return CouldNotCompute.
4255 const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4256 // If the value is a constant
4257 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4258 // If the value is already zero, the branch will execute zero times.
4259 if (C->getValue()->isZero()) return C;
4260 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4263 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4264 if (!AddRec || AddRec->getLoop() != L)
4265 return getCouldNotCompute();
4267 if (AddRec->isAffine()) {
4268 // If this is an affine expression, the execution count of this branch is
4269 // the minimum unsigned root of the following equation:
4271 // Start + Step*N = 0 (mod 2^BW)
4275 // Step*N = -Start (mod 2^BW)
4277 // where BW is the common bit width of Start and Step.
4279 // Get the initial value for the loop.
4280 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4281 L->getParentLoop());
4282 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4283 L->getParentLoop());
4285 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4286 // For now we handle only constant steps.
4288 // First, handle unitary steps.
4289 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4290 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4291 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4292 return Start; // N = Start (as unsigned)
4294 // Then, try to solve the above equation provided that Start is constant.
4295 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4296 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4297 -StartC->getValue()->getValue(),
4300 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
4301 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4302 // the quadratic equation to solve it.
4303 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4305 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4306 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4309 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
4310 << " sol#2: " << *R2 << "\n";
4312 // Pick the smallest positive root value.
4313 if (ConstantInt *CB =
4314 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4315 R1->getValue(), R2->getValue()))) {
4316 if (CB->getZExtValue() == false)
4317 std::swap(R1, R2); // R1 is the minimum root now.
4319 // We can only use this value if the chrec ends up with an exact zero
4320 // value at this index. When solving for "X*X != 5", for example, we
4321 // should not accept a root of 2.
4322 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4324 return R1; // We found a quadratic root!
4329 return getCouldNotCompute();
4332 /// HowFarToNonZero - Return the number of times a backedge checking the
4333 /// specified value for nonzero will execute. If not computable, return
4335 const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4336 // Loops that look like: while (X == 0) are very strange indeed. We don't
4337 // handle them yet except for the trivial case. This could be expanded in the
4338 // future as needed.
4340 // If the value is a constant, check to see if it is known to be non-zero
4341 // already. If so, the backedge will execute zero times.
4342 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4343 if (!C->getValue()->isNullValue())
4344 return getIntegerSCEV(0, C->getType());
4345 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4348 // We could implement others, but I really doubt anyone writes loops like
4349 // this, and if they did, they would already be constant folded.
4350 return getCouldNotCompute();
4353 /// getLoopPredecessor - If the given loop's header has exactly one unique
4354 /// predecessor outside the loop, return it. Otherwise return null.
4356 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
4357 BasicBlock *Header = L->getHeader();
4358 BasicBlock *Pred = 0;
4359 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
4361 if (!L->contains(*PI)) {
4362 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
4368 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4369 /// (which may not be an immediate predecessor) which has exactly one
4370 /// successor from which BB is reachable, or null if no such block is
4374 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4375 // If the block has a unique predecessor, then there is no path from the
4376 // predecessor to the block that does not go through the direct edge
4377 // from the predecessor to the block.
4378 if (BasicBlock *Pred = BB->getSinglePredecessor())
4381 // A loop's header is defined to be a block that dominates the loop.
4382 // If the header has a unique predecessor outside the loop, it must be
4383 // a block that has exactly one successor that can reach the loop.
4384 if (Loop *L = LI->getLoopFor(BB))
4385 return getLoopPredecessor(L);
4390 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4391 /// testing whether two expressions are equal, however for the purposes of
4392 /// looking for a condition guarding a loop, it can be useful to be a little
4393 /// more general, since a front-end may have replicated the controlling
4396 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4397 // Quick check to see if they are the same SCEV.
4398 if (A == B) return true;
4400 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4401 // two different instructions with the same value. Check for this case.
4402 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4403 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4404 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4405 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4406 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4409 // Otherwise assume they may have a different value.
4413 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
4414 return getSignedRange(S).getSignedMax().isNegative();
4417 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
4418 return getSignedRange(S).getSignedMin().isStrictlyPositive();
4421 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
4422 return !getSignedRange(S).getSignedMin().isNegative();
4425 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
4426 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
4429 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
4430 return isKnownNegative(S) || isKnownPositive(S);
4433 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
4434 const SCEV *LHS, const SCEV *RHS) {
4436 if (HasSameValue(LHS, RHS))
4437 return ICmpInst::isTrueWhenEqual(Pred);
4441 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4443 case ICmpInst::ICMP_SGT:
4444 Pred = ICmpInst::ICMP_SLT;
4445 std::swap(LHS, RHS);
4446 case ICmpInst::ICMP_SLT: {
4447 ConstantRange LHSRange = getSignedRange(LHS);
4448 ConstantRange RHSRange = getSignedRange(RHS);
4449 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
4451 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
4455 case ICmpInst::ICMP_SGE:
4456 Pred = ICmpInst::ICMP_SLE;
4457 std::swap(LHS, RHS);
4458 case ICmpInst::ICMP_SLE: {
4459 ConstantRange LHSRange = getSignedRange(LHS);
4460 ConstantRange RHSRange = getSignedRange(RHS);
4461 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
4463 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
4467 case ICmpInst::ICMP_UGT:
4468 Pred = ICmpInst::ICMP_ULT;
4469 std::swap(LHS, RHS);
4470 case ICmpInst::ICMP_ULT: {
4471 ConstantRange LHSRange = getUnsignedRange(LHS);
4472 ConstantRange RHSRange = getUnsignedRange(RHS);
4473 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
4475 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
4479 case ICmpInst::ICMP_UGE:
4480 Pred = ICmpInst::ICMP_ULE;
4481 std::swap(LHS, RHS);
4482 case ICmpInst::ICMP_ULE: {
4483 ConstantRange LHSRange = getUnsignedRange(LHS);
4484 ConstantRange RHSRange = getUnsignedRange(RHS);
4485 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
4487 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
4491 case ICmpInst::ICMP_NE: {
4492 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
4494 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
4497 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4498 if (isKnownNonZero(Diff))
4502 case ICmpInst::ICMP_EQ:
4503 // The check at the top of the function catches the case where
4504 // the values are known to be equal.
4510 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
4511 /// protected by a conditional between LHS and RHS. This is used to
4512 /// to eliminate casts.
4514 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
4515 ICmpInst::Predicate Pred,
4516 const SCEV *LHS, const SCEV *RHS) {
4517 // Interpret a null as meaning no loop, where there is obviously no guard
4518 // (interprocedural conditions notwithstanding).
4519 if (!L) return true;
4521 BasicBlock *Latch = L->getLoopLatch();
4525 BranchInst *LoopContinuePredicate =
4526 dyn_cast<BranchInst>(Latch->getTerminator());
4527 if (!LoopContinuePredicate ||
4528 LoopContinuePredicate->isUnconditional())
4531 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
4532 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
4535 /// isLoopGuardedByCond - Test whether entry to the loop is protected
4536 /// by a conditional between LHS and RHS. This is used to help avoid max
4537 /// expressions in loop trip counts, and to eliminate casts.
4539 ScalarEvolution::isLoopGuardedByCond(const Loop *L,
4540 ICmpInst::Predicate Pred,
4541 const SCEV *LHS, const SCEV *RHS) {
4542 // Interpret a null as meaning no loop, where there is obviously no guard
4543 // (interprocedural conditions notwithstanding).
4544 if (!L) return false;
4546 BasicBlock *Predecessor = getLoopPredecessor(L);
4547 BasicBlock *PredecessorDest = L->getHeader();
4549 // Starting at the loop predecessor, climb up the predecessor chain, as long
4550 // as there are predecessors that can be found that have unique successors
4551 // leading to the original header.
4553 PredecessorDest = Predecessor,
4554 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4556 BranchInst *LoopEntryPredicate =
4557 dyn_cast<BranchInst>(Predecessor->getTerminator());
4558 if (!LoopEntryPredicate ||
4559 LoopEntryPredicate->isUnconditional())
4562 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4563 LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4570 /// isImpliedCond - Test whether the condition described by Pred, LHS,
4571 /// and RHS is true whenever the given Cond value evaluates to true.
4572 bool ScalarEvolution::isImpliedCond(Value *CondValue,
4573 ICmpInst::Predicate Pred,
4574 const SCEV *LHS, const SCEV *RHS,
4576 // Recursivly handle And and Or conditions.
4577 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4578 if (BO->getOpcode() == Instruction::And) {
4580 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4581 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4582 } else if (BO->getOpcode() == Instruction::Or) {
4584 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4585 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4589 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4590 if (!ICI) return false;
4592 // Bail if the ICmp's operands' types are wider than the needed type
4593 // before attempting to call getSCEV on them. This avoids infinite
4594 // recursion, since the analysis of widening casts can require loop
4595 // exit condition information for overflow checking, which would
4597 if (getTypeSizeInBits(LHS->getType()) <
4598 getTypeSizeInBits(ICI->getOperand(0)->getType()))
4601 // Now that we found a conditional branch that dominates the loop, check to
4602 // see if it is the comparison we are looking for.
4603 ICmpInst::Predicate FoundPred;
4605 FoundPred = ICI->getInversePredicate();
4607 FoundPred = ICI->getPredicate();
4609 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
4610 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
4612 // Balance the types. The case where FoundLHS' type is wider than
4613 // LHS' type is checked for above.
4614 if (getTypeSizeInBits(LHS->getType()) >
4615 getTypeSizeInBits(FoundLHS->getType())) {
4616 if (CmpInst::isSigned(Pred)) {
4617 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
4618 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
4620 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
4621 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
4625 // Canonicalize the query to match the way instcombine will have
4626 // canonicalized the comparison.
4627 // First, put a constant operand on the right.
4628 if (isa<SCEVConstant>(LHS)) {
4629 std::swap(LHS, RHS);
4630 Pred = ICmpInst::getSwappedPredicate(Pred);
4632 // Then, canonicalize comparisons with boundary cases.
4633 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4634 const APInt &RA = RC->getValue()->getValue();
4636 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4637 case ICmpInst::ICMP_EQ:
4638 case ICmpInst::ICMP_NE:
4640 case ICmpInst::ICMP_UGE:
4641 if ((RA - 1).isMinValue()) {
4642 Pred = ICmpInst::ICMP_NE;
4643 RHS = getConstant(RA - 1);
4646 if (RA.isMaxValue()) {
4647 Pred = ICmpInst::ICMP_EQ;
4650 if (RA.isMinValue()) return true;
4652 case ICmpInst::ICMP_ULE:
4653 if ((RA + 1).isMaxValue()) {
4654 Pred = ICmpInst::ICMP_NE;
4655 RHS = getConstant(RA + 1);
4658 if (RA.isMinValue()) {
4659 Pred = ICmpInst::ICMP_EQ;
4662 if (RA.isMaxValue()) return true;
4664 case ICmpInst::ICMP_SGE:
4665 if ((RA - 1).isMinSignedValue()) {
4666 Pred = ICmpInst::ICMP_NE;
4667 RHS = getConstant(RA - 1);
4670 if (RA.isMaxSignedValue()) {
4671 Pred = ICmpInst::ICMP_EQ;
4674 if (RA.isMinSignedValue()) return true;
4676 case ICmpInst::ICMP_SLE:
4677 if ((RA + 1).isMaxSignedValue()) {
4678 Pred = ICmpInst::ICMP_NE;
4679 RHS = getConstant(RA + 1);
4682 if (RA.isMinSignedValue()) {
4683 Pred = ICmpInst::ICMP_EQ;
4686 if (RA.isMaxSignedValue()) return true;
4688 case ICmpInst::ICMP_UGT:
4689 if (RA.isMinValue()) {
4690 Pred = ICmpInst::ICMP_NE;
4693 if ((RA + 1).isMaxValue()) {
4694 Pred = ICmpInst::ICMP_EQ;
4695 RHS = getConstant(RA + 1);
4698 if (RA.isMaxValue()) return false;
4700 case ICmpInst::ICMP_ULT:
4701 if (RA.isMaxValue()) {
4702 Pred = ICmpInst::ICMP_NE;
4705 if ((RA - 1).isMinValue()) {
4706 Pred = ICmpInst::ICMP_EQ;
4707 RHS = getConstant(RA - 1);
4710 if (RA.isMinValue()) return false;
4712 case ICmpInst::ICMP_SGT:
4713 if (RA.isMinSignedValue()) {
4714 Pred = ICmpInst::ICMP_NE;
4717 if ((RA + 1).isMaxSignedValue()) {
4718 Pred = ICmpInst::ICMP_EQ;
4719 RHS = getConstant(RA + 1);
4722 if (RA.isMaxSignedValue()) return false;
4724 case ICmpInst::ICMP_SLT:
4725 if (RA.isMaxSignedValue()) {
4726 Pred = ICmpInst::ICMP_NE;
4729 if ((RA - 1).isMinSignedValue()) {
4730 Pred = ICmpInst::ICMP_EQ;
4731 RHS = getConstant(RA - 1);
4734 if (RA.isMinSignedValue()) return false;
4739 // Check to see if we can make the LHS or RHS match.
4740 if (LHS == FoundRHS || RHS == FoundLHS) {
4741 if (isa<SCEVConstant>(RHS)) {
4742 std::swap(FoundLHS, FoundRHS);
4743 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
4745 std::swap(LHS, RHS);
4746 Pred = ICmpInst::getSwappedPredicate(Pred);
4750 // Check whether the found predicate is the same as the desired predicate.
4751 if (FoundPred == Pred)
4752 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
4754 // Check whether swapping the found predicate makes it the same as the
4755 // desired predicate.
4756 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
4757 if (isa<SCEVConstant>(RHS))
4758 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
4760 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
4761 RHS, LHS, FoundLHS, FoundRHS);
4764 // Check whether the actual condition is beyond sufficient.
4765 if (FoundPred == ICmpInst::ICMP_EQ)
4766 if (ICmpInst::isTrueWhenEqual(Pred))
4767 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
4769 if (Pred == ICmpInst::ICMP_NE)
4770 if (!ICmpInst::isTrueWhenEqual(FoundPred))
4771 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
4774 // Otherwise assume the worst.
4778 /// isImpliedCondOperands - Test whether the condition described by Pred,
4779 /// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS,
4780 /// and FoundRHS is true.
4781 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
4782 const SCEV *LHS, const SCEV *RHS,
4783 const SCEV *FoundLHS,
4784 const SCEV *FoundRHS) {
4785 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
4786 FoundLHS, FoundRHS) ||
4787 // ~x < ~y --> x > y
4788 isImpliedCondOperandsHelper(Pred, LHS, RHS,
4789 getNotSCEV(FoundRHS),
4790 getNotSCEV(FoundLHS));
4793 /// isImpliedCondOperandsHelper - Test whether the condition described by
4794 /// Pred, LHS, and RHS is true whenever the condition desribed by Pred,
4795 /// FoundLHS, and FoundRHS is true.
4797 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
4798 const SCEV *LHS, const SCEV *RHS,
4799 const SCEV *FoundLHS,
4800 const SCEV *FoundRHS) {
4802 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4803 case ICmpInst::ICMP_EQ:
4804 case ICmpInst::ICMP_NE:
4805 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
4808 case ICmpInst::ICMP_SLT:
4809 case ICmpInst::ICMP_SLE:
4810 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
4811 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS))
4814 case ICmpInst::ICMP_SGT:
4815 case ICmpInst::ICMP_SGE:
4816 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
4817 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS))
4820 case ICmpInst::ICMP_ULT:
4821 case ICmpInst::ICMP_ULE:
4822 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
4823 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS))
4826 case ICmpInst::ICMP_UGT:
4827 case ICmpInst::ICMP_UGE:
4828 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
4829 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS))
4837 /// getBECount - Subtract the end and start values and divide by the step,
4838 /// rounding up, to get the number of times the backedge is executed. Return
4839 /// CouldNotCompute if an intermediate computation overflows.
4840 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
4844 const Type *Ty = Start->getType();
4845 const SCEV *NegOne = getIntegerSCEV(-1, Ty);
4846 const SCEV *Diff = getMinusSCEV(End, Start);
4847 const SCEV *RoundUp = getAddExpr(Step, NegOne);
4849 // Add an adjustment to the difference between End and Start so that
4850 // the division will effectively round up.
4851 const SCEV *Add = getAddExpr(Diff, RoundUp);
4854 // Check Add for unsigned overflow.
4855 // TODO: More sophisticated things could be done here.
4856 const Type *WideTy = IntegerType::get(getContext(),
4857 getTypeSizeInBits(Ty) + 1);
4858 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
4859 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
4860 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
4861 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
4862 return getCouldNotCompute();
4865 return getUDivExpr(Add, Step);
4868 /// HowManyLessThans - Return the number of times a backedge containing the
4869 /// specified less-than comparison will execute. If not computable, return
4870 /// CouldNotCompute.
4871 ScalarEvolution::BackedgeTakenInfo
4872 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
4873 const Loop *L, bool isSigned) {
4874 // Only handle: "ADDREC < LoopInvariant".
4875 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
4877 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
4878 if (!AddRec || AddRec->getLoop() != L)
4879 return getCouldNotCompute();
4881 // Check to see if we have a flag which makes analysis easy.
4882 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
4883 AddRec->hasNoUnsignedWrap();
4885 if (AddRec->isAffine()) {
4886 // FORNOW: We only support unit strides.
4887 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
4888 const SCEV *Step = AddRec->getStepRecurrence(*this);
4890 // TODO: handle non-constant strides.
4891 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
4892 if (!CStep || CStep->isZero())
4893 return getCouldNotCompute();
4894 if (CStep->isOne()) {
4895 // With unit stride, the iteration never steps past the limit value.
4896 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
4898 // We know the iteration won't step past the maximum value for its type.
4900 } else if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
4901 // Test whether a positive iteration iteration can step past the limit
4902 // value and past the maximum value for its type in a single step.
4904 APInt Max = APInt::getSignedMaxValue(BitWidth);
4905 if ((Max - CStep->getValue()->getValue())
4906 .slt(CLimit->getValue()->getValue()))
4907 return getCouldNotCompute();
4909 APInt Max = APInt::getMaxValue(BitWidth);
4910 if ((Max - CStep->getValue()->getValue())
4911 .ult(CLimit->getValue()->getValue()))
4912 return getCouldNotCompute();
4915 // TODO: handle non-constant limit values below.
4916 return getCouldNotCompute();
4918 // TODO: handle negative strides below.
4919 return getCouldNotCompute();
4921 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
4922 // m. So, we count the number of iterations in which {n,+,s} < m is true.
4923 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
4924 // treat m-n as signed nor unsigned due to overflow possibility.
4926 // First, we get the value of the LHS in the first iteration: n
4927 const SCEV *Start = AddRec->getOperand(0);
4929 // Determine the minimum constant start value.
4930 const SCEV *MinStart = getConstant(isSigned ?
4931 getSignedRange(Start).getSignedMin() :
4932 getUnsignedRange(Start).getUnsignedMin());
4934 // If we know that the condition is true in order to enter the loop,
4935 // then we know that it will run exactly (m-n)/s times. Otherwise, we
4936 // only know that it will execute (max(m,n)-n)/s times. In both cases,
4937 // the division must round up.
4938 const SCEV *End = RHS;
4939 if (!isLoopGuardedByCond(L,
4940 isSigned ? ICmpInst::ICMP_SLT :
4942 getMinusSCEV(Start, Step), RHS))
4943 End = isSigned ? getSMaxExpr(RHS, Start)
4944 : getUMaxExpr(RHS, Start);
4946 // Determine the maximum constant end value.
4947 const SCEV *MaxEnd = getConstant(isSigned ?
4948 getSignedRange(End).getSignedMax() :
4949 getUnsignedRange(End).getUnsignedMax());
4951 // Finally, we subtract these two values and divide, rounding up, to get
4952 // the number of times the backedge is executed.
4953 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
4955 // The maximum backedge count is similar, except using the minimum start
4956 // value and the maximum end value.
4957 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
4959 return BackedgeTakenInfo(BECount, MaxBECount);
4962 return getCouldNotCompute();
4965 /// getNumIterationsInRange - Return the number of iterations of this loop that
4966 /// produce values in the specified constant range. Another way of looking at
4967 /// this is that it returns the first iteration number where the value is not in
4968 /// the condition, thus computing the exit count. If the iteration count can't
4969 /// be computed, an instance of SCEVCouldNotCompute is returned.
4970 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
4971 ScalarEvolution &SE) const {
4972 if (Range.isFullSet()) // Infinite loop.
4973 return SE.getCouldNotCompute();
4975 // If the start is a non-zero constant, shift the range to simplify things.
4976 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
4977 if (!SC->getValue()->isZero()) {
4978 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
4979 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
4980 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
4981 if (const SCEVAddRecExpr *ShiftedAddRec =
4982 dyn_cast<SCEVAddRecExpr>(Shifted))
4983 return ShiftedAddRec->getNumIterationsInRange(
4984 Range.subtract(SC->getValue()->getValue()), SE);
4985 // This is strange and shouldn't happen.
4986 return SE.getCouldNotCompute();
4989 // The only time we can solve this is when we have all constant indices.
4990 // Otherwise, we cannot determine the overflow conditions.
4991 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
4992 if (!isa<SCEVConstant>(getOperand(i)))
4993 return SE.getCouldNotCompute();
4996 // Okay at this point we know that all elements of the chrec are constants and
4997 // that the start element is zero.
4999 // First check to see if the range contains zero. If not, the first
5001 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5002 if (!Range.contains(APInt(BitWidth, 0)))
5003 return SE.getIntegerSCEV(0, getType());
5006 // If this is an affine expression then we have this situation:
5007 // Solve {0,+,A} in Range === Ax in Range
5009 // We know that zero is in the range. If A is positive then we know that
5010 // the upper value of the range must be the first possible exit value.
5011 // If A is negative then the lower of the range is the last possible loop
5012 // value. Also note that we already checked for a full range.
5013 APInt One(BitWidth,1);
5014 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5015 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5017 // The exit value should be (End+A)/A.
5018 APInt ExitVal = (End + A).udiv(A);
5019 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5021 // Evaluate at the exit value. If we really did fall out of the valid
5022 // range, then we computed our trip count, otherwise wrap around or other
5023 // things must have happened.
5024 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5025 if (Range.contains(Val->getValue()))
5026 return SE.getCouldNotCompute(); // Something strange happened
5028 // Ensure that the previous value is in the range. This is a sanity check.
5029 assert(Range.contains(
5030 EvaluateConstantChrecAtConstant(this,
5031 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5032 "Linear scev computation is off in a bad way!");
5033 return SE.getConstant(ExitValue);
5034 } else if (isQuadratic()) {
5035 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5036 // quadratic equation to solve it. To do this, we must frame our problem in
5037 // terms of figuring out when zero is crossed, instead of when
5038 // Range.getUpper() is crossed.
5039 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5040 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5041 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5043 // Next, solve the constructed addrec
5044 std::pair<const SCEV *,const SCEV *> Roots =
5045 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5046 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5047 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5049 // Pick the smallest positive root value.
5050 if (ConstantInt *CB =
5051 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5052 R1->getValue(), R2->getValue()))) {
5053 if (CB->getZExtValue() == false)
5054 std::swap(R1, R2); // R1 is the minimum root now.
5056 // Make sure the root is not off by one. The returned iteration should
5057 // not be in the range, but the previous one should be. When solving
5058 // for "X*X < 5", for example, we should not return a root of 2.
5059 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5062 if (Range.contains(R1Val->getValue())) {
5063 // The next iteration must be out of the range...
5064 ConstantInt *NextVal =
5065 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5067 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5068 if (!Range.contains(R1Val->getValue()))
5069 return SE.getConstant(NextVal);
5070 return SE.getCouldNotCompute(); // Something strange happened
5073 // If R1 was not in the range, then it is a good return value. Make
5074 // sure that R1-1 WAS in the range though, just in case.
5075 ConstantInt *NextVal =
5076 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5077 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5078 if (Range.contains(R1Val->getValue()))
5080 return SE.getCouldNotCompute(); // Something strange happened
5085 return SE.getCouldNotCompute();
5090 //===----------------------------------------------------------------------===//
5091 // SCEVCallbackVH Class Implementation
5092 //===----------------------------------------------------------------------===//
5094 void ScalarEvolution::SCEVCallbackVH::deleted() {
5095 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5096 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5097 SE->ConstantEvolutionLoopExitValue.erase(PN);
5098 SE->Scalars.erase(getValPtr());
5099 // this now dangles!
5102 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
5103 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5105 // Forget all the expressions associated with users of the old value,
5106 // so that future queries will recompute the expressions using the new
5108 SmallVector<User *, 16> Worklist;
5109 SmallPtrSet<User *, 8> Visited;
5110 Value *Old = getValPtr();
5111 bool DeleteOld = false;
5112 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5114 Worklist.push_back(*UI);
5115 while (!Worklist.empty()) {
5116 User *U = Worklist.pop_back_val();
5117 // Deleting the Old value will cause this to dangle. Postpone
5118 // that until everything else is done.
5123 if (!Visited.insert(U))
5125 if (PHINode *PN = dyn_cast<PHINode>(U))
5126 SE->ConstantEvolutionLoopExitValue.erase(PN);
5127 SE->Scalars.erase(U);
5128 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5130 Worklist.push_back(*UI);
5132 // Delete the Old value if it (indirectly) references itself.
5134 if (PHINode *PN = dyn_cast<PHINode>(Old))
5135 SE->ConstantEvolutionLoopExitValue.erase(PN);
5136 SE->Scalars.erase(Old);
5137 // this now dangles!
5142 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5143 : CallbackVH(V), SE(se) {}
5145 //===----------------------------------------------------------------------===//
5146 // ScalarEvolution Class Implementation
5147 //===----------------------------------------------------------------------===//
5149 ScalarEvolution::ScalarEvolution()
5150 : FunctionPass(&ID) {
5153 bool ScalarEvolution::runOnFunction(Function &F) {
5155 LI = &getAnalysis<LoopInfo>();
5156 TD = getAnalysisIfAvailable<TargetData>();
5160 void ScalarEvolution::releaseMemory() {
5162 BackedgeTakenCounts.clear();
5163 ConstantEvolutionLoopExitValue.clear();
5164 ValuesAtScopes.clear();
5165 UniqueSCEVs.clear();
5166 SCEVAllocator.Reset();
5169 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5170 AU.setPreservesAll();
5171 AU.addRequiredTransitive<LoopInfo>();
5174 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5175 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5178 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5180 // Print all inner loops first
5181 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5182 PrintLoopInfo(OS, SE, *I);
5184 OS << "Loop " << L->getHeader()->getName() << ": ";
5186 SmallVector<BasicBlock*, 8> ExitBlocks;
5187 L->getExitBlocks(ExitBlocks);
5188 if (ExitBlocks.size() != 1)
5189 OS << "<multiple exits> ";
5191 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5192 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5194 OS << "Unpredictable backedge-taken count. ";
5198 OS << "Loop " << L->getHeader()->getName() << ": ";
5200 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5201 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5203 OS << "Unpredictable max backedge-taken count. ";
5209 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
5210 // ScalarEvolution's implementaiton of the print method is to print
5211 // out SCEV values of all instructions that are interesting. Doing
5212 // this potentially causes it to create new SCEV objects though,
5213 // which technically conflicts with the const qualifier. This isn't
5214 // observable from outside the class though, so casting away the
5215 // const isn't dangerous.
5216 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
5218 OS << "Classifying expressions for: " << F->getName() << "\n";
5219 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5220 if (isSCEVable(I->getType())) {
5223 const SCEV *SV = SE.getSCEV(&*I);
5226 const Loop *L = LI->getLoopFor((*I).getParent());
5228 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5235 OS << "\t\t" "Exits: ";
5236 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5237 if (!ExitValue->isLoopInvariant(L)) {
5238 OS << "<<Unknown>>";
5247 OS << "Determining loop execution counts for: " << F->getName() << "\n";
5248 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5249 PrintLoopInfo(OS, &SE, *I);