1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #define DEBUG_TYPE "scalar-evolution"
62 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/GlobalAlias.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/Operator.h"
70 #include "llvm/Analysis/ConstantFolding.h"
71 #include "llvm/Analysis/Dominators.h"
72 #include "llvm/Analysis/LoopInfo.h"
73 #include "llvm/Analysis/ValueTracking.h"
74 #include "llvm/Assembly/Writer.h"
75 #include "llvm/Target/TargetData.h"
76 #include "llvm/Support/CommandLine.h"
77 #include "llvm/Support/ConstantRange.h"
78 #include "llvm/Support/ErrorHandling.h"
79 #include "llvm/Support/GetElementPtrTypeIterator.h"
80 #include "llvm/Support/InstIterator.h"
81 #include "llvm/Support/MathExtras.h"
82 #include "llvm/Support/raw_ostream.h"
83 #include "llvm/ADT/Statistic.h"
84 #include "llvm/ADT/STLExtras.h"
85 #include "llvm/ADT/SmallPtrSet.h"
89 STATISTIC(NumArrayLenItCounts,
90 "Number of trip counts computed with array length");
91 STATISTIC(NumTripCountsComputed,
92 "Number of loops with predictable loop counts");
93 STATISTIC(NumTripCountsNotComputed,
94 "Number of loops without predictable loop counts");
95 STATISTIC(NumBruteForceTripCountsComputed,
96 "Number of loops with trip counts computed by force");
98 static cl::opt<unsigned>
99 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
100 cl::desc("Maximum number of iterations SCEV will "
101 "symbolically execute a constant "
105 static RegisterPass<ScalarEvolution>
106 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
107 char ScalarEvolution::ID = 0;
109 //===----------------------------------------------------------------------===//
110 // SCEV class definitions
111 //===----------------------------------------------------------------------===//
113 //===----------------------------------------------------------------------===//
114 // Implementation of the SCEV class.
119 void SCEV::dump() const {
124 bool SCEV::isZero() const {
125 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
126 return SC->getValue()->isZero();
130 bool SCEV::isOne() const {
131 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
132 return SC->getValue()->isOne();
136 bool SCEV::isAllOnesValue() const {
137 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
138 return SC->getValue()->isAllOnesValue();
142 SCEVCouldNotCompute::SCEVCouldNotCompute() :
143 SCEV(FoldingSetNodeID(), scCouldNotCompute) {}
145 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
146 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
150 const Type *SCEVCouldNotCompute::getType() const {
151 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
155 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
156 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
160 bool SCEVCouldNotCompute::hasOperand(const SCEV *) const {
161 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
165 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
166 OS << "***COULDNOTCOMPUTE***";
169 bool SCEVCouldNotCompute::classof(const SCEV *S) {
170 return S->getSCEVType() == scCouldNotCompute;
173 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
175 ID.AddInteger(scConstant);
178 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
179 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>();
180 new (S) SCEVConstant(ID, V);
181 UniqueSCEVs.InsertNode(S, IP);
185 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
186 return getConstant(ConstantInt::get(getContext(), Val));
190 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
192 ConstantInt::get(cast<IntegerType>(Ty), V, isSigned));
195 const Type *SCEVConstant::getType() const { return V->getType(); }
197 void SCEVConstant::print(raw_ostream &OS) const {
198 WriteAsOperand(OS, V, false);
201 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID,
202 unsigned SCEVTy, const SCEV *op, const Type *ty)
203 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
205 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
206 return Op->dominates(BB, DT);
209 bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
210 return Op->properlyDominates(BB, DT);
213 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID,
214 const SCEV *op, const Type *ty)
215 : SCEVCastExpr(ID, scTruncate, op, ty) {
216 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
217 (Ty->isInteger() || isa<PointerType>(Ty)) &&
218 "Cannot truncate non-integer value!");
221 void SCEVTruncateExpr::print(raw_ostream &OS) const {
222 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
225 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID,
226 const SCEV *op, const Type *ty)
227 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
228 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
229 (Ty->isInteger() || isa<PointerType>(Ty)) &&
230 "Cannot zero extend non-integer value!");
233 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
234 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
237 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID,
238 const SCEV *op, const Type *ty)
239 : SCEVCastExpr(ID, scSignExtend, op, ty) {
240 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
241 (Ty->isInteger() || isa<PointerType>(Ty)) &&
242 "Cannot sign extend non-integer value!");
245 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
246 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
249 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
250 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
251 const char *OpStr = getOperationStr();
252 OS << "(" << *Operands[0];
253 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
254 OS << OpStr << *Operands[i];
258 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
259 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
260 if (!getOperand(i)->dominates(BB, DT))
266 bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
267 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
268 if (!getOperand(i)->properlyDominates(BB, DT))
274 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
275 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
278 bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
279 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT);
282 void SCEVUDivExpr::print(raw_ostream &OS) const {
283 OS << "(" << *LHS << " /u " << *RHS << ")";
286 const Type *SCEVUDivExpr::getType() const {
287 // In most cases the types of LHS and RHS will be the same, but in some
288 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
289 // depend on the type for correctness, but handling types carefully can
290 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
291 // a pointer type than the RHS, so use the RHS' type here.
292 return RHS->getType();
295 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
296 // Add recurrences are never invariant in the function-body (null loop).
300 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
301 if (QueryLoop->contains(L))
304 // This recurrence is variant w.r.t. QueryLoop if any of its operands
306 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
307 if (!getOperand(i)->isLoopInvariant(QueryLoop))
310 // Otherwise it's loop-invariant.
314 void SCEVAddRecExpr::print(raw_ostream &OS) const {
315 OS << "{" << *Operands[0];
316 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
317 OS << ",+," << *Operands[i];
318 OS << "}<" << L->getHeader()->getName() + ">";
321 void SCEVFieldOffsetExpr::print(raw_ostream &OS) const {
322 // LLVM struct fields don't have names, so just print the field number.
323 OS << "offsetof(" << *STy << ", " << FieldNo << ")";
326 void SCEVAllocSizeExpr::print(raw_ostream &OS) const {
327 OS << "sizeof(" << *AllocTy << ")";
330 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
331 // All non-instruction values are loop invariant. All instructions are loop
332 // invariant if they are not contained in the specified loop.
333 // Instructions are never considered invariant in the function body
334 // (null loop) because they are defined within the "loop".
335 if (Instruction *I = dyn_cast<Instruction>(V))
336 return L && !L->contains(I);
340 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
341 if (Instruction *I = dyn_cast<Instruction>(getValue()))
342 return DT->dominates(I->getParent(), BB);
346 bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
347 if (Instruction *I = dyn_cast<Instruction>(getValue()))
348 return DT->properlyDominates(I->getParent(), BB);
352 const Type *SCEVUnknown::getType() const {
356 void SCEVUnknown::print(raw_ostream &OS) const {
357 WriteAsOperand(OS, V, false);
360 //===----------------------------------------------------------------------===//
362 //===----------------------------------------------------------------------===//
364 static bool CompareTypes(const Type *A, const Type *B) {
365 if (A->getTypeID() != B->getTypeID())
366 return A->getTypeID() < B->getTypeID();
367 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) {
368 const IntegerType *BI = cast<IntegerType>(B);
369 return AI->getBitWidth() < BI->getBitWidth();
371 if (const PointerType *AI = dyn_cast<PointerType>(A)) {
372 const PointerType *BI = cast<PointerType>(B);
373 return CompareTypes(AI->getElementType(), BI->getElementType());
375 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) {
376 const ArrayType *BI = cast<ArrayType>(B);
377 if (AI->getNumElements() != BI->getNumElements())
378 return AI->getNumElements() < BI->getNumElements();
379 return CompareTypes(AI->getElementType(), BI->getElementType());
381 if (const VectorType *AI = dyn_cast<VectorType>(A)) {
382 const VectorType *BI = cast<VectorType>(B);
383 if (AI->getNumElements() != BI->getNumElements())
384 return AI->getNumElements() < BI->getNumElements();
385 return CompareTypes(AI->getElementType(), BI->getElementType());
387 if (const StructType *AI = dyn_cast<StructType>(A)) {
388 const StructType *BI = cast<StructType>(B);
389 if (AI->getNumElements() != BI->getNumElements())
390 return AI->getNumElements() < BI->getNumElements();
391 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i)
392 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) ||
393 CompareTypes(BI->getElementType(i), AI->getElementType(i)))
394 return CompareTypes(AI->getElementType(i), BI->getElementType(i));
400 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
401 /// than the complexity of the RHS. This comparator is used to canonicalize
403 class SCEVComplexityCompare {
406 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
408 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
409 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
413 // Primarily, sort the SCEVs by their getSCEVType().
414 if (LHS->getSCEVType() != RHS->getSCEVType())
415 return LHS->getSCEVType() < RHS->getSCEVType();
417 // Aside from the getSCEVType() ordering, the particular ordering
418 // isn't very important except that it's beneficial to be consistent,
419 // so that (a + b) and (b + a) don't end up as different expressions.
421 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
422 // not as complete as it could be.
423 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
424 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
426 // Order pointer values after integer values. This helps SCEVExpander
428 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
430 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
433 // Compare getValueID values.
434 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
435 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
437 // Sort arguments by their position.
438 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
439 const Argument *RA = cast<Argument>(RU->getValue());
440 return LA->getArgNo() < RA->getArgNo();
443 // For instructions, compare their loop depth, and their opcode.
444 // This is pretty loose.
445 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
446 Instruction *RV = cast<Instruction>(RU->getValue());
448 // Compare loop depths.
449 if (LI->getLoopDepth(LV->getParent()) !=
450 LI->getLoopDepth(RV->getParent()))
451 return LI->getLoopDepth(LV->getParent()) <
452 LI->getLoopDepth(RV->getParent());
455 if (LV->getOpcode() != RV->getOpcode())
456 return LV->getOpcode() < RV->getOpcode();
458 // Compare the number of operands.
459 if (LV->getNumOperands() != RV->getNumOperands())
460 return LV->getNumOperands() < RV->getNumOperands();
466 // Compare constant values.
467 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
468 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
469 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
470 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
471 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
474 // Compare addrec loop depths.
475 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
476 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
477 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
478 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
481 // Lexicographically compare n-ary expressions.
482 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
483 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
484 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
485 if (i >= RC->getNumOperands())
487 if (operator()(LC->getOperand(i), RC->getOperand(i)))
489 if (operator()(RC->getOperand(i), LC->getOperand(i)))
492 return LC->getNumOperands() < RC->getNumOperands();
495 // Lexicographically compare udiv expressions.
496 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
497 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
498 if (operator()(LC->getLHS(), RC->getLHS()))
500 if (operator()(RC->getLHS(), LC->getLHS()))
502 if (operator()(LC->getRHS(), RC->getRHS()))
504 if (operator()(RC->getRHS(), LC->getRHS()))
509 // Compare cast expressions by operand.
510 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
511 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
512 return operator()(LC->getOperand(), RC->getOperand());
515 // Compare offsetof expressions.
516 if (const SCEVFieldOffsetExpr *LA = dyn_cast<SCEVFieldOffsetExpr>(LHS)) {
517 const SCEVFieldOffsetExpr *RA = cast<SCEVFieldOffsetExpr>(RHS);
518 if (CompareTypes(LA->getStructType(), RA->getStructType()) ||
519 CompareTypes(RA->getStructType(), LA->getStructType()))
520 return CompareTypes(LA->getStructType(), RA->getStructType());
521 return LA->getFieldNo() < RA->getFieldNo();
524 // Compare sizeof expressions by the allocation type.
525 if (const SCEVAllocSizeExpr *LA = dyn_cast<SCEVAllocSizeExpr>(LHS)) {
526 const SCEVAllocSizeExpr *RA = cast<SCEVAllocSizeExpr>(RHS);
527 return CompareTypes(LA->getAllocType(), RA->getAllocType());
530 llvm_unreachable("Unknown SCEV kind!");
536 /// GroupByComplexity - Given a list of SCEV objects, order them by their
537 /// complexity, and group objects of the same complexity together by value.
538 /// When this routine is finished, we know that any duplicates in the vector are
539 /// consecutive and that complexity is monotonically increasing.
541 /// Note that we go take special precautions to ensure that we get determinstic
542 /// results from this routine. In other words, we don't want the results of
543 /// this to depend on where the addresses of various SCEV objects happened to
546 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
548 if (Ops.size() < 2) return; // Noop
549 if (Ops.size() == 2) {
550 // This is the common case, which also happens to be trivially simple.
552 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
553 std::swap(Ops[0], Ops[1]);
557 // Do the rough sort by complexity.
558 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
560 // Now that we are sorted by complexity, group elements of the same
561 // complexity. Note that this is, at worst, N^2, but the vector is likely to
562 // be extremely short in practice. Note that we take this approach because we
563 // do not want to depend on the addresses of the objects we are grouping.
564 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
565 const SCEV *S = Ops[i];
566 unsigned Complexity = S->getSCEVType();
568 // If there are any objects of the same complexity and same value as this
570 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
571 if (Ops[j] == S) { // Found a duplicate.
572 // Move it to immediately after i'th element.
573 std::swap(Ops[i+1], Ops[j]);
574 ++i; // no need to rescan it.
575 if (i == e-2) return; // Done!
583 //===----------------------------------------------------------------------===//
584 // Simple SCEV method implementations
585 //===----------------------------------------------------------------------===//
587 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
589 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
591 const Type* ResultTy) {
592 // Handle the simplest case efficiently.
594 return SE.getTruncateOrZeroExtend(It, ResultTy);
596 // We are using the following formula for BC(It, K):
598 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
600 // Suppose, W is the bitwidth of the return value. We must be prepared for
601 // overflow. Hence, we must assure that the result of our computation is
602 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
603 // safe in modular arithmetic.
605 // However, this code doesn't use exactly that formula; the formula it uses
606 // is something like the following, where T is the number of factors of 2 in
607 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
610 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
612 // This formula is trivially equivalent to the previous formula. However,
613 // this formula can be implemented much more efficiently. The trick is that
614 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
615 // arithmetic. To do exact division in modular arithmetic, all we have
616 // to do is multiply by the inverse. Therefore, this step can be done at
619 // The next issue is how to safely do the division by 2^T. The way this
620 // is done is by doing the multiplication step at a width of at least W + T
621 // bits. This way, the bottom W+T bits of the product are accurate. Then,
622 // when we perform the division by 2^T (which is equivalent to a right shift
623 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
624 // truncated out after the division by 2^T.
626 // In comparison to just directly using the first formula, this technique
627 // is much more efficient; using the first formula requires W * K bits,
628 // but this formula less than W + K bits. Also, the first formula requires
629 // a division step, whereas this formula only requires multiplies and shifts.
631 // It doesn't matter whether the subtraction step is done in the calculation
632 // width or the input iteration count's width; if the subtraction overflows,
633 // the result must be zero anyway. We prefer here to do it in the width of
634 // the induction variable because it helps a lot for certain cases; CodeGen
635 // isn't smart enough to ignore the overflow, which leads to much less
636 // efficient code if the width of the subtraction is wider than the native
639 // (It's possible to not widen at all by pulling out factors of 2 before
640 // the multiplication; for example, K=2 can be calculated as
641 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
642 // extra arithmetic, so it's not an obvious win, and it gets
643 // much more complicated for K > 3.)
645 // Protection from insane SCEVs; this bound is conservative,
646 // but it probably doesn't matter.
648 return SE.getCouldNotCompute();
650 unsigned W = SE.getTypeSizeInBits(ResultTy);
652 // Calculate K! / 2^T and T; we divide out the factors of two before
653 // multiplying for calculating K! / 2^T to avoid overflow.
654 // Other overflow doesn't matter because we only care about the bottom
655 // W bits of the result.
656 APInt OddFactorial(W, 1);
658 for (unsigned i = 3; i <= K; ++i) {
660 unsigned TwoFactors = Mult.countTrailingZeros();
662 Mult = Mult.lshr(TwoFactors);
663 OddFactorial *= Mult;
666 // We need at least W + T bits for the multiplication step
667 unsigned CalculationBits = W + T;
669 // Calcuate 2^T, at width T+W.
670 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
672 // Calculate the multiplicative inverse of K! / 2^T;
673 // this multiplication factor will perform the exact division by
675 APInt Mod = APInt::getSignedMinValue(W+1);
676 APInt MultiplyFactor = OddFactorial.zext(W+1);
677 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
678 MultiplyFactor = MultiplyFactor.trunc(W);
680 // Calculate the product, at width T+W
681 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
683 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
684 for (unsigned i = 1; i != K; ++i) {
685 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
686 Dividend = SE.getMulExpr(Dividend,
687 SE.getTruncateOrZeroExtend(S, CalculationTy));
691 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
693 // Truncate the result, and divide by K! / 2^T.
695 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
696 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
699 /// evaluateAtIteration - Return the value of this chain of recurrences at
700 /// the specified iteration number. We can evaluate this recurrence by
701 /// multiplying each element in the chain by the binomial coefficient
702 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
704 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
706 /// where BC(It, k) stands for binomial coefficient.
708 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
709 ScalarEvolution &SE) const {
710 const SCEV *Result = getStart();
711 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
712 // The computation is correct in the face of overflow provided that the
713 // multiplication is performed _after_ the evaluation of the binomial
715 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
716 if (isa<SCEVCouldNotCompute>(Coeff))
719 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
724 //===----------------------------------------------------------------------===//
725 // SCEV Expression folder implementations
726 //===----------------------------------------------------------------------===//
728 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
730 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
731 "This is not a truncating conversion!");
732 assert(isSCEVable(Ty) &&
733 "This is not a conversion to a SCEVable type!");
734 Ty = getEffectiveSCEVType(Ty);
737 ID.AddInteger(scTruncate);
741 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
743 // Fold if the operand is constant.
744 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
746 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
748 // trunc(trunc(x)) --> trunc(x)
749 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
750 return getTruncateExpr(ST->getOperand(), Ty);
752 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
753 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
754 return getTruncateOrSignExtend(SS->getOperand(), Ty);
756 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
757 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
758 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
760 // If the input value is a chrec scev, truncate the chrec's operands.
761 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
762 SmallVector<const SCEV *, 4> Operands;
763 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
764 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
765 return getAddRecExpr(Operands, AddRec->getLoop());
768 // The cast wasn't folded; create an explicit cast node.
769 // Recompute the insert position, as it may have been invalidated.
770 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
771 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>();
772 new (S) SCEVTruncateExpr(ID, Op, Ty);
773 UniqueSCEVs.InsertNode(S, IP);
777 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
779 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
780 "This is not an extending conversion!");
781 assert(isSCEVable(Ty) &&
782 "This is not a conversion to a SCEVable type!");
783 Ty = getEffectiveSCEVType(Ty);
785 // Fold if the operand is constant.
786 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
787 const Type *IntTy = getEffectiveSCEVType(Ty);
788 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
789 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
790 return getConstant(cast<ConstantInt>(C));
793 // zext(zext(x)) --> zext(x)
794 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
795 return getZeroExtendExpr(SZ->getOperand(), Ty);
797 // Before doing any expensive analysis, check to see if we've already
798 // computed a SCEV for this Op and Ty.
800 ID.AddInteger(scZeroExtend);
804 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
806 // If the input value is a chrec scev, and we can prove that the value
807 // did not overflow the old, smaller, value, we can zero extend all of the
808 // operands (often constants). This allows analysis of something like
809 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
810 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
811 if (AR->isAffine()) {
812 const SCEV *Start = AR->getStart();
813 const SCEV *Step = AR->getStepRecurrence(*this);
814 unsigned BitWidth = getTypeSizeInBits(AR->getType());
815 const Loop *L = AR->getLoop();
817 // If we have special knowledge that this addrec won't overflow,
818 // we don't need to do any further analysis.
819 if (AR->hasNoUnsignedWrap())
820 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
821 getZeroExtendExpr(Step, Ty),
824 // Check whether the backedge-taken count is SCEVCouldNotCompute.
825 // Note that this serves two purposes: It filters out loops that are
826 // simply not analyzable, and it covers the case where this code is
827 // being called from within backedge-taken count analysis, such that
828 // attempting to ask for the backedge-taken count would likely result
829 // in infinite recursion. In the later case, the analysis code will
830 // cope with a conservative value, and it will take care to purge
831 // that value once it has finished.
832 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
833 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
834 // Manually compute the final value for AR, checking for
837 // Check whether the backedge-taken count can be losslessly casted to
838 // the addrec's type. The count is always unsigned.
839 const SCEV *CastedMaxBECount =
840 getTruncateOrZeroExtend(MaxBECount, Start->getType());
841 const SCEV *RecastedMaxBECount =
842 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
843 if (MaxBECount == RecastedMaxBECount) {
844 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
845 // Check whether Start+Step*MaxBECount has no unsigned overflow.
847 getMulExpr(CastedMaxBECount,
848 getTruncateOrZeroExtend(Step, Start->getType()));
849 const SCEV *Add = getAddExpr(Start, ZMul);
850 const SCEV *OperandExtendedAdd =
851 getAddExpr(getZeroExtendExpr(Start, WideTy),
852 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
853 getZeroExtendExpr(Step, WideTy)));
854 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
855 // Return the expression with the addrec on the outside.
856 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
857 getZeroExtendExpr(Step, Ty),
860 // Similar to above, only this time treat the step value as signed.
861 // This covers loops that count down.
863 getMulExpr(CastedMaxBECount,
864 getTruncateOrSignExtend(Step, Start->getType()));
865 Add = getAddExpr(Start, SMul);
867 getAddExpr(getZeroExtendExpr(Start, WideTy),
868 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
869 getSignExtendExpr(Step, WideTy)));
870 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
871 // Return the expression with the addrec on the outside.
872 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
873 getSignExtendExpr(Step, Ty),
877 // If the backedge is guarded by a comparison with the pre-inc value
878 // the addrec is safe. Also, if the entry is guarded by a comparison
879 // with the start value and the backedge is guarded by a comparison
880 // with the post-inc value, the addrec is safe.
881 if (isKnownPositive(Step)) {
882 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
883 getUnsignedRange(Step).getUnsignedMax());
884 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
885 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
886 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
887 AR->getPostIncExpr(*this), N)))
888 // Return the expression with the addrec on the outside.
889 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
890 getZeroExtendExpr(Step, Ty),
892 } else if (isKnownNegative(Step)) {
893 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
894 getSignedRange(Step).getSignedMin());
895 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) &&
896 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) ||
897 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
898 AR->getPostIncExpr(*this), N)))
899 // Return the expression with the addrec on the outside.
900 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
901 getSignExtendExpr(Step, Ty),
907 // The cast wasn't folded; create an explicit cast node.
908 // Recompute the insert position, as it may have been invalidated.
909 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
910 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>();
911 new (S) SCEVZeroExtendExpr(ID, Op, Ty);
912 UniqueSCEVs.InsertNode(S, IP);
916 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
918 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
919 "This is not an extending conversion!");
920 assert(isSCEVable(Ty) &&
921 "This is not a conversion to a SCEVable type!");
922 Ty = getEffectiveSCEVType(Ty);
924 // Fold if the operand is constant.
925 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
926 const Type *IntTy = getEffectiveSCEVType(Ty);
927 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
928 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
929 return getConstant(cast<ConstantInt>(C));
932 // sext(sext(x)) --> sext(x)
933 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
934 return getSignExtendExpr(SS->getOperand(), Ty);
936 // Before doing any expensive analysis, check to see if we've already
937 // computed a SCEV for this Op and Ty.
939 ID.AddInteger(scSignExtend);
943 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
945 // If the input value is a chrec scev, and we can prove that the value
946 // did not overflow the old, smaller, value, we can sign extend all of the
947 // operands (often constants). This allows analysis of something like
948 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
949 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
950 if (AR->isAffine()) {
951 const SCEV *Start = AR->getStart();
952 const SCEV *Step = AR->getStepRecurrence(*this);
953 unsigned BitWidth = getTypeSizeInBits(AR->getType());
954 const Loop *L = AR->getLoop();
956 // If we have special knowledge that this addrec won't overflow,
957 // we don't need to do any further analysis.
958 if (AR->hasNoSignedWrap())
959 return getAddRecExpr(getSignExtendExpr(Start, Ty),
960 getSignExtendExpr(Step, Ty),
963 // Check whether the backedge-taken count is SCEVCouldNotCompute.
964 // Note that this serves two purposes: It filters out loops that are
965 // simply not analyzable, and it covers the case where this code is
966 // being called from within backedge-taken count analysis, such that
967 // attempting to ask for the backedge-taken count would likely result
968 // in infinite recursion. In the later case, the analysis code will
969 // cope with a conservative value, and it will take care to purge
970 // that value once it has finished.
971 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
972 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
973 // Manually compute the final value for AR, checking for
976 // Check whether the backedge-taken count can be losslessly casted to
977 // the addrec's type. The count is always unsigned.
978 const SCEV *CastedMaxBECount =
979 getTruncateOrZeroExtend(MaxBECount, Start->getType());
980 const SCEV *RecastedMaxBECount =
981 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
982 if (MaxBECount == RecastedMaxBECount) {
983 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
984 // Check whether Start+Step*MaxBECount has no signed overflow.
986 getMulExpr(CastedMaxBECount,
987 getTruncateOrSignExtend(Step, Start->getType()));
988 const SCEV *Add = getAddExpr(Start, SMul);
989 const SCEV *OperandExtendedAdd =
990 getAddExpr(getSignExtendExpr(Start, WideTy),
991 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
992 getSignExtendExpr(Step, WideTy)));
993 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
994 // Return the expression with the addrec on the outside.
995 return getAddRecExpr(getSignExtendExpr(Start, Ty),
996 getSignExtendExpr(Step, Ty),
999 // Similar to above, only this time treat the step value as unsigned.
1000 // This covers loops that count up with an unsigned step.
1002 getMulExpr(CastedMaxBECount,
1003 getTruncateOrZeroExtend(Step, Start->getType()));
1004 Add = getAddExpr(Start, UMul);
1005 OperandExtendedAdd =
1006 getAddExpr(getSignExtendExpr(Start, WideTy),
1007 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1008 getZeroExtendExpr(Step, WideTy)));
1009 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1010 // Return the expression with the addrec on the outside.
1011 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1012 getZeroExtendExpr(Step, Ty),
1016 // If the backedge is guarded by a comparison with the pre-inc value
1017 // the addrec is safe. Also, if the entry is guarded by a comparison
1018 // with the start value and the backedge is guarded by a comparison
1019 // with the post-inc value, the addrec is safe.
1020 if (isKnownPositive(Step)) {
1021 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1022 getSignedRange(Step).getSignedMax());
1023 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1024 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1025 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1026 AR->getPostIncExpr(*this), N)))
1027 // Return the expression with the addrec on the outside.
1028 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1029 getSignExtendExpr(Step, Ty),
1031 } else if (isKnownNegative(Step)) {
1032 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1033 getSignedRange(Step).getSignedMin());
1034 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1035 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1036 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1037 AR->getPostIncExpr(*this), N)))
1038 // Return the expression with the addrec on the outside.
1039 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1040 getSignExtendExpr(Step, Ty),
1046 // The cast wasn't folded; create an explicit cast node.
1047 // Recompute the insert position, as it may have been invalidated.
1048 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1049 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>();
1050 new (S) SCEVSignExtendExpr(ID, Op, Ty);
1051 UniqueSCEVs.InsertNode(S, IP);
1055 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1056 /// unspecified bits out to the given type.
1058 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1060 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1061 "This is not an extending conversion!");
1062 assert(isSCEVable(Ty) &&
1063 "This is not a conversion to a SCEVable type!");
1064 Ty = getEffectiveSCEVType(Ty);
1066 // Sign-extend negative constants.
1067 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1068 if (SC->getValue()->getValue().isNegative())
1069 return getSignExtendExpr(Op, Ty);
1071 // Peel off a truncate cast.
1072 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1073 const SCEV *NewOp = T->getOperand();
1074 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1075 return getAnyExtendExpr(NewOp, Ty);
1076 return getTruncateOrNoop(NewOp, Ty);
1079 // Next try a zext cast. If the cast is folded, use it.
1080 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1081 if (!isa<SCEVZeroExtendExpr>(ZExt))
1084 // Next try a sext cast. If the cast is folded, use it.
1085 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1086 if (!isa<SCEVSignExtendExpr>(SExt))
1089 // If the expression is obviously signed, use the sext cast value.
1090 if (isa<SCEVSMaxExpr>(Op))
1093 // Absent any other information, use the zext cast value.
1097 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1098 /// a list of operands to be added under the given scale, update the given
1099 /// map. This is a helper function for getAddRecExpr. As an example of
1100 /// what it does, given a sequence of operands that would form an add
1101 /// expression like this:
1103 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1105 /// where A and B are constants, update the map with these values:
1107 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1109 /// and add 13 + A*B*29 to AccumulatedConstant.
1110 /// This will allow getAddRecExpr to produce this:
1112 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1114 /// This form often exposes folding opportunities that are hidden in
1115 /// the original operand list.
1117 /// Return true iff it appears that any interesting folding opportunities
1118 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1119 /// the common case where no interesting opportunities are present, and
1120 /// is also used as a check to avoid infinite recursion.
1123 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1124 SmallVector<const SCEV *, 8> &NewOps,
1125 APInt &AccumulatedConstant,
1126 const SmallVectorImpl<const SCEV *> &Ops,
1128 ScalarEvolution &SE) {
1129 bool Interesting = false;
1131 // Iterate over the add operands.
1132 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1133 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1134 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1136 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1137 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1138 // A multiplication of a constant with another add; recurse.
1140 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1141 cast<SCEVAddExpr>(Mul->getOperand(1))
1145 // A multiplication of a constant with some other value. Update
1147 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1148 const SCEV *Key = SE.getMulExpr(MulOps);
1149 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1150 M.insert(std::make_pair(Key, NewScale));
1152 NewOps.push_back(Pair.first->first);
1154 Pair.first->second += NewScale;
1155 // The map already had an entry for this value, which may indicate
1156 // a folding opportunity.
1160 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1161 // Pull a buried constant out to the outside.
1162 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
1164 AccumulatedConstant += Scale * C->getValue()->getValue();
1166 // An ordinary operand. Update the map.
1167 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1168 M.insert(std::make_pair(Ops[i], Scale));
1170 NewOps.push_back(Pair.first->first);
1172 Pair.first->second += Scale;
1173 // The map already had an entry for this value, which may indicate
1174 // a folding opportunity.
1184 struct APIntCompare {
1185 bool operator()(const APInt &LHS, const APInt &RHS) const {
1186 return LHS.ult(RHS);
1191 /// getAddExpr - Get a canonical add expression, or something simpler if
1193 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1194 bool HasNUW, bool HasNSW) {
1195 assert(!Ops.empty() && "Cannot get empty add!");
1196 if (Ops.size() == 1) return Ops[0];
1198 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1199 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1200 getEffectiveSCEVType(Ops[0]->getType()) &&
1201 "SCEVAddExpr operand types don't match!");
1204 // Sort by complexity, this groups all similar expression types together.
1205 GroupByComplexity(Ops, LI);
1207 // If there are any constants, fold them together.
1209 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1211 assert(Idx < Ops.size());
1212 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1213 // We found two constants, fold them together!
1214 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1215 RHSC->getValue()->getValue());
1216 if (Ops.size() == 2) return Ops[0];
1217 Ops.erase(Ops.begin()+1); // Erase the folded element
1218 LHSC = cast<SCEVConstant>(Ops[0]);
1221 // If we are left with a constant zero being added, strip it off.
1222 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1223 Ops.erase(Ops.begin());
1228 if (Ops.size() == 1) return Ops[0];
1230 // Okay, check to see if the same value occurs in the operand list twice. If
1231 // so, merge them together into an multiply expression. Since we sorted the
1232 // list, these values are required to be adjacent.
1233 const Type *Ty = Ops[0]->getType();
1234 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1235 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1236 // Found a match, merge the two values into a multiply, and add any
1237 // remaining values to the result.
1238 const SCEV *Two = getIntegerSCEV(2, Ty);
1239 const SCEV *Mul = getMulExpr(Ops[i], Two);
1240 if (Ops.size() == 2)
1242 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1244 return getAddExpr(Ops, HasNUW, HasNSW);
1247 // Check for truncates. If all the operands are truncated from the same
1248 // type, see if factoring out the truncate would permit the result to be
1249 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1250 // if the contents of the resulting outer trunc fold to something simple.
1251 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1252 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1253 const Type *DstType = Trunc->getType();
1254 const Type *SrcType = Trunc->getOperand()->getType();
1255 SmallVector<const SCEV *, 8> LargeOps;
1257 // Check all the operands to see if they can be represented in the
1258 // source type of the truncate.
1259 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1260 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1261 if (T->getOperand()->getType() != SrcType) {
1265 LargeOps.push_back(T->getOperand());
1266 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1267 // This could be either sign or zero extension, but sign extension
1268 // is much more likely to be foldable here.
1269 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1270 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1271 SmallVector<const SCEV *, 8> LargeMulOps;
1272 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1273 if (const SCEVTruncateExpr *T =
1274 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1275 if (T->getOperand()->getType() != SrcType) {
1279 LargeMulOps.push_back(T->getOperand());
1280 } else if (const SCEVConstant *C =
1281 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1282 // This could be either sign or zero extension, but sign extension
1283 // is much more likely to be foldable here.
1284 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1291 LargeOps.push_back(getMulExpr(LargeMulOps));
1298 // Evaluate the expression in the larger type.
1299 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1300 // If it folds to something simple, use it. Otherwise, don't.
1301 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1302 return getTruncateExpr(Fold, DstType);
1306 // Skip past any other cast SCEVs.
1307 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1310 // If there are add operands they would be next.
1311 if (Idx < Ops.size()) {
1312 bool DeletedAdd = false;
1313 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1314 // If we have an add, expand the add operands onto the end of the operands
1316 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1317 Ops.erase(Ops.begin()+Idx);
1321 // If we deleted at least one add, we added operands to the end of the list,
1322 // and they are not necessarily sorted. Recurse to resort and resimplify
1323 // any operands we just aquired.
1325 return getAddExpr(Ops);
1328 // Skip over the add expression until we get to a multiply.
1329 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1332 // Check to see if there are any folding opportunities present with
1333 // operands multiplied by constant values.
1334 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1335 uint64_t BitWidth = getTypeSizeInBits(Ty);
1336 DenseMap<const SCEV *, APInt> M;
1337 SmallVector<const SCEV *, 8> NewOps;
1338 APInt AccumulatedConstant(BitWidth, 0);
1339 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1340 Ops, APInt(BitWidth, 1), *this)) {
1341 // Some interesting folding opportunity is present, so its worthwhile to
1342 // re-generate the operands list. Group the operands by constant scale,
1343 // to avoid multiplying by the same constant scale multiple times.
1344 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1345 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1346 E = NewOps.end(); I != E; ++I)
1347 MulOpLists[M.find(*I)->second].push_back(*I);
1348 // Re-generate the operands list.
1350 if (AccumulatedConstant != 0)
1351 Ops.push_back(getConstant(AccumulatedConstant));
1352 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1353 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1355 Ops.push_back(getMulExpr(getConstant(I->first),
1356 getAddExpr(I->second)));
1358 return getIntegerSCEV(0, Ty);
1359 if (Ops.size() == 1)
1361 return getAddExpr(Ops);
1365 // If we are adding something to a multiply expression, make sure the
1366 // something is not already an operand of the multiply. If so, merge it into
1368 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1369 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1370 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1371 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1372 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1373 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1374 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1375 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1376 if (Mul->getNumOperands() != 2) {
1377 // If the multiply has more than two operands, we must get the
1379 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1380 MulOps.erase(MulOps.begin()+MulOp);
1381 InnerMul = getMulExpr(MulOps);
1383 const SCEV *One = getIntegerSCEV(1, Ty);
1384 const SCEV *AddOne = getAddExpr(InnerMul, One);
1385 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1386 if (Ops.size() == 2) return OuterMul;
1388 Ops.erase(Ops.begin()+AddOp);
1389 Ops.erase(Ops.begin()+Idx-1);
1391 Ops.erase(Ops.begin()+Idx);
1392 Ops.erase(Ops.begin()+AddOp-1);
1394 Ops.push_back(OuterMul);
1395 return getAddExpr(Ops);
1398 // Check this multiply against other multiplies being added together.
1399 for (unsigned OtherMulIdx = Idx+1;
1400 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1402 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1403 // If MulOp occurs in OtherMul, we can fold the two multiplies
1405 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1406 OMulOp != e; ++OMulOp)
1407 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1408 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1409 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1410 if (Mul->getNumOperands() != 2) {
1411 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1413 MulOps.erase(MulOps.begin()+MulOp);
1414 InnerMul1 = getMulExpr(MulOps);
1416 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1417 if (OtherMul->getNumOperands() != 2) {
1418 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1419 OtherMul->op_end());
1420 MulOps.erase(MulOps.begin()+OMulOp);
1421 InnerMul2 = getMulExpr(MulOps);
1423 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1424 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1425 if (Ops.size() == 2) return OuterMul;
1426 Ops.erase(Ops.begin()+Idx);
1427 Ops.erase(Ops.begin()+OtherMulIdx-1);
1428 Ops.push_back(OuterMul);
1429 return getAddExpr(Ops);
1435 // If there are any add recurrences in the operands list, see if any other
1436 // added values are loop invariant. If so, we can fold them into the
1438 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1441 // Scan over all recurrences, trying to fold loop invariants into them.
1442 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1443 // Scan all of the other operands to this add and add them to the vector if
1444 // they are loop invariant w.r.t. the recurrence.
1445 SmallVector<const SCEV *, 8> LIOps;
1446 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1447 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1448 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1449 LIOps.push_back(Ops[i]);
1450 Ops.erase(Ops.begin()+i);
1454 // If we found some loop invariants, fold them into the recurrence.
1455 if (!LIOps.empty()) {
1456 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1457 LIOps.push_back(AddRec->getStart());
1459 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1461 AddRecOps[0] = getAddExpr(LIOps);
1463 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
1464 AddRec->hasNoUnsignedWrap() && HasNUW,
1465 AddRec->hasNoSignedWrap() && HasNSW);
1466 // If all of the other operands were loop invariant, we are done.
1467 if (Ops.size() == 1) return NewRec;
1469 // Otherwise, add the folded AddRec by the non-liv parts.
1470 for (unsigned i = 0;; ++i)
1471 if (Ops[i] == AddRec) {
1475 return getAddExpr(Ops);
1478 // Okay, if there weren't any loop invariants to be folded, check to see if
1479 // there are multiple AddRec's with the same loop induction variable being
1480 // added together. If so, we can fold them.
1481 for (unsigned OtherIdx = Idx+1;
1482 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1483 if (OtherIdx != Idx) {
1484 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1485 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1486 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1487 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1489 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1490 if (i >= NewOps.size()) {
1491 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1492 OtherAddRec->op_end());
1495 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1497 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1499 if (Ops.size() == 2) return NewAddRec;
1501 Ops.erase(Ops.begin()+Idx);
1502 Ops.erase(Ops.begin()+OtherIdx-1);
1503 Ops.push_back(NewAddRec);
1504 return getAddExpr(Ops);
1508 // Otherwise couldn't fold anything into this recurrence. Move onto the
1512 // Okay, it looks like we really DO need an add expr. Check to see if we
1513 // already have one, otherwise create a new one.
1514 FoldingSetNodeID ID;
1515 ID.AddInteger(scAddExpr);
1516 ID.AddInteger(Ops.size());
1517 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1518 ID.AddPointer(Ops[i]);
1520 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1521 SCEVAddExpr *S = SCEVAllocator.Allocate<SCEVAddExpr>();
1522 new (S) SCEVAddExpr(ID, Ops);
1523 UniqueSCEVs.InsertNode(S, IP);
1524 if (HasNUW) S->setHasNoUnsignedWrap(true);
1525 if (HasNSW) S->setHasNoSignedWrap(true);
1530 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1532 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1533 bool HasNUW, bool HasNSW) {
1534 assert(!Ops.empty() && "Cannot get empty mul!");
1536 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1537 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1538 getEffectiveSCEVType(Ops[0]->getType()) &&
1539 "SCEVMulExpr operand types don't match!");
1542 // Sort by complexity, this groups all similar expression types together.
1543 GroupByComplexity(Ops, LI);
1545 // If there are any constants, fold them together.
1547 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1549 // C1*(C2+V) -> C1*C2 + C1*V
1550 if (Ops.size() == 2)
1551 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1552 if (Add->getNumOperands() == 2 &&
1553 isa<SCEVConstant>(Add->getOperand(0)))
1554 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1555 getMulExpr(LHSC, Add->getOperand(1)));
1559 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1560 // We found two constants, fold them together!
1561 ConstantInt *Fold = ConstantInt::get(getContext(),
1562 LHSC->getValue()->getValue() *
1563 RHSC->getValue()->getValue());
1564 Ops[0] = getConstant(Fold);
1565 Ops.erase(Ops.begin()+1); // Erase the folded element
1566 if (Ops.size() == 1) return Ops[0];
1567 LHSC = cast<SCEVConstant>(Ops[0]);
1570 // If we are left with a constant one being multiplied, strip it off.
1571 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1572 Ops.erase(Ops.begin());
1574 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1575 // If we have a multiply of zero, it will always be zero.
1580 // Skip over the add expression until we get to a multiply.
1581 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1584 if (Ops.size() == 1)
1587 // If there are mul operands inline them all into this expression.
1588 if (Idx < Ops.size()) {
1589 bool DeletedMul = false;
1590 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1591 // If we have an mul, expand the mul operands onto the end of the operands
1593 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1594 Ops.erase(Ops.begin()+Idx);
1598 // If we deleted at least one mul, we added operands to the end of the list,
1599 // and they are not necessarily sorted. Recurse to resort and resimplify
1600 // any operands we just aquired.
1602 return getMulExpr(Ops);
1605 // If there are any add recurrences in the operands list, see if any other
1606 // added values are loop invariant. If so, we can fold them into the
1608 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1611 // Scan over all recurrences, trying to fold loop invariants into them.
1612 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1613 // Scan all of the other operands to this mul and add them to the vector if
1614 // they are loop invariant w.r.t. the recurrence.
1615 SmallVector<const SCEV *, 8> LIOps;
1616 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1617 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1618 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1619 LIOps.push_back(Ops[i]);
1620 Ops.erase(Ops.begin()+i);
1624 // If we found some loop invariants, fold them into the recurrence.
1625 if (!LIOps.empty()) {
1626 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1627 SmallVector<const SCEV *, 4> NewOps;
1628 NewOps.reserve(AddRec->getNumOperands());
1629 if (LIOps.size() == 1) {
1630 const SCEV *Scale = LIOps[0];
1631 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1632 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1634 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1635 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
1636 MulOps.push_back(AddRec->getOperand(i));
1637 NewOps.push_back(getMulExpr(MulOps));
1641 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
1642 AddRec->hasNoUnsignedWrap() && HasNUW,
1643 AddRec->hasNoSignedWrap() && HasNSW);
1645 // If all of the other operands were loop invariant, we are done.
1646 if (Ops.size() == 1) return NewRec;
1648 // Otherwise, multiply the folded AddRec by the non-liv parts.
1649 for (unsigned i = 0;; ++i)
1650 if (Ops[i] == AddRec) {
1654 return getMulExpr(Ops);
1657 // Okay, if there weren't any loop invariants to be folded, check to see if
1658 // there are multiple AddRec's with the same loop induction variable being
1659 // multiplied together. If so, we can fold them.
1660 for (unsigned OtherIdx = Idx+1;
1661 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1662 if (OtherIdx != Idx) {
1663 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1664 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1665 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1666 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1667 const SCEV *NewStart = getMulExpr(F->getStart(),
1669 const SCEV *B = F->getStepRecurrence(*this);
1670 const SCEV *D = G->getStepRecurrence(*this);
1671 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1674 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1676 if (Ops.size() == 2) return NewAddRec;
1678 Ops.erase(Ops.begin()+Idx);
1679 Ops.erase(Ops.begin()+OtherIdx-1);
1680 Ops.push_back(NewAddRec);
1681 return getMulExpr(Ops);
1685 // Otherwise couldn't fold anything into this recurrence. Move onto the
1689 // Okay, it looks like we really DO need an mul expr. Check to see if we
1690 // already have one, otherwise create a new one.
1691 FoldingSetNodeID ID;
1692 ID.AddInteger(scMulExpr);
1693 ID.AddInteger(Ops.size());
1694 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1695 ID.AddPointer(Ops[i]);
1697 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1698 SCEVMulExpr *S = SCEVAllocator.Allocate<SCEVMulExpr>();
1699 new (S) SCEVMulExpr(ID, Ops);
1700 UniqueSCEVs.InsertNode(S, IP);
1701 if (HasNUW) S->setHasNoUnsignedWrap(true);
1702 if (HasNSW) S->setHasNoSignedWrap(true);
1706 /// getUDivExpr - Get a canonical unsigned division expression, or something
1707 /// simpler if possible.
1708 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1710 assert(getEffectiveSCEVType(LHS->getType()) ==
1711 getEffectiveSCEVType(RHS->getType()) &&
1712 "SCEVUDivExpr operand types don't match!");
1714 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1715 if (RHSC->getValue()->equalsInt(1))
1716 return LHS; // X udiv 1 --> x
1718 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1720 // Determine if the division can be folded into the operands of
1722 // TODO: Generalize this to non-constants by using known-bits information.
1723 const Type *Ty = LHS->getType();
1724 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1725 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1726 // For non-power-of-two values, effectively round the value up to the
1727 // nearest power of two.
1728 if (!RHSC->getValue()->getValue().isPowerOf2())
1730 const IntegerType *ExtTy =
1731 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1732 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1733 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1734 if (const SCEVConstant *Step =
1735 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1736 if (!Step->getValue()->getValue()
1737 .urem(RHSC->getValue()->getValue()) &&
1738 getZeroExtendExpr(AR, ExtTy) ==
1739 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1740 getZeroExtendExpr(Step, ExtTy),
1742 SmallVector<const SCEV *, 4> Operands;
1743 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1744 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1745 return getAddRecExpr(Operands, AR->getLoop());
1747 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1748 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1749 SmallVector<const SCEV *, 4> Operands;
1750 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1751 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1752 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1753 // Find an operand that's safely divisible.
1754 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1755 const SCEV *Op = M->getOperand(i);
1756 const SCEV *Div = getUDivExpr(Op, RHSC);
1757 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1758 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands();
1759 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(),
1762 return getMulExpr(Operands);
1766 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1767 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1768 SmallVector<const SCEV *, 4> Operands;
1769 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1770 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1771 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1773 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1774 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1775 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1777 Operands.push_back(Op);
1779 if (Operands.size() == A->getNumOperands())
1780 return getAddExpr(Operands);
1784 // Fold if both operands are constant.
1785 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1786 Constant *LHSCV = LHSC->getValue();
1787 Constant *RHSCV = RHSC->getValue();
1788 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1793 FoldingSetNodeID ID;
1794 ID.AddInteger(scUDivExpr);
1798 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1799 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>();
1800 new (S) SCEVUDivExpr(ID, LHS, RHS);
1801 UniqueSCEVs.InsertNode(S, IP);
1806 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1807 /// Simplify the expression as much as possible.
1808 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1809 const SCEV *Step, const Loop *L,
1810 bool HasNUW, bool HasNSW) {
1811 SmallVector<const SCEV *, 4> Operands;
1812 Operands.push_back(Start);
1813 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1814 if (StepChrec->getLoop() == L) {
1815 Operands.insert(Operands.end(), StepChrec->op_begin(),
1816 StepChrec->op_end());
1817 return getAddRecExpr(Operands, L);
1820 Operands.push_back(Step);
1821 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
1824 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1825 /// Simplify the expression as much as possible.
1827 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1829 bool HasNUW, bool HasNSW) {
1830 if (Operands.size() == 1) return Operands[0];
1832 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1833 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1834 getEffectiveSCEVType(Operands[0]->getType()) &&
1835 "SCEVAddRecExpr operand types don't match!");
1838 if (Operands.back()->isZero()) {
1839 Operands.pop_back();
1840 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
1843 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1844 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1845 const Loop *NestedLoop = NestedAR->getLoop();
1846 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1847 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
1848 NestedAR->op_end());
1849 Operands[0] = NestedAR->getStart();
1850 // AddRecs require their operands be loop-invariant with respect to their
1851 // loops. Don't perform this transformation if it would break this
1853 bool AllInvariant = true;
1854 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1855 if (!Operands[i]->isLoopInvariant(L)) {
1856 AllInvariant = false;
1860 NestedOperands[0] = getAddRecExpr(Operands, L);
1861 AllInvariant = true;
1862 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
1863 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
1864 AllInvariant = false;
1868 // Ok, both add recurrences are valid after the transformation.
1869 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
1871 // Reset Operands to its original state.
1872 Operands[0] = NestedAR;
1876 FoldingSetNodeID ID;
1877 ID.AddInteger(scAddRecExpr);
1878 ID.AddInteger(Operands.size());
1879 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1880 ID.AddPointer(Operands[i]);
1883 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1884 SCEVAddRecExpr *S = SCEVAllocator.Allocate<SCEVAddRecExpr>();
1885 new (S) SCEVAddRecExpr(ID, Operands, L);
1886 UniqueSCEVs.InsertNode(S, IP);
1887 if (HasNUW) S->setHasNoUnsignedWrap(true);
1888 if (HasNSW) S->setHasNoSignedWrap(true);
1892 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
1894 SmallVector<const SCEV *, 2> Ops;
1897 return getSMaxExpr(Ops);
1901 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1902 assert(!Ops.empty() && "Cannot get empty smax!");
1903 if (Ops.size() == 1) return Ops[0];
1905 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1906 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1907 getEffectiveSCEVType(Ops[0]->getType()) &&
1908 "SCEVSMaxExpr operand types don't match!");
1911 // Sort by complexity, this groups all similar expression types together.
1912 GroupByComplexity(Ops, LI);
1914 // If there are any constants, fold them together.
1916 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1918 assert(Idx < Ops.size());
1919 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1920 // We found two constants, fold them together!
1921 ConstantInt *Fold = ConstantInt::get(getContext(),
1922 APIntOps::smax(LHSC->getValue()->getValue(),
1923 RHSC->getValue()->getValue()));
1924 Ops[0] = getConstant(Fold);
1925 Ops.erase(Ops.begin()+1); // Erase the folded element
1926 if (Ops.size() == 1) return Ops[0];
1927 LHSC = cast<SCEVConstant>(Ops[0]);
1930 // If we are left with a constant minimum-int, strip it off.
1931 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1932 Ops.erase(Ops.begin());
1934 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
1935 // If we have an smax with a constant maximum-int, it will always be
1941 if (Ops.size() == 1) return Ops[0];
1943 // Find the first SMax
1944 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1947 // Check to see if one of the operands is an SMax. If so, expand its operands
1948 // onto our operand list, and recurse to simplify.
1949 if (Idx < Ops.size()) {
1950 bool DeletedSMax = false;
1951 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1952 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1953 Ops.erase(Ops.begin()+Idx);
1958 return getSMaxExpr(Ops);
1961 // Okay, check to see if the same value occurs in the operand list twice. If
1962 // so, delete one. Since we sorted the list, these values are required to
1964 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1965 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1966 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1970 if (Ops.size() == 1) return Ops[0];
1972 assert(!Ops.empty() && "Reduced smax down to nothing!");
1974 // Okay, it looks like we really DO need an smax expr. Check to see if we
1975 // already have one, otherwise create a new one.
1976 FoldingSetNodeID ID;
1977 ID.AddInteger(scSMaxExpr);
1978 ID.AddInteger(Ops.size());
1979 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1980 ID.AddPointer(Ops[i]);
1982 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1983 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>();
1984 new (S) SCEVSMaxExpr(ID, Ops);
1985 UniqueSCEVs.InsertNode(S, IP);
1989 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
1991 SmallVector<const SCEV *, 2> Ops;
1994 return getUMaxExpr(Ops);
1998 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1999 assert(!Ops.empty() && "Cannot get empty umax!");
2000 if (Ops.size() == 1) return Ops[0];
2002 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2003 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2004 getEffectiveSCEVType(Ops[0]->getType()) &&
2005 "SCEVUMaxExpr operand types don't match!");
2008 // Sort by complexity, this groups all similar expression types together.
2009 GroupByComplexity(Ops, LI);
2011 // If there are any constants, fold them together.
2013 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2015 assert(Idx < Ops.size());
2016 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2017 // We found two constants, fold them together!
2018 ConstantInt *Fold = ConstantInt::get(getContext(),
2019 APIntOps::umax(LHSC->getValue()->getValue(),
2020 RHSC->getValue()->getValue()));
2021 Ops[0] = getConstant(Fold);
2022 Ops.erase(Ops.begin()+1); // Erase the folded element
2023 if (Ops.size() == 1) return Ops[0];
2024 LHSC = cast<SCEVConstant>(Ops[0]);
2027 // If we are left with a constant minimum-int, strip it off.
2028 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2029 Ops.erase(Ops.begin());
2031 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2032 // If we have an umax with a constant maximum-int, it will always be
2038 if (Ops.size() == 1) return Ops[0];
2040 // Find the first UMax
2041 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2044 // Check to see if one of the operands is a UMax. If so, expand its operands
2045 // onto our operand list, and recurse to simplify.
2046 if (Idx < Ops.size()) {
2047 bool DeletedUMax = false;
2048 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2049 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
2050 Ops.erase(Ops.begin()+Idx);
2055 return getUMaxExpr(Ops);
2058 // Okay, check to see if the same value occurs in the operand list twice. If
2059 // so, delete one. Since we sorted the list, these values are required to
2061 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2062 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
2063 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2067 if (Ops.size() == 1) return Ops[0];
2069 assert(!Ops.empty() && "Reduced umax down to nothing!");
2071 // Okay, it looks like we really DO need a umax expr. Check to see if we
2072 // already have one, otherwise create a new one.
2073 FoldingSetNodeID ID;
2074 ID.AddInteger(scUMaxExpr);
2075 ID.AddInteger(Ops.size());
2076 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2077 ID.AddPointer(Ops[i]);
2079 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2080 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>();
2081 new (S) SCEVUMaxExpr(ID, Ops);
2082 UniqueSCEVs.InsertNode(S, IP);
2086 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2088 // ~smax(~x, ~y) == smin(x, y).
2089 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2092 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2094 // ~umax(~x, ~y) == umin(x, y)
2095 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2098 const SCEV *ScalarEvolution::getFieldOffsetExpr(const StructType *STy,
2100 // If we have TargetData we can determine the constant offset.
2102 const Type *IntPtrTy = TD->getIntPtrType(getContext());
2103 const StructLayout &SL = *TD->getStructLayout(STy);
2104 uint64_t Offset = SL.getElementOffset(FieldNo);
2105 return getIntegerSCEV(Offset, IntPtrTy);
2108 // Field 0 is always at offset 0.
2110 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2111 return getIntegerSCEV(0, Ty);
2114 // Okay, it looks like we really DO need an offsetof expr. Check to see if we
2115 // already have one, otherwise create a new one.
2116 FoldingSetNodeID ID;
2117 ID.AddInteger(scFieldOffset);
2119 ID.AddInteger(FieldNo);
2121 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2122 SCEV *S = SCEVAllocator.Allocate<SCEVFieldOffsetExpr>();
2123 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2124 new (S) SCEVFieldOffsetExpr(ID, Ty, STy, FieldNo);
2125 UniqueSCEVs.InsertNode(S, IP);
2129 const SCEV *ScalarEvolution::getAllocSizeExpr(const Type *AllocTy) {
2130 // If we have TargetData we can determine the constant size.
2131 if (TD && AllocTy->isSized()) {
2132 const Type *IntPtrTy = TD->getIntPtrType(getContext());
2133 return getIntegerSCEV(TD->getTypeAllocSize(AllocTy), IntPtrTy);
2136 // Expand an array size into the element size times the number
2138 if (const ArrayType *ATy = dyn_cast<ArrayType>(AllocTy)) {
2139 const SCEV *E = getAllocSizeExpr(ATy->getElementType());
2141 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()),
2142 ATy->getNumElements())));
2145 // Expand a vector size into the element size times the number
2147 if (const VectorType *VTy = dyn_cast<VectorType>(AllocTy)) {
2148 const SCEV *E = getAllocSizeExpr(VTy->getElementType());
2150 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()),
2151 VTy->getNumElements())));
2154 // Okay, it looks like we really DO need a sizeof expr. Check to see if we
2155 // already have one, otherwise create a new one.
2156 FoldingSetNodeID ID;
2157 ID.AddInteger(scAllocSize);
2158 ID.AddPointer(AllocTy);
2160 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2161 SCEV *S = SCEVAllocator.Allocate<SCEVAllocSizeExpr>();
2162 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2163 new (S) SCEVAllocSizeExpr(ID, Ty, AllocTy);
2164 UniqueSCEVs.InsertNode(S, IP);
2168 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2169 // Don't attempt to do anything other than create a SCEVUnknown object
2170 // here. createSCEV only calls getUnknown after checking for all other
2171 // interesting possibilities, and any other code that calls getUnknown
2172 // is doing so in order to hide a value from SCEV canonicalization.
2174 FoldingSetNodeID ID;
2175 ID.AddInteger(scUnknown);
2178 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2179 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>();
2180 new (S) SCEVUnknown(ID, V);
2181 UniqueSCEVs.InsertNode(S, IP);
2185 //===----------------------------------------------------------------------===//
2186 // Basic SCEV Analysis and PHI Idiom Recognition Code
2189 /// isSCEVable - Test if values of the given type are analyzable within
2190 /// the SCEV framework. This primarily includes integer types, and it
2191 /// can optionally include pointer types if the ScalarEvolution class
2192 /// has access to target-specific information.
2193 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2194 // Integers and pointers are always SCEVable.
2195 return Ty->isInteger() || isa<PointerType>(Ty);
2198 /// getTypeSizeInBits - Return the size in bits of the specified type,
2199 /// for which isSCEVable must return true.
2200 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2201 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2203 // If we have a TargetData, use it!
2205 return TD->getTypeSizeInBits(Ty);
2207 // Integer types have fixed sizes.
2208 if (Ty->isInteger())
2209 return Ty->getPrimitiveSizeInBits();
2211 // The only other support type is pointer. Without TargetData, conservatively
2212 // assume pointers are 64-bit.
2213 assert(isa<PointerType>(Ty) && "isSCEVable permitted a non-SCEVable type!");
2217 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2218 /// the given type and which represents how SCEV will treat the given
2219 /// type, for which isSCEVable must return true. For pointer types,
2220 /// this is the pointer-sized integer type.
2221 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2222 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2224 if (Ty->isInteger())
2227 // The only other support type is pointer.
2228 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
2229 if (TD) return TD->getIntPtrType(getContext());
2231 // Without TargetData, conservatively assume pointers are 64-bit.
2232 return Type::getInt64Ty(getContext());
2235 const SCEV *ScalarEvolution::getCouldNotCompute() {
2236 return &CouldNotCompute;
2239 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2240 /// expression and create a new one.
2241 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2242 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2244 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2245 if (I != Scalars.end()) return I->second;
2246 const SCEV *S = createSCEV(V);
2247 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2251 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
2252 /// specified signed integer value and return a SCEV for the constant.
2253 const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
2254 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2255 return getConstant(ConstantInt::get(ITy, Val));
2258 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2260 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2261 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2263 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2265 const Type *Ty = V->getType();
2266 Ty = getEffectiveSCEVType(Ty);
2267 return getMulExpr(V,
2268 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2271 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2272 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2273 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2275 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2277 const Type *Ty = V->getType();
2278 Ty = getEffectiveSCEVType(Ty);
2279 const SCEV *AllOnes =
2280 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2281 return getMinusSCEV(AllOnes, V);
2284 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2286 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2289 return getAddExpr(LHS, getNegativeSCEV(RHS));
2292 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2293 /// input value to the specified type. If the type must be extended, it is zero
2296 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2298 const Type *SrcTy = V->getType();
2299 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2300 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2301 "Cannot truncate or zero extend with non-integer arguments!");
2302 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2303 return V; // No conversion
2304 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2305 return getTruncateExpr(V, Ty);
2306 return getZeroExtendExpr(V, Ty);
2309 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2310 /// input value to the specified type. If the type must be extended, it is sign
2313 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2315 const Type *SrcTy = V->getType();
2316 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2317 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2318 "Cannot truncate or zero extend with non-integer arguments!");
2319 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2320 return V; // No conversion
2321 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2322 return getTruncateExpr(V, Ty);
2323 return getSignExtendExpr(V, Ty);
2326 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2327 /// input value to the specified type. If the type must be extended, it is zero
2328 /// extended. The conversion must not be narrowing.
2330 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2331 const Type *SrcTy = V->getType();
2332 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2333 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2334 "Cannot noop or zero extend with non-integer arguments!");
2335 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2336 "getNoopOrZeroExtend cannot truncate!");
2337 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2338 return V; // No conversion
2339 return getZeroExtendExpr(V, Ty);
2342 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2343 /// input value to the specified type. If the type must be extended, it is sign
2344 /// extended. The conversion must not be narrowing.
2346 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2347 const Type *SrcTy = V->getType();
2348 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2349 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2350 "Cannot noop or sign extend with non-integer arguments!");
2351 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2352 "getNoopOrSignExtend cannot truncate!");
2353 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2354 return V; // No conversion
2355 return getSignExtendExpr(V, Ty);
2358 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2359 /// the input value to the specified type. If the type must be extended,
2360 /// it is extended with unspecified bits. The conversion must not be
2363 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2364 const Type *SrcTy = V->getType();
2365 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2366 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2367 "Cannot noop or any extend with non-integer arguments!");
2368 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2369 "getNoopOrAnyExtend cannot truncate!");
2370 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2371 return V; // No conversion
2372 return getAnyExtendExpr(V, Ty);
2375 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2376 /// input value to the specified type. The conversion must not be widening.
2378 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2379 const Type *SrcTy = V->getType();
2380 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
2381 (Ty->isInteger() || isa<PointerType>(Ty)) &&
2382 "Cannot truncate or noop with non-integer arguments!");
2383 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2384 "getTruncateOrNoop cannot extend!");
2385 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2386 return V; // No conversion
2387 return getTruncateExpr(V, Ty);
2390 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2391 /// the types using zero-extension, and then perform a umax operation
2393 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2395 const SCEV *PromotedLHS = LHS;
2396 const SCEV *PromotedRHS = RHS;
2398 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2399 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2401 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2403 return getUMaxExpr(PromotedLHS, PromotedRHS);
2406 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2407 /// the types using zero-extension, and then perform a umin operation
2409 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2411 const SCEV *PromotedLHS = LHS;
2412 const SCEV *PromotedRHS = RHS;
2414 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2415 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2417 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2419 return getUMinExpr(PromotedLHS, PromotedRHS);
2422 /// PushDefUseChildren - Push users of the given Instruction
2423 /// onto the given Worklist.
2425 PushDefUseChildren(Instruction *I,
2426 SmallVectorImpl<Instruction *> &Worklist) {
2427 // Push the def-use children onto the Worklist stack.
2428 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2430 Worklist.push_back(cast<Instruction>(UI));
2433 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2434 /// instructions that depend on the given instruction and removes them from
2435 /// the Scalars map if they reference SymName. This is used during PHI
2438 ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) {
2439 SmallVector<Instruction *, 16> Worklist;
2440 PushDefUseChildren(I, Worklist);
2442 SmallPtrSet<Instruction *, 8> Visited;
2444 while (!Worklist.empty()) {
2445 Instruction *I = Worklist.pop_back_val();
2446 if (!Visited.insert(I)) continue;
2448 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
2449 Scalars.find(static_cast<Value *>(I));
2450 if (It != Scalars.end()) {
2451 // Short-circuit the def-use traversal if the symbolic name
2452 // ceases to appear in expressions.
2453 if (!It->second->hasOperand(SymName))
2456 // SCEVUnknown for a PHI either means that it has an unrecognized
2457 // structure, or it's a PHI that's in the progress of being computed
2458 // by createNodeForPHI. In the former case, additional loop trip
2459 // count information isn't going to change anything. In the later
2460 // case, createNodeForPHI will perform the necessary updates on its
2461 // own when it gets to that point.
2462 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
2463 ValuesAtScopes.erase(It->second);
2468 PushDefUseChildren(I, Worklist);
2472 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2473 /// a loop header, making it a potential recurrence, or it doesn't.
2475 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2476 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2477 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2478 if (L->getHeader() == PN->getParent()) {
2479 // If it lives in the loop header, it has two incoming values, one
2480 // from outside the loop, and one from inside.
2481 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2482 unsigned BackEdge = IncomingEdge^1;
2484 // While we are analyzing this PHI node, handle its value symbolically.
2485 const SCEV *SymbolicName = getUnknown(PN);
2486 assert(Scalars.find(PN) == Scalars.end() &&
2487 "PHI node already processed?");
2488 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2490 // Using this symbolic name for the PHI, analyze the value coming around
2492 Value *BEValueV = PN->getIncomingValue(BackEdge);
2493 const SCEV *BEValue = getSCEV(BEValueV);
2495 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2496 // has a special value for the first iteration of the loop.
2498 // If the value coming around the backedge is an add with the symbolic
2499 // value we just inserted, then we found a simple induction variable!
2500 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2501 // If there is a single occurrence of the symbolic value, replace it
2502 // with a recurrence.
2503 unsigned FoundIndex = Add->getNumOperands();
2504 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2505 if (Add->getOperand(i) == SymbolicName)
2506 if (FoundIndex == e) {
2511 if (FoundIndex != Add->getNumOperands()) {
2512 // Create an add with everything but the specified operand.
2513 SmallVector<const SCEV *, 8> Ops;
2514 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2515 if (i != FoundIndex)
2516 Ops.push_back(Add->getOperand(i));
2517 const SCEV *Accum = getAddExpr(Ops);
2519 // This is not a valid addrec if the step amount is varying each
2520 // loop iteration, but is not itself an addrec in this loop.
2521 if (Accum->isLoopInvariant(L) ||
2522 (isa<SCEVAddRecExpr>(Accum) &&
2523 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2524 const SCEV *StartVal =
2525 getSCEV(PN->getIncomingValue(IncomingEdge));
2526 const SCEVAddRecExpr *PHISCEV =
2527 cast<SCEVAddRecExpr>(getAddRecExpr(StartVal, Accum, L));
2529 // If the increment doesn't overflow, then neither the addrec nor the
2530 // post-increment will overflow.
2531 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV))
2532 if (OBO->getOperand(0) == PN &&
2533 getSCEV(OBO->getOperand(1)) ==
2534 PHISCEV->getStepRecurrence(*this)) {
2535 const SCEVAddRecExpr *PostInc = PHISCEV->getPostIncExpr(*this);
2536 if (OBO->hasNoUnsignedWrap()) {
2537 const_cast<SCEVAddRecExpr *>(PHISCEV)
2538 ->setHasNoUnsignedWrap(true);
2539 const_cast<SCEVAddRecExpr *>(PostInc)
2540 ->setHasNoUnsignedWrap(true);
2542 if (OBO->hasNoSignedWrap()) {
2543 const_cast<SCEVAddRecExpr *>(PHISCEV)
2544 ->setHasNoSignedWrap(true);
2545 const_cast<SCEVAddRecExpr *>(PostInc)
2546 ->setHasNoSignedWrap(true);
2550 // Okay, for the entire analysis of this edge we assumed the PHI
2551 // to be symbolic. We now need to go back and purge all of the
2552 // entries for the scalars that use the symbolic expression.
2553 ForgetSymbolicName(PN, SymbolicName);
2554 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2558 } else if (const SCEVAddRecExpr *AddRec =
2559 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2560 // Otherwise, this could be a loop like this:
2561 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2562 // In this case, j = {1,+,1} and BEValue is j.
2563 // Because the other in-value of i (0) fits the evolution of BEValue
2564 // i really is an addrec evolution.
2565 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2566 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2568 // If StartVal = j.start - j.stride, we can use StartVal as the
2569 // initial step of the addrec evolution.
2570 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2571 AddRec->getOperand(1))) {
2572 const SCEV *PHISCEV =
2573 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2575 // Okay, for the entire analysis of this edge we assumed the PHI
2576 // to be symbolic. We now need to go back and purge all of the
2577 // entries for the scalars that use the symbolic expression.
2578 ForgetSymbolicName(PN, SymbolicName);
2579 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2585 return SymbolicName;
2588 // It's tempting to recognize PHIs with a unique incoming value, however
2589 // this leads passes like indvars to break LCSSA form. Fortunately, such
2590 // PHIs are rare, as instcombine zaps them.
2592 // If it's not a loop phi, we can't handle it yet.
2593 return getUnknown(PN);
2596 /// createNodeForGEP - Expand GEP instructions into add and multiply
2597 /// operations. This allows them to be analyzed by regular SCEV code.
2599 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2601 bool InBounds = GEP->isInBounds();
2602 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2603 Value *Base = GEP->getOperand(0);
2604 // Don't attempt to analyze GEPs over unsized objects.
2605 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2606 return getUnknown(GEP);
2607 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
2608 gep_type_iterator GTI = gep_type_begin(GEP);
2609 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2613 // Compute the (potentially symbolic) offset in bytes for this index.
2614 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2615 // For a struct, add the member offset.
2616 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2617 TotalOffset = getAddExpr(TotalOffset,
2618 getFieldOffsetExpr(STy, FieldNo),
2619 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2621 // For an array, add the element offset, explicitly scaled.
2622 const SCEV *LocalOffset = getSCEV(Index);
2623 if (!isa<PointerType>(LocalOffset->getType()))
2624 // Getelementptr indicies are signed.
2625 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
2626 // Lower "inbounds" GEPs to NSW arithmetic.
2627 LocalOffset = getMulExpr(LocalOffset, getAllocSizeExpr(*GTI),
2628 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2629 TotalOffset = getAddExpr(TotalOffset, LocalOffset,
2630 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2633 return getAddExpr(getSCEV(Base), TotalOffset,
2634 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2637 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2638 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2639 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2640 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2642 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2643 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2644 return C->getValue()->getValue().countTrailingZeros();
2646 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2647 return std::min(GetMinTrailingZeros(T->getOperand()),
2648 (uint32_t)getTypeSizeInBits(T->getType()));
2650 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2651 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2652 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2653 getTypeSizeInBits(E->getType()) : OpRes;
2656 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2657 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2658 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2659 getTypeSizeInBits(E->getType()) : OpRes;
2662 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2663 // The result is the min of all operands results.
2664 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2665 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2666 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2670 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2671 // The result is the sum of all operands results.
2672 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2673 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2674 for (unsigned i = 1, e = M->getNumOperands();
2675 SumOpRes != BitWidth && i != e; ++i)
2676 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2681 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2682 // The result is the min of all operands results.
2683 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2684 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2685 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2689 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2690 // The result is the min of all operands results.
2691 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2692 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2693 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2697 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2698 // The result is the min of all operands results.
2699 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2700 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2701 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2705 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2706 // For a SCEVUnknown, ask ValueTracking.
2707 unsigned BitWidth = getTypeSizeInBits(U->getType());
2708 APInt Mask = APInt::getAllOnesValue(BitWidth);
2709 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2710 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2711 return Zeros.countTrailingOnes();
2718 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2721 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2723 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2724 return ConstantRange(C->getValue()->getValue());
2726 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2727 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2728 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2729 X = X.add(getUnsignedRange(Add->getOperand(i)));
2733 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2734 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2735 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2736 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2740 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2741 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2742 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2743 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2747 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2748 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2749 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2750 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2754 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2755 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2756 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2760 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2761 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2762 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
2765 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2766 ConstantRange X = getUnsignedRange(SExt->getOperand());
2767 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
2770 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2771 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2772 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
2775 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
2777 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2778 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
2779 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
2780 if (!Trip) return FullSet;
2782 // TODO: non-affine addrec
2783 if (AddRec->isAffine()) {
2784 const Type *Ty = AddRec->getType();
2785 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2786 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
2787 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2789 const SCEV *Start = AddRec->getStart();
2790 const SCEV *Step = AddRec->getStepRecurrence(*this);
2791 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2793 // Check for overflow.
2794 // TODO: This is very conservative.
2795 if (!(Step->isOne() &&
2796 isKnownPredicate(ICmpInst::ICMP_ULT, Start, End)) &&
2797 !(Step->isAllOnesValue() &&
2798 isKnownPredicate(ICmpInst::ICMP_UGT, Start, End)))
2801 ConstantRange StartRange = getUnsignedRange(Start);
2802 ConstantRange EndRange = getUnsignedRange(End);
2803 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
2804 EndRange.getUnsignedMin());
2805 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
2806 EndRange.getUnsignedMax());
2807 if (Min.isMinValue() && Max.isMaxValue())
2809 return ConstantRange(Min, Max+1);
2814 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2815 // For a SCEVUnknown, ask ValueTracking.
2816 unsigned BitWidth = getTypeSizeInBits(U->getType());
2817 APInt Mask = APInt::getAllOnesValue(BitWidth);
2818 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2819 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
2820 if (Ones == ~Zeros + 1)
2822 return ConstantRange(Ones, ~Zeros + 1);
2828 /// getSignedRange - Determine the signed range for a particular SCEV.
2831 ScalarEvolution::getSignedRange(const SCEV *S) {
2833 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2834 return ConstantRange(C->getValue()->getValue());
2836 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2837 ConstantRange X = getSignedRange(Add->getOperand(0));
2838 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2839 X = X.add(getSignedRange(Add->getOperand(i)));
2843 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2844 ConstantRange X = getSignedRange(Mul->getOperand(0));
2845 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2846 X = X.multiply(getSignedRange(Mul->getOperand(i)));
2850 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2851 ConstantRange X = getSignedRange(SMax->getOperand(0));
2852 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2853 X = X.smax(getSignedRange(SMax->getOperand(i)));
2857 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2858 ConstantRange X = getSignedRange(UMax->getOperand(0));
2859 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2860 X = X.umax(getSignedRange(UMax->getOperand(i)));
2864 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2865 ConstantRange X = getSignedRange(UDiv->getLHS());
2866 ConstantRange Y = getSignedRange(UDiv->getRHS());
2870 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2871 ConstantRange X = getSignedRange(ZExt->getOperand());
2872 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
2875 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2876 ConstantRange X = getSignedRange(SExt->getOperand());
2877 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
2880 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2881 ConstantRange X = getSignedRange(Trunc->getOperand());
2882 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
2885 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
2887 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2888 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
2889 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
2890 if (!Trip) return FullSet;
2892 // TODO: non-affine addrec
2893 if (AddRec->isAffine()) {
2894 const Type *Ty = AddRec->getType();
2895 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2896 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
2897 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2899 const SCEV *Start = AddRec->getStart();
2900 const SCEV *Step = AddRec->getStepRecurrence(*this);
2901 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2903 // Check for overflow.
2904 // TODO: This is very conservative.
2905 if (!(Step->isOne() &&
2906 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) &&
2907 !(Step->isAllOnesValue() &&
2908 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End)))
2911 ConstantRange StartRange = getSignedRange(Start);
2912 ConstantRange EndRange = getSignedRange(End);
2913 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
2914 EndRange.getSignedMin());
2915 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
2916 EndRange.getSignedMax());
2917 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
2919 return ConstantRange(Min, Max+1);
2924 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2925 // For a SCEVUnknown, ask ValueTracking.
2926 unsigned BitWidth = getTypeSizeInBits(U->getType());
2927 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
2931 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
2932 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1);
2938 /// createSCEV - We know that there is no SCEV for the specified value.
2939 /// Analyze the expression.
2941 const SCEV *ScalarEvolution::createSCEV(Value *V) {
2942 if (!isSCEVable(V->getType()))
2943 return getUnknown(V);
2945 unsigned Opcode = Instruction::UserOp1;
2946 if (Instruction *I = dyn_cast<Instruction>(V))
2947 Opcode = I->getOpcode();
2948 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2949 Opcode = CE->getOpcode();
2950 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
2951 return getConstant(CI);
2952 else if (isa<ConstantPointerNull>(V))
2953 return getIntegerSCEV(0, V->getType());
2954 else if (isa<UndefValue>(V))
2955 return getIntegerSCEV(0, V->getType());
2956 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
2957 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
2959 return getUnknown(V);
2961 Operator *U = cast<Operator>(V);
2963 case Instruction::Add:
2964 // Don't transfer the NSW and NUW bits from the Add instruction to the
2965 // Add expression, because the Instruction may be guarded by control
2966 // flow and the no-overflow bits may not be valid for the expression in
2968 return getAddExpr(getSCEV(U->getOperand(0)),
2969 getSCEV(U->getOperand(1)));
2970 case Instruction::Mul:
2971 // Don't transfer the NSW and NUW bits from the Mul instruction to the
2972 // Mul expression, as with Add.
2973 return getMulExpr(getSCEV(U->getOperand(0)),
2974 getSCEV(U->getOperand(1)));
2975 case Instruction::UDiv:
2976 return getUDivExpr(getSCEV(U->getOperand(0)),
2977 getSCEV(U->getOperand(1)));
2978 case Instruction::Sub:
2979 return getMinusSCEV(getSCEV(U->getOperand(0)),
2980 getSCEV(U->getOperand(1)));
2981 case Instruction::And:
2982 // For an expression like x&255 that merely masks off the high bits,
2983 // use zext(trunc(x)) as the SCEV expression.
2984 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2985 if (CI->isNullValue())
2986 return getSCEV(U->getOperand(1));
2987 if (CI->isAllOnesValue())
2988 return getSCEV(U->getOperand(0));
2989 const APInt &A = CI->getValue();
2991 // Instcombine's ShrinkDemandedConstant may strip bits out of
2992 // constants, obscuring what would otherwise be a low-bits mask.
2993 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
2994 // knew about to reconstruct a low-bits mask value.
2995 unsigned LZ = A.countLeadingZeros();
2996 unsigned BitWidth = A.getBitWidth();
2997 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
2998 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
2999 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3001 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3003 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3005 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3006 IntegerType::get(getContext(), BitWidth - LZ)),
3011 case Instruction::Or:
3012 // If the RHS of the Or is a constant, we may have something like:
3013 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3014 // optimizations will transparently handle this case.
3016 // In order for this transformation to be safe, the LHS must be of the
3017 // form X*(2^n) and the Or constant must be less than 2^n.
3018 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3019 const SCEV *LHS = getSCEV(U->getOperand(0));
3020 const APInt &CIVal = CI->getValue();
3021 if (GetMinTrailingZeros(LHS) >=
3022 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3023 // Build a plain add SCEV.
3024 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3025 // If the LHS of the add was an addrec and it has no-wrap flags,
3026 // transfer the no-wrap flags, since an or won't introduce a wrap.
3027 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3028 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3029 if (OldAR->hasNoUnsignedWrap())
3030 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3031 if (OldAR->hasNoSignedWrap())
3032 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3038 case Instruction::Xor:
3039 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3040 // If the RHS of the xor is a signbit, then this is just an add.
3041 // Instcombine turns add of signbit into xor as a strength reduction step.
3042 if (CI->getValue().isSignBit())
3043 return getAddExpr(getSCEV(U->getOperand(0)),
3044 getSCEV(U->getOperand(1)));
3046 // If the RHS of xor is -1, then this is a not operation.
3047 if (CI->isAllOnesValue())
3048 return getNotSCEV(getSCEV(U->getOperand(0)));
3050 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3051 // This is a variant of the check for xor with -1, and it handles
3052 // the case where instcombine has trimmed non-demanded bits out
3053 // of an xor with -1.
3054 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3055 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3056 if (BO->getOpcode() == Instruction::And &&
3057 LCI->getValue() == CI->getValue())
3058 if (const SCEVZeroExtendExpr *Z =
3059 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3060 const Type *UTy = U->getType();
3061 const SCEV *Z0 = Z->getOperand();
3062 const Type *Z0Ty = Z0->getType();
3063 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3065 // If C is a low-bits mask, the zero extend is zerving to
3066 // mask off the high bits. Complement the operand and
3067 // re-apply the zext.
3068 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3069 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3071 // If C is a single bit, it may be in the sign-bit position
3072 // before the zero-extend. In this case, represent the xor
3073 // using an add, which is equivalent, and re-apply the zext.
3074 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3075 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3077 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3083 case Instruction::Shl:
3084 // Turn shift left of a constant amount into a multiply.
3085 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3086 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
3087 Constant *X = ConstantInt::get(getContext(),
3088 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3089 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3093 case Instruction::LShr:
3094 // Turn logical shift right of a constant into a unsigned divide.
3095 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3096 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
3097 Constant *X = ConstantInt::get(getContext(),
3098 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3099 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3103 case Instruction::AShr:
3104 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3105 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3106 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
3107 if (L->getOpcode() == Instruction::Shl &&
3108 L->getOperand(1) == U->getOperand(1)) {
3109 unsigned BitWidth = getTypeSizeInBits(U->getType());
3110 uint64_t Amt = BitWidth - CI->getZExtValue();
3111 if (Amt == BitWidth)
3112 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3114 return getIntegerSCEV(0, U->getType()); // value is undefined
3116 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3117 IntegerType::get(getContext(), Amt)),
3122 case Instruction::Trunc:
3123 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3125 case Instruction::ZExt:
3126 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3128 case Instruction::SExt:
3129 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3131 case Instruction::BitCast:
3132 // BitCasts are no-op casts so we just eliminate the cast.
3133 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3134 return getSCEV(U->getOperand(0));
3137 // It's tempting to handle inttoptr and ptrtoint, however this can
3138 // lead to pointer expressions which cannot be expanded to GEPs
3139 // (because they may overflow). For now, the only pointer-typed
3140 // expressions we handle are GEPs and address literals.
3142 case Instruction::GetElementPtr:
3143 return createNodeForGEP(cast<GEPOperator>(U));
3145 case Instruction::PHI:
3146 return createNodeForPHI(cast<PHINode>(U));
3148 case Instruction::Select:
3149 // This could be a smax or umax that was lowered earlier.
3150 // Try to recover it.
3151 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3152 Value *LHS = ICI->getOperand(0);
3153 Value *RHS = ICI->getOperand(1);
3154 switch (ICI->getPredicate()) {
3155 case ICmpInst::ICMP_SLT:
3156 case ICmpInst::ICMP_SLE:
3157 std::swap(LHS, RHS);
3159 case ICmpInst::ICMP_SGT:
3160 case ICmpInst::ICMP_SGE:
3161 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3162 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
3163 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3164 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
3166 case ICmpInst::ICMP_ULT:
3167 case ICmpInst::ICMP_ULE:
3168 std::swap(LHS, RHS);
3170 case ICmpInst::ICMP_UGT:
3171 case ICmpInst::ICMP_UGE:
3172 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3173 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
3174 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3175 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
3177 case ICmpInst::ICMP_NE:
3178 // n != 0 ? n : 1 -> umax(n, 1)
3179 if (LHS == U->getOperand(1) &&
3180 isa<ConstantInt>(U->getOperand(2)) &&
3181 cast<ConstantInt>(U->getOperand(2))->isOne() &&
3182 isa<ConstantInt>(RHS) &&
3183 cast<ConstantInt>(RHS)->isZero())
3184 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
3186 case ICmpInst::ICMP_EQ:
3187 // n == 0 ? 1 : n -> umax(n, 1)
3188 if (LHS == U->getOperand(2) &&
3189 isa<ConstantInt>(U->getOperand(1)) &&
3190 cast<ConstantInt>(U->getOperand(1))->isOne() &&
3191 isa<ConstantInt>(RHS) &&
3192 cast<ConstantInt>(RHS)->isZero())
3193 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
3200 default: // We cannot analyze this expression.
3204 return getUnknown(V);
3209 //===----------------------------------------------------------------------===//
3210 // Iteration Count Computation Code
3213 /// getBackedgeTakenCount - If the specified loop has a predictable
3214 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3215 /// object. The backedge-taken count is the number of times the loop header
3216 /// will be branched to from within the loop. This is one less than the
3217 /// trip count of the loop, since it doesn't count the first iteration,
3218 /// when the header is branched to from outside the loop.
3220 /// Note that it is not valid to call this method on a loop without a
3221 /// loop-invariant backedge-taken count (see
3222 /// hasLoopInvariantBackedgeTakenCount).
3224 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3225 return getBackedgeTakenInfo(L).Exact;
3228 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3229 /// return the least SCEV value that is known never to be less than the
3230 /// actual backedge taken count.
3231 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3232 return getBackedgeTakenInfo(L).Max;
3235 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3236 /// onto the given Worklist.
3238 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3239 BasicBlock *Header = L->getHeader();
3241 // Push all Loop-header PHIs onto the Worklist stack.
3242 for (BasicBlock::iterator I = Header->begin();
3243 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3244 Worklist.push_back(PN);
3247 const ScalarEvolution::BackedgeTakenInfo &
3248 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3249 // Initially insert a CouldNotCompute for this loop. If the insertion
3250 // succeeds, procede to actually compute a backedge-taken count and
3251 // update the value. The temporary CouldNotCompute value tells SCEV
3252 // code elsewhere that it shouldn't attempt to request a new
3253 // backedge-taken count, which could result in infinite recursion.
3254 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3255 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3257 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
3258 if (ItCount.Exact != getCouldNotCompute()) {
3259 assert(ItCount.Exact->isLoopInvariant(L) &&
3260 ItCount.Max->isLoopInvariant(L) &&
3261 "Computed trip count isn't loop invariant for loop!");
3262 ++NumTripCountsComputed;
3264 // Update the value in the map.
3265 Pair.first->second = ItCount;
3267 if (ItCount.Max != getCouldNotCompute())
3268 // Update the value in the map.
3269 Pair.first->second = ItCount;
3270 if (isa<PHINode>(L->getHeader()->begin()))
3271 // Only count loops that have phi nodes as not being computable.
3272 ++NumTripCountsNotComputed;
3275 // Now that we know more about the trip count for this loop, forget any
3276 // existing SCEV values for PHI nodes in this loop since they are only
3277 // conservative estimates made without the benefit of trip count
3278 // information. This is similar to the code in forgetLoop, except that
3279 // it handles SCEVUnknown PHI nodes specially.
3280 if (ItCount.hasAnyInfo()) {
3281 SmallVector<Instruction *, 16> Worklist;
3282 PushLoopPHIs(L, Worklist);
3284 SmallPtrSet<Instruction *, 8> Visited;
3285 while (!Worklist.empty()) {
3286 Instruction *I = Worklist.pop_back_val();
3287 if (!Visited.insert(I)) continue;
3289 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3290 Scalars.find(static_cast<Value *>(I));
3291 if (It != Scalars.end()) {
3292 // SCEVUnknown for a PHI either means that it has an unrecognized
3293 // structure, or it's a PHI that's in the progress of being computed
3294 // by createNodeForPHI. In the former case, additional loop trip
3295 // count information isn't going to change anything. In the later
3296 // case, createNodeForPHI will perform the necessary updates on its
3297 // own when it gets to that point.
3298 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3299 ValuesAtScopes.erase(It->second);
3302 if (PHINode *PN = dyn_cast<PHINode>(I))
3303 ConstantEvolutionLoopExitValue.erase(PN);
3306 PushDefUseChildren(I, Worklist);
3310 return Pair.first->second;
3313 /// forgetLoop - This method should be called by the client when it has
3314 /// changed a loop in a way that may effect ScalarEvolution's ability to
3315 /// compute a trip count, or if the loop is deleted.
3316 void ScalarEvolution::forgetLoop(const Loop *L) {
3317 // Drop any stored trip count value.
3318 BackedgeTakenCounts.erase(L);
3320 // Drop information about expressions based on loop-header PHIs.
3321 SmallVector<Instruction *, 16> Worklist;
3322 PushLoopPHIs(L, Worklist);
3324 SmallPtrSet<Instruction *, 8> Visited;
3325 while (!Worklist.empty()) {
3326 Instruction *I = Worklist.pop_back_val();
3327 if (!Visited.insert(I)) continue;
3329 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3330 Scalars.find(static_cast<Value *>(I));
3331 if (It != Scalars.end()) {
3332 ValuesAtScopes.erase(It->second);
3334 if (PHINode *PN = dyn_cast<PHINode>(I))
3335 ConstantEvolutionLoopExitValue.erase(PN);
3338 PushDefUseChildren(I, Worklist);
3342 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3343 /// of the specified loop will execute.
3344 ScalarEvolution::BackedgeTakenInfo
3345 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3346 SmallVector<BasicBlock *, 8> ExitingBlocks;
3347 L->getExitingBlocks(ExitingBlocks);
3349 // Examine all exits and pick the most conservative values.
3350 const SCEV *BECount = getCouldNotCompute();
3351 const SCEV *MaxBECount = getCouldNotCompute();
3352 bool CouldNotComputeBECount = false;
3353 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3354 BackedgeTakenInfo NewBTI =
3355 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3357 if (NewBTI.Exact == getCouldNotCompute()) {
3358 // We couldn't compute an exact value for this exit, so
3359 // we won't be able to compute an exact value for the loop.
3360 CouldNotComputeBECount = true;
3361 BECount = getCouldNotCompute();
3362 } else if (!CouldNotComputeBECount) {
3363 if (BECount == getCouldNotCompute())
3364 BECount = NewBTI.Exact;
3366 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3368 if (MaxBECount == getCouldNotCompute())
3369 MaxBECount = NewBTI.Max;
3370 else if (NewBTI.Max != getCouldNotCompute())
3371 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3374 return BackedgeTakenInfo(BECount, MaxBECount);
3377 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3378 /// of the specified loop will execute if it exits via the specified block.
3379 ScalarEvolution::BackedgeTakenInfo
3380 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3381 BasicBlock *ExitingBlock) {
3383 // Okay, we've chosen an exiting block. See what condition causes us to
3384 // exit at this block.
3386 // FIXME: we should be able to handle switch instructions (with a single exit)
3387 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3388 if (ExitBr == 0) return getCouldNotCompute();
3389 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3391 // At this point, we know we have a conditional branch that determines whether
3392 // the loop is exited. However, we don't know if the branch is executed each
3393 // time through the loop. If not, then the execution count of the branch will
3394 // not be equal to the trip count of the loop.
3396 // Currently we check for this by checking to see if the Exit branch goes to
3397 // the loop header. If so, we know it will always execute the same number of
3398 // times as the loop. We also handle the case where the exit block *is* the
3399 // loop header. This is common for un-rotated loops.
3401 // If both of those tests fail, walk up the unique predecessor chain to the
3402 // header, stopping if there is an edge that doesn't exit the loop. If the
3403 // header is reached, the execution count of the branch will be equal to the
3404 // trip count of the loop.
3406 // More extensive analysis could be done to handle more cases here.
3408 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3409 ExitBr->getSuccessor(1) != L->getHeader() &&
3410 ExitBr->getParent() != L->getHeader()) {
3411 // The simple checks failed, try climbing the unique predecessor chain
3412 // up to the header.
3414 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3415 BasicBlock *Pred = BB->getUniquePredecessor();
3417 return getCouldNotCompute();
3418 TerminatorInst *PredTerm = Pred->getTerminator();
3419 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3420 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3423 // If the predecessor has a successor that isn't BB and isn't
3424 // outside the loop, assume the worst.
3425 if (L->contains(PredSucc))
3426 return getCouldNotCompute();
3428 if (Pred == L->getHeader()) {
3435 return getCouldNotCompute();
3438 // Procede to the next level to examine the exit condition expression.
3439 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3440 ExitBr->getSuccessor(0),
3441 ExitBr->getSuccessor(1));
3444 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3445 /// backedge of the specified loop will execute if its exit condition
3446 /// were a conditional branch of ExitCond, TBB, and FBB.
3447 ScalarEvolution::BackedgeTakenInfo
3448 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3452 // Check if the controlling expression for this loop is an And or Or.
3453 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3454 if (BO->getOpcode() == Instruction::And) {
3455 // Recurse on the operands of the and.
3456 BackedgeTakenInfo BTI0 =
3457 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3458 BackedgeTakenInfo BTI1 =
3459 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3460 const SCEV *BECount = getCouldNotCompute();
3461 const SCEV *MaxBECount = getCouldNotCompute();
3462 if (L->contains(TBB)) {
3463 // Both conditions must be true for the loop to continue executing.
3464 // Choose the less conservative count.
3465 if (BTI0.Exact == getCouldNotCompute() ||
3466 BTI1.Exact == getCouldNotCompute())
3467 BECount = getCouldNotCompute();
3469 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3470 if (BTI0.Max == getCouldNotCompute())
3471 MaxBECount = BTI1.Max;
3472 else if (BTI1.Max == getCouldNotCompute())
3473 MaxBECount = BTI0.Max;
3475 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3477 // Both conditions must be true for the loop to exit.
3478 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3479 if (BTI0.Exact != getCouldNotCompute() &&
3480 BTI1.Exact != getCouldNotCompute())
3481 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3482 if (BTI0.Max != getCouldNotCompute() &&
3483 BTI1.Max != getCouldNotCompute())
3484 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3487 return BackedgeTakenInfo(BECount, MaxBECount);
3489 if (BO->getOpcode() == Instruction::Or) {
3490 // Recurse on the operands of the or.
3491 BackedgeTakenInfo BTI0 =
3492 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3493 BackedgeTakenInfo BTI1 =
3494 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3495 const SCEV *BECount = getCouldNotCompute();
3496 const SCEV *MaxBECount = getCouldNotCompute();
3497 if (L->contains(FBB)) {
3498 // Both conditions must be false for the loop to continue executing.
3499 // Choose the less conservative count.
3500 if (BTI0.Exact == getCouldNotCompute() ||
3501 BTI1.Exact == getCouldNotCompute())
3502 BECount = getCouldNotCompute();
3504 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3505 if (BTI0.Max == getCouldNotCompute())
3506 MaxBECount = BTI1.Max;
3507 else if (BTI1.Max == getCouldNotCompute())
3508 MaxBECount = BTI0.Max;
3510 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3512 // Both conditions must be false for the loop to exit.
3513 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3514 if (BTI0.Exact != getCouldNotCompute() &&
3515 BTI1.Exact != getCouldNotCompute())
3516 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3517 if (BTI0.Max != getCouldNotCompute() &&
3518 BTI1.Max != getCouldNotCompute())
3519 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3522 return BackedgeTakenInfo(BECount, MaxBECount);
3526 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3527 // Procede to the next level to examine the icmp.
3528 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3529 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3531 // If it's not an integer or pointer comparison then compute it the hard way.
3532 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3535 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3536 /// backedge of the specified loop will execute if its exit condition
3537 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3538 ScalarEvolution::BackedgeTakenInfo
3539 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3544 // If the condition was exit on true, convert the condition to exit on false
3545 ICmpInst::Predicate Cond;
3546 if (!L->contains(FBB))
3547 Cond = ExitCond->getPredicate();
3549 Cond = ExitCond->getInversePredicate();
3551 // Handle common loops like: for (X = "string"; *X; ++X)
3552 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3553 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3555 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3556 if (!isa<SCEVCouldNotCompute>(ItCnt)) {
3557 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType());
3558 return BackedgeTakenInfo(ItCnt,
3559 isa<SCEVConstant>(ItCnt) ? ItCnt :
3560 getConstant(APInt::getMaxValue(BitWidth)-1));
3564 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3565 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3567 // Try to evaluate any dependencies out of the loop.
3568 LHS = getSCEVAtScope(LHS, L);
3569 RHS = getSCEVAtScope(RHS, L);
3571 // At this point, we would like to compute how many iterations of the
3572 // loop the predicate will return true for these inputs.
3573 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3574 // If there is a loop-invariant, force it into the RHS.
3575 std::swap(LHS, RHS);
3576 Cond = ICmpInst::getSwappedPredicate(Cond);
3579 // If we have a comparison of a chrec against a constant, try to use value
3580 // ranges to answer this query.
3581 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3582 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3583 if (AddRec->getLoop() == L) {
3584 // Form the constant range.
3585 ConstantRange CompRange(
3586 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3588 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3589 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3593 case ICmpInst::ICMP_NE: { // while (X != Y)
3594 // Convert to: while (X-Y != 0)
3595 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3596 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3599 case ICmpInst::ICMP_EQ: { // while (X == Y)
3600 // Convert to: while (X-Y == 0)
3601 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3602 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3605 case ICmpInst::ICMP_SLT: {
3606 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3607 if (BTI.hasAnyInfo()) return BTI;
3610 case ICmpInst::ICMP_SGT: {
3611 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3612 getNotSCEV(RHS), L, true);
3613 if (BTI.hasAnyInfo()) return BTI;
3616 case ICmpInst::ICMP_ULT: {
3617 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3618 if (BTI.hasAnyInfo()) return BTI;
3621 case ICmpInst::ICMP_UGT: {
3622 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3623 getNotSCEV(RHS), L, false);
3624 if (BTI.hasAnyInfo()) return BTI;
3629 errs() << "ComputeBackedgeTakenCount ";
3630 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3631 errs() << "[unsigned] ";
3632 errs() << *LHS << " "
3633 << Instruction::getOpcodeName(Instruction::ICmp)
3634 << " " << *RHS << "\n";
3639 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3642 static ConstantInt *
3643 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3644 ScalarEvolution &SE) {
3645 const SCEV *InVal = SE.getConstant(C);
3646 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3647 assert(isa<SCEVConstant>(Val) &&
3648 "Evaluation of SCEV at constant didn't fold correctly?");
3649 return cast<SCEVConstant>(Val)->getValue();
3652 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3653 /// and a GEP expression (missing the pointer index) indexing into it, return
3654 /// the addressed element of the initializer or null if the index expression is
3657 GetAddressedElementFromGlobal(GlobalVariable *GV,
3658 const std::vector<ConstantInt*> &Indices) {
3659 Constant *Init = GV->getInitializer();
3660 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3661 uint64_t Idx = Indices[i]->getZExtValue();
3662 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3663 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3664 Init = cast<Constant>(CS->getOperand(Idx));
3665 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3666 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3667 Init = cast<Constant>(CA->getOperand(Idx));
3668 } else if (isa<ConstantAggregateZero>(Init)) {
3669 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3670 assert(Idx < STy->getNumElements() && "Bad struct index!");
3671 Init = Constant::getNullValue(STy->getElementType(Idx));
3672 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3673 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3674 Init = Constant::getNullValue(ATy->getElementType());
3676 llvm_unreachable("Unknown constant aggregate type!");
3680 return 0; // Unknown initializer type
3686 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3687 /// 'icmp op load X, cst', try to see if we can compute the backedge
3688 /// execution count.
3690 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3694 ICmpInst::Predicate predicate) {
3695 if (LI->isVolatile()) return getCouldNotCompute();
3697 // Check to see if the loaded pointer is a getelementptr of a global.
3698 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3699 if (!GEP) return getCouldNotCompute();
3701 // Make sure that it is really a constant global we are gepping, with an
3702 // initializer, and make sure the first IDX is really 0.
3703 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3704 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
3705 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3706 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3707 return getCouldNotCompute();
3709 // Okay, we allow one non-constant index into the GEP instruction.
3711 std::vector<ConstantInt*> Indexes;
3712 unsigned VarIdxNum = 0;
3713 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3714 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3715 Indexes.push_back(CI);
3716 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3717 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3718 VarIdx = GEP->getOperand(i);
3720 Indexes.push_back(0);
3723 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3724 // Check to see if X is a loop variant variable value now.
3725 const SCEV *Idx = getSCEV(VarIdx);
3726 Idx = getSCEVAtScope(Idx, L);
3728 // We can only recognize very limited forms of loop index expressions, in
3729 // particular, only affine AddRec's like {C1,+,C2}.
3730 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3731 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3732 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3733 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
3734 return getCouldNotCompute();
3736 unsigned MaxSteps = MaxBruteForceIterations;
3737 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3738 ConstantInt *ItCst = ConstantInt::get(
3739 cast<IntegerType>(IdxExpr->getType()), IterationNum);
3740 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
3742 // Form the GEP offset.
3743 Indexes[VarIdxNum] = Val;
3745 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
3746 if (Result == 0) break; // Cannot compute!
3748 // Evaluate the condition for this iteration.
3749 Result = ConstantExpr::getICmp(predicate, Result, RHS);
3750 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
3751 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
3753 errs() << "\n***\n*** Computed loop count " << *ItCst
3754 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
3757 ++NumArrayLenItCounts;
3758 return getConstant(ItCst); // Found terminating iteration!
3761 return getCouldNotCompute();
3765 /// CanConstantFold - Return true if we can constant fold an instruction of the
3766 /// specified type, assuming that all operands were constants.
3767 static bool CanConstantFold(const Instruction *I) {
3768 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
3769 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
3772 if (const CallInst *CI = dyn_cast<CallInst>(I))
3773 if (const Function *F = CI->getCalledFunction())
3774 return canConstantFoldCallTo(F);
3778 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
3779 /// in the loop that V is derived from. We allow arbitrary operations along the
3780 /// way, but the operands of an operation must either be constants or a value
3781 /// derived from a constant PHI. If this expression does not fit with these
3782 /// constraints, return null.
3783 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
3784 // If this is not an instruction, or if this is an instruction outside of the
3785 // loop, it can't be derived from a loop PHI.
3786 Instruction *I = dyn_cast<Instruction>(V);
3787 if (I == 0 || !L->contains(I)) return 0;
3789 if (PHINode *PN = dyn_cast<PHINode>(I)) {
3790 if (L->getHeader() == I->getParent())
3793 // We don't currently keep track of the control flow needed to evaluate
3794 // PHIs, so we cannot handle PHIs inside of loops.
3798 // If we won't be able to constant fold this expression even if the operands
3799 // are constants, return early.
3800 if (!CanConstantFold(I)) return 0;
3802 // Otherwise, we can evaluate this instruction if all of its operands are
3803 // constant or derived from a PHI node themselves.
3805 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
3806 if (!(isa<Constant>(I->getOperand(Op)) ||
3807 isa<GlobalValue>(I->getOperand(Op)))) {
3808 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
3809 if (P == 0) return 0; // Not evolving from PHI
3813 return 0; // Evolving from multiple different PHIs.
3816 // This is a expression evolving from a constant PHI!
3820 /// EvaluateExpression - Given an expression that passes the
3821 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
3822 /// in the loop has the value PHIVal. If we can't fold this expression for some
3823 /// reason, return null.
3824 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
3825 const TargetData *TD) {
3826 if (isa<PHINode>(V)) return PHIVal;
3827 if (Constant *C = dyn_cast<Constant>(V)) return C;
3828 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
3829 Instruction *I = cast<Instruction>(V);
3831 std::vector<Constant*> Operands;
3832 Operands.resize(I->getNumOperands());
3834 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3835 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
3836 if (Operands[i] == 0) return 0;
3839 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3840 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
3842 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3843 &Operands[0], Operands.size(), TD);
3846 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
3847 /// in the header of its containing loop, we know the loop executes a
3848 /// constant number of times, and the PHI node is just a recurrence
3849 /// involving constants, fold it.
3851 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
3854 std::map<PHINode*, Constant*>::iterator I =
3855 ConstantEvolutionLoopExitValue.find(PN);
3856 if (I != ConstantEvolutionLoopExitValue.end())
3859 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
3860 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
3862 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
3864 // Since the loop is canonicalized, the PHI node must have two entries. One
3865 // entry must be a constant (coming in from outside of the loop), and the
3866 // second must be derived from the same PHI.
3867 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3868 Constant *StartCST =
3869 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3871 return RetVal = 0; // Must be a constant.
3873 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3874 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3876 return RetVal = 0; // Not derived from same PHI.
3878 // Execute the loop symbolically to determine the exit value.
3879 if (BEs.getActiveBits() >= 32)
3880 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
3882 unsigned NumIterations = BEs.getZExtValue(); // must be in range
3883 unsigned IterationNum = 0;
3884 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
3885 if (IterationNum == NumIterations)
3886 return RetVal = PHIVal; // Got exit value!
3888 // Compute the value of the PHI node for the next iteration.
3889 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
3890 if (NextPHI == PHIVal)
3891 return RetVal = NextPHI; // Stopped evolving!
3893 return 0; // Couldn't evaluate!
3898 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
3899 /// constant number of times (the condition evolves only from constants),
3900 /// try to evaluate a few iterations of the loop until we get the exit
3901 /// condition gets a value of ExitWhen (true or false). If we cannot
3902 /// evaluate the trip count of the loop, return getCouldNotCompute().
3904 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
3907 PHINode *PN = getConstantEvolvingPHI(Cond, L);
3908 if (PN == 0) return getCouldNotCompute();
3910 // Since the loop is canonicalized, the PHI node must have two entries. One
3911 // entry must be a constant (coming in from outside of the loop), and the
3912 // second must be derived from the same PHI.
3913 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3914 Constant *StartCST =
3915 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3916 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
3918 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3919 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3920 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
3922 // Okay, we find a PHI node that defines the trip count of this loop. Execute
3923 // the loop symbolically to determine when the condition gets a value of
3925 unsigned IterationNum = 0;
3926 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
3927 for (Constant *PHIVal = StartCST;
3928 IterationNum != MaxIterations; ++IterationNum) {
3929 ConstantInt *CondVal =
3930 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
3932 // Couldn't symbolically evaluate.
3933 if (!CondVal) return getCouldNotCompute();
3935 if (CondVal->getValue() == uint64_t(ExitWhen)) {
3936 ++NumBruteForceTripCountsComputed;
3937 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
3940 // Compute the value of the PHI node for the next iteration.
3941 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
3942 if (NextPHI == 0 || NextPHI == PHIVal)
3943 return getCouldNotCompute();// Couldn't evaluate or not making progress...
3947 // Too many iterations were needed to evaluate.
3948 return getCouldNotCompute();
3951 /// getSCEVAtScope - Return a SCEV expression for the specified value
3952 /// at the specified scope in the program. The L value specifies a loop
3953 /// nest to evaluate the expression at, where null is the top-level or a
3954 /// specified loop is immediately inside of the loop.
3956 /// This method can be used to compute the exit value for a variable defined
3957 /// in a loop by querying what the value will hold in the parent loop.
3959 /// In the case that a relevant loop exit value cannot be computed, the
3960 /// original value V is returned.
3961 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
3962 // Check to see if we've folded this expression at this loop before.
3963 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
3964 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
3965 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
3967 return Pair.first->second ? Pair.first->second : V;
3969 // Otherwise compute it.
3970 const SCEV *C = computeSCEVAtScope(V, L);
3971 ValuesAtScopes[V][L] = C;
3975 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
3976 if (isa<SCEVConstant>(V)) return V;
3978 // If this instruction is evolved from a constant-evolving PHI, compute the
3979 // exit value from the loop without using SCEVs.
3980 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
3981 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
3982 const Loop *LI = (*this->LI)[I->getParent()];
3983 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
3984 if (PHINode *PN = dyn_cast<PHINode>(I))
3985 if (PN->getParent() == LI->getHeader()) {
3986 // Okay, there is no closed form solution for the PHI node. Check
3987 // to see if the loop that contains it has a known backedge-taken
3988 // count. If so, we may be able to force computation of the exit
3990 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
3991 if (const SCEVConstant *BTCC =
3992 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
3993 // Okay, we know how many times the containing loop executes. If
3994 // this is a constant evolving PHI node, get the final value at
3995 // the specified iteration number.
3996 Constant *RV = getConstantEvolutionLoopExitValue(PN,
3997 BTCC->getValue()->getValue(),
3999 if (RV) return getSCEV(RV);
4003 // Okay, this is an expression that we cannot symbolically evaluate
4004 // into a SCEV. Check to see if it's possible to symbolically evaluate
4005 // the arguments into constants, and if so, try to constant propagate the
4006 // result. This is particularly useful for computing loop exit values.
4007 if (CanConstantFold(I)) {
4008 std::vector<Constant*> Operands;
4009 Operands.reserve(I->getNumOperands());
4010 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4011 Value *Op = I->getOperand(i);
4012 if (Constant *C = dyn_cast<Constant>(Op)) {
4013 Operands.push_back(C);
4015 // If any of the operands is non-constant and if they are
4016 // non-integer and non-pointer, don't even try to analyze them
4017 // with scev techniques.
4018 if (!isSCEVable(Op->getType()))
4021 const SCEV *OpV = getSCEVAtScope(Op, L);
4022 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
4023 Constant *C = SC->getValue();
4024 if (C->getType() != Op->getType())
4025 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4029 Operands.push_back(C);
4030 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
4031 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
4032 if (C->getType() != Op->getType())
4034 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4038 Operands.push_back(C);
4048 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4049 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4050 Operands[0], Operands[1], TD);
4052 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4053 &Operands[0], Operands.size(), TD);
4058 // This is some other type of SCEVUnknown, just return it.
4062 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4063 // Avoid performing the look-up in the common case where the specified
4064 // expression has no loop-variant portions.
4065 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4066 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4067 if (OpAtScope != Comm->getOperand(i)) {
4068 // Okay, at least one of these operands is loop variant but might be
4069 // foldable. Build a new instance of the folded commutative expression.
4070 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4071 Comm->op_begin()+i);
4072 NewOps.push_back(OpAtScope);
4074 for (++i; i != e; ++i) {
4075 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4076 NewOps.push_back(OpAtScope);
4078 if (isa<SCEVAddExpr>(Comm))
4079 return getAddExpr(NewOps);
4080 if (isa<SCEVMulExpr>(Comm))
4081 return getMulExpr(NewOps);
4082 if (isa<SCEVSMaxExpr>(Comm))
4083 return getSMaxExpr(NewOps);
4084 if (isa<SCEVUMaxExpr>(Comm))
4085 return getUMaxExpr(NewOps);
4086 llvm_unreachable("Unknown commutative SCEV type!");
4089 // If we got here, all operands are loop invariant.
4093 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4094 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4095 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4096 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4097 return Div; // must be loop invariant
4098 return getUDivExpr(LHS, RHS);
4101 // If this is a loop recurrence for a loop that does not contain L, then we
4102 // are dealing with the final value computed by the loop.
4103 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4104 if (!L || !AddRec->getLoop()->contains(L)) {
4105 // To evaluate this recurrence, we need to know how many times the AddRec
4106 // loop iterates. Compute this now.
4107 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4108 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4110 // Then, evaluate the AddRec.
4111 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4116 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4117 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4118 if (Op == Cast->getOperand())
4119 return Cast; // must be loop invariant
4120 return getZeroExtendExpr(Op, Cast->getType());
4123 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4124 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4125 if (Op == Cast->getOperand())
4126 return Cast; // must be loop invariant
4127 return getSignExtendExpr(Op, Cast->getType());
4130 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4131 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4132 if (Op == Cast->getOperand())
4133 return Cast; // must be loop invariant
4134 return getTruncateExpr(Op, Cast->getType());
4137 if (isa<SCEVTargetDataConstant>(V))
4140 llvm_unreachable("Unknown SCEV type!");
4144 /// getSCEVAtScope - This is a convenience function which does
4145 /// getSCEVAtScope(getSCEV(V), L).
4146 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4147 return getSCEVAtScope(getSCEV(V), L);
4150 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4151 /// following equation:
4153 /// A * X = B (mod N)
4155 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4156 /// A and B isn't important.
4158 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4159 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4160 ScalarEvolution &SE) {
4161 uint32_t BW = A.getBitWidth();
4162 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4163 assert(A != 0 && "A must be non-zero.");
4167 // The gcd of A and N may have only one prime factor: 2. The number of
4168 // trailing zeros in A is its multiplicity
4169 uint32_t Mult2 = A.countTrailingZeros();
4172 // 2. Check if B is divisible by D.
4174 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4175 // is not less than multiplicity of this prime factor for D.
4176 if (B.countTrailingZeros() < Mult2)
4177 return SE.getCouldNotCompute();
4179 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4182 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4183 // bit width during computations.
4184 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4185 APInt Mod(BW + 1, 0);
4186 Mod.set(BW - Mult2); // Mod = N / D
4187 APInt I = AD.multiplicativeInverse(Mod);
4189 // 4. Compute the minimum unsigned root of the equation:
4190 // I * (B / D) mod (N / D)
4191 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4193 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4195 return SE.getConstant(Result.trunc(BW));
4198 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4199 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4200 /// might be the same) or two SCEVCouldNotCompute objects.
4202 static std::pair<const SCEV *,const SCEV *>
4203 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4204 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4205 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4206 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4207 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4209 // We currently can only solve this if the coefficients are constants.
4210 if (!LC || !MC || !NC) {
4211 const SCEV *CNC = SE.getCouldNotCompute();
4212 return std::make_pair(CNC, CNC);
4215 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4216 const APInt &L = LC->getValue()->getValue();
4217 const APInt &M = MC->getValue()->getValue();
4218 const APInt &N = NC->getValue()->getValue();
4219 APInt Two(BitWidth, 2);
4220 APInt Four(BitWidth, 4);
4223 using namespace APIntOps;
4225 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4226 // The B coefficient is M-N/2
4230 // The A coefficient is N/2
4231 APInt A(N.sdiv(Two));
4233 // Compute the B^2-4ac term.
4236 SqrtTerm -= Four * (A * C);
4238 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4239 // integer value or else APInt::sqrt() will assert.
4240 APInt SqrtVal(SqrtTerm.sqrt());
4242 // Compute the two solutions for the quadratic formula.
4243 // The divisions must be performed as signed divisions.
4245 APInt TwoA( A << 1 );
4246 if (TwoA.isMinValue()) {
4247 const SCEV *CNC = SE.getCouldNotCompute();
4248 return std::make_pair(CNC, CNC);
4251 LLVMContext &Context = SE.getContext();
4253 ConstantInt *Solution1 =
4254 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4255 ConstantInt *Solution2 =
4256 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4258 return std::make_pair(SE.getConstant(Solution1),
4259 SE.getConstant(Solution2));
4260 } // end APIntOps namespace
4263 /// HowFarToZero - Return the number of times a backedge comparing the specified
4264 /// value to zero will execute. If not computable, return CouldNotCompute.
4265 const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4266 // If the value is a constant
4267 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4268 // If the value is already zero, the branch will execute zero times.
4269 if (C->getValue()->isZero()) return C;
4270 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4273 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4274 if (!AddRec || AddRec->getLoop() != L)
4275 return getCouldNotCompute();
4277 if (AddRec->isAffine()) {
4278 // If this is an affine expression, the execution count of this branch is
4279 // the minimum unsigned root of the following equation:
4281 // Start + Step*N = 0 (mod 2^BW)
4285 // Step*N = -Start (mod 2^BW)
4287 // where BW is the common bit width of Start and Step.
4289 // Get the initial value for the loop.
4290 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4291 L->getParentLoop());
4292 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4293 L->getParentLoop());
4295 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4296 // For now we handle only constant steps.
4298 // First, handle unitary steps.
4299 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4300 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4301 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4302 return Start; // N = Start (as unsigned)
4304 // Then, try to solve the above equation provided that Start is constant.
4305 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4306 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4307 -StartC->getValue()->getValue(),
4310 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
4311 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4312 // the quadratic equation to solve it.
4313 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4315 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4316 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4319 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
4320 << " sol#2: " << *R2 << "\n";
4322 // Pick the smallest positive root value.
4323 if (ConstantInt *CB =
4324 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4325 R1->getValue(), R2->getValue()))) {
4326 if (CB->getZExtValue() == false)
4327 std::swap(R1, R2); // R1 is the minimum root now.
4329 // We can only use this value if the chrec ends up with an exact zero
4330 // value at this index. When solving for "X*X != 5", for example, we
4331 // should not accept a root of 2.
4332 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4334 return R1; // We found a quadratic root!
4339 return getCouldNotCompute();
4342 /// HowFarToNonZero - Return the number of times a backedge checking the
4343 /// specified value for nonzero will execute. If not computable, return
4345 const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4346 // Loops that look like: while (X == 0) are very strange indeed. We don't
4347 // handle them yet except for the trivial case. This could be expanded in the
4348 // future as needed.
4350 // If the value is a constant, check to see if it is known to be non-zero
4351 // already. If so, the backedge will execute zero times.
4352 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4353 if (!C->getValue()->isNullValue())
4354 return getIntegerSCEV(0, C->getType());
4355 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4358 // We could implement others, but I really doubt anyone writes loops like
4359 // this, and if they did, they would already be constant folded.
4360 return getCouldNotCompute();
4363 /// getLoopPredecessor - If the given loop's header has exactly one unique
4364 /// predecessor outside the loop, return it. Otherwise return null.
4366 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
4367 BasicBlock *Header = L->getHeader();
4368 BasicBlock *Pred = 0;
4369 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
4371 if (!L->contains(*PI)) {
4372 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
4378 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4379 /// (which may not be an immediate predecessor) which has exactly one
4380 /// successor from which BB is reachable, or null if no such block is
4384 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4385 // If the block has a unique predecessor, then there is no path from the
4386 // predecessor to the block that does not go through the direct edge
4387 // from the predecessor to the block.
4388 if (BasicBlock *Pred = BB->getSinglePredecessor())
4391 // A loop's header is defined to be a block that dominates the loop.
4392 // If the header has a unique predecessor outside the loop, it must be
4393 // a block that has exactly one successor that can reach the loop.
4394 if (Loop *L = LI->getLoopFor(BB))
4395 return getLoopPredecessor(L);
4400 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4401 /// testing whether two expressions are equal, however for the purposes of
4402 /// looking for a condition guarding a loop, it can be useful to be a little
4403 /// more general, since a front-end may have replicated the controlling
4406 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4407 // Quick check to see if they are the same SCEV.
4408 if (A == B) return true;
4410 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4411 // two different instructions with the same value. Check for this case.
4412 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4413 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4414 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4415 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4416 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4419 // Otherwise assume they may have a different value.
4423 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
4424 return getSignedRange(S).getSignedMax().isNegative();
4427 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
4428 return getSignedRange(S).getSignedMin().isStrictlyPositive();
4431 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
4432 return !getSignedRange(S).getSignedMin().isNegative();
4435 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
4436 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
4439 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
4440 return isKnownNegative(S) || isKnownPositive(S);
4443 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
4444 const SCEV *LHS, const SCEV *RHS) {
4446 if (HasSameValue(LHS, RHS))
4447 return ICmpInst::isTrueWhenEqual(Pred);
4451 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4453 case ICmpInst::ICMP_SGT:
4454 Pred = ICmpInst::ICMP_SLT;
4455 std::swap(LHS, RHS);
4456 case ICmpInst::ICMP_SLT: {
4457 ConstantRange LHSRange = getSignedRange(LHS);
4458 ConstantRange RHSRange = getSignedRange(RHS);
4459 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
4461 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
4465 case ICmpInst::ICMP_SGE:
4466 Pred = ICmpInst::ICMP_SLE;
4467 std::swap(LHS, RHS);
4468 case ICmpInst::ICMP_SLE: {
4469 ConstantRange LHSRange = getSignedRange(LHS);
4470 ConstantRange RHSRange = getSignedRange(RHS);
4471 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
4473 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
4477 case ICmpInst::ICMP_UGT:
4478 Pred = ICmpInst::ICMP_ULT;
4479 std::swap(LHS, RHS);
4480 case ICmpInst::ICMP_ULT: {
4481 ConstantRange LHSRange = getUnsignedRange(LHS);
4482 ConstantRange RHSRange = getUnsignedRange(RHS);
4483 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
4485 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
4489 case ICmpInst::ICMP_UGE:
4490 Pred = ICmpInst::ICMP_ULE;
4491 std::swap(LHS, RHS);
4492 case ICmpInst::ICMP_ULE: {
4493 ConstantRange LHSRange = getUnsignedRange(LHS);
4494 ConstantRange RHSRange = getUnsignedRange(RHS);
4495 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
4497 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
4501 case ICmpInst::ICMP_NE: {
4502 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
4504 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
4507 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4508 if (isKnownNonZero(Diff))
4512 case ICmpInst::ICMP_EQ:
4513 // The check at the top of the function catches the case where
4514 // the values are known to be equal.
4520 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
4521 /// protected by a conditional between LHS and RHS. This is used to
4522 /// to eliminate casts.
4524 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
4525 ICmpInst::Predicate Pred,
4526 const SCEV *LHS, const SCEV *RHS) {
4527 // Interpret a null as meaning no loop, where there is obviously no guard
4528 // (interprocedural conditions notwithstanding).
4529 if (!L) return true;
4531 BasicBlock *Latch = L->getLoopLatch();
4535 BranchInst *LoopContinuePredicate =
4536 dyn_cast<BranchInst>(Latch->getTerminator());
4537 if (!LoopContinuePredicate ||
4538 LoopContinuePredicate->isUnconditional())
4541 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
4542 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
4545 /// isLoopGuardedByCond - Test whether entry to the loop is protected
4546 /// by a conditional between LHS and RHS. This is used to help avoid max
4547 /// expressions in loop trip counts, and to eliminate casts.
4549 ScalarEvolution::isLoopGuardedByCond(const Loop *L,
4550 ICmpInst::Predicate Pred,
4551 const SCEV *LHS, const SCEV *RHS) {
4552 // Interpret a null as meaning no loop, where there is obviously no guard
4553 // (interprocedural conditions notwithstanding).
4554 if (!L) return false;
4556 BasicBlock *Predecessor = getLoopPredecessor(L);
4557 BasicBlock *PredecessorDest = L->getHeader();
4559 // Starting at the loop predecessor, climb up the predecessor chain, as long
4560 // as there are predecessors that can be found that have unique successors
4561 // leading to the original header.
4563 PredecessorDest = Predecessor,
4564 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4566 BranchInst *LoopEntryPredicate =
4567 dyn_cast<BranchInst>(Predecessor->getTerminator());
4568 if (!LoopEntryPredicate ||
4569 LoopEntryPredicate->isUnconditional())
4572 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4573 LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4580 /// isImpliedCond - Test whether the condition described by Pred, LHS,
4581 /// and RHS is true whenever the given Cond value evaluates to true.
4582 bool ScalarEvolution::isImpliedCond(Value *CondValue,
4583 ICmpInst::Predicate Pred,
4584 const SCEV *LHS, const SCEV *RHS,
4586 // Recursivly handle And and Or conditions.
4587 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4588 if (BO->getOpcode() == Instruction::And) {
4590 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4591 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4592 } else if (BO->getOpcode() == Instruction::Or) {
4594 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4595 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4599 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4600 if (!ICI) return false;
4602 // Bail if the ICmp's operands' types are wider than the needed type
4603 // before attempting to call getSCEV on them. This avoids infinite
4604 // recursion, since the analysis of widening casts can require loop
4605 // exit condition information for overflow checking, which would
4607 if (getTypeSizeInBits(LHS->getType()) <
4608 getTypeSizeInBits(ICI->getOperand(0)->getType()))
4611 // Now that we found a conditional branch that dominates the loop, check to
4612 // see if it is the comparison we are looking for.
4613 ICmpInst::Predicate FoundPred;
4615 FoundPred = ICI->getInversePredicate();
4617 FoundPred = ICI->getPredicate();
4619 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
4620 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
4622 // Balance the types. The case where FoundLHS' type is wider than
4623 // LHS' type is checked for above.
4624 if (getTypeSizeInBits(LHS->getType()) >
4625 getTypeSizeInBits(FoundLHS->getType())) {
4626 if (CmpInst::isSigned(Pred)) {
4627 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
4628 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
4630 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
4631 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
4635 // Canonicalize the query to match the way instcombine will have
4636 // canonicalized the comparison.
4637 // First, put a constant operand on the right.
4638 if (isa<SCEVConstant>(LHS)) {
4639 std::swap(LHS, RHS);
4640 Pred = ICmpInst::getSwappedPredicate(Pred);
4642 // Then, canonicalize comparisons with boundary cases.
4643 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4644 const APInt &RA = RC->getValue()->getValue();
4646 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4647 case ICmpInst::ICMP_EQ:
4648 case ICmpInst::ICMP_NE:
4650 case ICmpInst::ICMP_UGE:
4651 if ((RA - 1).isMinValue()) {
4652 Pred = ICmpInst::ICMP_NE;
4653 RHS = getConstant(RA - 1);
4656 if (RA.isMaxValue()) {
4657 Pred = ICmpInst::ICMP_EQ;
4660 if (RA.isMinValue()) return true;
4662 case ICmpInst::ICMP_ULE:
4663 if ((RA + 1).isMaxValue()) {
4664 Pred = ICmpInst::ICMP_NE;
4665 RHS = getConstant(RA + 1);
4668 if (RA.isMinValue()) {
4669 Pred = ICmpInst::ICMP_EQ;
4672 if (RA.isMaxValue()) return true;
4674 case ICmpInst::ICMP_SGE:
4675 if ((RA - 1).isMinSignedValue()) {
4676 Pred = ICmpInst::ICMP_NE;
4677 RHS = getConstant(RA - 1);
4680 if (RA.isMaxSignedValue()) {
4681 Pred = ICmpInst::ICMP_EQ;
4684 if (RA.isMinSignedValue()) return true;
4686 case ICmpInst::ICMP_SLE:
4687 if ((RA + 1).isMaxSignedValue()) {
4688 Pred = ICmpInst::ICMP_NE;
4689 RHS = getConstant(RA + 1);
4692 if (RA.isMinSignedValue()) {
4693 Pred = ICmpInst::ICMP_EQ;
4696 if (RA.isMaxSignedValue()) return true;
4698 case ICmpInst::ICMP_UGT:
4699 if (RA.isMinValue()) {
4700 Pred = ICmpInst::ICMP_NE;
4703 if ((RA + 1).isMaxValue()) {
4704 Pred = ICmpInst::ICMP_EQ;
4705 RHS = getConstant(RA + 1);
4708 if (RA.isMaxValue()) return false;
4710 case ICmpInst::ICMP_ULT:
4711 if (RA.isMaxValue()) {
4712 Pred = ICmpInst::ICMP_NE;
4715 if ((RA - 1).isMinValue()) {
4716 Pred = ICmpInst::ICMP_EQ;
4717 RHS = getConstant(RA - 1);
4720 if (RA.isMinValue()) return false;
4722 case ICmpInst::ICMP_SGT:
4723 if (RA.isMinSignedValue()) {
4724 Pred = ICmpInst::ICMP_NE;
4727 if ((RA + 1).isMaxSignedValue()) {
4728 Pred = ICmpInst::ICMP_EQ;
4729 RHS = getConstant(RA + 1);
4732 if (RA.isMaxSignedValue()) return false;
4734 case ICmpInst::ICMP_SLT:
4735 if (RA.isMaxSignedValue()) {
4736 Pred = ICmpInst::ICMP_NE;
4739 if ((RA - 1).isMinSignedValue()) {
4740 Pred = ICmpInst::ICMP_EQ;
4741 RHS = getConstant(RA - 1);
4744 if (RA.isMinSignedValue()) return false;
4749 // Check to see if we can make the LHS or RHS match.
4750 if (LHS == FoundRHS || RHS == FoundLHS) {
4751 if (isa<SCEVConstant>(RHS)) {
4752 std::swap(FoundLHS, FoundRHS);
4753 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
4755 std::swap(LHS, RHS);
4756 Pred = ICmpInst::getSwappedPredicate(Pred);
4760 // Check whether the found predicate is the same as the desired predicate.
4761 if (FoundPred == Pred)
4762 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
4764 // Check whether swapping the found predicate makes it the same as the
4765 // desired predicate.
4766 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
4767 if (isa<SCEVConstant>(RHS))
4768 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
4770 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
4771 RHS, LHS, FoundLHS, FoundRHS);
4774 // Check whether the actual condition is beyond sufficient.
4775 if (FoundPred == ICmpInst::ICMP_EQ)
4776 if (ICmpInst::isTrueWhenEqual(Pred))
4777 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
4779 if (Pred == ICmpInst::ICMP_NE)
4780 if (!ICmpInst::isTrueWhenEqual(FoundPred))
4781 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
4784 // Otherwise assume the worst.
4788 /// isImpliedCondOperands - Test whether the condition described by Pred,
4789 /// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS,
4790 /// and FoundRHS is true.
4791 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
4792 const SCEV *LHS, const SCEV *RHS,
4793 const SCEV *FoundLHS,
4794 const SCEV *FoundRHS) {
4795 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
4796 FoundLHS, FoundRHS) ||
4797 // ~x < ~y --> x > y
4798 isImpliedCondOperandsHelper(Pred, LHS, RHS,
4799 getNotSCEV(FoundRHS),
4800 getNotSCEV(FoundLHS));
4803 /// isImpliedCondOperandsHelper - Test whether the condition described by
4804 /// Pred, LHS, and RHS is true whenever the condition desribed by Pred,
4805 /// FoundLHS, and FoundRHS is true.
4807 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
4808 const SCEV *LHS, const SCEV *RHS,
4809 const SCEV *FoundLHS,
4810 const SCEV *FoundRHS) {
4812 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4813 case ICmpInst::ICMP_EQ:
4814 case ICmpInst::ICMP_NE:
4815 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
4818 case ICmpInst::ICMP_SLT:
4819 case ICmpInst::ICMP_SLE:
4820 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
4821 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS))
4824 case ICmpInst::ICMP_SGT:
4825 case ICmpInst::ICMP_SGE:
4826 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
4827 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS))
4830 case ICmpInst::ICMP_ULT:
4831 case ICmpInst::ICMP_ULE:
4832 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
4833 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS))
4836 case ICmpInst::ICMP_UGT:
4837 case ICmpInst::ICMP_UGE:
4838 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
4839 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS))
4847 /// getBECount - Subtract the end and start values and divide by the step,
4848 /// rounding up, to get the number of times the backedge is executed. Return
4849 /// CouldNotCompute if an intermediate computation overflows.
4850 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
4854 const Type *Ty = Start->getType();
4855 const SCEV *NegOne = getIntegerSCEV(-1, Ty);
4856 const SCEV *Diff = getMinusSCEV(End, Start);
4857 const SCEV *RoundUp = getAddExpr(Step, NegOne);
4859 // Add an adjustment to the difference between End and Start so that
4860 // the division will effectively round up.
4861 const SCEV *Add = getAddExpr(Diff, RoundUp);
4864 // Check Add for unsigned overflow.
4865 // TODO: More sophisticated things could be done here.
4866 const Type *WideTy = IntegerType::get(getContext(),
4867 getTypeSizeInBits(Ty) + 1);
4868 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
4869 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
4870 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
4871 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
4872 return getCouldNotCompute();
4875 return getUDivExpr(Add, Step);
4878 /// HowManyLessThans - Return the number of times a backedge containing the
4879 /// specified less-than comparison will execute. If not computable, return
4880 /// CouldNotCompute.
4881 ScalarEvolution::BackedgeTakenInfo
4882 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
4883 const Loop *L, bool isSigned) {
4884 // Only handle: "ADDREC < LoopInvariant".
4885 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
4887 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
4888 if (!AddRec || AddRec->getLoop() != L)
4889 return getCouldNotCompute();
4891 // Check to see if we have a flag which makes analysis easy.
4892 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
4893 AddRec->hasNoUnsignedWrap();
4895 if (AddRec->isAffine()) {
4896 // FORNOW: We only support unit strides.
4897 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
4898 const SCEV *Step = AddRec->getStepRecurrence(*this);
4900 // TODO: handle non-constant strides.
4901 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
4902 if (!CStep || CStep->isZero())
4903 return getCouldNotCompute();
4904 if (CStep->isOne()) {
4905 // With unit stride, the iteration never steps past the limit value.
4906 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
4908 // We know the iteration won't step past the maximum value for its type.
4910 } else if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
4911 // Test whether a positive iteration iteration can step past the limit
4912 // value and past the maximum value for its type in a single step.
4914 APInt Max = APInt::getSignedMaxValue(BitWidth);
4915 if ((Max - CStep->getValue()->getValue())
4916 .slt(CLimit->getValue()->getValue()))
4917 return getCouldNotCompute();
4919 APInt Max = APInt::getMaxValue(BitWidth);
4920 if ((Max - CStep->getValue()->getValue())
4921 .ult(CLimit->getValue()->getValue()))
4922 return getCouldNotCompute();
4925 // TODO: handle non-constant limit values below.
4926 return getCouldNotCompute();
4928 // TODO: handle negative strides below.
4929 return getCouldNotCompute();
4931 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
4932 // m. So, we count the number of iterations in which {n,+,s} < m is true.
4933 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
4934 // treat m-n as signed nor unsigned due to overflow possibility.
4936 // First, we get the value of the LHS in the first iteration: n
4937 const SCEV *Start = AddRec->getOperand(0);
4939 // Determine the minimum constant start value.
4940 const SCEV *MinStart = getConstant(isSigned ?
4941 getSignedRange(Start).getSignedMin() :
4942 getUnsignedRange(Start).getUnsignedMin());
4944 // If we know that the condition is true in order to enter the loop,
4945 // then we know that it will run exactly (m-n)/s times. Otherwise, we
4946 // only know that it will execute (max(m,n)-n)/s times. In both cases,
4947 // the division must round up.
4948 const SCEV *End = RHS;
4949 if (!isLoopGuardedByCond(L,
4950 isSigned ? ICmpInst::ICMP_SLT :
4952 getMinusSCEV(Start, Step), RHS))
4953 End = isSigned ? getSMaxExpr(RHS, Start)
4954 : getUMaxExpr(RHS, Start);
4956 // Determine the maximum constant end value.
4957 const SCEV *MaxEnd = getConstant(isSigned ?
4958 getSignedRange(End).getSignedMax() :
4959 getUnsignedRange(End).getUnsignedMax());
4961 // Finally, we subtract these two values and divide, rounding up, to get
4962 // the number of times the backedge is executed.
4963 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
4965 // The maximum backedge count is similar, except using the minimum start
4966 // value and the maximum end value.
4967 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
4969 return BackedgeTakenInfo(BECount, MaxBECount);
4972 return getCouldNotCompute();
4975 /// getNumIterationsInRange - Return the number of iterations of this loop that
4976 /// produce values in the specified constant range. Another way of looking at
4977 /// this is that it returns the first iteration number where the value is not in
4978 /// the condition, thus computing the exit count. If the iteration count can't
4979 /// be computed, an instance of SCEVCouldNotCompute is returned.
4980 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
4981 ScalarEvolution &SE) const {
4982 if (Range.isFullSet()) // Infinite loop.
4983 return SE.getCouldNotCompute();
4985 // If the start is a non-zero constant, shift the range to simplify things.
4986 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
4987 if (!SC->getValue()->isZero()) {
4988 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
4989 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
4990 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
4991 if (const SCEVAddRecExpr *ShiftedAddRec =
4992 dyn_cast<SCEVAddRecExpr>(Shifted))
4993 return ShiftedAddRec->getNumIterationsInRange(
4994 Range.subtract(SC->getValue()->getValue()), SE);
4995 // This is strange and shouldn't happen.
4996 return SE.getCouldNotCompute();
4999 // The only time we can solve this is when we have all constant indices.
5000 // Otherwise, we cannot determine the overflow conditions.
5001 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5002 if (!isa<SCEVConstant>(getOperand(i)))
5003 return SE.getCouldNotCompute();
5006 // Okay at this point we know that all elements of the chrec are constants and
5007 // that the start element is zero.
5009 // First check to see if the range contains zero. If not, the first
5011 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5012 if (!Range.contains(APInt(BitWidth, 0)))
5013 return SE.getIntegerSCEV(0, getType());
5016 // If this is an affine expression then we have this situation:
5017 // Solve {0,+,A} in Range === Ax in Range
5019 // We know that zero is in the range. If A is positive then we know that
5020 // the upper value of the range must be the first possible exit value.
5021 // If A is negative then the lower of the range is the last possible loop
5022 // value. Also note that we already checked for a full range.
5023 APInt One(BitWidth,1);
5024 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5025 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5027 // The exit value should be (End+A)/A.
5028 APInt ExitVal = (End + A).udiv(A);
5029 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5031 // Evaluate at the exit value. If we really did fall out of the valid
5032 // range, then we computed our trip count, otherwise wrap around or other
5033 // things must have happened.
5034 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5035 if (Range.contains(Val->getValue()))
5036 return SE.getCouldNotCompute(); // Something strange happened
5038 // Ensure that the previous value is in the range. This is a sanity check.
5039 assert(Range.contains(
5040 EvaluateConstantChrecAtConstant(this,
5041 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5042 "Linear scev computation is off in a bad way!");
5043 return SE.getConstant(ExitValue);
5044 } else if (isQuadratic()) {
5045 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5046 // quadratic equation to solve it. To do this, we must frame our problem in
5047 // terms of figuring out when zero is crossed, instead of when
5048 // Range.getUpper() is crossed.
5049 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5050 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5051 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5053 // Next, solve the constructed addrec
5054 std::pair<const SCEV *,const SCEV *> Roots =
5055 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5056 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5057 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5059 // Pick the smallest positive root value.
5060 if (ConstantInt *CB =
5061 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5062 R1->getValue(), R2->getValue()))) {
5063 if (CB->getZExtValue() == false)
5064 std::swap(R1, R2); // R1 is the minimum root now.
5066 // Make sure the root is not off by one. The returned iteration should
5067 // not be in the range, but the previous one should be. When solving
5068 // for "X*X < 5", for example, we should not return a root of 2.
5069 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5072 if (Range.contains(R1Val->getValue())) {
5073 // The next iteration must be out of the range...
5074 ConstantInt *NextVal =
5075 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5077 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5078 if (!Range.contains(R1Val->getValue()))
5079 return SE.getConstant(NextVal);
5080 return SE.getCouldNotCompute(); // Something strange happened
5083 // If R1 was not in the range, then it is a good return value. Make
5084 // sure that R1-1 WAS in the range though, just in case.
5085 ConstantInt *NextVal =
5086 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5087 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5088 if (Range.contains(R1Val->getValue()))
5090 return SE.getCouldNotCompute(); // Something strange happened
5095 return SE.getCouldNotCompute();
5100 //===----------------------------------------------------------------------===//
5101 // SCEVCallbackVH Class Implementation
5102 //===----------------------------------------------------------------------===//
5104 void ScalarEvolution::SCEVCallbackVH::deleted() {
5105 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5106 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5107 SE->ConstantEvolutionLoopExitValue.erase(PN);
5108 SE->Scalars.erase(getValPtr());
5109 // this now dangles!
5112 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
5113 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5115 // Forget all the expressions associated with users of the old value,
5116 // so that future queries will recompute the expressions using the new
5118 SmallVector<User *, 16> Worklist;
5119 SmallPtrSet<User *, 8> Visited;
5120 Value *Old = getValPtr();
5121 bool DeleteOld = false;
5122 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5124 Worklist.push_back(*UI);
5125 while (!Worklist.empty()) {
5126 User *U = Worklist.pop_back_val();
5127 // Deleting the Old value will cause this to dangle. Postpone
5128 // that until everything else is done.
5133 if (!Visited.insert(U))
5135 if (PHINode *PN = dyn_cast<PHINode>(U))
5136 SE->ConstantEvolutionLoopExitValue.erase(PN);
5137 SE->Scalars.erase(U);
5138 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5140 Worklist.push_back(*UI);
5142 // Delete the Old value if it (indirectly) references itself.
5144 if (PHINode *PN = dyn_cast<PHINode>(Old))
5145 SE->ConstantEvolutionLoopExitValue.erase(PN);
5146 SE->Scalars.erase(Old);
5147 // this now dangles!
5152 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5153 : CallbackVH(V), SE(se) {}
5155 //===----------------------------------------------------------------------===//
5156 // ScalarEvolution Class Implementation
5157 //===----------------------------------------------------------------------===//
5159 ScalarEvolution::ScalarEvolution()
5160 : FunctionPass(&ID) {
5163 bool ScalarEvolution::runOnFunction(Function &F) {
5165 LI = &getAnalysis<LoopInfo>();
5166 TD = getAnalysisIfAvailable<TargetData>();
5170 void ScalarEvolution::releaseMemory() {
5172 BackedgeTakenCounts.clear();
5173 ConstantEvolutionLoopExitValue.clear();
5174 ValuesAtScopes.clear();
5175 UniqueSCEVs.clear();
5176 SCEVAllocator.Reset();
5179 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5180 AU.setPreservesAll();
5181 AU.addRequiredTransitive<LoopInfo>();
5184 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5185 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5188 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5190 // Print all inner loops first
5191 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5192 PrintLoopInfo(OS, SE, *I);
5194 OS << "Loop " << L->getHeader()->getName() << ": ";
5196 SmallVector<BasicBlock *, 8> ExitBlocks;
5197 L->getExitBlocks(ExitBlocks);
5198 if (ExitBlocks.size() != 1)
5199 OS << "<multiple exits> ";
5201 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5202 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5204 OS << "Unpredictable backedge-taken count. ";
5208 OS << "Loop " << L->getHeader()->getName() << ": ";
5210 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5211 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5213 OS << "Unpredictable max backedge-taken count. ";
5219 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5220 // ScalarEvolution's implementaiton of the print method is to print
5221 // out SCEV values of all instructions that are interesting. Doing
5222 // this potentially causes it to create new SCEV objects though,
5223 // which technically conflicts with the const qualifier. This isn't
5224 // observable from outside the class though, so casting away the
5225 // const isn't dangerous.
5226 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5228 OS << "Classifying expressions for: " << F->getName() << "\n";
5229 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5230 if (isSCEVable(I->getType())) {
5233 const SCEV *SV = SE.getSCEV(&*I);
5236 const Loop *L = LI->getLoopFor((*I).getParent());
5238 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5245 OS << "\t\t" "Exits: ";
5246 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5247 if (!ExitValue->isLoopInvariant(L)) {
5248 OS << "<<Unknown>>";
5257 OS << "Determining loop execution counts for: " << F->getName() << "\n";
5258 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5259 PrintLoopInfo(OS, &SE, *I);