1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
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 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/Support/CommandLine.h"
87 #include "llvm/Support/Debug.h"
88 #include "llvm/Support/ErrorHandling.h"
89 #include "llvm/Support/MathExtras.h"
90 #include "llvm/Support/raw_ostream.h"
94 #define DEBUG_TYPE "scalar-evolution"
96 STATISTIC(NumArrayLenItCounts,
97 "Number of trip counts computed with array length");
98 STATISTIC(NumTripCountsComputed,
99 "Number of loops with predictable loop counts");
100 STATISTIC(NumTripCountsNotComputed,
101 "Number of loops without predictable loop counts");
102 STATISTIC(NumBruteForceTripCountsComputed,
103 "Number of loops with trip counts computed by force");
105 static cl::opt<unsigned>
106 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
107 cl::desc("Maximum number of iterations SCEV will "
108 "symbolically execute a constant "
112 // FIXME: Enable this with XDEBUG when the test suite is clean.
114 VerifySCEV("verify-scev",
115 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
117 //===----------------------------------------------------------------------===//
118 // SCEV class definitions
119 //===----------------------------------------------------------------------===//
121 //===----------------------------------------------------------------------===//
122 // Implementation of the SCEV class.
125 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
126 void SCEV::dump() const {
132 void SCEV::print(raw_ostream &OS) const {
133 switch (static_cast<SCEVTypes>(getSCEVType())) {
135 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
138 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
139 const SCEV *Op = Trunc->getOperand();
140 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
141 << *Trunc->getType() << ")";
145 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
146 const SCEV *Op = ZExt->getOperand();
147 OS << "(zext " << *Op->getType() << " " << *Op << " to "
148 << *ZExt->getType() << ")";
152 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
153 const SCEV *Op = SExt->getOperand();
154 OS << "(sext " << *Op->getType() << " " << *Op << " to "
155 << *SExt->getType() << ")";
159 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
160 OS << "{" << *AR->getOperand(0);
161 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
162 OS << ",+," << *AR->getOperand(i);
164 if (AR->getNoWrapFlags(FlagNUW))
166 if (AR->getNoWrapFlags(FlagNSW))
168 if (AR->getNoWrapFlags(FlagNW) &&
169 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
171 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
179 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
180 const char *OpStr = nullptr;
181 switch (NAry->getSCEVType()) {
182 case scAddExpr: OpStr = " + "; break;
183 case scMulExpr: OpStr = " * "; break;
184 case scUMaxExpr: OpStr = " umax "; break;
185 case scSMaxExpr: OpStr = " smax "; break;
188 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
191 if (std::next(I) != E)
195 switch (NAry->getSCEVType()) {
198 if (NAry->getNoWrapFlags(FlagNUW))
200 if (NAry->getNoWrapFlags(FlagNSW))
206 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
207 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
211 const SCEVUnknown *U = cast<SCEVUnknown>(this);
213 if (U->isSizeOf(AllocTy)) {
214 OS << "sizeof(" << *AllocTy << ")";
217 if (U->isAlignOf(AllocTy)) {
218 OS << "alignof(" << *AllocTy << ")";
224 if (U->isOffsetOf(CTy, FieldNo)) {
225 OS << "offsetof(" << *CTy << ", ";
226 FieldNo->printAsOperand(OS, false);
231 // Otherwise just print it normally.
232 U->getValue()->printAsOperand(OS, false);
235 case scCouldNotCompute:
236 OS << "***COULDNOTCOMPUTE***";
239 llvm_unreachable("Unknown SCEV kind!");
242 Type *SCEV::getType() const {
243 switch (static_cast<SCEVTypes>(getSCEVType())) {
245 return cast<SCEVConstant>(this)->getType();
249 return cast<SCEVCastExpr>(this)->getType();
254 return cast<SCEVNAryExpr>(this)->getType();
256 return cast<SCEVAddExpr>(this)->getType();
258 return cast<SCEVUDivExpr>(this)->getType();
260 return cast<SCEVUnknown>(this)->getType();
261 case scCouldNotCompute:
262 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
264 llvm_unreachable("Unknown SCEV kind!");
267 bool SCEV::isZero() const {
268 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
269 return SC->getValue()->isZero();
273 bool SCEV::isOne() const {
274 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
275 return SC->getValue()->isOne();
279 bool SCEV::isAllOnesValue() const {
280 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
281 return SC->getValue()->isAllOnesValue();
285 /// isNonConstantNegative - Return true if the specified scev is negated, but
287 bool SCEV::isNonConstantNegative() const {
288 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
289 if (!Mul) return false;
291 // If there is a constant factor, it will be first.
292 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
293 if (!SC) return false;
295 // Return true if the value is negative, this matches things like (-42 * V).
296 return SC->getValue()->getValue().isNegative();
299 SCEVCouldNotCompute::SCEVCouldNotCompute() :
300 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
302 bool SCEVCouldNotCompute::classof(const SCEV *S) {
303 return S->getSCEVType() == scCouldNotCompute;
306 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
308 ID.AddInteger(scConstant);
311 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
312 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
313 UniqueSCEVs.InsertNode(S, IP);
317 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
318 return getConstant(ConstantInt::get(getContext(), Val));
322 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
323 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
324 return getConstant(ConstantInt::get(ITy, V, isSigned));
327 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
328 unsigned SCEVTy, const SCEV *op, Type *ty)
329 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
331 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
332 const SCEV *op, Type *ty)
333 : SCEVCastExpr(ID, scTruncate, op, ty) {
334 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
335 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
336 "Cannot truncate non-integer value!");
339 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
340 const SCEV *op, Type *ty)
341 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
342 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
343 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
344 "Cannot zero extend non-integer value!");
347 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
348 const SCEV *op, Type *ty)
349 : SCEVCastExpr(ID, scSignExtend, op, ty) {
350 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
351 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
352 "Cannot sign extend non-integer value!");
355 void SCEVUnknown::deleted() {
356 // Clear this SCEVUnknown from various maps.
357 SE->forgetMemoizedResults(this);
359 // Remove this SCEVUnknown from the uniquing map.
360 SE->UniqueSCEVs.RemoveNode(this);
362 // Release the value.
366 void SCEVUnknown::allUsesReplacedWith(Value *New) {
367 // Clear this SCEVUnknown from various maps.
368 SE->forgetMemoizedResults(this);
370 // Remove this SCEVUnknown from the uniquing map.
371 SE->UniqueSCEVs.RemoveNode(this);
373 // Update this SCEVUnknown to point to the new value. This is needed
374 // because there may still be outstanding SCEVs which still point to
379 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
380 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
381 if (VCE->getOpcode() == Instruction::PtrToInt)
382 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
383 if (CE->getOpcode() == Instruction::GetElementPtr &&
384 CE->getOperand(0)->isNullValue() &&
385 CE->getNumOperands() == 2)
386 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
388 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
396 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
397 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
398 if (VCE->getOpcode() == Instruction::PtrToInt)
399 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
400 if (CE->getOpcode() == Instruction::GetElementPtr &&
401 CE->getOperand(0)->isNullValue()) {
403 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
404 if (StructType *STy = dyn_cast<StructType>(Ty))
405 if (!STy->isPacked() &&
406 CE->getNumOperands() == 3 &&
407 CE->getOperand(1)->isNullValue()) {
408 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
410 STy->getNumElements() == 2 &&
411 STy->getElementType(0)->isIntegerTy(1)) {
412 AllocTy = STy->getElementType(1);
421 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
422 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
423 if (VCE->getOpcode() == Instruction::PtrToInt)
424 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
425 if (CE->getOpcode() == Instruction::GetElementPtr &&
426 CE->getNumOperands() == 3 &&
427 CE->getOperand(0)->isNullValue() &&
428 CE->getOperand(1)->isNullValue()) {
430 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
431 // Ignore vector types here so that ScalarEvolutionExpander doesn't
432 // emit getelementptrs that index into vectors.
433 if (Ty->isStructTy() || Ty->isArrayTy()) {
435 FieldNo = CE->getOperand(2);
443 //===----------------------------------------------------------------------===//
445 //===----------------------------------------------------------------------===//
448 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
449 /// than the complexity of the RHS. This comparator is used to canonicalize
451 class SCEVComplexityCompare {
452 const LoopInfo *const LI;
454 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
456 // Return true or false if LHS is less than, or at least RHS, respectively.
457 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
458 return compare(LHS, RHS) < 0;
461 // Return negative, zero, or positive, if LHS is less than, equal to, or
462 // greater than RHS, respectively. A three-way result allows recursive
463 // comparisons to be more efficient.
464 int compare(const SCEV *LHS, const SCEV *RHS) const {
465 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
469 // Primarily, sort the SCEVs by their getSCEVType().
470 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
472 return (int)LType - (int)RType;
474 // Aside from the getSCEVType() ordering, the particular ordering
475 // isn't very important except that it's beneficial to be consistent,
476 // so that (a + b) and (b + a) don't end up as different expressions.
477 switch (static_cast<SCEVTypes>(LType)) {
479 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
480 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
482 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
483 // not as complete as it could be.
484 const Value *LV = LU->getValue(), *RV = RU->getValue();
486 // Order pointer values after integer values. This helps SCEVExpander
488 bool LIsPointer = LV->getType()->isPointerTy(),
489 RIsPointer = RV->getType()->isPointerTy();
490 if (LIsPointer != RIsPointer)
491 return (int)LIsPointer - (int)RIsPointer;
493 // Compare getValueID values.
494 unsigned LID = LV->getValueID(),
495 RID = RV->getValueID();
497 return (int)LID - (int)RID;
499 // Sort arguments by their position.
500 if (const Argument *LA = dyn_cast<Argument>(LV)) {
501 const Argument *RA = cast<Argument>(RV);
502 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
503 return (int)LArgNo - (int)RArgNo;
506 // For instructions, compare their loop depth, and their operand
507 // count. This is pretty loose.
508 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
509 const Instruction *RInst = cast<Instruction>(RV);
511 // Compare loop depths.
512 const BasicBlock *LParent = LInst->getParent(),
513 *RParent = RInst->getParent();
514 if (LParent != RParent) {
515 unsigned LDepth = LI->getLoopDepth(LParent),
516 RDepth = LI->getLoopDepth(RParent);
517 if (LDepth != RDepth)
518 return (int)LDepth - (int)RDepth;
521 // Compare the number of operands.
522 unsigned LNumOps = LInst->getNumOperands(),
523 RNumOps = RInst->getNumOperands();
524 return (int)LNumOps - (int)RNumOps;
531 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
532 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
534 // Compare constant values.
535 const APInt &LA = LC->getValue()->getValue();
536 const APInt &RA = RC->getValue()->getValue();
537 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
538 if (LBitWidth != RBitWidth)
539 return (int)LBitWidth - (int)RBitWidth;
540 return LA.ult(RA) ? -1 : 1;
544 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
545 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
547 // Compare addrec loop depths.
548 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
549 if (LLoop != RLoop) {
550 unsigned LDepth = LLoop->getLoopDepth(),
551 RDepth = RLoop->getLoopDepth();
552 if (LDepth != RDepth)
553 return (int)LDepth - (int)RDepth;
556 // Addrec complexity grows with operand count.
557 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
558 if (LNumOps != RNumOps)
559 return (int)LNumOps - (int)RNumOps;
561 // Lexicographically compare.
562 for (unsigned i = 0; i != LNumOps; ++i) {
563 long X = compare(LA->getOperand(i), RA->getOperand(i));
575 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
576 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
578 // Lexicographically compare n-ary expressions.
579 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
580 if (LNumOps != RNumOps)
581 return (int)LNumOps - (int)RNumOps;
583 for (unsigned i = 0; i != LNumOps; ++i) {
586 long X = compare(LC->getOperand(i), RC->getOperand(i));
590 return (int)LNumOps - (int)RNumOps;
594 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
595 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
597 // Lexicographically compare udiv expressions.
598 long X = compare(LC->getLHS(), RC->getLHS());
601 return compare(LC->getRHS(), RC->getRHS());
607 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
608 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
610 // Compare cast expressions by operand.
611 return compare(LC->getOperand(), RC->getOperand());
614 case scCouldNotCompute:
615 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
617 llvm_unreachable("Unknown SCEV kind!");
622 /// GroupByComplexity - Given a list of SCEV objects, order them by their
623 /// complexity, and group objects of the same complexity together by value.
624 /// When this routine is finished, we know that any duplicates in the vector are
625 /// consecutive and that complexity is monotonically increasing.
627 /// Note that we go take special precautions to ensure that we get deterministic
628 /// results from this routine. In other words, we don't want the results of
629 /// this to depend on where the addresses of various SCEV objects happened to
632 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
634 if (Ops.size() < 2) return; // Noop
635 if (Ops.size() == 2) {
636 // This is the common case, which also happens to be trivially simple.
638 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
639 if (SCEVComplexityCompare(LI)(RHS, LHS))
644 // Do the rough sort by complexity.
645 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
647 // Now that we are sorted by complexity, group elements of the same
648 // complexity. Note that this is, at worst, N^2, but the vector is likely to
649 // be extremely short in practice. Note that we take this approach because we
650 // do not want to depend on the addresses of the objects we are grouping.
651 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
652 const SCEV *S = Ops[i];
653 unsigned Complexity = S->getSCEVType();
655 // If there are any objects of the same complexity and same value as this
657 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
658 if (Ops[j] == S) { // Found a duplicate.
659 // Move it to immediately after i'th element.
660 std::swap(Ops[i+1], Ops[j]);
661 ++i; // no need to rescan it.
662 if (i == e-2) return; // Done!
669 struct FindSCEVSize {
671 FindSCEVSize() : Size(0) {}
673 bool follow(const SCEV *S) {
675 // Keep looking at all operands of S.
678 bool isDone() const {
684 // Returns the size of the SCEV S.
685 static inline int sizeOfSCEV(const SCEV *S) {
687 SCEVTraversal<FindSCEVSize> ST(F);
694 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
696 // Computes the Quotient and Remainder of the division of Numerator by
698 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
699 const SCEV *Denominator, const SCEV **Quotient,
700 const SCEV **Remainder) {
701 assert(Numerator && Denominator && "Uninitialized SCEV");
703 SCEVDivision D(SE, Numerator, Denominator);
705 // Check for the trivial case here to avoid having to check for it in the
707 if (Numerator == Denominator) {
713 if (Numerator->isZero()) {
719 // A simple case when N/1. The quotient is N.
720 if (Denominator->isOne()) {
721 *Quotient = Numerator;
726 // Split the Denominator when it is a product.
727 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
729 *Quotient = Numerator;
730 for (const SCEV *Op : T->operands()) {
731 divide(SE, *Quotient, Op, &Q, &R);
734 // Bail out when the Numerator is not divisible by one of the terms of
738 *Remainder = Numerator;
747 *Quotient = D.Quotient;
748 *Remainder = D.Remainder;
751 // Except in the trivial case described above, we do not know how to divide
752 // Expr by Denominator for the following functions with empty implementation.
753 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
754 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
755 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
756 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
757 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
758 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
759 void visitUnknown(const SCEVUnknown *Numerator) {}
760 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
762 void visitConstant(const SCEVConstant *Numerator) {
763 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
764 APInt NumeratorVal = Numerator->getValue()->getValue();
765 APInt DenominatorVal = D->getValue()->getValue();
766 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
767 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
769 if (NumeratorBW > DenominatorBW)
770 DenominatorVal = DenominatorVal.sext(NumeratorBW);
771 else if (NumeratorBW < DenominatorBW)
772 NumeratorVal = NumeratorVal.sext(DenominatorBW);
774 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
775 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
776 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
777 Quotient = SE.getConstant(QuotientVal);
778 Remainder = SE.getConstant(RemainderVal);
783 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
784 const SCEV *StartQ, *StartR, *StepQ, *StepR;
785 assert(Numerator->isAffine() && "Numerator should be affine");
786 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
787 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
788 // Bail out if the types do not match.
789 Type *Ty = Denominator->getType();
790 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
791 Ty != StepQ->getType() || Ty != StepR->getType()) {
793 Remainder = Numerator;
796 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
797 Numerator->getNoWrapFlags());
798 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
799 Numerator->getNoWrapFlags());
802 void visitAddExpr(const SCEVAddExpr *Numerator) {
803 SmallVector<const SCEV *, 2> Qs, Rs;
804 Type *Ty = Denominator->getType();
806 for (const SCEV *Op : Numerator->operands()) {
808 divide(SE, Op, Denominator, &Q, &R);
810 // Bail out if types do not match.
811 if (Ty != Q->getType() || Ty != R->getType()) {
813 Remainder = Numerator;
821 if (Qs.size() == 1) {
827 Quotient = SE.getAddExpr(Qs);
828 Remainder = SE.getAddExpr(Rs);
831 void visitMulExpr(const SCEVMulExpr *Numerator) {
832 SmallVector<const SCEV *, 2> Qs;
833 Type *Ty = Denominator->getType();
835 bool FoundDenominatorTerm = false;
836 for (const SCEV *Op : Numerator->operands()) {
837 // Bail out if types do not match.
838 if (Ty != Op->getType()) {
840 Remainder = Numerator;
844 if (FoundDenominatorTerm) {
849 // Check whether Denominator divides one of the product operands.
851 divide(SE, Op, Denominator, &Q, &R);
857 // Bail out if types do not match.
858 if (Ty != Q->getType()) {
860 Remainder = Numerator;
864 FoundDenominatorTerm = true;
868 if (FoundDenominatorTerm) {
873 Quotient = SE.getMulExpr(Qs);
877 if (!isa<SCEVUnknown>(Denominator)) {
879 Remainder = Numerator;
883 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
884 ValueToValueMap RewriteMap;
885 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
886 cast<SCEVConstant>(Zero)->getValue();
887 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
889 if (Remainder->isZero()) {
890 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
891 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
892 cast<SCEVConstant>(One)->getValue();
894 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
898 // Quotient is (Numerator - Remainder) divided by Denominator.
900 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
901 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
902 // This SCEV does not seem to simplify: fail the division here.
904 Remainder = Numerator;
907 divide(SE, Diff, Denominator, &Q, &R);
909 "(Numerator - Remainder) should evenly divide Denominator");
914 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
915 const SCEV *Denominator)
916 : SE(S), Denominator(Denominator) {
917 Zero = SE.getConstant(Denominator->getType(), 0);
918 One = SE.getConstant(Denominator->getType(), 1);
920 // By default, we don't know how to divide Expr by Denominator.
921 // Providing the default here simplifies the rest of the code.
923 Remainder = Numerator;
927 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
932 //===----------------------------------------------------------------------===//
933 // Simple SCEV method implementations
934 //===----------------------------------------------------------------------===//
936 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
938 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
941 // Handle the simplest case efficiently.
943 return SE.getTruncateOrZeroExtend(It, ResultTy);
945 // We are using the following formula for BC(It, K):
947 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
949 // Suppose, W is the bitwidth of the return value. We must be prepared for
950 // overflow. Hence, we must assure that the result of our computation is
951 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
952 // safe in modular arithmetic.
954 // However, this code doesn't use exactly that formula; the formula it uses
955 // is something like the following, where T is the number of factors of 2 in
956 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
959 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
961 // This formula is trivially equivalent to the previous formula. However,
962 // this formula can be implemented much more efficiently. The trick is that
963 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
964 // arithmetic. To do exact division in modular arithmetic, all we have
965 // to do is multiply by the inverse. Therefore, this step can be done at
968 // The next issue is how to safely do the division by 2^T. The way this
969 // is done is by doing the multiplication step at a width of at least W + T
970 // bits. This way, the bottom W+T bits of the product are accurate. Then,
971 // when we perform the division by 2^T (which is equivalent to a right shift
972 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
973 // truncated out after the division by 2^T.
975 // In comparison to just directly using the first formula, this technique
976 // is much more efficient; using the first formula requires W * K bits,
977 // but this formula less than W + K bits. Also, the first formula requires
978 // a division step, whereas this formula only requires multiplies and shifts.
980 // It doesn't matter whether the subtraction step is done in the calculation
981 // width or the input iteration count's width; if the subtraction overflows,
982 // the result must be zero anyway. We prefer here to do it in the width of
983 // the induction variable because it helps a lot for certain cases; CodeGen
984 // isn't smart enough to ignore the overflow, which leads to much less
985 // efficient code if the width of the subtraction is wider than the native
988 // (It's possible to not widen at all by pulling out factors of 2 before
989 // the multiplication; for example, K=2 can be calculated as
990 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
991 // extra arithmetic, so it's not an obvious win, and it gets
992 // much more complicated for K > 3.)
994 // Protection from insane SCEVs; this bound is conservative,
995 // but it probably doesn't matter.
997 return SE.getCouldNotCompute();
999 unsigned W = SE.getTypeSizeInBits(ResultTy);
1001 // Calculate K! / 2^T and T; we divide out the factors of two before
1002 // multiplying for calculating K! / 2^T to avoid overflow.
1003 // Other overflow doesn't matter because we only care about the bottom
1004 // W bits of the result.
1005 APInt OddFactorial(W, 1);
1007 for (unsigned i = 3; i <= K; ++i) {
1009 unsigned TwoFactors = Mult.countTrailingZeros();
1011 Mult = Mult.lshr(TwoFactors);
1012 OddFactorial *= Mult;
1015 // We need at least W + T bits for the multiplication step
1016 unsigned CalculationBits = W + T;
1018 // Calculate 2^T, at width T+W.
1019 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1021 // Calculate the multiplicative inverse of K! / 2^T;
1022 // this multiplication factor will perform the exact division by
1024 APInt Mod = APInt::getSignedMinValue(W+1);
1025 APInt MultiplyFactor = OddFactorial.zext(W+1);
1026 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1027 MultiplyFactor = MultiplyFactor.trunc(W);
1029 // Calculate the product, at width T+W
1030 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1032 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1033 for (unsigned i = 1; i != K; ++i) {
1034 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1035 Dividend = SE.getMulExpr(Dividend,
1036 SE.getTruncateOrZeroExtend(S, CalculationTy));
1040 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1042 // Truncate the result, and divide by K! / 2^T.
1044 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1045 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1048 /// evaluateAtIteration - Return the value of this chain of recurrences at
1049 /// the specified iteration number. We can evaluate this recurrence by
1050 /// multiplying each element in the chain by the binomial coefficient
1051 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1053 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1055 /// where BC(It, k) stands for binomial coefficient.
1057 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1058 ScalarEvolution &SE) const {
1059 const SCEV *Result = getStart();
1060 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1061 // The computation is correct in the face of overflow provided that the
1062 // multiplication is performed _after_ the evaluation of the binomial
1064 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1065 if (isa<SCEVCouldNotCompute>(Coeff))
1068 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1073 //===----------------------------------------------------------------------===//
1074 // SCEV Expression folder implementations
1075 //===----------------------------------------------------------------------===//
1077 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1079 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1080 "This is not a truncating conversion!");
1081 assert(isSCEVable(Ty) &&
1082 "This is not a conversion to a SCEVable type!");
1083 Ty = getEffectiveSCEVType(Ty);
1085 FoldingSetNodeID ID;
1086 ID.AddInteger(scTruncate);
1090 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1092 // Fold if the operand is constant.
1093 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1095 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1097 // trunc(trunc(x)) --> trunc(x)
1098 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1099 return getTruncateExpr(ST->getOperand(), Ty);
1101 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1102 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1103 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1105 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1106 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1107 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1109 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1110 // eliminate all the truncates, or we replace other casts with truncates.
1111 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1112 SmallVector<const SCEV *, 4> Operands;
1113 bool hasTrunc = false;
1114 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1115 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1116 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1117 hasTrunc = isa<SCEVTruncateExpr>(S);
1118 Operands.push_back(S);
1121 return getAddExpr(Operands);
1122 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1125 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1126 // eliminate all the truncates, or we replace other casts with truncates.
1127 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1128 SmallVector<const SCEV *, 4> Operands;
1129 bool hasTrunc = false;
1130 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1131 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1132 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1133 hasTrunc = isa<SCEVTruncateExpr>(S);
1134 Operands.push_back(S);
1137 return getMulExpr(Operands);
1138 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1141 // If the input value is a chrec scev, truncate the chrec's operands.
1142 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1143 SmallVector<const SCEV *, 4> Operands;
1144 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1145 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
1146 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1149 // The cast wasn't folded; create an explicit cast node. We can reuse
1150 // the existing insert position since if we get here, we won't have
1151 // made any changes which would invalidate it.
1152 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1154 UniqueSCEVs.InsertNode(S, IP);
1158 // Get the limit of a recurrence such that incrementing by Step cannot cause
1159 // signed overflow as long as the value of the recurrence within the
1160 // loop does not exceed this limit before incrementing.
1161 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1162 ICmpInst::Predicate *Pred,
1163 ScalarEvolution *SE) {
1164 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1165 if (SE->isKnownPositive(Step)) {
1166 *Pred = ICmpInst::ICMP_SLT;
1167 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1168 SE->getSignedRange(Step).getSignedMax());
1170 if (SE->isKnownNegative(Step)) {
1171 *Pred = ICmpInst::ICMP_SGT;
1172 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1173 SE->getSignedRange(Step).getSignedMin());
1178 // Get the limit of a recurrence such that incrementing by Step cannot cause
1179 // unsigned overflow as long as the value of the recurrence within the loop does
1180 // not exceed this limit before incrementing.
1181 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1182 ICmpInst::Predicate *Pred,
1183 ScalarEvolution *SE) {
1184 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1185 *Pred = ICmpInst::ICMP_ULT;
1187 return SE->getConstant(APInt::getMinValue(BitWidth) -
1188 SE->getUnsignedRange(Step).getUnsignedMax());
1193 struct ExtendOpTraitsBase {
1194 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1197 // Used to make code generic over signed and unsigned overflow.
1198 template <typename ExtendOp> struct ExtendOpTraits {
1201 // static const SCEV::NoWrapFlags WrapType;
1203 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1205 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1206 // ICmpInst::Predicate *Pred,
1207 // ScalarEvolution *SE);
1211 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1212 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1214 static const GetExtendExprTy GetExtendExpr;
1216 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1217 ICmpInst::Predicate *Pred,
1218 ScalarEvolution *SE) {
1219 return getSignedOverflowLimitForStep(Step, Pred, SE);
1223 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1224 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1227 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1228 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1230 static const GetExtendExprTy GetExtendExpr;
1232 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1233 ICmpInst::Predicate *Pred,
1234 ScalarEvolution *SE) {
1235 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1239 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1240 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1243 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1244 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1245 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1246 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1247 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1248 // expression "Step + sext/zext(PreIncAR)" is congruent with
1249 // "sext/zext(PostIncAR)"
1250 template <typename ExtendOpTy>
1251 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1252 ScalarEvolution *SE) {
1253 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1254 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1256 const Loop *L = AR->getLoop();
1257 const SCEV *Start = AR->getStart();
1258 const SCEV *Step = AR->getStepRecurrence(*SE);
1260 // Check for a simple looking step prior to loop entry.
1261 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1265 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1266 // subtraction is expensive. For this purpose, perform a quick and dirty
1267 // difference, by checking for Step in the operand list.
1268 SmallVector<const SCEV *, 4> DiffOps;
1269 for (const SCEV *Op : SA->operands())
1271 DiffOps.push_back(Op);
1273 if (DiffOps.size() == SA->getNumOperands())
1276 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1279 // 1. NSW/NUW flags on the step increment.
1280 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1281 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1282 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1284 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1285 // "S+X does not sign/unsign-overflow".
1288 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1289 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1290 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1293 // 2. Direct overflow check on the step operation's expression.
1294 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1295 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1296 const SCEV *OperandExtendedStart =
1297 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1298 (SE->*GetExtendExpr)(Step, WideTy));
1299 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1300 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1301 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1302 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1303 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1304 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1309 // 3. Loop precondition.
1310 ICmpInst::Predicate Pred;
1311 const SCEV *OverflowLimit =
1312 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1314 if (OverflowLimit &&
1315 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1321 // Get the normalized zero or sign extended expression for this AddRec's Start.
1322 template <typename ExtendOpTy>
1323 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1324 ScalarEvolution *SE) {
1325 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1327 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1329 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1331 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1332 (SE->*GetExtendExpr)(PreStart, Ty));
1335 // Try to prove away overflow by looking at "nearby" add recurrences. A
1336 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1337 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1341 // {S,+,X} == {S-T,+,X} + T
1342 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1344 // If ({S-T,+,X} + T) does not overflow ... (1)
1346 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1348 // If {S-T,+,X} does not overflow ... (2)
1350 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1351 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1353 // If (S-T)+T does not overflow ... (3)
1355 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1356 // == {Ext(S),+,Ext(X)} == LHS
1358 // Thus, if (1), (2) and (3) are true for some T, then
1359 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1361 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1362 // does not overflow" restricted to the 0th iteration. Therefore we only need
1363 // to check for (1) and (2).
1365 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1366 // is `Delta` (defined below).
1368 template <typename ExtendOpTy>
1369 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1372 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1374 // We restrict `Start` to a constant to prevent SCEV from spending too much
1375 // time here. It is correct (but more expensive) to continue with a
1376 // non-constant `Start` and do a general SCEV subtraction to compute
1377 // `PreStart` below.
1379 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1383 APInt StartAI = StartC->getValue()->getValue();
1385 for (unsigned Delta : {-2, -1, 1, 2}) {
1386 const SCEV *PreStart = getConstant(StartAI - Delta);
1388 // Give up if we don't already have the add recurrence we need because
1389 // actually constructing an add recurrence is relatively expensive.
1390 const SCEVAddRecExpr *PreAR = [&]() {
1391 FoldingSetNodeID ID;
1392 ID.AddInteger(scAddRecExpr);
1393 ID.AddPointer(PreStart);
1394 ID.AddPointer(Step);
1397 return static_cast<SCEVAddRecExpr *>(
1398 this->UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1401 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1402 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1403 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1404 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1405 DeltaS, &Pred, this);
1406 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1414 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1416 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1417 "This is not an extending conversion!");
1418 assert(isSCEVable(Ty) &&
1419 "This is not a conversion to a SCEVable type!");
1420 Ty = getEffectiveSCEVType(Ty);
1422 // Fold if the operand is constant.
1423 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1425 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1427 // zext(zext(x)) --> zext(x)
1428 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1429 return getZeroExtendExpr(SZ->getOperand(), Ty);
1431 // Before doing any expensive analysis, check to see if we've already
1432 // computed a SCEV for this Op and Ty.
1433 FoldingSetNodeID ID;
1434 ID.AddInteger(scZeroExtend);
1438 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1440 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1441 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1442 // It's possible the bits taken off by the truncate were all zero bits. If
1443 // so, we should be able to simplify this further.
1444 const SCEV *X = ST->getOperand();
1445 ConstantRange CR = getUnsignedRange(X);
1446 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1447 unsigned NewBits = getTypeSizeInBits(Ty);
1448 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1449 CR.zextOrTrunc(NewBits)))
1450 return getTruncateOrZeroExtend(X, Ty);
1453 // If the input value is a chrec scev, and we can prove that the value
1454 // did not overflow the old, smaller, value, we can zero extend all of the
1455 // operands (often constants). This allows analysis of something like
1456 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1457 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1458 if (AR->isAffine()) {
1459 const SCEV *Start = AR->getStart();
1460 const SCEV *Step = AR->getStepRecurrence(*this);
1461 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1462 const Loop *L = AR->getLoop();
1464 // If we have special knowledge that this addrec won't overflow,
1465 // we don't need to do any further analysis.
1466 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1467 return getAddRecExpr(
1468 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1469 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1471 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1472 // Note that this serves two purposes: It filters out loops that are
1473 // simply not analyzable, and it covers the case where this code is
1474 // being called from within backedge-taken count analysis, such that
1475 // attempting to ask for the backedge-taken count would likely result
1476 // in infinite recursion. In the later case, the analysis code will
1477 // cope with a conservative value, and it will take care to purge
1478 // that value once it has finished.
1479 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1480 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1481 // Manually compute the final value for AR, checking for
1484 // Check whether the backedge-taken count can be losslessly casted to
1485 // the addrec's type. The count is always unsigned.
1486 const SCEV *CastedMaxBECount =
1487 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1488 const SCEV *RecastedMaxBECount =
1489 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1490 if (MaxBECount == RecastedMaxBECount) {
1491 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1492 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1493 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1494 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1495 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1496 const SCEV *WideMaxBECount =
1497 getZeroExtendExpr(CastedMaxBECount, WideTy);
1498 const SCEV *OperandExtendedAdd =
1499 getAddExpr(WideStart,
1500 getMulExpr(WideMaxBECount,
1501 getZeroExtendExpr(Step, WideTy)));
1502 if (ZAdd == OperandExtendedAdd) {
1503 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1504 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1505 // Return the expression with the addrec on the outside.
1506 return getAddRecExpr(
1507 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1508 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1510 // Similar to above, only this time treat the step value as signed.
1511 // This covers loops that count down.
1512 OperandExtendedAdd =
1513 getAddExpr(WideStart,
1514 getMulExpr(WideMaxBECount,
1515 getSignExtendExpr(Step, WideTy)));
1516 if (ZAdd == OperandExtendedAdd) {
1517 // Cache knowledge of AR NW, which is propagated to this AddRec.
1518 // Negative step causes unsigned wrap, but it still can't self-wrap.
1519 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1520 // Return the expression with the addrec on the outside.
1521 return getAddRecExpr(
1522 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1523 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1527 // If the backedge is guarded by a comparison with the pre-inc value
1528 // the addrec is safe. Also, if the entry is guarded by a comparison
1529 // with the start value and the backedge is guarded by a comparison
1530 // with the post-inc value, the addrec is safe.
1531 if (isKnownPositive(Step)) {
1532 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1533 getUnsignedRange(Step).getUnsignedMax());
1534 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1535 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1536 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1537 AR->getPostIncExpr(*this), N))) {
1538 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1539 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1540 // Return the expression with the addrec on the outside.
1541 return getAddRecExpr(
1542 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1543 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1545 } else if (isKnownNegative(Step)) {
1546 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1547 getSignedRange(Step).getSignedMin());
1548 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1549 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1550 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1551 AR->getPostIncExpr(*this), N))) {
1552 // Cache knowledge of AR NW, which is propagated to this AddRec.
1553 // Negative step causes unsigned wrap, but it still can't self-wrap.
1554 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1555 // Return the expression with the addrec on the outside.
1556 return getAddRecExpr(
1557 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1558 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1563 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1564 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1565 return getAddRecExpr(
1566 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1567 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1571 // The cast wasn't folded; create an explicit cast node.
1572 // Recompute the insert position, as it may have been invalidated.
1573 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1574 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1576 UniqueSCEVs.InsertNode(S, IP);
1580 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1582 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1583 "This is not an extending conversion!");
1584 assert(isSCEVable(Ty) &&
1585 "This is not a conversion to a SCEVable type!");
1586 Ty = getEffectiveSCEVType(Ty);
1588 // Fold if the operand is constant.
1589 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1591 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1593 // sext(sext(x)) --> sext(x)
1594 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1595 return getSignExtendExpr(SS->getOperand(), Ty);
1597 // sext(zext(x)) --> zext(x)
1598 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1599 return getZeroExtendExpr(SZ->getOperand(), Ty);
1601 // Before doing any expensive analysis, check to see if we've already
1602 // computed a SCEV for this Op and Ty.
1603 FoldingSetNodeID ID;
1604 ID.AddInteger(scSignExtend);
1608 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1610 // If the input value is provably positive, build a zext instead.
1611 if (isKnownNonNegative(Op))
1612 return getZeroExtendExpr(Op, Ty);
1614 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1615 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1616 // It's possible the bits taken off by the truncate were all sign bits. If
1617 // so, we should be able to simplify this further.
1618 const SCEV *X = ST->getOperand();
1619 ConstantRange CR = getSignedRange(X);
1620 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1621 unsigned NewBits = getTypeSizeInBits(Ty);
1622 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1623 CR.sextOrTrunc(NewBits)))
1624 return getTruncateOrSignExtend(X, Ty);
1627 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1628 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1629 if (SA->getNumOperands() == 2) {
1630 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1631 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1633 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1634 const APInt &C1 = SC1->getValue()->getValue();
1635 const APInt &C2 = SC2->getValue()->getValue();
1636 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1637 C2.ugt(C1) && C2.isPowerOf2())
1638 return getAddExpr(getSignExtendExpr(SC1, Ty),
1639 getSignExtendExpr(SMul, Ty));
1644 // If the input value is a chrec scev, and we can prove that the value
1645 // did not overflow the old, smaller, value, we can sign extend all of the
1646 // operands (often constants). This allows analysis of something like
1647 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1648 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1649 if (AR->isAffine()) {
1650 const SCEV *Start = AR->getStart();
1651 const SCEV *Step = AR->getStepRecurrence(*this);
1652 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1653 const Loop *L = AR->getLoop();
1655 // If we have special knowledge that this addrec won't overflow,
1656 // we don't need to do any further analysis.
1657 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1658 return getAddRecExpr(
1659 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1660 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1662 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1663 // Note that this serves two purposes: It filters out loops that are
1664 // simply not analyzable, and it covers the case where this code is
1665 // being called from within backedge-taken count analysis, such that
1666 // attempting to ask for the backedge-taken count would likely result
1667 // in infinite recursion. In the later case, the analysis code will
1668 // cope with a conservative value, and it will take care to purge
1669 // that value once it has finished.
1670 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1671 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1672 // Manually compute the final value for AR, checking for
1675 // Check whether the backedge-taken count can be losslessly casted to
1676 // the addrec's type. The count is always unsigned.
1677 const SCEV *CastedMaxBECount =
1678 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1679 const SCEV *RecastedMaxBECount =
1680 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1681 if (MaxBECount == RecastedMaxBECount) {
1682 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1683 // Check whether Start+Step*MaxBECount has no signed overflow.
1684 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1685 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1686 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1687 const SCEV *WideMaxBECount =
1688 getZeroExtendExpr(CastedMaxBECount, WideTy);
1689 const SCEV *OperandExtendedAdd =
1690 getAddExpr(WideStart,
1691 getMulExpr(WideMaxBECount,
1692 getSignExtendExpr(Step, WideTy)));
1693 if (SAdd == OperandExtendedAdd) {
1694 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1695 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1696 // Return the expression with the addrec on the outside.
1697 return getAddRecExpr(
1698 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1699 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1701 // Similar to above, only this time treat the step value as unsigned.
1702 // This covers loops that count up with an unsigned step.
1703 OperandExtendedAdd =
1704 getAddExpr(WideStart,
1705 getMulExpr(WideMaxBECount,
1706 getZeroExtendExpr(Step, WideTy)));
1707 if (SAdd == OperandExtendedAdd) {
1708 // If AR wraps around then
1710 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1711 // => SAdd != OperandExtendedAdd
1713 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1714 // (SAdd == OperandExtendedAdd => AR is NW)
1716 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1718 // Return the expression with the addrec on the outside.
1719 return getAddRecExpr(
1720 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1721 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1725 // If the backedge is guarded by a comparison with the pre-inc value
1726 // the addrec is safe. Also, if the entry is guarded by a comparison
1727 // with the start value and the backedge is guarded by a comparison
1728 // with the post-inc value, the addrec is safe.
1729 ICmpInst::Predicate Pred;
1730 const SCEV *OverflowLimit =
1731 getSignedOverflowLimitForStep(Step, &Pred, this);
1732 if (OverflowLimit &&
1733 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1734 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1735 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1737 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1738 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1739 return getAddRecExpr(
1740 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1741 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1744 // If Start and Step are constants, check if we can apply this
1746 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1747 auto SC1 = dyn_cast<SCEVConstant>(Start);
1748 auto SC2 = dyn_cast<SCEVConstant>(Step);
1750 const APInt &C1 = SC1->getValue()->getValue();
1751 const APInt &C2 = SC2->getValue()->getValue();
1752 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1754 Start = getSignExtendExpr(Start, Ty);
1755 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1756 L, AR->getNoWrapFlags());
1757 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1761 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1762 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1763 return getAddRecExpr(
1764 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1765 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1769 // The cast wasn't folded; create an explicit cast node.
1770 // Recompute the insert position, as it may have been invalidated.
1771 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1772 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1774 UniqueSCEVs.InsertNode(S, IP);
1778 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1779 /// unspecified bits out to the given type.
1781 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1783 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1784 "This is not an extending conversion!");
1785 assert(isSCEVable(Ty) &&
1786 "This is not a conversion to a SCEVable type!");
1787 Ty = getEffectiveSCEVType(Ty);
1789 // Sign-extend negative constants.
1790 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1791 if (SC->getValue()->getValue().isNegative())
1792 return getSignExtendExpr(Op, Ty);
1794 // Peel off a truncate cast.
1795 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1796 const SCEV *NewOp = T->getOperand();
1797 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1798 return getAnyExtendExpr(NewOp, Ty);
1799 return getTruncateOrNoop(NewOp, Ty);
1802 // Next try a zext cast. If the cast is folded, use it.
1803 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1804 if (!isa<SCEVZeroExtendExpr>(ZExt))
1807 // Next try a sext cast. If the cast is folded, use it.
1808 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1809 if (!isa<SCEVSignExtendExpr>(SExt))
1812 // Force the cast to be folded into the operands of an addrec.
1813 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1814 SmallVector<const SCEV *, 4> Ops;
1815 for (const SCEV *Op : AR->operands())
1816 Ops.push_back(getAnyExtendExpr(Op, Ty));
1817 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1820 // If the expression is obviously signed, use the sext cast value.
1821 if (isa<SCEVSMaxExpr>(Op))
1824 // Absent any other information, use the zext cast value.
1828 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1829 /// a list of operands to be added under the given scale, update the given
1830 /// map. This is a helper function for getAddRecExpr. As an example of
1831 /// what it does, given a sequence of operands that would form an add
1832 /// expression like this:
1834 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1836 /// where A and B are constants, update the map with these values:
1838 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1840 /// and add 13 + A*B*29 to AccumulatedConstant.
1841 /// This will allow getAddRecExpr to produce this:
1843 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1845 /// This form often exposes folding opportunities that are hidden in
1846 /// the original operand list.
1848 /// Return true iff it appears that any interesting folding opportunities
1849 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1850 /// the common case where no interesting opportunities are present, and
1851 /// is also used as a check to avoid infinite recursion.
1854 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1855 SmallVectorImpl<const SCEV *> &NewOps,
1856 APInt &AccumulatedConstant,
1857 const SCEV *const *Ops, size_t NumOperands,
1859 ScalarEvolution &SE) {
1860 bool Interesting = false;
1862 // Iterate over the add operands. They are sorted, with constants first.
1864 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1866 // Pull a buried constant out to the outside.
1867 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1869 AccumulatedConstant += Scale * C->getValue()->getValue();
1872 // Next comes everything else. We're especially interested in multiplies
1873 // here, but they're in the middle, so just visit the rest with one loop.
1874 for (; i != NumOperands; ++i) {
1875 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1876 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1878 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1879 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1880 // A multiplication of a constant with another add; recurse.
1881 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1883 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1884 Add->op_begin(), Add->getNumOperands(),
1887 // A multiplication of a constant with some other value. Update
1889 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1890 const SCEV *Key = SE.getMulExpr(MulOps);
1891 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1892 M.insert(std::make_pair(Key, NewScale));
1894 NewOps.push_back(Pair.first->first);
1896 Pair.first->second += NewScale;
1897 // The map already had an entry for this value, which may indicate
1898 // a folding opportunity.
1903 // An ordinary operand. Update the map.
1904 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1905 M.insert(std::make_pair(Ops[i], Scale));
1907 NewOps.push_back(Pair.first->first);
1909 Pair.first->second += Scale;
1910 // The map already had an entry for this value, which may indicate
1911 // a folding opportunity.
1921 struct APIntCompare {
1922 bool operator()(const APInt &LHS, const APInt &RHS) const {
1923 return LHS.ult(RHS);
1928 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1929 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1930 // can't-overflow flags for the operation if possible.
1931 static SCEV::NoWrapFlags
1932 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1933 const SmallVectorImpl<const SCEV *> &Ops,
1934 SCEV::NoWrapFlags OldFlags) {
1935 using namespace std::placeholders;
1938 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1940 assert(CanAnalyze && "don't call from other places!");
1942 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1943 SCEV::NoWrapFlags SignOrUnsignWrap =
1944 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1946 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1947 auto IsKnownNonNegative =
1948 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1950 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1951 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1952 return ScalarEvolution::setFlags(OldFlags,
1953 (SCEV::NoWrapFlags)SignOrUnsignMask);
1958 /// getAddExpr - Get a canonical add expression, or something simpler if
1960 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1961 SCEV::NoWrapFlags Flags) {
1962 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1963 "only nuw or nsw allowed");
1964 assert(!Ops.empty() && "Cannot get empty add!");
1965 if (Ops.size() == 1) return Ops[0];
1967 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1968 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1969 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1970 "SCEVAddExpr operand types don't match!");
1973 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1975 // Sort by complexity, this groups all similar expression types together.
1976 GroupByComplexity(Ops, &LI);
1978 // If there are any constants, fold them together.
1980 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1982 assert(Idx < Ops.size());
1983 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1984 // We found two constants, fold them together!
1985 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1986 RHSC->getValue()->getValue());
1987 if (Ops.size() == 2) return Ops[0];
1988 Ops.erase(Ops.begin()+1); // Erase the folded element
1989 LHSC = cast<SCEVConstant>(Ops[0]);
1992 // If we are left with a constant zero being added, strip it off.
1993 if (LHSC->getValue()->isZero()) {
1994 Ops.erase(Ops.begin());
1998 if (Ops.size() == 1) return Ops[0];
2001 // Okay, check to see if the same value occurs in the operand list more than
2002 // once. If so, merge them together into an multiply expression. Since we
2003 // sorted the list, these values are required to be adjacent.
2004 Type *Ty = Ops[0]->getType();
2005 bool FoundMatch = false;
2006 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2007 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2008 // Scan ahead to count how many equal operands there are.
2010 while (i+Count != e && Ops[i+Count] == Ops[i])
2012 // Merge the values into a multiply.
2013 const SCEV *Scale = getConstant(Ty, Count);
2014 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2015 if (Ops.size() == Count)
2018 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2019 --i; e -= Count - 1;
2023 return getAddExpr(Ops, Flags);
2025 // Check for truncates. If all the operands are truncated from the same
2026 // type, see if factoring out the truncate would permit the result to be
2027 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2028 // if the contents of the resulting outer trunc fold to something simple.
2029 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2030 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2031 Type *DstType = Trunc->getType();
2032 Type *SrcType = Trunc->getOperand()->getType();
2033 SmallVector<const SCEV *, 8> LargeOps;
2035 // Check all the operands to see if they can be represented in the
2036 // source type of the truncate.
2037 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2038 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2039 if (T->getOperand()->getType() != SrcType) {
2043 LargeOps.push_back(T->getOperand());
2044 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2045 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2046 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2047 SmallVector<const SCEV *, 8> LargeMulOps;
2048 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2049 if (const SCEVTruncateExpr *T =
2050 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2051 if (T->getOperand()->getType() != SrcType) {
2055 LargeMulOps.push_back(T->getOperand());
2056 } else if (const SCEVConstant *C =
2057 dyn_cast<SCEVConstant>(M->getOperand(j))) {
2058 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2065 LargeOps.push_back(getMulExpr(LargeMulOps));
2072 // Evaluate the expression in the larger type.
2073 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2074 // If it folds to something simple, use it. Otherwise, don't.
2075 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2076 return getTruncateExpr(Fold, DstType);
2080 // Skip past any other cast SCEVs.
2081 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2084 // If there are add operands they would be next.
2085 if (Idx < Ops.size()) {
2086 bool DeletedAdd = false;
2087 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2088 // If we have an add, expand the add operands onto the end of the operands
2090 Ops.erase(Ops.begin()+Idx);
2091 Ops.append(Add->op_begin(), Add->op_end());
2095 // If we deleted at least one add, we added operands to the end of the list,
2096 // and they are not necessarily sorted. Recurse to resort and resimplify
2097 // any operands we just acquired.
2099 return getAddExpr(Ops);
2102 // Skip over the add expression until we get to a multiply.
2103 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2106 // Check to see if there are any folding opportunities present with
2107 // operands multiplied by constant values.
2108 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2109 uint64_t BitWidth = getTypeSizeInBits(Ty);
2110 DenseMap<const SCEV *, APInt> M;
2111 SmallVector<const SCEV *, 8> NewOps;
2112 APInt AccumulatedConstant(BitWidth, 0);
2113 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2114 Ops.data(), Ops.size(),
2115 APInt(BitWidth, 1), *this)) {
2116 // Some interesting folding opportunity is present, so its worthwhile to
2117 // re-generate the operands list. Group the operands by constant scale,
2118 // to avoid multiplying by the same constant scale multiple times.
2119 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2120 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
2121 E = NewOps.end(); I != E; ++I)
2122 MulOpLists[M.find(*I)->second].push_back(*I);
2123 // Re-generate the operands list.
2125 if (AccumulatedConstant != 0)
2126 Ops.push_back(getConstant(AccumulatedConstant));
2127 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
2128 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
2130 Ops.push_back(getMulExpr(getConstant(I->first),
2131 getAddExpr(I->second)));
2133 return getConstant(Ty, 0);
2134 if (Ops.size() == 1)
2136 return getAddExpr(Ops);
2140 // If we are adding something to a multiply expression, make sure the
2141 // something is not already an operand of the multiply. If so, merge it into
2143 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2144 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2145 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2146 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2147 if (isa<SCEVConstant>(MulOpSCEV))
2149 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2150 if (MulOpSCEV == Ops[AddOp]) {
2151 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2152 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2153 if (Mul->getNumOperands() != 2) {
2154 // If the multiply has more than two operands, we must get the
2156 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2157 Mul->op_begin()+MulOp);
2158 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2159 InnerMul = getMulExpr(MulOps);
2161 const SCEV *One = getConstant(Ty, 1);
2162 const SCEV *AddOne = getAddExpr(One, InnerMul);
2163 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2164 if (Ops.size() == 2) return OuterMul;
2166 Ops.erase(Ops.begin()+AddOp);
2167 Ops.erase(Ops.begin()+Idx-1);
2169 Ops.erase(Ops.begin()+Idx);
2170 Ops.erase(Ops.begin()+AddOp-1);
2172 Ops.push_back(OuterMul);
2173 return getAddExpr(Ops);
2176 // Check this multiply against other multiplies being added together.
2177 for (unsigned OtherMulIdx = Idx+1;
2178 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2180 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2181 // If MulOp occurs in OtherMul, we can fold the two multiplies
2183 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2184 OMulOp != e; ++OMulOp)
2185 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2186 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2187 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2188 if (Mul->getNumOperands() != 2) {
2189 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2190 Mul->op_begin()+MulOp);
2191 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2192 InnerMul1 = getMulExpr(MulOps);
2194 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2195 if (OtherMul->getNumOperands() != 2) {
2196 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2197 OtherMul->op_begin()+OMulOp);
2198 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2199 InnerMul2 = getMulExpr(MulOps);
2201 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2202 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2203 if (Ops.size() == 2) return OuterMul;
2204 Ops.erase(Ops.begin()+Idx);
2205 Ops.erase(Ops.begin()+OtherMulIdx-1);
2206 Ops.push_back(OuterMul);
2207 return getAddExpr(Ops);
2213 // If there are any add recurrences in the operands list, see if any other
2214 // added values are loop invariant. If so, we can fold them into the
2216 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2219 // Scan over all recurrences, trying to fold loop invariants into them.
2220 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2221 // Scan all of the other operands to this add and add them to the vector if
2222 // they are loop invariant w.r.t. the recurrence.
2223 SmallVector<const SCEV *, 8> LIOps;
2224 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2225 const Loop *AddRecLoop = AddRec->getLoop();
2226 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2227 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2228 LIOps.push_back(Ops[i]);
2229 Ops.erase(Ops.begin()+i);
2233 // If we found some loop invariants, fold them into the recurrence.
2234 if (!LIOps.empty()) {
2235 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2236 LIOps.push_back(AddRec->getStart());
2238 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2240 AddRecOps[0] = getAddExpr(LIOps);
2242 // Build the new addrec. Propagate the NUW and NSW flags if both the
2243 // outer add and the inner addrec are guaranteed to have no overflow.
2244 // Always propagate NW.
2245 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2246 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2248 // If all of the other operands were loop invariant, we are done.
2249 if (Ops.size() == 1) return NewRec;
2251 // Otherwise, add the folded AddRec by the non-invariant parts.
2252 for (unsigned i = 0;; ++i)
2253 if (Ops[i] == AddRec) {
2257 return getAddExpr(Ops);
2260 // Okay, if there weren't any loop invariants to be folded, check to see if
2261 // there are multiple AddRec's with the same loop induction variable being
2262 // added together. If so, we can fold them.
2263 for (unsigned OtherIdx = Idx+1;
2264 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2266 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2267 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2268 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2270 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2272 if (const SCEVAddRecExpr *OtherAddRec =
2273 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2274 if (OtherAddRec->getLoop() == AddRecLoop) {
2275 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2277 if (i >= AddRecOps.size()) {
2278 AddRecOps.append(OtherAddRec->op_begin()+i,
2279 OtherAddRec->op_end());
2282 AddRecOps[i] = getAddExpr(AddRecOps[i],
2283 OtherAddRec->getOperand(i));
2285 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2287 // Step size has changed, so we cannot guarantee no self-wraparound.
2288 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2289 return getAddExpr(Ops);
2292 // Otherwise couldn't fold anything into this recurrence. Move onto the
2296 // Okay, it looks like we really DO need an add expr. Check to see if we
2297 // already have one, otherwise create a new one.
2298 FoldingSetNodeID ID;
2299 ID.AddInteger(scAddExpr);
2300 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2301 ID.AddPointer(Ops[i]);
2304 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2306 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2307 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2308 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2310 UniqueSCEVs.InsertNode(S, IP);
2312 S->setNoWrapFlags(Flags);
2316 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2318 if (j > 1 && k / j != i) Overflow = true;
2322 /// Compute the result of "n choose k", the binomial coefficient. If an
2323 /// intermediate computation overflows, Overflow will be set and the return will
2324 /// be garbage. Overflow is not cleared on absence of overflow.
2325 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2326 // We use the multiplicative formula:
2327 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2328 // At each iteration, we take the n-th term of the numeral and divide by the
2329 // (k-n)th term of the denominator. This division will always produce an
2330 // integral result, and helps reduce the chance of overflow in the
2331 // intermediate computations. However, we can still overflow even when the
2332 // final result would fit.
2334 if (n == 0 || n == k) return 1;
2335 if (k > n) return 0;
2341 for (uint64_t i = 1; i <= k; ++i) {
2342 r = umul_ov(r, n-(i-1), Overflow);
2348 /// Determine if any of the operands in this SCEV are a constant or if
2349 /// any of the add or multiply expressions in this SCEV contain a constant.
2350 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2351 SmallVector<const SCEV *, 4> Ops;
2352 Ops.push_back(StartExpr);
2353 while (!Ops.empty()) {
2354 const SCEV *CurrentExpr = Ops.pop_back_val();
2355 if (isa<SCEVConstant>(*CurrentExpr))
2358 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2359 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2360 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2366 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2368 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2369 SCEV::NoWrapFlags Flags) {
2370 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2371 "only nuw or nsw allowed");
2372 assert(!Ops.empty() && "Cannot get empty mul!");
2373 if (Ops.size() == 1) return Ops[0];
2375 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2376 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2377 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2378 "SCEVMulExpr operand types don't match!");
2381 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2383 // Sort by complexity, this groups all similar expression types together.
2384 GroupByComplexity(Ops, &LI);
2386 // If there are any constants, fold them together.
2388 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2390 // C1*(C2+V) -> C1*C2 + C1*V
2391 if (Ops.size() == 2)
2392 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2393 // If any of Add's ops are Adds or Muls with a constant,
2394 // apply this transformation as well.
2395 if (Add->getNumOperands() == 2)
2396 if (containsConstantSomewhere(Add))
2397 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2398 getMulExpr(LHSC, Add->getOperand(1)));
2401 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2402 // We found two constants, fold them together!
2403 ConstantInt *Fold = ConstantInt::get(getContext(),
2404 LHSC->getValue()->getValue() *
2405 RHSC->getValue()->getValue());
2406 Ops[0] = getConstant(Fold);
2407 Ops.erase(Ops.begin()+1); // Erase the folded element
2408 if (Ops.size() == 1) return Ops[0];
2409 LHSC = cast<SCEVConstant>(Ops[0]);
2412 // If we are left with a constant one being multiplied, strip it off.
2413 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2414 Ops.erase(Ops.begin());
2416 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2417 // If we have a multiply of zero, it will always be zero.
2419 } else if (Ops[0]->isAllOnesValue()) {
2420 // If we have a mul by -1 of an add, try distributing the -1 among the
2422 if (Ops.size() == 2) {
2423 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2424 SmallVector<const SCEV *, 4> NewOps;
2425 bool AnyFolded = false;
2426 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2427 E = Add->op_end(); I != E; ++I) {
2428 const SCEV *Mul = getMulExpr(Ops[0], *I);
2429 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2430 NewOps.push_back(Mul);
2433 return getAddExpr(NewOps);
2435 else if (const SCEVAddRecExpr *
2436 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2437 // Negation preserves a recurrence's no self-wrap property.
2438 SmallVector<const SCEV *, 4> Operands;
2439 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2440 E = AddRec->op_end(); I != E; ++I) {
2441 Operands.push_back(getMulExpr(Ops[0], *I));
2443 return getAddRecExpr(Operands, AddRec->getLoop(),
2444 AddRec->getNoWrapFlags(SCEV::FlagNW));
2449 if (Ops.size() == 1)
2453 // Skip over the add expression until we get to a multiply.
2454 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2457 // If there are mul operands inline them all into this expression.
2458 if (Idx < Ops.size()) {
2459 bool DeletedMul = false;
2460 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2461 // If we have an mul, expand the mul operands onto the end of the operands
2463 Ops.erase(Ops.begin()+Idx);
2464 Ops.append(Mul->op_begin(), Mul->op_end());
2468 // If we deleted at least one mul, we added operands to the end of the list,
2469 // and they are not necessarily sorted. Recurse to resort and resimplify
2470 // any operands we just acquired.
2472 return getMulExpr(Ops);
2475 // If there are any add recurrences in the operands list, see if any other
2476 // added values are loop invariant. If so, we can fold them into the
2478 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2481 // Scan over all recurrences, trying to fold loop invariants into them.
2482 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2483 // Scan all of the other operands to this mul and add them to the vector if
2484 // they are loop invariant w.r.t. the recurrence.
2485 SmallVector<const SCEV *, 8> LIOps;
2486 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2487 const Loop *AddRecLoop = AddRec->getLoop();
2488 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2489 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2490 LIOps.push_back(Ops[i]);
2491 Ops.erase(Ops.begin()+i);
2495 // If we found some loop invariants, fold them into the recurrence.
2496 if (!LIOps.empty()) {
2497 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2498 SmallVector<const SCEV *, 4> NewOps;
2499 NewOps.reserve(AddRec->getNumOperands());
2500 const SCEV *Scale = getMulExpr(LIOps);
2501 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2502 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2504 // Build the new addrec. Propagate the NUW and NSW flags if both the
2505 // outer mul and the inner addrec are guaranteed to have no overflow.
2507 // No self-wrap cannot be guaranteed after changing the step size, but
2508 // will be inferred if either NUW or NSW is true.
2509 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2510 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2512 // If all of the other operands were loop invariant, we are done.
2513 if (Ops.size() == 1) return NewRec;
2515 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2516 for (unsigned i = 0;; ++i)
2517 if (Ops[i] == AddRec) {
2521 return getMulExpr(Ops);
2524 // Okay, if there weren't any loop invariants to be folded, check to see if
2525 // there are multiple AddRec's with the same loop induction variable being
2526 // multiplied together. If so, we can fold them.
2528 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2529 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2530 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2531 // ]]],+,...up to x=2n}.
2532 // Note that the arguments to choose() are always integers with values
2533 // known at compile time, never SCEV objects.
2535 // The implementation avoids pointless extra computations when the two
2536 // addrec's are of different length (mathematically, it's equivalent to
2537 // an infinite stream of zeros on the right).
2538 bool OpsModified = false;
2539 for (unsigned OtherIdx = Idx+1;
2540 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2542 const SCEVAddRecExpr *OtherAddRec =
2543 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2544 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2547 bool Overflow = false;
2548 Type *Ty = AddRec->getType();
2549 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2550 SmallVector<const SCEV*, 7> AddRecOps;
2551 for (int x = 0, xe = AddRec->getNumOperands() +
2552 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2553 const SCEV *Term = getConstant(Ty, 0);
2554 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2555 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2556 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2557 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2558 z < ze && !Overflow; ++z) {
2559 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2561 if (LargerThan64Bits)
2562 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2564 Coeff = Coeff1*Coeff2;
2565 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2566 const SCEV *Term1 = AddRec->getOperand(y-z);
2567 const SCEV *Term2 = OtherAddRec->getOperand(z);
2568 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2571 AddRecOps.push_back(Term);
2574 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2576 if (Ops.size() == 2) return NewAddRec;
2577 Ops[Idx] = NewAddRec;
2578 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2580 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2586 return getMulExpr(Ops);
2588 // Otherwise couldn't fold anything into this recurrence. Move onto the
2592 // Okay, it looks like we really DO need an mul expr. Check to see if we
2593 // already have one, otherwise create a new one.
2594 FoldingSetNodeID ID;
2595 ID.AddInteger(scMulExpr);
2596 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2597 ID.AddPointer(Ops[i]);
2600 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2602 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2603 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2604 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2606 UniqueSCEVs.InsertNode(S, IP);
2608 S->setNoWrapFlags(Flags);
2612 /// getUDivExpr - Get a canonical unsigned division expression, or something
2613 /// simpler if possible.
2614 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2616 assert(getEffectiveSCEVType(LHS->getType()) ==
2617 getEffectiveSCEVType(RHS->getType()) &&
2618 "SCEVUDivExpr operand types don't match!");
2620 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2621 if (RHSC->getValue()->equalsInt(1))
2622 return LHS; // X udiv 1 --> x
2623 // If the denominator is zero, the result of the udiv is undefined. Don't
2624 // try to analyze it, because the resolution chosen here may differ from
2625 // the resolution chosen in other parts of the compiler.
2626 if (!RHSC->getValue()->isZero()) {
2627 // Determine if the division can be folded into the operands of
2629 // TODO: Generalize this to non-constants by using known-bits information.
2630 Type *Ty = LHS->getType();
2631 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2632 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2633 // For non-power-of-two values, effectively round the value up to the
2634 // nearest power of two.
2635 if (!RHSC->getValue()->getValue().isPowerOf2())
2637 IntegerType *ExtTy =
2638 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2639 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2640 if (const SCEVConstant *Step =
2641 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2642 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2643 const APInt &StepInt = Step->getValue()->getValue();
2644 const APInt &DivInt = RHSC->getValue()->getValue();
2645 if (!StepInt.urem(DivInt) &&
2646 getZeroExtendExpr(AR, ExtTy) ==
2647 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2648 getZeroExtendExpr(Step, ExtTy),
2649 AR->getLoop(), SCEV::FlagAnyWrap)) {
2650 SmallVector<const SCEV *, 4> Operands;
2651 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2652 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2653 return getAddRecExpr(Operands, AR->getLoop(),
2656 /// Get a canonical UDivExpr for a recurrence.
2657 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2658 // We can currently only fold X%N if X is constant.
2659 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2660 if (StartC && !DivInt.urem(StepInt) &&
2661 getZeroExtendExpr(AR, ExtTy) ==
2662 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2663 getZeroExtendExpr(Step, ExtTy),
2664 AR->getLoop(), SCEV::FlagAnyWrap)) {
2665 const APInt &StartInt = StartC->getValue()->getValue();
2666 const APInt &StartRem = StartInt.urem(StepInt);
2668 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2669 AR->getLoop(), SCEV::FlagNW);
2672 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2673 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2674 SmallVector<const SCEV *, 4> Operands;
2675 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2676 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2677 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2678 // Find an operand that's safely divisible.
2679 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2680 const SCEV *Op = M->getOperand(i);
2681 const SCEV *Div = getUDivExpr(Op, RHSC);
2682 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2683 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2686 return getMulExpr(Operands);
2690 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2691 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2692 SmallVector<const SCEV *, 4> Operands;
2693 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2694 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2695 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2697 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2698 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2699 if (isa<SCEVUDivExpr>(Op) ||
2700 getMulExpr(Op, RHS) != A->getOperand(i))
2702 Operands.push_back(Op);
2704 if (Operands.size() == A->getNumOperands())
2705 return getAddExpr(Operands);
2709 // Fold if both operands are constant.
2710 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2711 Constant *LHSCV = LHSC->getValue();
2712 Constant *RHSCV = RHSC->getValue();
2713 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2719 FoldingSetNodeID ID;
2720 ID.AddInteger(scUDivExpr);
2724 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2725 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2727 UniqueSCEVs.InsertNode(S, IP);
2731 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2732 APInt A = C1->getValue()->getValue().abs();
2733 APInt B = C2->getValue()->getValue().abs();
2734 uint32_t ABW = A.getBitWidth();
2735 uint32_t BBW = B.getBitWidth();
2742 return APIntOps::GreatestCommonDivisor(A, B);
2745 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2746 /// something simpler if possible. There is no representation for an exact udiv
2747 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2748 /// We can't do this when it's not exact because the udiv may be clearing bits.
2749 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2751 // TODO: we could try to find factors in all sorts of things, but for now we
2752 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2753 // end of this file for inspiration.
2755 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2757 return getUDivExpr(LHS, RHS);
2759 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2760 // If the mulexpr multiplies by a constant, then that constant must be the
2761 // first element of the mulexpr.
2762 if (const SCEVConstant *LHSCst =
2763 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2764 if (LHSCst == RHSCst) {
2765 SmallVector<const SCEV *, 2> Operands;
2766 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2767 return getMulExpr(Operands);
2770 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2771 // that there's a factor provided by one of the other terms. We need to
2773 APInt Factor = gcd(LHSCst, RHSCst);
2774 if (!Factor.isIntN(1)) {
2775 LHSCst = cast<SCEVConstant>(
2776 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2777 RHSCst = cast<SCEVConstant>(
2778 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2779 SmallVector<const SCEV *, 2> Operands;
2780 Operands.push_back(LHSCst);
2781 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2782 LHS = getMulExpr(Operands);
2784 Mul = dyn_cast<SCEVMulExpr>(LHS);
2786 return getUDivExactExpr(LHS, RHS);
2791 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2792 if (Mul->getOperand(i) == RHS) {
2793 SmallVector<const SCEV *, 2> Operands;
2794 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2795 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2796 return getMulExpr(Operands);
2800 return getUDivExpr(LHS, RHS);
2803 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2804 /// Simplify the expression as much as possible.
2805 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2807 SCEV::NoWrapFlags Flags) {
2808 SmallVector<const SCEV *, 4> Operands;
2809 Operands.push_back(Start);
2810 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2811 if (StepChrec->getLoop() == L) {
2812 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2813 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2816 Operands.push_back(Step);
2817 return getAddRecExpr(Operands, L, Flags);
2820 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2821 /// Simplify the expression as much as possible.
2823 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2824 const Loop *L, SCEV::NoWrapFlags Flags) {
2825 if (Operands.size() == 1) return Operands[0];
2827 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2828 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2829 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2830 "SCEVAddRecExpr operand types don't match!");
2831 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2832 assert(isLoopInvariant(Operands[i], L) &&
2833 "SCEVAddRecExpr operand is not loop-invariant!");
2836 if (Operands.back()->isZero()) {
2837 Operands.pop_back();
2838 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2841 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2842 // use that information to infer NUW and NSW flags. However, computing a
2843 // BE count requires calling getAddRecExpr, so we may not yet have a
2844 // meaningful BE count at this point (and if we don't, we'd be stuck
2845 // with a SCEVCouldNotCompute as the cached BE count).
2847 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2849 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2850 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2851 const Loop *NestedLoop = NestedAR->getLoop();
2852 if (L->contains(NestedLoop)
2853 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2854 : (!NestedLoop->contains(L) &&
2855 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2856 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2857 NestedAR->op_end());
2858 Operands[0] = NestedAR->getStart();
2859 // AddRecs require their operands be loop-invariant with respect to their
2860 // loops. Don't perform this transformation if it would break this
2862 bool AllInvariant = true;
2863 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2864 if (!isLoopInvariant(Operands[i], L)) {
2865 AllInvariant = false;
2869 // Create a recurrence for the outer loop with the same step size.
2871 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2872 // inner recurrence has the same property.
2873 SCEV::NoWrapFlags OuterFlags =
2874 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2876 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2877 AllInvariant = true;
2878 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2879 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2880 AllInvariant = false;
2884 // Ok, both add recurrences are valid after the transformation.
2886 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2887 // the outer recurrence has the same property.
2888 SCEV::NoWrapFlags InnerFlags =
2889 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2890 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2893 // Reset Operands to its original state.
2894 Operands[0] = NestedAR;
2898 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2899 // already have one, otherwise create a new one.
2900 FoldingSetNodeID ID;
2901 ID.AddInteger(scAddRecExpr);
2902 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2903 ID.AddPointer(Operands[i]);
2907 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2909 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2910 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2911 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2912 O, Operands.size(), L);
2913 UniqueSCEVs.InsertNode(S, IP);
2915 S->setNoWrapFlags(Flags);
2920 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2921 const SmallVectorImpl<const SCEV *> &IndexExprs,
2923 // getSCEV(Base)->getType() has the same address space as Base->getType()
2924 // because SCEV::getType() preserves the address space.
2925 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2926 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2927 // instruction to its SCEV, because the Instruction may be guarded by control
2928 // flow and the no-overflow bits may not be valid for the expression in any
2929 // context. This can be fixed similarly to how these flags are handled for
2931 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2933 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2934 // The address space is unimportant. The first thing we do on CurTy is getting
2935 // its element type.
2936 Type *CurTy = PointerType::getUnqual(PointeeType);
2937 for (const SCEV *IndexExpr : IndexExprs) {
2938 // Compute the (potentially symbolic) offset in bytes for this index.
2939 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2940 // For a struct, add the member offset.
2941 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2942 unsigned FieldNo = Index->getZExtValue();
2943 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2945 // Add the field offset to the running total offset.
2946 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2948 // Update CurTy to the type of the field at Index.
2949 CurTy = STy->getTypeAtIndex(Index);
2951 // Update CurTy to its element type.
2952 CurTy = cast<SequentialType>(CurTy)->getElementType();
2953 // For an array, add the element offset, explicitly scaled.
2954 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2955 // Getelementptr indices are signed.
2956 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2958 // Multiply the index by the element size to compute the element offset.
2959 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2961 // Add the element offset to the running total offset.
2962 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2966 // Add the total offset from all the GEP indices to the base.
2967 return getAddExpr(BaseExpr, TotalOffset, Wrap);
2970 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2972 SmallVector<const SCEV *, 2> Ops;
2975 return getSMaxExpr(Ops);
2979 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2980 assert(!Ops.empty() && "Cannot get empty smax!");
2981 if (Ops.size() == 1) return Ops[0];
2983 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2984 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2985 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2986 "SCEVSMaxExpr operand types don't match!");
2989 // Sort by complexity, this groups all similar expression types together.
2990 GroupByComplexity(Ops, &LI);
2992 // If there are any constants, fold them together.
2994 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2996 assert(Idx < Ops.size());
2997 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2998 // We found two constants, fold them together!
2999 ConstantInt *Fold = ConstantInt::get(getContext(),
3000 APIntOps::smax(LHSC->getValue()->getValue(),
3001 RHSC->getValue()->getValue()));
3002 Ops[0] = getConstant(Fold);
3003 Ops.erase(Ops.begin()+1); // Erase the folded element
3004 if (Ops.size() == 1) return Ops[0];
3005 LHSC = cast<SCEVConstant>(Ops[0]);
3008 // If we are left with a constant minimum-int, strip it off.
3009 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3010 Ops.erase(Ops.begin());
3012 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3013 // If we have an smax with a constant maximum-int, it will always be
3018 if (Ops.size() == 1) return Ops[0];
3021 // Find the first SMax
3022 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3025 // Check to see if one of the operands is an SMax. If so, expand its operands
3026 // onto our operand list, and recurse to simplify.
3027 if (Idx < Ops.size()) {
3028 bool DeletedSMax = false;
3029 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3030 Ops.erase(Ops.begin()+Idx);
3031 Ops.append(SMax->op_begin(), SMax->op_end());
3036 return getSMaxExpr(Ops);
3039 // Okay, check to see if the same value occurs in the operand list twice. If
3040 // so, delete one. Since we sorted the list, these values are required to
3042 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3043 // X smax Y smax Y --> X smax Y
3044 // X smax Y --> X, if X is always greater than Y
3045 if (Ops[i] == Ops[i+1] ||
3046 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3047 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3049 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3050 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3054 if (Ops.size() == 1) return Ops[0];
3056 assert(!Ops.empty() && "Reduced smax down to nothing!");
3058 // Okay, it looks like we really DO need an smax expr. Check to see if we
3059 // already have one, otherwise create a new one.
3060 FoldingSetNodeID ID;
3061 ID.AddInteger(scSMaxExpr);
3062 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3063 ID.AddPointer(Ops[i]);
3065 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3066 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3067 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3068 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3070 UniqueSCEVs.InsertNode(S, IP);
3074 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3076 SmallVector<const SCEV *, 2> Ops;
3079 return getUMaxExpr(Ops);
3083 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3084 assert(!Ops.empty() && "Cannot get empty umax!");
3085 if (Ops.size() == 1) return Ops[0];
3087 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3088 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3089 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3090 "SCEVUMaxExpr operand types don't match!");
3093 // Sort by complexity, this groups all similar expression types together.
3094 GroupByComplexity(Ops, &LI);
3096 // If there are any constants, fold them together.
3098 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3100 assert(Idx < Ops.size());
3101 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3102 // We found two constants, fold them together!
3103 ConstantInt *Fold = ConstantInt::get(getContext(),
3104 APIntOps::umax(LHSC->getValue()->getValue(),
3105 RHSC->getValue()->getValue()));
3106 Ops[0] = getConstant(Fold);
3107 Ops.erase(Ops.begin()+1); // Erase the folded element
3108 if (Ops.size() == 1) return Ops[0];
3109 LHSC = cast<SCEVConstant>(Ops[0]);
3112 // If we are left with a constant minimum-int, strip it off.
3113 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3114 Ops.erase(Ops.begin());
3116 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3117 // If we have an umax with a constant maximum-int, it will always be
3122 if (Ops.size() == 1) return Ops[0];
3125 // Find the first UMax
3126 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3129 // Check to see if one of the operands is a UMax. If so, expand its operands
3130 // onto our operand list, and recurse to simplify.
3131 if (Idx < Ops.size()) {
3132 bool DeletedUMax = false;
3133 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3134 Ops.erase(Ops.begin()+Idx);
3135 Ops.append(UMax->op_begin(), UMax->op_end());
3140 return getUMaxExpr(Ops);
3143 // Okay, check to see if the same value occurs in the operand list twice. If
3144 // so, delete one. Since we sorted the list, these values are required to
3146 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3147 // X umax Y umax Y --> X umax Y
3148 // X umax Y --> X, if X is always greater than Y
3149 if (Ops[i] == Ops[i+1] ||
3150 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3151 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3153 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3154 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3158 if (Ops.size() == 1) return Ops[0];
3160 assert(!Ops.empty() && "Reduced umax down to nothing!");
3162 // Okay, it looks like we really DO need a umax expr. Check to see if we
3163 // already have one, otherwise create a new one.
3164 FoldingSetNodeID ID;
3165 ID.AddInteger(scUMaxExpr);
3166 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3167 ID.AddPointer(Ops[i]);
3169 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3170 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3171 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3172 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3174 UniqueSCEVs.InsertNode(S, IP);
3178 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3180 // ~smax(~x, ~y) == smin(x, y).
3181 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3184 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3186 // ~umax(~x, ~y) == umin(x, y)
3187 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3190 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3191 // We can bypass creating a target-independent
3192 // constant expression and then folding it back into a ConstantInt.
3193 // This is just a compile-time optimization.
3194 return getConstant(IntTy,
3195 F.getParent()->getDataLayout().getTypeAllocSize(AllocTy));
3198 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3201 // We can bypass creating a target-independent
3202 // constant expression and then folding it back into a ConstantInt.
3203 // This is just a compile-time optimization.
3206 F.getParent()->getDataLayout().getStructLayout(STy)->getElementOffset(
3210 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3211 // Don't attempt to do anything other than create a SCEVUnknown object
3212 // here. createSCEV only calls getUnknown after checking for all other
3213 // interesting possibilities, and any other code that calls getUnknown
3214 // is doing so in order to hide a value from SCEV canonicalization.
3216 FoldingSetNodeID ID;
3217 ID.AddInteger(scUnknown);
3220 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3221 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3222 "Stale SCEVUnknown in uniquing map!");
3225 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3227 FirstUnknown = cast<SCEVUnknown>(S);
3228 UniqueSCEVs.InsertNode(S, IP);
3232 //===----------------------------------------------------------------------===//
3233 // Basic SCEV Analysis and PHI Idiom Recognition Code
3236 /// isSCEVable - Test if values of the given type are analyzable within
3237 /// the SCEV framework. This primarily includes integer types, and it
3238 /// can optionally include pointer types if the ScalarEvolution class
3239 /// has access to target-specific information.
3240 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3241 // Integers and pointers are always SCEVable.
3242 return Ty->isIntegerTy() || Ty->isPointerTy();
3245 /// getTypeSizeInBits - Return the size in bits of the specified type,
3246 /// for which isSCEVable must return true.
3247 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3248 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3249 return F.getParent()->getDataLayout().getTypeSizeInBits(Ty);
3252 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3253 /// the given type and which represents how SCEV will treat the given
3254 /// type, for which isSCEVable must return true. For pointer types,
3255 /// this is the pointer-sized integer type.
3256 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3257 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3259 if (Ty->isIntegerTy()) {
3263 // The only other support type is pointer.
3264 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3265 return F.getParent()->getDataLayout().getIntPtrType(Ty);
3268 const SCEV *ScalarEvolution::getCouldNotCompute() {
3269 return CouldNotCompute.get();
3273 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3274 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3275 // is set iff if find such SCEVUnknown.
3277 struct FindInvalidSCEVUnknown {
3279 FindInvalidSCEVUnknown() { FindOne = false; }
3280 bool follow(const SCEV *S) {
3281 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3285 if (!cast<SCEVUnknown>(S)->getValue())
3292 bool isDone() const { return FindOne; }
3296 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3297 FindInvalidSCEVUnknown F;
3298 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3304 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3305 /// expression and create a new one.
3306 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3307 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3309 const SCEV *S = getExistingSCEV(V);
3312 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3317 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3318 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3320 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3321 if (I != ValueExprMap.end()) {
3322 const SCEV *S = I->second;
3323 if (checkValidity(S))
3325 ValueExprMap.erase(I);
3330 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3332 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3333 SCEV::NoWrapFlags Flags) {
3334 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3336 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3338 Type *Ty = V->getType();
3339 Ty = getEffectiveSCEVType(Ty);
3341 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3344 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3345 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3346 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3348 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3350 Type *Ty = V->getType();
3351 Ty = getEffectiveSCEVType(Ty);
3352 const SCEV *AllOnes =
3353 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3354 return getMinusSCEV(AllOnes, V);
3357 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3358 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3359 SCEV::NoWrapFlags Flags) {
3360 // Fast path: X - X --> 0.
3362 return getConstant(LHS->getType(), 0);
3364 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3365 // makes it so that we cannot make much use of NUW.
3366 auto AddFlags = SCEV::FlagAnyWrap;
3367 const bool RHSIsNotMinSigned =
3368 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3369 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3370 // Let M be the minimum representable signed value. Then (-1)*RHS
3371 // signed-wraps if and only if RHS is M. That can happen even for
3372 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3373 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3374 // (-1)*RHS, we need to prove that RHS != M.
3376 // If LHS is non-negative and we know that LHS - RHS does not
3377 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3378 // either by proving that RHS > M or that LHS >= 0.
3379 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3380 AddFlags = SCEV::FlagNSW;
3384 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3385 // RHS is NSW and LHS >= 0.
3387 // The difficulty here is that the NSW flag may have been proven
3388 // relative to a loop that is to be found in a recurrence in LHS and
3389 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3390 // larger scope than intended.
3391 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3393 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3396 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3397 /// input value to the specified type. If the type must be extended, it is zero
3400 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3401 Type *SrcTy = V->getType();
3402 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3403 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3404 "Cannot truncate or zero extend with non-integer arguments!");
3405 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3406 return V; // No conversion
3407 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3408 return getTruncateExpr(V, Ty);
3409 return getZeroExtendExpr(V, Ty);
3412 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3413 /// input value to the specified type. If the type must be extended, it is sign
3416 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3418 Type *SrcTy = V->getType();
3419 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3420 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3421 "Cannot truncate or zero extend with non-integer arguments!");
3422 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3423 return V; // No conversion
3424 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3425 return getTruncateExpr(V, Ty);
3426 return getSignExtendExpr(V, Ty);
3429 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3430 /// input value to the specified type. If the type must be extended, it is zero
3431 /// extended. The conversion must not be narrowing.
3433 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3434 Type *SrcTy = V->getType();
3435 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3436 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3437 "Cannot noop or zero extend with non-integer arguments!");
3438 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3439 "getNoopOrZeroExtend cannot truncate!");
3440 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3441 return V; // No conversion
3442 return getZeroExtendExpr(V, Ty);
3445 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3446 /// input value to the specified type. If the type must be extended, it is sign
3447 /// extended. The conversion must not be narrowing.
3449 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3450 Type *SrcTy = V->getType();
3451 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3452 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3453 "Cannot noop or sign extend with non-integer arguments!");
3454 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3455 "getNoopOrSignExtend cannot truncate!");
3456 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3457 return V; // No conversion
3458 return getSignExtendExpr(V, Ty);
3461 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3462 /// the input value to the specified type. If the type must be extended,
3463 /// it is extended with unspecified bits. The conversion must not be
3466 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3467 Type *SrcTy = V->getType();
3468 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3469 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3470 "Cannot noop or any extend with non-integer arguments!");
3471 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3472 "getNoopOrAnyExtend cannot truncate!");
3473 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3474 return V; // No conversion
3475 return getAnyExtendExpr(V, Ty);
3478 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3479 /// input value to the specified type. The conversion must not be widening.
3481 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3482 Type *SrcTy = V->getType();
3483 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3484 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3485 "Cannot truncate or noop with non-integer arguments!");
3486 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3487 "getTruncateOrNoop cannot extend!");
3488 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3489 return V; // No conversion
3490 return getTruncateExpr(V, Ty);
3493 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3494 /// the types using zero-extension, and then perform a umax operation
3496 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3498 const SCEV *PromotedLHS = LHS;
3499 const SCEV *PromotedRHS = RHS;
3501 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3502 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3504 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3506 return getUMaxExpr(PromotedLHS, PromotedRHS);
3509 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3510 /// the types using zero-extension, and then perform a umin operation
3512 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3514 const SCEV *PromotedLHS = LHS;
3515 const SCEV *PromotedRHS = RHS;
3517 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3518 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3520 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3522 return getUMinExpr(PromotedLHS, PromotedRHS);
3525 /// getPointerBase - Transitively follow the chain of pointer-type operands
3526 /// until reaching a SCEV that does not have a single pointer operand. This
3527 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3528 /// but corner cases do exist.
3529 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3530 // A pointer operand may evaluate to a nonpointer expression, such as null.
3531 if (!V->getType()->isPointerTy())
3534 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3535 return getPointerBase(Cast->getOperand());
3537 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3538 const SCEV *PtrOp = nullptr;
3539 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3541 if ((*I)->getType()->isPointerTy()) {
3542 // Cannot find the base of an expression with multiple pointer operands.
3550 return getPointerBase(PtrOp);
3555 /// PushDefUseChildren - Push users of the given Instruction
3556 /// onto the given Worklist.
3558 PushDefUseChildren(Instruction *I,
3559 SmallVectorImpl<Instruction *> &Worklist) {
3560 // Push the def-use children onto the Worklist stack.
3561 for (User *U : I->users())
3562 Worklist.push_back(cast<Instruction>(U));
3565 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3566 /// instructions that depend on the given instruction and removes them from
3567 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3570 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3571 SmallVector<Instruction *, 16> Worklist;
3572 PushDefUseChildren(PN, Worklist);
3574 SmallPtrSet<Instruction *, 8> Visited;
3576 while (!Worklist.empty()) {
3577 Instruction *I = Worklist.pop_back_val();
3578 if (!Visited.insert(I).second)
3581 ValueExprMapType::iterator It =
3582 ValueExprMap.find_as(static_cast<Value *>(I));
3583 if (It != ValueExprMap.end()) {
3584 const SCEV *Old = It->second;
3586 // Short-circuit the def-use traversal if the symbolic name
3587 // ceases to appear in expressions.
3588 if (Old != SymName && !hasOperand(Old, SymName))
3591 // SCEVUnknown for a PHI either means that it has an unrecognized
3592 // structure, it's a PHI that's in the progress of being computed
3593 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3594 // additional loop trip count information isn't going to change anything.
3595 // In the second case, createNodeForPHI will perform the necessary
3596 // updates on its own when it gets to that point. In the third, we do
3597 // want to forget the SCEVUnknown.
3598 if (!isa<PHINode>(I) ||
3599 !isa<SCEVUnknown>(Old) ||
3600 (I != PN && Old == SymName)) {
3601 forgetMemoizedResults(Old);
3602 ValueExprMap.erase(It);
3606 PushDefUseChildren(I, Worklist);
3610 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3611 /// a loop header, making it a potential recurrence, or it doesn't.
3613 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3614 if (const Loop *L = LI.getLoopFor(PN->getParent()))
3615 if (L->getHeader() == PN->getParent()) {
3616 // The loop may have multiple entrances or multiple exits; we can analyze
3617 // this phi as an addrec if it has a unique entry value and a unique
3619 Value *BEValueV = nullptr, *StartValueV = nullptr;
3620 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3621 Value *V = PN->getIncomingValue(i);
3622 if (L->contains(PN->getIncomingBlock(i))) {
3625 } else if (BEValueV != V) {
3629 } else if (!StartValueV) {
3631 } else if (StartValueV != V) {
3632 StartValueV = nullptr;
3636 if (BEValueV && StartValueV) {
3637 // While we are analyzing this PHI node, handle its value symbolically.
3638 const SCEV *SymbolicName = getUnknown(PN);
3639 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3640 "PHI node already processed?");
3641 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3643 // Using this symbolic name for the PHI, analyze the value coming around
3645 const SCEV *BEValue = getSCEV(BEValueV);
3647 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3648 // has a special value for the first iteration of the loop.
3650 // If the value coming around the backedge is an add with the symbolic
3651 // value we just inserted, then we found a simple induction variable!
3652 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3653 // If there is a single occurrence of the symbolic value, replace it
3654 // with a recurrence.
3655 unsigned FoundIndex = Add->getNumOperands();
3656 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3657 if (Add->getOperand(i) == SymbolicName)
3658 if (FoundIndex == e) {
3663 if (FoundIndex != Add->getNumOperands()) {
3664 // Create an add with everything but the specified operand.
3665 SmallVector<const SCEV *, 8> Ops;
3666 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3667 if (i != FoundIndex)
3668 Ops.push_back(Add->getOperand(i));
3669 const SCEV *Accum = getAddExpr(Ops);
3671 // This is not a valid addrec if the step amount is varying each
3672 // loop iteration, but is not itself an addrec in this loop.
3673 if (isLoopInvariant(Accum, L) ||
3674 (isa<SCEVAddRecExpr>(Accum) &&
3675 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3676 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3678 // If the increment doesn't overflow, then neither the addrec nor
3679 // the post-increment will overflow.
3680 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3681 if (OBO->getOperand(0) == PN) {
3682 if (OBO->hasNoUnsignedWrap())
3683 Flags = setFlags(Flags, SCEV::FlagNUW);
3684 if (OBO->hasNoSignedWrap())
3685 Flags = setFlags(Flags, SCEV::FlagNSW);
3687 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3688 // If the increment is an inbounds GEP, then we know the address
3689 // space cannot be wrapped around. We cannot make any guarantee
3690 // about signed or unsigned overflow because pointers are
3691 // unsigned but we may have a negative index from the base
3692 // pointer. We can guarantee that no unsigned wrap occurs if the
3693 // indices form a positive value.
3694 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3695 Flags = setFlags(Flags, SCEV::FlagNW);
3697 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3698 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3699 Flags = setFlags(Flags, SCEV::FlagNUW);
3702 // We cannot transfer nuw and nsw flags from subtraction
3703 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3707 const SCEV *StartVal = getSCEV(StartValueV);
3708 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3710 // Since the no-wrap flags are on the increment, they apply to the
3711 // post-incremented value as well.
3712 if (isLoopInvariant(Accum, L))
3713 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3716 // Okay, for the entire analysis of this edge we assumed the PHI
3717 // to be symbolic. We now need to go back and purge all of the
3718 // entries for the scalars that use the symbolic expression.
3719 ForgetSymbolicName(PN, SymbolicName);
3720 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3724 } else if (const SCEVAddRecExpr *AddRec =
3725 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3726 // Otherwise, this could be a loop like this:
3727 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3728 // In this case, j = {1,+,1} and BEValue is j.
3729 // Because the other in-value of i (0) fits the evolution of BEValue
3730 // i really is an addrec evolution.
3731 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3732 const SCEV *StartVal = getSCEV(StartValueV);
3734 // If StartVal = j.start - j.stride, we can use StartVal as the
3735 // initial step of the addrec evolution.
3736 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3737 AddRec->getOperand(1))) {
3738 // FIXME: For constant StartVal, we should be able to infer
3740 const SCEV *PHISCEV =
3741 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3744 // Okay, for the entire analysis of this edge we assumed the PHI
3745 // to be symbolic. We now need to go back and purge all of the
3746 // entries for the scalars that use the symbolic expression.
3747 ForgetSymbolicName(PN, SymbolicName);
3748 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3756 // If the PHI has a single incoming value, follow that value, unless the
3757 // PHI's incoming blocks are in a different loop, in which case doing so
3758 // risks breaking LCSSA form. Instcombine would normally zap these, but
3759 // it doesn't have DominatorTree information, so it may miss cases.
3760 if (Value *V = SimplifyInstruction(PN, F.getParent()->getDataLayout(), &TLI,
3762 if (LI.replacementPreservesLCSSAForm(PN, V))
3765 // If it's not a loop phi, we can't handle it yet.
3766 return getUnknown(PN);
3769 /// createNodeForGEP - Expand GEP instructions into add and multiply
3770 /// operations. This allows them to be analyzed by regular SCEV code.
3772 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3773 Value *Base = GEP->getOperand(0);
3774 // Don't attempt to analyze GEPs over unsized objects.
3775 if (!Base->getType()->getPointerElementType()->isSized())
3776 return getUnknown(GEP);
3778 SmallVector<const SCEV *, 4> IndexExprs;
3779 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
3780 IndexExprs.push_back(getSCEV(*Index));
3781 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
3785 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3786 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3787 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3788 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3790 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3791 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3792 return C->getValue()->getValue().countTrailingZeros();
3794 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3795 return std::min(GetMinTrailingZeros(T->getOperand()),
3796 (uint32_t)getTypeSizeInBits(T->getType()));
3798 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3799 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3800 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3801 getTypeSizeInBits(E->getType()) : OpRes;
3804 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3805 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3806 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3807 getTypeSizeInBits(E->getType()) : OpRes;
3810 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3811 // The result is the min of all operands results.
3812 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3813 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3814 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3818 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3819 // The result is the sum of all operands results.
3820 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3821 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3822 for (unsigned i = 1, e = M->getNumOperands();
3823 SumOpRes != BitWidth && i != e; ++i)
3824 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3829 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3830 // The result is the min of all operands results.
3831 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3832 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3833 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3837 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3838 // The result is the min of all operands results.
3839 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3840 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3841 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3845 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3846 // The result is the min of all operands results.
3847 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3848 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3849 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3853 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3854 // For a SCEVUnknown, ask ValueTracking.
3855 unsigned BitWidth = getTypeSizeInBits(U->getType());
3856 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3857 computeKnownBits(U->getValue(), Zeros, Ones, F.getParent()->getDataLayout(),
3858 0, &AC, nullptr, &DT);
3859 return Zeros.countTrailingOnes();
3866 /// GetRangeFromMetadata - Helper method to assign a range to V from
3867 /// metadata present in the IR.
3868 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3869 if (Instruction *I = dyn_cast<Instruction>(V)) {
3870 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3871 ConstantRange TotalRange(
3872 cast<IntegerType>(I->getType())->getBitWidth(), false);
3874 unsigned NumRanges = MD->getNumOperands() / 2;
3875 assert(NumRanges >= 1);
3877 for (unsigned i = 0; i < NumRanges; ++i) {
3878 ConstantInt *Lower =
3879 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3880 ConstantInt *Upper =
3881 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3882 ConstantRange Range(Lower->getValue(), Upper->getValue());
3883 TotalRange = TotalRange.unionWith(Range);
3893 /// getRange - Determine the range for a particular SCEV. If SignHint is
3894 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
3895 /// with a "cleaner" unsigned (resp. signed) representation.
3898 ScalarEvolution::getRange(const SCEV *S,
3899 ScalarEvolution::RangeSignHint SignHint) {
3900 DenseMap<const SCEV *, ConstantRange> &Cache =
3901 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
3904 // See if we've computed this range already.
3905 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
3906 if (I != Cache.end())
3909 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3910 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
3912 unsigned BitWidth = getTypeSizeInBits(S->getType());
3913 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3915 // If the value has known zeros, the maximum value will have those known zeros
3917 uint32_t TZ = GetMinTrailingZeros(S);
3919 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
3920 ConservativeResult =
3921 ConstantRange(APInt::getMinValue(BitWidth),
3922 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3924 ConservativeResult = ConstantRange(
3925 APInt::getSignedMinValue(BitWidth),
3926 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3929 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3930 ConstantRange X = getRange(Add->getOperand(0), SignHint);
3931 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3932 X = X.add(getRange(Add->getOperand(i), SignHint));
3933 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
3936 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3937 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
3938 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3939 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
3940 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
3943 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3944 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
3945 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3946 X = X.smax(getRange(SMax->getOperand(i), SignHint));
3947 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
3950 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3951 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
3952 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3953 X = X.umax(getRange(UMax->getOperand(i), SignHint));
3954 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
3957 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3958 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
3959 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
3960 return setRange(UDiv, SignHint,
3961 ConservativeResult.intersectWith(X.udiv(Y)));
3964 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3965 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
3966 return setRange(ZExt, SignHint,
3967 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3970 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3971 ConstantRange X = getRange(SExt->getOperand(), SignHint);
3972 return setRange(SExt, SignHint,
3973 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3976 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3977 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
3978 return setRange(Trunc, SignHint,
3979 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3982 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3983 // If there's no unsigned wrap, the value will never be less than its
3985 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3986 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3987 if (!C->getValue()->isZero())
3988 ConservativeResult =
3989 ConservativeResult.intersectWith(
3990 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3992 // If there's no signed wrap, and all the operands have the same sign or
3993 // zero, the value won't ever change sign.
3994 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3995 bool AllNonNeg = true;
3996 bool AllNonPos = true;
3997 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3998 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3999 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4002 ConservativeResult = ConservativeResult.intersectWith(
4003 ConstantRange(APInt(BitWidth, 0),
4004 APInt::getSignedMinValue(BitWidth)));
4006 ConservativeResult = ConservativeResult.intersectWith(
4007 ConstantRange(APInt::getSignedMinValue(BitWidth),
4008 APInt(BitWidth, 1)));
4011 // TODO: non-affine addrec
4012 if (AddRec->isAffine()) {
4013 Type *Ty = AddRec->getType();
4014 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4015 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4016 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4018 // Check for overflow. This must be done with ConstantRange arithmetic
4019 // because we could be called from within the ScalarEvolution overflow
4022 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4023 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4024 ConstantRange ZExtMaxBECountRange =
4025 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4027 const SCEV *Start = AddRec->getStart();
4028 const SCEV *Step = AddRec->getStepRecurrence(*this);
4029 ConstantRange StepSRange = getSignedRange(Step);
4030 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4032 ConstantRange StartURange = getUnsignedRange(Start);
4033 ConstantRange EndURange =
4034 StartURange.add(MaxBECountRange.multiply(StepSRange));
4036 // Check for unsigned overflow.
4037 ConstantRange ZExtStartURange =
4038 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4039 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4040 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4042 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4043 EndURange.getUnsignedMin());
4044 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4045 EndURange.getUnsignedMax());
4046 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4048 ConservativeResult =
4049 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4052 ConstantRange StartSRange = getSignedRange(Start);
4053 ConstantRange EndSRange =
4054 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4056 // Check for signed overflow. This must be done with ConstantRange
4057 // arithmetic because we could be called from within the ScalarEvolution
4058 // overflow checking code.
4059 ConstantRange SExtStartSRange =
4060 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4061 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4062 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4064 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4065 EndSRange.getSignedMin());
4066 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4067 EndSRange.getSignedMax());
4068 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4070 ConservativeResult =
4071 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4076 return setRange(AddRec, SignHint, ConservativeResult);
4079 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4080 // Check if the IR explicitly contains !range metadata.
4081 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4082 if (MDRange.hasValue())
4083 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4085 // Split here to avoid paying the compile-time cost of calling both
4086 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4088 const DataLayout &DL = F.getParent()->getDataLayout();
4089 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4090 // For a SCEVUnknown, ask ValueTracking.
4091 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4092 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4093 if (Ones != ~Zeros + 1)
4094 ConservativeResult =
4095 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4097 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4098 "generalize as needed!");
4099 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4101 ConservativeResult = ConservativeResult.intersectWith(
4102 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4103 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4106 return setRange(U, SignHint, ConservativeResult);
4109 return setRange(S, SignHint, ConservativeResult);
4112 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4113 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4114 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4116 // Return early if there are no flags to propagate to the SCEV.
4117 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4118 if (BinOp->hasNoUnsignedWrap())
4119 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4120 if (BinOp->hasNoSignedWrap())
4121 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4122 if (Flags == SCEV::FlagAnyWrap) {
4123 return SCEV::FlagAnyWrap;
4126 // Here we check that BinOp is in the header of the innermost loop
4127 // containing BinOp, since we only deal with instructions in the loop
4128 // header. The actual loop we need to check later will come from an add
4129 // recurrence, but getting that requires computing the SCEV of the operands,
4130 // which can be expensive. This check we can do cheaply to rule out some
4132 Loop *innermostContainingLoop = LI.getLoopFor(BinOp->getParent());
4133 if (innermostContainingLoop == nullptr ||
4134 innermostContainingLoop->getHeader() != BinOp->getParent())
4135 return SCEV::FlagAnyWrap;
4137 // Only proceed if we can prove that BinOp does not yield poison.
4138 if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
4140 // At this point we know that if V is executed, then it does not wrap
4141 // according to at least one of NSW or NUW. If V is not executed, then we do
4142 // not know if the calculation that V represents would wrap. Multiple
4143 // instructions can map to the same SCEV. If we apply NSW or NUW from V to
4144 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4145 // derived from other instructions that map to the same SCEV. We cannot make
4146 // that guarantee for cases where V is not executed. So we need to find the
4147 // loop that V is considered in relation to and prove that V is executed for
4148 // every iteration of that loop. That implies that the value that V
4149 // calculates does not wrap anywhere in the loop, so then we can apply the
4150 // flags to the SCEV.
4152 // We check isLoopInvariant to disambiguate in case we are adding two
4153 // recurrences from different loops, so that we know which loop to prove
4154 // that V is executed in.
4155 for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
4156 const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
4157 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4158 const int OtherOpIndex = 1 - OpIndex;
4159 const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
4160 if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
4161 isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
4165 return SCEV::FlagAnyWrap;
4168 /// createSCEV - We know that there is no SCEV for the specified value. Analyze
4171 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4172 if (!isSCEVable(V->getType()))
4173 return getUnknown(V);
4175 unsigned Opcode = Instruction::UserOp1;
4176 if (Instruction *I = dyn_cast<Instruction>(V)) {
4177 Opcode = I->getOpcode();
4179 // Don't attempt to analyze instructions in blocks that aren't
4180 // reachable. Such instructions don't matter, and they aren't required
4181 // to obey basic rules for definitions dominating uses which this
4182 // analysis depends on.
4183 if (!DT.isReachableFromEntry(I->getParent()))
4184 return getUnknown(V);
4185 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4186 Opcode = CE->getOpcode();
4187 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4188 return getConstant(CI);
4189 else if (isa<ConstantPointerNull>(V))
4190 return getConstant(V->getType(), 0);
4191 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4192 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4194 return getUnknown(V);
4196 Operator *U = cast<Operator>(V);
4198 case Instruction::Add: {
4199 // The simple thing to do would be to just call getSCEV on both operands
4200 // and call getAddExpr with the result. However if we're looking at a
4201 // bunch of things all added together, this can be quite inefficient,
4202 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4203 // Instead, gather up all the operands and make a single getAddExpr call.
4204 // LLVM IR canonical form means we need only traverse the left operands.
4205 SmallVector<const SCEV *, 4> AddOps;
4206 for (Value *Op = U;; Op = U->getOperand(0)) {
4207 U = dyn_cast<Operator>(Op);
4208 unsigned Opcode = U ? U->getOpcode() : 0;
4209 if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
4210 assert(Op != V && "V should be an add");
4211 AddOps.push_back(getSCEV(Op));
4215 if (auto *OpSCEV = getExistingSCEV(U)) {
4216 AddOps.push_back(OpSCEV);
4220 // If a NUW or NSW flag can be applied to the SCEV for this
4221 // addition, then compute the SCEV for this addition by itself
4222 // with a separate call to getAddExpr. We need to do that
4223 // instead of pushing the operands of the addition onto AddOps,
4224 // since the flags are only known to apply to this particular
4225 // addition - they may not apply to other additions that can be
4226 // formed with operands from AddOps.
4227 const SCEV *RHS = getSCEV(U->getOperand(1));
4228 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4229 if (Flags != SCEV::FlagAnyWrap) {
4230 const SCEV *LHS = getSCEV(U->getOperand(0));
4231 if (Opcode == Instruction::Sub)
4232 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4234 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4238 if (Opcode == Instruction::Sub)
4239 AddOps.push_back(getNegativeSCEV(RHS));
4241 AddOps.push_back(RHS);
4243 return getAddExpr(AddOps);
4246 case Instruction::Mul: {
4247 SmallVector<const SCEV *, 4> MulOps;
4248 for (Value *Op = U;; Op = U->getOperand(0)) {
4249 U = dyn_cast<Operator>(Op);
4250 if (!U || U->getOpcode() != Instruction::Mul) {
4251 assert(Op != V && "V should be a mul");
4252 MulOps.push_back(getSCEV(Op));
4256 if (auto *OpSCEV = getExistingSCEV(U)) {
4257 MulOps.push_back(OpSCEV);
4261 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4262 if (Flags != SCEV::FlagAnyWrap) {
4263 MulOps.push_back(getMulExpr(getSCEV(U->getOperand(0)),
4264 getSCEV(U->getOperand(1)), Flags));
4268 MulOps.push_back(getSCEV(U->getOperand(1)));
4270 return getMulExpr(MulOps);
4272 case Instruction::UDiv:
4273 return getUDivExpr(getSCEV(U->getOperand(0)),
4274 getSCEV(U->getOperand(1)));
4275 case Instruction::Sub:
4276 return getMinusSCEV(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)),
4277 getNoWrapFlagsFromUB(U));
4278 case Instruction::And:
4279 // For an expression like x&255 that merely masks off the high bits,
4280 // use zext(trunc(x)) as the SCEV expression.
4281 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4282 if (CI->isNullValue())
4283 return getSCEV(U->getOperand(1));
4284 if (CI->isAllOnesValue())
4285 return getSCEV(U->getOperand(0));
4286 const APInt &A = CI->getValue();
4288 // Instcombine's ShrinkDemandedConstant may strip bits out of
4289 // constants, obscuring what would otherwise be a low-bits mask.
4290 // Use computeKnownBits to compute what ShrinkDemandedConstant
4291 // knew about to reconstruct a low-bits mask value.
4292 unsigned LZ = A.countLeadingZeros();
4293 unsigned TZ = A.countTrailingZeros();
4294 unsigned BitWidth = A.getBitWidth();
4295 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4296 computeKnownBits(U->getOperand(0), KnownZero, KnownOne,
4297 F.getParent()->getDataLayout(), 0, &AC, nullptr, &DT);
4299 APInt EffectiveMask =
4300 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4301 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4302 const SCEV *MulCount = getConstant(
4303 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4307 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4308 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4315 case Instruction::Or:
4316 // If the RHS of the Or is a constant, we may have something like:
4317 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4318 // optimizations will transparently handle this case.
4320 // In order for this transformation to be safe, the LHS must be of the
4321 // form X*(2^n) and the Or constant must be less than 2^n.
4322 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4323 const SCEV *LHS = getSCEV(U->getOperand(0));
4324 const APInt &CIVal = CI->getValue();
4325 if (GetMinTrailingZeros(LHS) >=
4326 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4327 // Build a plain add SCEV.
4328 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4329 // If the LHS of the add was an addrec and it has no-wrap flags,
4330 // transfer the no-wrap flags, since an or won't introduce a wrap.
4331 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4332 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4333 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4334 OldAR->getNoWrapFlags());
4340 case Instruction::Xor:
4341 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4342 // If the RHS of the xor is a signbit, then this is just an add.
4343 // Instcombine turns add of signbit into xor as a strength reduction step.
4344 if (CI->getValue().isSignBit())
4345 return getAddExpr(getSCEV(U->getOperand(0)),
4346 getSCEV(U->getOperand(1)));
4348 // If the RHS of xor is -1, then this is a not operation.
4349 if (CI->isAllOnesValue())
4350 return getNotSCEV(getSCEV(U->getOperand(0)));
4352 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4353 // This is a variant of the check for xor with -1, and it handles
4354 // the case where instcombine has trimmed non-demanded bits out
4355 // of an xor with -1.
4356 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4357 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4358 if (BO->getOpcode() == Instruction::And &&
4359 LCI->getValue() == CI->getValue())
4360 if (const SCEVZeroExtendExpr *Z =
4361 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4362 Type *UTy = U->getType();
4363 const SCEV *Z0 = Z->getOperand();
4364 Type *Z0Ty = Z0->getType();
4365 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4367 // If C is a low-bits mask, the zero extend is serving to
4368 // mask off the high bits. Complement the operand and
4369 // re-apply the zext.
4370 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4371 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4373 // If C is a single bit, it may be in the sign-bit position
4374 // before the zero-extend. In this case, represent the xor
4375 // using an add, which is equivalent, and re-apply the zext.
4376 APInt Trunc = CI->getValue().trunc(Z0TySize);
4377 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4379 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4385 case Instruction::Shl:
4386 // Turn shift left of a constant amount into a multiply.
4387 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4388 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4390 // If the shift count is not less than the bitwidth, the result of
4391 // the shift is undefined. Don't try to analyze it, because the
4392 // resolution chosen here may differ from the resolution chosen in
4393 // other parts of the compiler.
4394 if (SA->getValue().uge(BitWidth))
4397 // It is currently not resolved how to interpret NSW for left
4398 // shift by BitWidth - 1, so we avoid applying flags in that
4399 // case. Remove this check (or this comment) once the situation
4401 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
4402 // and http://reviews.llvm.org/D8890 .
4403 auto Flags = SCEV::FlagAnyWrap;
4404 if (SA->getValue().ult(BitWidth - 1)) Flags = getNoWrapFlagsFromUB(U);
4406 Constant *X = ConstantInt::get(getContext(),
4407 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4408 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X), Flags);
4412 case Instruction::LShr:
4413 // Turn logical shift right of a constant into a unsigned divide.
4414 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4415 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4417 // If the shift count is not less than the bitwidth, the result of
4418 // the shift is undefined. Don't try to analyze it, because the
4419 // resolution chosen here may differ from the resolution chosen in
4420 // other parts of the compiler.
4421 if (SA->getValue().uge(BitWidth))
4424 Constant *X = ConstantInt::get(getContext(),
4425 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4426 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4430 case Instruction::AShr:
4431 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4432 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4433 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4434 if (L->getOpcode() == Instruction::Shl &&
4435 L->getOperand(1) == U->getOperand(1)) {
4436 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4438 // If the shift count is not less than the bitwidth, the result of
4439 // the shift is undefined. Don't try to analyze it, because the
4440 // resolution chosen here may differ from the resolution chosen in
4441 // other parts of the compiler.
4442 if (CI->getValue().uge(BitWidth))
4445 uint64_t Amt = BitWidth - CI->getZExtValue();
4446 if (Amt == BitWidth)
4447 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4449 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4450 IntegerType::get(getContext(),
4456 case Instruction::Trunc:
4457 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4459 case Instruction::ZExt:
4460 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4462 case Instruction::SExt:
4463 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4465 case Instruction::BitCast:
4466 // BitCasts are no-op casts so we just eliminate the cast.
4467 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4468 return getSCEV(U->getOperand(0));
4471 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4472 // lead to pointer expressions which cannot safely be expanded to GEPs,
4473 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4474 // simplifying integer expressions.
4476 case Instruction::GetElementPtr:
4477 return createNodeForGEP(cast<GEPOperator>(U));
4479 case Instruction::PHI:
4480 return createNodeForPHI(cast<PHINode>(U));
4482 case Instruction::Select:
4483 // This could be a smax or umax that was lowered earlier.
4484 // Try to recover it.
4485 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4486 Value *LHS = ICI->getOperand(0);
4487 Value *RHS = ICI->getOperand(1);
4488 switch (ICI->getPredicate()) {
4489 case ICmpInst::ICMP_SLT:
4490 case ICmpInst::ICMP_SLE:
4491 std::swap(LHS, RHS);
4493 case ICmpInst::ICMP_SGT:
4494 case ICmpInst::ICMP_SGE:
4495 // a >s b ? a+x : b+x -> smax(a, b)+x
4496 // a >s b ? b+x : a+x -> smin(a, b)+x
4497 if (getTypeSizeInBits(LHS->getType()) <=
4498 getTypeSizeInBits(U->getType())) {
4499 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType());
4500 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType());
4501 const SCEV *LA = getSCEV(U->getOperand(1));
4502 const SCEV *RA = getSCEV(U->getOperand(2));
4503 const SCEV *LDiff = getMinusSCEV(LA, LS);
4504 const SCEV *RDiff = getMinusSCEV(RA, RS);
4506 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4507 LDiff = getMinusSCEV(LA, RS);
4508 RDiff = getMinusSCEV(RA, LS);
4510 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4513 case ICmpInst::ICMP_ULT:
4514 case ICmpInst::ICMP_ULE:
4515 std::swap(LHS, RHS);
4517 case ICmpInst::ICMP_UGT:
4518 case ICmpInst::ICMP_UGE:
4519 // a >u b ? a+x : b+x -> umax(a, b)+x
4520 // a >u b ? b+x : a+x -> umin(a, b)+x
4521 if (getTypeSizeInBits(LHS->getType()) <=
4522 getTypeSizeInBits(U->getType())) {
4523 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4524 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType());
4525 const SCEV *LA = getSCEV(U->getOperand(1));
4526 const SCEV *RA = getSCEV(U->getOperand(2));
4527 const SCEV *LDiff = getMinusSCEV(LA, LS);
4528 const SCEV *RDiff = getMinusSCEV(RA, RS);
4530 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4531 LDiff = getMinusSCEV(LA, RS);
4532 RDiff = getMinusSCEV(RA, LS);
4534 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4537 case ICmpInst::ICMP_NE:
4538 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4539 if (getTypeSizeInBits(LHS->getType()) <=
4540 getTypeSizeInBits(U->getType()) &&
4541 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4542 const SCEV *One = getConstant(U->getType(), 1);
4543 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4544 const SCEV *LA = getSCEV(U->getOperand(1));
4545 const SCEV *RA = getSCEV(U->getOperand(2));
4546 const SCEV *LDiff = getMinusSCEV(LA, LS);
4547 const SCEV *RDiff = getMinusSCEV(RA, One);
4549 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4552 case ICmpInst::ICMP_EQ:
4553 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4554 if (getTypeSizeInBits(LHS->getType()) <=
4555 getTypeSizeInBits(U->getType()) &&
4556 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4557 const SCEV *One = getConstant(U->getType(), 1);
4558 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4559 const SCEV *LA = getSCEV(U->getOperand(1));
4560 const SCEV *RA = getSCEV(U->getOperand(2));
4561 const SCEV *LDiff = getMinusSCEV(LA, One);
4562 const SCEV *RDiff = getMinusSCEV(RA, LS);
4564 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4572 default: // We cannot analyze this expression.
4576 return getUnknown(V);
4581 //===----------------------------------------------------------------------===//
4582 // Iteration Count Computation Code
4585 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4586 if (BasicBlock *ExitingBB = L->getExitingBlock())
4587 return getSmallConstantTripCount(L, ExitingBB);
4589 // No trip count information for multiple exits.
4593 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4594 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4595 /// constant. Will also return 0 if the maximum trip count is very large (>=
4598 /// This "trip count" assumes that control exits via ExitingBlock. More
4599 /// precisely, it is the number of times that control may reach ExitingBlock
4600 /// before taking the branch. For loops with multiple exits, it may not be the
4601 /// number times that the loop header executes because the loop may exit
4602 /// prematurely via another branch.
4603 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4604 BasicBlock *ExitingBlock) {
4605 assert(ExitingBlock && "Must pass a non-null exiting block!");
4606 assert(L->isLoopExiting(ExitingBlock) &&
4607 "Exiting block must actually branch out of the loop!");
4608 const SCEVConstant *ExitCount =
4609 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4613 ConstantInt *ExitConst = ExitCount->getValue();
4615 // Guard against huge trip counts.
4616 if (ExitConst->getValue().getActiveBits() > 32)
4619 // In case of integer overflow, this returns 0, which is correct.
4620 return ((unsigned)ExitConst->getZExtValue()) + 1;
4623 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4624 if (BasicBlock *ExitingBB = L->getExitingBlock())
4625 return getSmallConstantTripMultiple(L, ExitingBB);
4627 // No trip multiple information for multiple exits.
4631 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4632 /// trip count of this loop as a normal unsigned value, if possible. This
4633 /// means that the actual trip count is always a multiple of the returned
4634 /// value (don't forget the trip count could very well be zero as well!).
4636 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4637 /// multiple of a constant (which is also the case if the trip count is simply
4638 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4639 /// if the trip count is very large (>= 2^32).
4641 /// As explained in the comments for getSmallConstantTripCount, this assumes
4642 /// that control exits the loop via ExitingBlock.
4644 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4645 BasicBlock *ExitingBlock) {
4646 assert(ExitingBlock && "Must pass a non-null exiting block!");
4647 assert(L->isLoopExiting(ExitingBlock) &&
4648 "Exiting block must actually branch out of the loop!");
4649 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4650 if (ExitCount == getCouldNotCompute())
4653 // Get the trip count from the BE count by adding 1.
4654 const SCEV *TCMul = getAddExpr(ExitCount,
4655 getConstant(ExitCount->getType(), 1));
4656 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4657 // to factor simple cases.
4658 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4659 TCMul = Mul->getOperand(0);
4661 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4665 ConstantInt *Result = MulC->getValue();
4667 // Guard against huge trip counts (this requires checking
4668 // for zero to handle the case where the trip count == -1 and the
4670 if (!Result || Result->getValue().getActiveBits() > 32 ||
4671 Result->getValue().getActiveBits() == 0)
4674 return (unsigned)Result->getZExtValue();
4677 // getExitCount - Get the expression for the number of loop iterations for which
4678 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4679 // SCEVCouldNotCompute.
4680 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4681 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4684 /// getBackedgeTakenCount - If the specified loop has a predictable
4685 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4686 /// object. The backedge-taken count is the number of times the loop header
4687 /// will be branched to from within the loop. This is one less than the
4688 /// trip count of the loop, since it doesn't count the first iteration,
4689 /// when the header is branched to from outside the loop.
4691 /// Note that it is not valid to call this method on a loop without a
4692 /// loop-invariant backedge-taken count (see
4693 /// hasLoopInvariantBackedgeTakenCount).
4695 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4696 return getBackedgeTakenInfo(L).getExact(this);
4699 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4700 /// return the least SCEV value that is known never to be less than the
4701 /// actual backedge taken count.
4702 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4703 return getBackedgeTakenInfo(L).getMax(this);
4706 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4707 /// onto the given Worklist.
4709 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4710 BasicBlock *Header = L->getHeader();
4712 // Push all Loop-header PHIs onto the Worklist stack.
4713 for (BasicBlock::iterator I = Header->begin();
4714 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4715 Worklist.push_back(PN);
4718 const ScalarEvolution::BackedgeTakenInfo &
4719 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4720 // Initially insert an invalid entry for this loop. If the insertion
4721 // succeeds, proceed to actually compute a backedge-taken count and
4722 // update the value. The temporary CouldNotCompute value tells SCEV
4723 // code elsewhere that it shouldn't attempt to request a new
4724 // backedge-taken count, which could result in infinite recursion.
4725 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4726 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4728 return Pair.first->second;
4730 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4731 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4732 // must be cleared in this scope.
4733 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4735 if (Result.getExact(this) != getCouldNotCompute()) {
4736 assert(isLoopInvariant(Result.getExact(this), L) &&
4737 isLoopInvariant(Result.getMax(this), L) &&
4738 "Computed backedge-taken count isn't loop invariant for loop!");
4739 ++NumTripCountsComputed;
4741 else if (Result.getMax(this) == getCouldNotCompute() &&
4742 isa<PHINode>(L->getHeader()->begin())) {
4743 // Only count loops that have phi nodes as not being computable.
4744 ++NumTripCountsNotComputed;
4747 // Now that we know more about the trip count for this loop, forget any
4748 // existing SCEV values for PHI nodes in this loop since they are only
4749 // conservative estimates made without the benefit of trip count
4750 // information. This is similar to the code in forgetLoop, except that
4751 // it handles SCEVUnknown PHI nodes specially.
4752 if (Result.hasAnyInfo()) {
4753 SmallVector<Instruction *, 16> Worklist;
4754 PushLoopPHIs(L, Worklist);
4756 SmallPtrSet<Instruction *, 8> Visited;
4757 while (!Worklist.empty()) {
4758 Instruction *I = Worklist.pop_back_val();
4759 if (!Visited.insert(I).second)
4762 ValueExprMapType::iterator It =
4763 ValueExprMap.find_as(static_cast<Value *>(I));
4764 if (It != ValueExprMap.end()) {
4765 const SCEV *Old = It->second;
4767 // SCEVUnknown for a PHI either means that it has an unrecognized
4768 // structure, or it's a PHI that's in the progress of being computed
4769 // by createNodeForPHI. In the former case, additional loop trip
4770 // count information isn't going to change anything. In the later
4771 // case, createNodeForPHI will perform the necessary updates on its
4772 // own when it gets to that point.
4773 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4774 forgetMemoizedResults(Old);
4775 ValueExprMap.erase(It);
4777 if (PHINode *PN = dyn_cast<PHINode>(I))
4778 ConstantEvolutionLoopExitValue.erase(PN);
4781 PushDefUseChildren(I, Worklist);
4785 // Re-lookup the insert position, since the call to
4786 // ComputeBackedgeTakenCount above could result in a
4787 // recusive call to getBackedgeTakenInfo (on a different
4788 // loop), which would invalidate the iterator computed
4790 return BackedgeTakenCounts.find(L)->second = Result;
4793 /// forgetLoop - This method should be called by the client when it has
4794 /// changed a loop in a way that may effect ScalarEvolution's ability to
4795 /// compute a trip count, or if the loop is deleted.
4796 void ScalarEvolution::forgetLoop(const Loop *L) {
4797 // Drop any stored trip count value.
4798 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4799 BackedgeTakenCounts.find(L);
4800 if (BTCPos != BackedgeTakenCounts.end()) {
4801 BTCPos->second.clear();
4802 BackedgeTakenCounts.erase(BTCPos);
4805 // Drop information about expressions based on loop-header PHIs.
4806 SmallVector<Instruction *, 16> Worklist;
4807 PushLoopPHIs(L, Worklist);
4809 SmallPtrSet<Instruction *, 8> Visited;
4810 while (!Worklist.empty()) {
4811 Instruction *I = Worklist.pop_back_val();
4812 if (!Visited.insert(I).second)
4815 ValueExprMapType::iterator It =
4816 ValueExprMap.find_as(static_cast<Value *>(I));
4817 if (It != ValueExprMap.end()) {
4818 forgetMemoizedResults(It->second);
4819 ValueExprMap.erase(It);
4820 if (PHINode *PN = dyn_cast<PHINode>(I))
4821 ConstantEvolutionLoopExitValue.erase(PN);
4824 PushDefUseChildren(I, Worklist);
4827 // Forget all contained loops too, to avoid dangling entries in the
4828 // ValuesAtScopes map.
4829 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4833 /// forgetValue - This method should be called by the client when it has
4834 /// changed a value in a way that may effect its value, or which may
4835 /// disconnect it from a def-use chain linking it to a loop.
4836 void ScalarEvolution::forgetValue(Value *V) {
4837 Instruction *I = dyn_cast<Instruction>(V);
4840 // Drop information about expressions based on loop-header PHIs.
4841 SmallVector<Instruction *, 16> Worklist;
4842 Worklist.push_back(I);
4844 SmallPtrSet<Instruction *, 8> Visited;
4845 while (!Worklist.empty()) {
4846 I = Worklist.pop_back_val();
4847 if (!Visited.insert(I).second)
4850 ValueExprMapType::iterator It =
4851 ValueExprMap.find_as(static_cast<Value *>(I));
4852 if (It != ValueExprMap.end()) {
4853 forgetMemoizedResults(It->second);
4854 ValueExprMap.erase(It);
4855 if (PHINode *PN = dyn_cast<PHINode>(I))
4856 ConstantEvolutionLoopExitValue.erase(PN);
4859 PushDefUseChildren(I, Worklist);
4863 /// getExact - Get the exact loop backedge taken count considering all loop
4864 /// exits. A computable result can only be returned for loops with a single
4865 /// exit. Returning the minimum taken count among all exits is incorrect
4866 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
4867 /// assumes that the limit of each loop test is never skipped. This is a valid
4868 /// assumption as long as the loop exits via that test. For precise results, it
4869 /// is the caller's responsibility to specify the relevant loop exit using
4870 /// getExact(ExitingBlock, SE).
4872 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4873 // If any exits were not computable, the loop is not computable.
4874 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4876 // We need exactly one computable exit.
4877 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4878 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4880 const SCEV *BECount = nullptr;
4881 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4882 ENT != nullptr; ENT = ENT->getNextExit()) {
4884 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4887 BECount = ENT->ExactNotTaken;
4888 else if (BECount != ENT->ExactNotTaken)
4889 return SE->getCouldNotCompute();
4891 assert(BECount && "Invalid not taken count for loop exit");
4895 /// getExact - Get the exact not taken count for this loop exit.
4897 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4898 ScalarEvolution *SE) const {
4899 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4900 ENT != nullptr; ENT = ENT->getNextExit()) {
4902 if (ENT->ExitingBlock == ExitingBlock)
4903 return ENT->ExactNotTaken;
4905 return SE->getCouldNotCompute();
4908 /// getMax - Get the max backedge taken count for the loop.
4910 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4911 return Max ? Max : SE->getCouldNotCompute();
4914 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4915 ScalarEvolution *SE) const {
4916 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4919 if (!ExitNotTaken.ExitingBlock)
4922 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4923 ENT != nullptr; ENT = ENT->getNextExit()) {
4925 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4926 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4933 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4934 /// computable exit into a persistent ExitNotTakenInfo array.
4935 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4936 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4937 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4940 ExitNotTaken.setIncomplete();
4942 unsigned NumExits = ExitCounts.size();
4943 if (NumExits == 0) return;
4945 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4946 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4947 if (NumExits == 1) return;
4949 // Handle the rare case of multiple computable exits.
4950 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4952 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4953 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4954 PrevENT->setNextExit(ENT);
4955 ENT->ExitingBlock = ExitCounts[i].first;
4956 ENT->ExactNotTaken = ExitCounts[i].second;
4960 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4961 void ScalarEvolution::BackedgeTakenInfo::clear() {
4962 ExitNotTaken.ExitingBlock = nullptr;
4963 ExitNotTaken.ExactNotTaken = nullptr;
4964 delete[] ExitNotTaken.getNextExit();
4967 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4968 /// of the specified loop will execute.
4969 ScalarEvolution::BackedgeTakenInfo
4970 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4971 SmallVector<BasicBlock *, 8> ExitingBlocks;
4972 L->getExitingBlocks(ExitingBlocks);
4974 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4975 bool CouldComputeBECount = true;
4976 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4977 const SCEV *MustExitMaxBECount = nullptr;
4978 const SCEV *MayExitMaxBECount = nullptr;
4980 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4981 // and compute maxBECount.
4982 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4983 BasicBlock *ExitBB = ExitingBlocks[i];
4984 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4986 // 1. For each exit that can be computed, add an entry to ExitCounts.
4987 // CouldComputeBECount is true only if all exits can be computed.
4988 if (EL.Exact == getCouldNotCompute())
4989 // We couldn't compute an exact value for this exit, so
4990 // we won't be able to compute an exact value for the loop.
4991 CouldComputeBECount = false;
4993 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4995 // 2. Derive the loop's MaxBECount from each exit's max number of
4996 // non-exiting iterations. Partition the loop exits into two kinds:
4997 // LoopMustExits and LoopMayExits.
4999 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5000 // is a LoopMayExit. If any computable LoopMustExit is found, then
5001 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
5002 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
5003 // considered greater than any computable EL.Max.
5004 if (EL.Max != getCouldNotCompute() && Latch &&
5005 DT.dominates(ExitBB, Latch)) {
5006 if (!MustExitMaxBECount)
5007 MustExitMaxBECount = EL.Max;
5009 MustExitMaxBECount =
5010 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5012 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5013 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5014 MayExitMaxBECount = EL.Max;
5017 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5021 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5022 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5023 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5026 /// ComputeExitLimit - Compute the number of times the backedge of the specified
5027 /// loop will execute if it exits via the specified block.
5028 ScalarEvolution::ExitLimit
5029 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
5031 // Okay, we've chosen an exiting block. See what condition causes us to
5032 // exit at this block and remember the exit block and whether all other targets
5033 // lead to the loop header.
5034 bool MustExecuteLoopHeader = true;
5035 BasicBlock *Exit = nullptr;
5036 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5038 if (!L->contains(*SI)) {
5039 if (Exit) // Multiple exit successors.
5040 return getCouldNotCompute();
5042 } else if (*SI != L->getHeader()) {
5043 MustExecuteLoopHeader = false;
5046 // At this point, we know we have a conditional branch that determines whether
5047 // the loop is exited. However, we don't know if the branch is executed each
5048 // time through the loop. If not, then the execution count of the branch will
5049 // not be equal to the trip count of the loop.
5051 // Currently we check for this by checking to see if the Exit branch goes to
5052 // the loop header. If so, we know it will always execute the same number of
5053 // times as the loop. We also handle the case where the exit block *is* the
5054 // loop header. This is common for un-rotated loops.
5056 // If both of those tests fail, walk up the unique predecessor chain to the
5057 // header, stopping if there is an edge that doesn't exit the loop. If the
5058 // header is reached, the execution count of the branch will be equal to the
5059 // trip count of the loop.
5061 // More extensive analysis could be done to handle more cases here.
5063 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5064 // The simple checks failed, try climbing the unique predecessor chain
5065 // up to the header.
5067 for (BasicBlock *BB = ExitingBlock; BB; ) {
5068 BasicBlock *Pred = BB->getUniquePredecessor();
5070 return getCouldNotCompute();
5071 TerminatorInst *PredTerm = Pred->getTerminator();
5072 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5075 // If the predecessor has a successor that isn't BB and isn't
5076 // outside the loop, assume the worst.
5077 if (L->contains(PredSucc))
5078 return getCouldNotCompute();
5080 if (Pred == L->getHeader()) {
5087 return getCouldNotCompute();
5090 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5091 TerminatorInst *Term = ExitingBlock->getTerminator();
5092 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5093 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5094 // Proceed to the next level to examine the exit condition expression.
5095 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5096 BI->getSuccessor(1),
5097 /*ControlsExit=*/IsOnlyExit);
5100 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5101 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
5102 /*ControlsExit=*/IsOnlyExit);
5104 return getCouldNotCompute();
5107 /// ComputeExitLimitFromCond - Compute the number of times the
5108 /// backedge of the specified loop will execute if its exit condition
5109 /// were a conditional branch of ExitCond, TBB, and FBB.
5111 /// @param ControlsExit is true if ExitCond directly controls the exit
5112 /// branch. In this case, we can assume that the loop exits only if the
5113 /// condition is true and can infer that failing to meet the condition prior to
5114 /// integer wraparound results in undefined behavior.
5115 ScalarEvolution::ExitLimit
5116 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
5120 bool ControlsExit) {
5121 // Check if the controlling expression for this loop is an And or Or.
5122 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5123 if (BO->getOpcode() == Instruction::And) {
5124 // Recurse on the operands of the and.
5125 bool EitherMayExit = L->contains(TBB);
5126 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5127 ControlsExit && !EitherMayExit);
5128 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5129 ControlsExit && !EitherMayExit);
5130 const SCEV *BECount = getCouldNotCompute();
5131 const SCEV *MaxBECount = getCouldNotCompute();
5132 if (EitherMayExit) {
5133 // Both conditions must be true for the loop to continue executing.
5134 // Choose the less conservative count.
5135 if (EL0.Exact == getCouldNotCompute() ||
5136 EL1.Exact == getCouldNotCompute())
5137 BECount = getCouldNotCompute();
5139 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5140 if (EL0.Max == getCouldNotCompute())
5141 MaxBECount = EL1.Max;
5142 else if (EL1.Max == getCouldNotCompute())
5143 MaxBECount = EL0.Max;
5145 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5147 // Both conditions must be true at the same time for the loop to exit.
5148 // For now, be conservative.
5149 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5150 if (EL0.Max == EL1.Max)
5151 MaxBECount = EL0.Max;
5152 if (EL0.Exact == EL1.Exact)
5153 BECount = EL0.Exact;
5156 return ExitLimit(BECount, MaxBECount);
5158 if (BO->getOpcode() == Instruction::Or) {
5159 // Recurse on the operands of the or.
5160 bool EitherMayExit = L->contains(FBB);
5161 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5162 ControlsExit && !EitherMayExit);
5163 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5164 ControlsExit && !EitherMayExit);
5165 const SCEV *BECount = getCouldNotCompute();
5166 const SCEV *MaxBECount = getCouldNotCompute();
5167 if (EitherMayExit) {
5168 // Both conditions must be false for the loop to continue executing.
5169 // Choose the less conservative count.
5170 if (EL0.Exact == getCouldNotCompute() ||
5171 EL1.Exact == getCouldNotCompute())
5172 BECount = getCouldNotCompute();
5174 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5175 if (EL0.Max == getCouldNotCompute())
5176 MaxBECount = EL1.Max;
5177 else if (EL1.Max == getCouldNotCompute())
5178 MaxBECount = EL0.Max;
5180 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5182 // Both conditions must be false at the same time for the loop to exit.
5183 // For now, be conservative.
5184 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5185 if (EL0.Max == EL1.Max)
5186 MaxBECount = EL0.Max;
5187 if (EL0.Exact == EL1.Exact)
5188 BECount = EL0.Exact;
5191 return ExitLimit(BECount, MaxBECount);
5195 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5196 // Proceed to the next level to examine the icmp.
5197 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5198 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5200 // Check for a constant condition. These are normally stripped out by
5201 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5202 // preserve the CFG and is temporarily leaving constant conditions
5204 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5205 if (L->contains(FBB) == !CI->getZExtValue())
5206 // The backedge is always taken.
5207 return getCouldNotCompute();
5209 // The backedge is never taken.
5210 return getConstant(CI->getType(), 0);
5213 // If it's not an integer or pointer comparison then compute it the hard way.
5214 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5217 /// ComputeExitLimitFromICmp - Compute the number of times the
5218 /// backedge of the specified loop will execute if its exit condition
5219 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5220 ScalarEvolution::ExitLimit
5221 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5225 bool ControlsExit) {
5227 // If the condition was exit on true, convert the condition to exit on false
5228 ICmpInst::Predicate Cond;
5229 if (!L->contains(FBB))
5230 Cond = ExitCond->getPredicate();
5232 Cond = ExitCond->getInversePredicate();
5234 // Handle common loops like: for (X = "string"; *X; ++X)
5235 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5236 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5238 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5239 if (ItCnt.hasAnyInfo())
5243 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5244 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5246 // Try to evaluate any dependencies out of the loop.
5247 LHS = getSCEVAtScope(LHS, L);
5248 RHS = getSCEVAtScope(RHS, L);
5250 // At this point, we would like to compute how many iterations of the
5251 // loop the predicate will return true for these inputs.
5252 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5253 // If there is a loop-invariant, force it into the RHS.
5254 std::swap(LHS, RHS);
5255 Cond = ICmpInst::getSwappedPredicate(Cond);
5258 // Simplify the operands before analyzing them.
5259 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5261 // If we have a comparison of a chrec against a constant, try to use value
5262 // ranges to answer this query.
5263 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5264 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5265 if (AddRec->getLoop() == L) {
5266 // Form the constant range.
5267 ConstantRange CompRange(
5268 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5270 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5271 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5275 case ICmpInst::ICMP_NE: { // while (X != Y)
5276 // Convert to: while (X-Y != 0)
5277 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5278 if (EL.hasAnyInfo()) return EL;
5281 case ICmpInst::ICMP_EQ: { // while (X == Y)
5282 // Convert to: while (X-Y == 0)
5283 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5284 if (EL.hasAnyInfo()) return EL;
5287 case ICmpInst::ICMP_SLT:
5288 case ICmpInst::ICMP_ULT: { // while (X < Y)
5289 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5290 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5291 if (EL.hasAnyInfo()) return EL;
5294 case ICmpInst::ICMP_SGT:
5295 case ICmpInst::ICMP_UGT: { // while (X > Y)
5296 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5297 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5298 if (EL.hasAnyInfo()) return EL;
5303 dbgs() << "ComputeBackedgeTakenCount ";
5304 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5305 dbgs() << "[unsigned] ";
5306 dbgs() << *LHS << " "
5307 << Instruction::getOpcodeName(Instruction::ICmp)
5308 << " " << *RHS << "\n";
5312 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5315 ScalarEvolution::ExitLimit
5316 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5318 BasicBlock *ExitingBlock,
5319 bool ControlsExit) {
5320 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5322 // Give up if the exit is the default dest of a switch.
5323 if (Switch->getDefaultDest() == ExitingBlock)
5324 return getCouldNotCompute();
5326 assert(L->contains(Switch->getDefaultDest()) &&
5327 "Default case must not exit the loop!");
5328 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5329 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5331 // while (X != Y) --> while (X-Y != 0)
5332 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5333 if (EL.hasAnyInfo())
5336 return getCouldNotCompute();
5339 static ConstantInt *
5340 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5341 ScalarEvolution &SE) {
5342 const SCEV *InVal = SE.getConstant(C);
5343 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5344 assert(isa<SCEVConstant>(Val) &&
5345 "Evaluation of SCEV at constant didn't fold correctly?");
5346 return cast<SCEVConstant>(Val)->getValue();
5349 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5350 /// 'icmp op load X, cst', try to see if we can compute the backedge
5351 /// execution count.
5352 ScalarEvolution::ExitLimit
5353 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5357 ICmpInst::Predicate predicate) {
5359 if (LI->isVolatile()) return getCouldNotCompute();
5361 // Check to see if the loaded pointer is a getelementptr of a global.
5362 // TODO: Use SCEV instead of manually grubbing with GEPs.
5363 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5364 if (!GEP) return getCouldNotCompute();
5366 // Make sure that it is really a constant global we are gepping, with an
5367 // initializer, and make sure the first IDX is really 0.
5368 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5369 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5370 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5371 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5372 return getCouldNotCompute();
5374 // Okay, we allow one non-constant index into the GEP instruction.
5375 Value *VarIdx = nullptr;
5376 std::vector<Constant*> Indexes;
5377 unsigned VarIdxNum = 0;
5378 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5379 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5380 Indexes.push_back(CI);
5381 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5382 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5383 VarIdx = GEP->getOperand(i);
5385 Indexes.push_back(nullptr);
5388 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5390 return getCouldNotCompute();
5392 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5393 // Check to see if X is a loop variant variable value now.
5394 const SCEV *Idx = getSCEV(VarIdx);
5395 Idx = getSCEVAtScope(Idx, L);
5397 // We can only recognize very limited forms of loop index expressions, in
5398 // particular, only affine AddRec's like {C1,+,C2}.
5399 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5400 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5401 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5402 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5403 return getCouldNotCompute();
5405 unsigned MaxSteps = MaxBruteForceIterations;
5406 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5407 ConstantInt *ItCst = ConstantInt::get(
5408 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5409 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5411 // Form the GEP offset.
5412 Indexes[VarIdxNum] = Val;
5414 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5416 if (!Result) break; // Cannot compute!
5418 // Evaluate the condition for this iteration.
5419 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5420 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5421 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5423 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5424 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5427 ++NumArrayLenItCounts;
5428 return getConstant(ItCst); // Found terminating iteration!
5431 return getCouldNotCompute();
5435 /// CanConstantFold - Return true if we can constant fold an instruction of the
5436 /// specified type, assuming that all operands were constants.
5437 static bool CanConstantFold(const Instruction *I) {
5438 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5439 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5443 if (const CallInst *CI = dyn_cast<CallInst>(I))
5444 if (const Function *F = CI->getCalledFunction())
5445 return canConstantFoldCallTo(F);
5449 /// Determine whether this instruction can constant evolve within this loop
5450 /// assuming its operands can all constant evolve.
5451 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5452 // An instruction outside of the loop can't be derived from a loop PHI.
5453 if (!L->contains(I)) return false;
5455 if (isa<PHINode>(I)) {
5456 // We don't currently keep track of the control flow needed to evaluate
5457 // PHIs, so we cannot handle PHIs inside of loops.
5458 return L->getHeader() == I->getParent();
5461 // If we won't be able to constant fold this expression even if the operands
5462 // are constants, bail early.
5463 return CanConstantFold(I);
5466 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5467 /// recursing through each instruction operand until reaching a loop header phi.
5469 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5470 DenseMap<Instruction *, PHINode *> &PHIMap) {
5472 // Otherwise, we can evaluate this instruction if all of its operands are
5473 // constant or derived from a PHI node themselves.
5474 PHINode *PHI = nullptr;
5475 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5476 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5478 if (isa<Constant>(*OpI)) continue;
5480 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5481 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5483 PHINode *P = dyn_cast<PHINode>(OpInst);
5485 // If this operand is already visited, reuse the prior result.
5486 // We may have P != PHI if this is the deepest point at which the
5487 // inconsistent paths meet.
5488 P = PHIMap.lookup(OpInst);
5490 // Recurse and memoize the results, whether a phi is found or not.
5491 // This recursive call invalidates pointers into PHIMap.
5492 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5496 return nullptr; // Not evolving from PHI
5497 if (PHI && PHI != P)
5498 return nullptr; // Evolving from multiple different PHIs.
5501 // This is a expression evolving from a constant PHI!
5505 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5506 /// in the loop that V is derived from. We allow arbitrary operations along the
5507 /// way, but the operands of an operation must either be constants or a value
5508 /// derived from a constant PHI. If this expression does not fit with these
5509 /// constraints, return null.
5510 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5511 Instruction *I = dyn_cast<Instruction>(V);
5512 if (!I || !canConstantEvolve(I, L)) return nullptr;
5514 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5518 // Record non-constant instructions contained by the loop.
5519 DenseMap<Instruction *, PHINode *> PHIMap;
5520 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5523 /// EvaluateExpression - Given an expression that passes the
5524 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5525 /// in the loop has the value PHIVal. If we can't fold this expression for some
5526 /// reason, return null.
5527 static Constant *EvaluateExpression(Value *V, const Loop *L,
5528 DenseMap<Instruction *, Constant *> &Vals,
5529 const DataLayout &DL,
5530 const TargetLibraryInfo *TLI) {
5531 // Convenient constant check, but redundant for recursive calls.
5532 if (Constant *C = dyn_cast<Constant>(V)) return C;
5533 Instruction *I = dyn_cast<Instruction>(V);
5534 if (!I) return nullptr;
5536 if (Constant *C = Vals.lookup(I)) return C;
5538 // An instruction inside the loop depends on a value outside the loop that we
5539 // weren't given a mapping for, or a value such as a call inside the loop.
5540 if (!canConstantEvolve(I, L)) return nullptr;
5542 // An unmapped PHI can be due to a branch or another loop inside this loop,
5543 // or due to this not being the initial iteration through a loop where we
5544 // couldn't compute the evolution of this particular PHI last time.
5545 if (isa<PHINode>(I)) return nullptr;
5547 std::vector<Constant*> Operands(I->getNumOperands());
5549 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5550 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5552 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5553 if (!Operands[i]) return nullptr;
5556 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5558 if (!C) return nullptr;
5562 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5563 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5564 Operands[1], DL, TLI);
5565 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5566 if (!LI->isVolatile())
5567 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5569 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5573 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5574 /// in the header of its containing loop, we know the loop executes a
5575 /// constant number of times, and the PHI node is just a recurrence
5576 /// involving constants, fold it.
5578 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5581 DenseMap<PHINode*, Constant*>::const_iterator I =
5582 ConstantEvolutionLoopExitValue.find(PN);
5583 if (I != ConstantEvolutionLoopExitValue.end())
5586 if (BEs.ugt(MaxBruteForceIterations))
5587 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5589 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5591 DenseMap<Instruction *, Constant *> CurrentIterVals;
5592 BasicBlock *Header = L->getHeader();
5593 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5595 // Since the loop is canonicalized, the PHI node must have two entries. One
5596 // entry must be a constant (coming in from outside of the loop), and the
5597 // second must be derived from the same PHI.
5598 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5599 PHINode *PHI = nullptr;
5600 for (BasicBlock::iterator I = Header->begin();
5601 (PHI = dyn_cast<PHINode>(I)); ++I) {
5602 Constant *StartCST =
5603 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5604 if (!StartCST) continue;
5605 CurrentIterVals[PHI] = StartCST;
5607 if (!CurrentIterVals.count(PN))
5608 return RetVal = nullptr;
5610 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5612 // Execute the loop symbolically to determine the exit value.
5613 if (BEs.getActiveBits() >= 32)
5614 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5616 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5617 unsigned IterationNum = 0;
5618 const DataLayout &DL = F.getParent()->getDataLayout();
5619 for (; ; ++IterationNum) {
5620 if (IterationNum == NumIterations)
5621 return RetVal = CurrentIterVals[PN]; // Got exit value!
5623 // Compute the value of the PHIs for the next iteration.
5624 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5625 DenseMap<Instruction *, Constant *> NextIterVals;
5627 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5629 return nullptr; // Couldn't evaluate!
5630 NextIterVals[PN] = NextPHI;
5632 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5634 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5635 // cease to be able to evaluate one of them or if they stop evolving,
5636 // because that doesn't necessarily prevent us from computing PN.
5637 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5638 for (DenseMap<Instruction *, Constant *>::const_iterator
5639 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5640 PHINode *PHI = dyn_cast<PHINode>(I->first);
5641 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5642 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5644 // We use two distinct loops because EvaluateExpression may invalidate any
5645 // iterators into CurrentIterVals.
5646 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5647 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5648 PHINode *PHI = I->first;
5649 Constant *&NextPHI = NextIterVals[PHI];
5650 if (!NextPHI) { // Not already computed.
5651 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5652 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5654 if (NextPHI != I->second)
5655 StoppedEvolving = false;
5658 // If all entries in CurrentIterVals == NextIterVals then we can stop
5659 // iterating, the loop can't continue to change.
5660 if (StoppedEvolving)
5661 return RetVal = CurrentIterVals[PN];
5663 CurrentIterVals.swap(NextIterVals);
5667 /// ComputeExitCountExhaustively - If the loop is known to execute a
5668 /// constant number of times (the condition evolves only from constants),
5669 /// try to evaluate a few iterations of the loop until we get the exit
5670 /// condition gets a value of ExitWhen (true or false). If we cannot
5671 /// evaluate the trip count of the loop, return getCouldNotCompute().
5672 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5675 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5676 if (!PN) return getCouldNotCompute();
5678 // If the loop is canonicalized, the PHI will have exactly two entries.
5679 // That's the only form we support here.
5680 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5682 DenseMap<Instruction *, Constant *> CurrentIterVals;
5683 BasicBlock *Header = L->getHeader();
5684 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5686 // One entry must be a constant (coming in from outside of the loop), and the
5687 // second must be derived from the same PHI.
5688 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5689 PHINode *PHI = nullptr;
5690 for (BasicBlock::iterator I = Header->begin();
5691 (PHI = dyn_cast<PHINode>(I)); ++I) {
5692 Constant *StartCST =
5693 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5694 if (!StartCST) continue;
5695 CurrentIterVals[PHI] = StartCST;
5697 if (!CurrentIterVals.count(PN))
5698 return getCouldNotCompute();
5700 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5701 // the loop symbolically to determine when the condition gets a value of
5703 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5704 const DataLayout &DL = F.getParent()->getDataLayout();
5705 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5706 ConstantInt *CondVal = dyn_cast_or_null<ConstantInt>(
5707 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
5709 // Couldn't symbolically evaluate.
5710 if (!CondVal) return getCouldNotCompute();
5712 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5713 ++NumBruteForceTripCountsComputed;
5714 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5717 // Update all the PHI nodes for the next iteration.
5718 DenseMap<Instruction *, Constant *> NextIterVals;
5720 // Create a list of which PHIs we need to compute. We want to do this before
5721 // calling EvaluateExpression on them because that may invalidate iterators
5722 // into CurrentIterVals.
5723 SmallVector<PHINode *, 8> PHIsToCompute;
5724 for (DenseMap<Instruction *, Constant *>::const_iterator
5725 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5726 PHINode *PHI = dyn_cast<PHINode>(I->first);
5727 if (!PHI || PHI->getParent() != Header) continue;
5728 PHIsToCompute.push_back(PHI);
5730 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5731 E = PHIsToCompute.end(); I != E; ++I) {
5733 Constant *&NextPHI = NextIterVals[PHI];
5734 if (NextPHI) continue; // Already computed!
5736 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5737 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5739 CurrentIterVals.swap(NextIterVals);
5742 // Too many iterations were needed to evaluate.
5743 return getCouldNotCompute();
5746 /// getSCEVAtScope - Return a SCEV expression for the specified value
5747 /// at the specified scope in the program. The L value specifies a loop
5748 /// nest to evaluate the expression at, where null is the top-level or a
5749 /// specified loop is immediately inside of the loop.
5751 /// This method can be used to compute the exit value for a variable defined
5752 /// in a loop by querying what the value will hold in the parent loop.
5754 /// In the case that a relevant loop exit value cannot be computed, the
5755 /// original value V is returned.
5756 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5757 // Check to see if we've folded this expression at this loop before.
5758 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5759 for (unsigned u = 0; u < Values.size(); u++) {
5760 if (Values[u].first == L)
5761 return Values[u].second ? Values[u].second : V;
5763 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5764 // Otherwise compute it.
5765 const SCEV *C = computeSCEVAtScope(V, L);
5766 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5767 for (unsigned u = Values2.size(); u > 0; u--) {
5768 if (Values2[u - 1].first == L) {
5769 Values2[u - 1].second = C;
5776 /// This builds up a Constant using the ConstantExpr interface. That way, we
5777 /// will return Constants for objects which aren't represented by a
5778 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5779 /// Returns NULL if the SCEV isn't representable as a Constant.
5780 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5781 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5782 case scCouldNotCompute:
5786 return cast<SCEVConstant>(V)->getValue();
5788 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5789 case scSignExtend: {
5790 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5791 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5792 return ConstantExpr::getSExt(CastOp, SS->getType());
5795 case scZeroExtend: {
5796 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5797 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5798 return ConstantExpr::getZExt(CastOp, SZ->getType());
5802 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5803 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5804 return ConstantExpr::getTrunc(CastOp, ST->getType());
5808 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5809 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5810 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5811 unsigned AS = PTy->getAddressSpace();
5812 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5813 C = ConstantExpr::getBitCast(C, DestPtrTy);
5815 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5816 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5817 if (!C2) return nullptr;
5820 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5821 unsigned AS = C2->getType()->getPointerAddressSpace();
5823 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5824 // The offsets have been converted to bytes. We can add bytes to an
5825 // i8* by GEP with the byte count in the first index.
5826 C = ConstantExpr::getBitCast(C, DestPtrTy);
5829 // Don't bother trying to sum two pointers. We probably can't
5830 // statically compute a load that results from it anyway.
5831 if (C2->getType()->isPointerTy())
5834 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5835 if (PTy->getElementType()->isStructTy())
5836 C2 = ConstantExpr::getIntegerCast(
5837 C2, Type::getInt32Ty(C->getContext()), true);
5838 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
5840 C = ConstantExpr::getAdd(C, C2);
5847 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5848 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5849 // Don't bother with pointers at all.
5850 if (C->getType()->isPointerTy()) return nullptr;
5851 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5852 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5853 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5854 C = ConstantExpr::getMul(C, C2);
5861 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5862 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5863 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5864 if (LHS->getType() == RHS->getType())
5865 return ConstantExpr::getUDiv(LHS, RHS);
5870 break; // TODO: smax, umax.
5875 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5876 if (isa<SCEVConstant>(V)) return V;
5878 // If this instruction is evolved from a constant-evolving PHI, compute the
5879 // exit value from the loop without using SCEVs.
5880 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5881 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5882 const Loop *LI = this->LI[I->getParent()];
5883 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5884 if (PHINode *PN = dyn_cast<PHINode>(I))
5885 if (PN->getParent() == LI->getHeader()) {
5886 // Okay, there is no closed form solution for the PHI node. Check
5887 // to see if the loop that contains it has a known backedge-taken
5888 // count. If so, we may be able to force computation of the exit
5890 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5891 if (const SCEVConstant *BTCC =
5892 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5893 // Okay, we know how many times the containing loop executes. If
5894 // this is a constant evolving PHI node, get the final value at
5895 // the specified iteration number.
5896 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5897 BTCC->getValue()->getValue(),
5899 if (RV) return getSCEV(RV);
5903 // Okay, this is an expression that we cannot symbolically evaluate
5904 // into a SCEV. Check to see if it's possible to symbolically evaluate
5905 // the arguments into constants, and if so, try to constant propagate the
5906 // result. This is particularly useful for computing loop exit values.
5907 if (CanConstantFold(I)) {
5908 SmallVector<Constant *, 4> Operands;
5909 bool MadeImprovement = false;
5910 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5911 Value *Op = I->getOperand(i);
5912 if (Constant *C = dyn_cast<Constant>(Op)) {
5913 Operands.push_back(C);
5917 // If any of the operands is non-constant and if they are
5918 // non-integer and non-pointer, don't even try to analyze them
5919 // with scev techniques.
5920 if (!isSCEVable(Op->getType()))
5923 const SCEV *OrigV = getSCEV(Op);
5924 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5925 MadeImprovement |= OrigV != OpV;
5927 Constant *C = BuildConstantFromSCEV(OpV);
5929 if (C->getType() != Op->getType())
5930 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5934 Operands.push_back(C);
5937 // Check to see if getSCEVAtScope actually made an improvement.
5938 if (MadeImprovement) {
5939 Constant *C = nullptr;
5940 const DataLayout &DL = F.getParent()->getDataLayout();
5941 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5942 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5943 Operands[1], DL, &TLI);
5944 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5945 if (!LI->isVolatile())
5946 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5948 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
5956 // This is some other type of SCEVUnknown, just return it.
5960 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5961 // Avoid performing the look-up in the common case where the specified
5962 // expression has no loop-variant portions.
5963 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5964 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5965 if (OpAtScope != Comm->getOperand(i)) {
5966 // Okay, at least one of these operands is loop variant but might be
5967 // foldable. Build a new instance of the folded commutative expression.
5968 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5969 Comm->op_begin()+i);
5970 NewOps.push_back(OpAtScope);
5972 for (++i; i != e; ++i) {
5973 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5974 NewOps.push_back(OpAtScope);
5976 if (isa<SCEVAddExpr>(Comm))
5977 return getAddExpr(NewOps);
5978 if (isa<SCEVMulExpr>(Comm))
5979 return getMulExpr(NewOps);
5980 if (isa<SCEVSMaxExpr>(Comm))
5981 return getSMaxExpr(NewOps);
5982 if (isa<SCEVUMaxExpr>(Comm))
5983 return getUMaxExpr(NewOps);
5984 llvm_unreachable("Unknown commutative SCEV type!");
5987 // If we got here, all operands are loop invariant.
5991 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5992 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5993 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5994 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5995 return Div; // must be loop invariant
5996 return getUDivExpr(LHS, RHS);
5999 // If this is a loop recurrence for a loop that does not contain L, then we
6000 // are dealing with the final value computed by the loop.
6001 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6002 // First, attempt to evaluate each operand.
6003 // Avoid performing the look-up in the common case where the specified
6004 // expression has no loop-variant portions.
6005 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6006 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6007 if (OpAtScope == AddRec->getOperand(i))
6010 // Okay, at least one of these operands is loop variant but might be
6011 // foldable. Build a new instance of the folded commutative expression.
6012 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6013 AddRec->op_begin()+i);
6014 NewOps.push_back(OpAtScope);
6015 for (++i; i != e; ++i)
6016 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6018 const SCEV *FoldedRec =
6019 getAddRecExpr(NewOps, AddRec->getLoop(),
6020 AddRec->getNoWrapFlags(SCEV::FlagNW));
6021 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6022 // The addrec may be folded to a nonrecurrence, for example, if the
6023 // induction variable is multiplied by zero after constant folding. Go
6024 // ahead and return the folded value.
6030 // If the scope is outside the addrec's loop, evaluate it by using the
6031 // loop exit value of the addrec.
6032 if (!AddRec->getLoop()->contains(L)) {
6033 // To evaluate this recurrence, we need to know how many times the AddRec
6034 // loop iterates. Compute this now.
6035 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6036 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6038 // Then, evaluate the AddRec.
6039 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6045 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6046 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6047 if (Op == Cast->getOperand())
6048 return Cast; // must be loop invariant
6049 return getZeroExtendExpr(Op, Cast->getType());
6052 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6053 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6054 if (Op == Cast->getOperand())
6055 return Cast; // must be loop invariant
6056 return getSignExtendExpr(Op, Cast->getType());
6059 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6060 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6061 if (Op == Cast->getOperand())
6062 return Cast; // must be loop invariant
6063 return getTruncateExpr(Op, Cast->getType());
6066 llvm_unreachable("Unknown SCEV type!");
6069 /// getSCEVAtScope - This is a convenience function which does
6070 /// getSCEVAtScope(getSCEV(V), L).
6071 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6072 return getSCEVAtScope(getSCEV(V), L);
6075 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6076 /// following equation:
6078 /// A * X = B (mod N)
6080 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6081 /// A and B isn't important.
6083 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6084 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6085 ScalarEvolution &SE) {
6086 uint32_t BW = A.getBitWidth();
6087 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6088 assert(A != 0 && "A must be non-zero.");
6092 // The gcd of A and N may have only one prime factor: 2. The number of
6093 // trailing zeros in A is its multiplicity
6094 uint32_t Mult2 = A.countTrailingZeros();
6097 // 2. Check if B is divisible by D.
6099 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6100 // is not less than multiplicity of this prime factor for D.
6101 if (B.countTrailingZeros() < Mult2)
6102 return SE.getCouldNotCompute();
6104 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6107 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6108 // bit width during computations.
6109 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6110 APInt Mod(BW + 1, 0);
6111 Mod.setBit(BW - Mult2); // Mod = N / D
6112 APInt I = AD.multiplicativeInverse(Mod);
6114 // 4. Compute the minimum unsigned root of the equation:
6115 // I * (B / D) mod (N / D)
6116 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6118 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6120 return SE.getConstant(Result.trunc(BW));
6123 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6124 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6125 /// might be the same) or two SCEVCouldNotCompute objects.
6127 static std::pair<const SCEV *,const SCEV *>
6128 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6129 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6130 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6131 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6132 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6134 // We currently can only solve this if the coefficients are constants.
6135 if (!LC || !MC || !NC) {
6136 const SCEV *CNC = SE.getCouldNotCompute();
6137 return std::make_pair(CNC, CNC);
6140 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6141 const APInt &L = LC->getValue()->getValue();
6142 const APInt &M = MC->getValue()->getValue();
6143 const APInt &N = NC->getValue()->getValue();
6144 APInt Two(BitWidth, 2);
6145 APInt Four(BitWidth, 4);
6148 using namespace APIntOps;
6150 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6151 // The B coefficient is M-N/2
6155 // The A coefficient is N/2
6156 APInt A(N.sdiv(Two));
6158 // Compute the B^2-4ac term.
6161 SqrtTerm -= Four * (A * C);
6163 if (SqrtTerm.isNegative()) {
6164 // The loop is provably infinite.
6165 const SCEV *CNC = SE.getCouldNotCompute();
6166 return std::make_pair(CNC, CNC);
6169 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6170 // integer value or else APInt::sqrt() will assert.
6171 APInt SqrtVal(SqrtTerm.sqrt());
6173 // Compute the two solutions for the quadratic formula.
6174 // The divisions must be performed as signed divisions.
6177 if (TwoA.isMinValue()) {
6178 const SCEV *CNC = SE.getCouldNotCompute();
6179 return std::make_pair(CNC, CNC);
6182 LLVMContext &Context = SE.getContext();
6184 ConstantInt *Solution1 =
6185 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6186 ConstantInt *Solution2 =
6187 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6189 return std::make_pair(SE.getConstant(Solution1),
6190 SE.getConstant(Solution2));
6191 } // end APIntOps namespace
6194 /// HowFarToZero - Return the number of times a backedge comparing the specified
6195 /// value to zero will execute. If not computable, return CouldNotCompute.
6197 /// This is only used for loops with a "x != y" exit test. The exit condition is
6198 /// now expressed as a single expression, V = x-y. So the exit test is
6199 /// effectively V != 0. We know and take advantage of the fact that this
6200 /// expression only being used in a comparison by zero context.
6201 ScalarEvolution::ExitLimit
6202 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6203 // If the value is a constant
6204 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6205 // If the value is already zero, the branch will execute zero times.
6206 if (C->getValue()->isZero()) return C;
6207 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6210 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6211 if (!AddRec || AddRec->getLoop() != L)
6212 return getCouldNotCompute();
6214 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6215 // the quadratic equation to solve it.
6216 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6217 std::pair<const SCEV *,const SCEV *> Roots =
6218 SolveQuadraticEquation(AddRec, *this);
6219 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6220 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6223 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6224 << " sol#2: " << *R2 << "\n";
6226 // Pick the smallest positive root value.
6227 if (ConstantInt *CB =
6228 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6231 if (!CB->getZExtValue())
6232 std::swap(R1, R2); // R1 is the minimum root now.
6234 // We can only use this value if the chrec ends up with an exact zero
6235 // value at this index. When solving for "X*X != 5", for example, we
6236 // should not accept a root of 2.
6237 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6239 return R1; // We found a quadratic root!
6242 return getCouldNotCompute();
6245 // Otherwise we can only handle this if it is affine.
6246 if (!AddRec->isAffine())
6247 return getCouldNotCompute();
6249 // If this is an affine expression, the execution count of this branch is
6250 // the minimum unsigned root of the following equation:
6252 // Start + Step*N = 0 (mod 2^BW)
6256 // Step*N = -Start (mod 2^BW)
6258 // where BW is the common bit width of Start and Step.
6260 // Get the initial value for the loop.
6261 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6262 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6264 // For now we handle only constant steps.
6266 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6267 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6268 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6269 // We have not yet seen any such cases.
6270 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6271 if (!StepC || StepC->getValue()->equalsInt(0))
6272 return getCouldNotCompute();
6274 // For positive steps (counting up until unsigned overflow):
6275 // N = -Start/Step (as unsigned)
6276 // For negative steps (counting down to zero):
6278 // First compute the unsigned distance from zero in the direction of Step.
6279 bool CountDown = StepC->getValue()->getValue().isNegative();
6280 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6282 // Handle unitary steps, which cannot wraparound.
6283 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6284 // N = Distance (as unsigned)
6285 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6286 ConstantRange CR = getUnsignedRange(Start);
6287 const SCEV *MaxBECount;
6288 if (!CountDown && CR.getUnsignedMin().isMinValue())
6289 // When counting up, the worst starting value is 1, not 0.
6290 MaxBECount = CR.getUnsignedMax().isMinValue()
6291 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6292 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6294 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6295 : -CR.getUnsignedMin());
6296 return ExitLimit(Distance, MaxBECount);
6299 // As a special case, handle the instance where Step is a positive power of
6300 // two. In this case, determining whether Step divides Distance evenly can be
6301 // done by counting and comparing the number of trailing zeros of Step and
6304 const APInt &StepV = StepC->getValue()->getValue();
6305 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6306 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6307 // case is not handled as this code is guarded by !CountDown.
6308 if (StepV.isPowerOf2() &&
6309 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
6310 return getUDivExactExpr(Distance, Step);
6313 // If the condition controls loop exit (the loop exits only if the expression
6314 // is true) and the addition is no-wrap we can use unsigned divide to
6315 // compute the backedge count. In this case, the step may not divide the
6316 // distance, but we don't care because if the condition is "missed" the loop
6317 // will have undefined behavior due to wrapping.
6318 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6320 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6321 return ExitLimit(Exact, Exact);
6324 // Then, try to solve the above equation provided that Start is constant.
6325 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6326 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6327 -StartC->getValue()->getValue(),
6329 return getCouldNotCompute();
6332 /// HowFarToNonZero - Return the number of times a backedge checking the
6333 /// specified value for nonzero will execute. If not computable, return
6335 ScalarEvolution::ExitLimit
6336 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6337 // Loops that look like: while (X == 0) are very strange indeed. We don't
6338 // handle them yet except for the trivial case. This could be expanded in the
6339 // future as needed.
6341 // If the value is a constant, check to see if it is known to be non-zero
6342 // already. If so, the backedge will execute zero times.
6343 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6344 if (!C->getValue()->isNullValue())
6345 return getConstant(C->getType(), 0);
6346 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6349 // We could implement others, but I really doubt anyone writes loops like
6350 // this, and if they did, they would already be constant folded.
6351 return getCouldNotCompute();
6354 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6355 /// (which may not be an immediate predecessor) which has exactly one
6356 /// successor from which BB is reachable, or null if no such block is
6359 std::pair<BasicBlock *, BasicBlock *>
6360 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6361 // If the block has a unique predecessor, then there is no path from the
6362 // predecessor to the block that does not go through the direct edge
6363 // from the predecessor to the block.
6364 if (BasicBlock *Pred = BB->getSinglePredecessor())
6365 return std::make_pair(Pred, BB);
6367 // A loop's header is defined to be a block that dominates the loop.
6368 // If the header has a unique predecessor outside the loop, it must be
6369 // a block that has exactly one successor that can reach the loop.
6370 if (Loop *L = LI.getLoopFor(BB))
6371 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6373 return std::pair<BasicBlock *, BasicBlock *>();
6376 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6377 /// testing whether two expressions are equal, however for the purposes of
6378 /// looking for a condition guarding a loop, it can be useful to be a little
6379 /// more general, since a front-end may have replicated the controlling
6382 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6383 // Quick check to see if they are the same SCEV.
6384 if (A == B) return true;
6386 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6387 // two different instructions with the same value. Check for this case.
6388 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6389 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6390 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6391 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6392 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6395 // Otherwise assume they may have a different value.
6399 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6400 /// predicate Pred. Return true iff any changes were made.
6402 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6403 const SCEV *&LHS, const SCEV *&RHS,
6405 bool Changed = false;
6407 // If we hit the max recursion limit bail out.
6411 // Canonicalize a constant to the right side.
6412 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6413 // Check for both operands constant.
6414 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6415 if (ConstantExpr::getICmp(Pred,
6417 RHSC->getValue())->isNullValue())
6418 goto trivially_false;
6420 goto trivially_true;
6422 // Otherwise swap the operands to put the constant on the right.
6423 std::swap(LHS, RHS);
6424 Pred = ICmpInst::getSwappedPredicate(Pred);
6428 // If we're comparing an addrec with a value which is loop-invariant in the
6429 // addrec's loop, put the addrec on the left. Also make a dominance check,
6430 // as both operands could be addrecs loop-invariant in each other's loop.
6431 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6432 const Loop *L = AR->getLoop();
6433 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6434 std::swap(LHS, RHS);
6435 Pred = ICmpInst::getSwappedPredicate(Pred);
6440 // If there's a constant operand, canonicalize comparisons with boundary
6441 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6442 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6443 const APInt &RA = RC->getValue()->getValue();
6445 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6446 case ICmpInst::ICMP_EQ:
6447 case ICmpInst::ICMP_NE:
6448 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6450 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6451 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6452 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6453 ME->getOperand(0)->isAllOnesValue()) {
6454 RHS = AE->getOperand(1);
6455 LHS = ME->getOperand(1);
6459 case ICmpInst::ICMP_UGE:
6460 if ((RA - 1).isMinValue()) {
6461 Pred = ICmpInst::ICMP_NE;
6462 RHS = getConstant(RA - 1);
6466 if (RA.isMaxValue()) {
6467 Pred = ICmpInst::ICMP_EQ;
6471 if (RA.isMinValue()) goto trivially_true;
6473 Pred = ICmpInst::ICMP_UGT;
6474 RHS = getConstant(RA - 1);
6477 case ICmpInst::ICMP_ULE:
6478 if ((RA + 1).isMaxValue()) {
6479 Pred = ICmpInst::ICMP_NE;
6480 RHS = getConstant(RA + 1);
6484 if (RA.isMinValue()) {
6485 Pred = ICmpInst::ICMP_EQ;
6489 if (RA.isMaxValue()) goto trivially_true;
6491 Pred = ICmpInst::ICMP_ULT;
6492 RHS = getConstant(RA + 1);
6495 case ICmpInst::ICMP_SGE:
6496 if ((RA - 1).isMinSignedValue()) {
6497 Pred = ICmpInst::ICMP_NE;
6498 RHS = getConstant(RA - 1);
6502 if (RA.isMaxSignedValue()) {
6503 Pred = ICmpInst::ICMP_EQ;
6507 if (RA.isMinSignedValue()) goto trivially_true;
6509 Pred = ICmpInst::ICMP_SGT;
6510 RHS = getConstant(RA - 1);
6513 case ICmpInst::ICMP_SLE:
6514 if ((RA + 1).isMaxSignedValue()) {
6515 Pred = ICmpInst::ICMP_NE;
6516 RHS = getConstant(RA + 1);
6520 if (RA.isMinSignedValue()) {
6521 Pred = ICmpInst::ICMP_EQ;
6525 if (RA.isMaxSignedValue()) goto trivially_true;
6527 Pred = ICmpInst::ICMP_SLT;
6528 RHS = getConstant(RA + 1);
6531 case ICmpInst::ICMP_UGT:
6532 if (RA.isMinValue()) {
6533 Pred = ICmpInst::ICMP_NE;
6537 if ((RA + 1).isMaxValue()) {
6538 Pred = ICmpInst::ICMP_EQ;
6539 RHS = getConstant(RA + 1);
6543 if (RA.isMaxValue()) goto trivially_false;
6545 case ICmpInst::ICMP_ULT:
6546 if (RA.isMaxValue()) {
6547 Pred = ICmpInst::ICMP_NE;
6551 if ((RA - 1).isMinValue()) {
6552 Pred = ICmpInst::ICMP_EQ;
6553 RHS = getConstant(RA - 1);
6557 if (RA.isMinValue()) goto trivially_false;
6559 case ICmpInst::ICMP_SGT:
6560 if (RA.isMinSignedValue()) {
6561 Pred = ICmpInst::ICMP_NE;
6565 if ((RA + 1).isMaxSignedValue()) {
6566 Pred = ICmpInst::ICMP_EQ;
6567 RHS = getConstant(RA + 1);
6571 if (RA.isMaxSignedValue()) goto trivially_false;
6573 case ICmpInst::ICMP_SLT:
6574 if (RA.isMaxSignedValue()) {
6575 Pred = ICmpInst::ICMP_NE;
6579 if ((RA - 1).isMinSignedValue()) {
6580 Pred = ICmpInst::ICMP_EQ;
6581 RHS = getConstant(RA - 1);
6585 if (RA.isMinSignedValue()) goto trivially_false;
6590 // Check for obvious equality.
6591 if (HasSameValue(LHS, RHS)) {
6592 if (ICmpInst::isTrueWhenEqual(Pred))
6593 goto trivially_true;
6594 if (ICmpInst::isFalseWhenEqual(Pred))
6595 goto trivially_false;
6598 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6599 // adding or subtracting 1 from one of the operands.
6601 case ICmpInst::ICMP_SLE:
6602 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6603 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6605 Pred = ICmpInst::ICMP_SLT;
6607 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6608 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6610 Pred = ICmpInst::ICMP_SLT;
6614 case ICmpInst::ICMP_SGE:
6615 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6616 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6618 Pred = ICmpInst::ICMP_SGT;
6620 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6621 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6623 Pred = ICmpInst::ICMP_SGT;
6627 case ICmpInst::ICMP_ULE:
6628 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6629 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6631 Pred = ICmpInst::ICMP_ULT;
6633 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6634 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6636 Pred = ICmpInst::ICMP_ULT;
6640 case ICmpInst::ICMP_UGE:
6641 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6642 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6644 Pred = ICmpInst::ICMP_UGT;
6646 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6647 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6649 Pred = ICmpInst::ICMP_UGT;
6657 // TODO: More simplifications are possible here.
6659 // Recursively simplify until we either hit a recursion limit or nothing
6662 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6668 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6669 Pred = ICmpInst::ICMP_EQ;
6674 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6675 Pred = ICmpInst::ICMP_NE;
6679 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6680 return getSignedRange(S).getSignedMax().isNegative();
6683 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6684 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6687 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6688 return !getSignedRange(S).getSignedMin().isNegative();
6691 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6692 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6695 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6696 return isKnownNegative(S) || isKnownPositive(S);
6699 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6700 const SCEV *LHS, const SCEV *RHS) {
6701 // Canonicalize the inputs first.
6702 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6704 // If LHS or RHS is an addrec, check to see if the condition is true in
6705 // every iteration of the loop.
6706 // If LHS and RHS are both addrec, both conditions must be true in
6707 // every iteration of the loop.
6708 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6709 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6710 bool LeftGuarded = false;
6711 bool RightGuarded = false;
6713 const Loop *L = LAR->getLoop();
6714 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6715 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6716 if (!RAR) return true;
6721 const Loop *L = RAR->getLoop();
6722 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6723 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6724 if (!LAR) return true;
6725 RightGuarded = true;
6728 if (LeftGuarded && RightGuarded)
6731 // Otherwise see what can be done with known constant ranges.
6732 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6735 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
6736 ICmpInst::Predicate Pred,
6738 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
6741 // Verify an invariant: inverting the predicate should turn a monotonically
6742 // increasing change to a monotonically decreasing one, and vice versa.
6743 bool IncreasingSwapped;
6744 bool ResultSwapped = isMonotonicPredicateImpl(
6745 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
6747 assert(Result == ResultSwapped && "should be able to analyze both!");
6749 assert(Increasing == !IncreasingSwapped &&
6750 "monotonicity should flip as we flip the predicate");
6756 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
6757 ICmpInst::Predicate Pred,
6760 // A zero step value for LHS means the induction variable is essentially a
6761 // loop invariant value. We don't really depend on the predicate actually
6762 // flipping from false to true (for increasing predicates, and the other way
6763 // around for decreasing predicates), all we care about is that *if* the
6764 // predicate changes then it only changes from false to true.
6766 // A zero step value in itself is not very useful, but there may be places
6767 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
6768 // as general as possible.
6772 return false; // Conservative answer
6774 case ICmpInst::ICMP_UGT:
6775 case ICmpInst::ICMP_UGE:
6776 case ICmpInst::ICMP_ULT:
6777 case ICmpInst::ICMP_ULE:
6778 if (!LHS->getNoWrapFlags(SCEV::FlagNUW))
6781 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
6784 case ICmpInst::ICMP_SGT:
6785 case ICmpInst::ICMP_SGE:
6786 case ICmpInst::ICMP_SLT:
6787 case ICmpInst::ICMP_SLE: {
6788 if (!LHS->getNoWrapFlags(SCEV::FlagNSW))
6791 const SCEV *Step = LHS->getStepRecurrence(*this);
6793 if (isKnownNonNegative(Step)) {
6794 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
6798 if (isKnownNonPositive(Step)) {
6799 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
6808 llvm_unreachable("switch has default clause!");
6811 bool ScalarEvolution::isLoopInvariantPredicate(
6812 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
6813 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
6814 const SCEV *&InvariantRHS) {
6816 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
6817 if (!isLoopInvariant(RHS, L)) {
6818 if (!isLoopInvariant(LHS, L))
6821 std::swap(LHS, RHS);
6822 Pred = ICmpInst::getSwappedPredicate(Pred);
6825 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
6826 if (!ArLHS || ArLHS->getLoop() != L)
6830 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
6833 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
6834 // true as the loop iterates, and the backedge is control dependent on
6835 // "ArLHS `Pred` RHS" == true then we can reason as follows:
6837 // * if the predicate was false in the first iteration then the predicate
6838 // is never evaluated again, since the loop exits without taking the
6840 // * if the predicate was true in the first iteration then it will
6841 // continue to be true for all future iterations since it is
6842 // monotonically increasing.
6844 // For both the above possibilities, we can replace the loop varying
6845 // predicate with its value on the first iteration of the loop (which is
6848 // A similar reasoning applies for a monotonically decreasing predicate, by
6849 // replacing true with false and false with true in the above two bullets.
6851 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
6853 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
6856 InvariantPred = Pred;
6857 InvariantLHS = ArLHS->getStart();
6863 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6864 const SCEV *LHS, const SCEV *RHS) {
6865 if (HasSameValue(LHS, RHS))
6866 return ICmpInst::isTrueWhenEqual(Pred);
6868 // This code is split out from isKnownPredicate because it is called from
6869 // within isLoopEntryGuardedByCond.
6872 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6873 case ICmpInst::ICMP_SGT:
6874 std::swap(LHS, RHS);
6875 case ICmpInst::ICMP_SLT: {
6876 ConstantRange LHSRange = getSignedRange(LHS);
6877 ConstantRange RHSRange = getSignedRange(RHS);
6878 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6880 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6884 case ICmpInst::ICMP_SGE:
6885 std::swap(LHS, RHS);
6886 case ICmpInst::ICMP_SLE: {
6887 ConstantRange LHSRange = getSignedRange(LHS);
6888 ConstantRange RHSRange = getSignedRange(RHS);
6889 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6891 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6895 case ICmpInst::ICMP_UGT:
6896 std::swap(LHS, RHS);
6897 case ICmpInst::ICMP_ULT: {
6898 ConstantRange LHSRange = getUnsignedRange(LHS);
6899 ConstantRange RHSRange = getUnsignedRange(RHS);
6900 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6902 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6906 case ICmpInst::ICMP_UGE:
6907 std::swap(LHS, RHS);
6908 case ICmpInst::ICMP_ULE: {
6909 ConstantRange LHSRange = getUnsignedRange(LHS);
6910 ConstantRange RHSRange = getUnsignedRange(RHS);
6911 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6913 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6917 case ICmpInst::ICMP_NE: {
6918 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6920 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6923 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6924 if (isKnownNonZero(Diff))
6928 case ICmpInst::ICMP_EQ:
6929 // The check at the top of the function catches the case where
6930 // the values are known to be equal.
6936 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6937 /// protected by a conditional between LHS and RHS. This is used to
6938 /// to eliminate casts.
6940 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6941 ICmpInst::Predicate Pred,
6942 const SCEV *LHS, const SCEV *RHS) {
6943 // Interpret a null as meaning no loop, where there is obviously no guard
6944 // (interprocedural conditions notwithstanding).
6945 if (!L) return true;
6947 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6949 BasicBlock *Latch = L->getLoopLatch();
6953 BranchInst *LoopContinuePredicate =
6954 dyn_cast<BranchInst>(Latch->getTerminator());
6955 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6956 isImpliedCond(Pred, LHS, RHS,
6957 LoopContinuePredicate->getCondition(),
6958 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6961 struct ClearWalkingBEDominatingCondsOnExit {
6962 ScalarEvolution &SE;
6964 explicit ClearWalkingBEDominatingCondsOnExit(ScalarEvolution &SE)
6967 ~ClearWalkingBEDominatingCondsOnExit() {
6968 SE.WalkingBEDominatingConds = false;
6972 // We don't want more than one activation of the following loops on the stack
6973 // -- that can lead to O(n!) time complexity.
6974 if (WalkingBEDominatingConds)
6977 WalkingBEDominatingConds = true;
6978 ClearWalkingBEDominatingCondsOnExit ClearOnExit(*this);
6980 // Check conditions due to any @llvm.assume intrinsics.
6981 for (auto &AssumeVH : AC.assumptions()) {
6984 auto *CI = cast<CallInst>(AssumeVH);
6985 if (!DT.dominates(CI, Latch->getTerminator()))
6988 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6992 // If the loop is not reachable from the entry block, we risk running into an
6993 // infinite loop as we walk up into the dom tree. These loops do not matter
6994 // anyway, so we just return a conservative answer when we see them.
6995 if (!DT.isReachableFromEntry(L->getHeader()))
6998 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
6999 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7001 assert(DTN && "should reach the loop header before reaching the root!");
7003 BasicBlock *BB = DTN->getBlock();
7004 BasicBlock *PBB = BB->getSinglePredecessor();
7008 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7009 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7012 Value *Condition = ContinuePredicate->getCondition();
7014 // If we have an edge `E` within the loop body that dominates the only
7015 // latch, the condition guarding `E` also guards the backedge. This
7016 // reasoning works only for loops with a single latch.
7018 BasicBlockEdge DominatingEdge(PBB, BB);
7019 if (DominatingEdge.isSingleEdge()) {
7020 // We're constructively (and conservatively) enumerating edges within the
7021 // loop body that dominate the latch. The dominator tree better agree
7023 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7025 if (isImpliedCond(Pred, LHS, RHS, Condition,
7026 BB != ContinuePredicate->getSuccessor(0)))
7034 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7035 /// by a conditional between LHS and RHS. This is used to help avoid max
7036 /// expressions in loop trip counts, and to eliminate casts.
7038 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7039 ICmpInst::Predicate Pred,
7040 const SCEV *LHS, const SCEV *RHS) {
7041 // Interpret a null as meaning no loop, where there is obviously no guard
7042 // (interprocedural conditions notwithstanding).
7043 if (!L) return false;
7045 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7047 // Starting at the loop predecessor, climb up the predecessor chain, as long
7048 // as there are predecessors that can be found that have unique successors
7049 // leading to the original header.
7050 for (std::pair<BasicBlock *, BasicBlock *>
7051 Pair(L->getLoopPredecessor(), L->getHeader());
7053 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7055 BranchInst *LoopEntryPredicate =
7056 dyn_cast<BranchInst>(Pair.first->getTerminator());
7057 if (!LoopEntryPredicate ||
7058 LoopEntryPredicate->isUnconditional())
7061 if (isImpliedCond(Pred, LHS, RHS,
7062 LoopEntryPredicate->getCondition(),
7063 LoopEntryPredicate->getSuccessor(0) != Pair.second))
7067 // Check conditions due to any @llvm.assume intrinsics.
7068 for (auto &AssumeVH : AC.assumptions()) {
7071 auto *CI = cast<CallInst>(AssumeVH);
7072 if (!DT.dominates(CI, L->getHeader()))
7075 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7082 /// RAII wrapper to prevent recursive application of isImpliedCond.
7083 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7084 /// currently evaluating isImpliedCond.
7085 struct MarkPendingLoopPredicate {
7087 DenseSet<Value*> &LoopPreds;
7090 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7091 : Cond(C), LoopPreds(LP) {
7092 Pending = !LoopPreds.insert(Cond).second;
7094 ~MarkPendingLoopPredicate() {
7096 LoopPreds.erase(Cond);
7100 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7101 /// and RHS is true whenever the given Cond value evaluates to true.
7102 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7103 const SCEV *LHS, const SCEV *RHS,
7104 Value *FoundCondValue,
7106 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7110 // Recursively handle And and Or conditions.
7111 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7112 if (BO->getOpcode() == Instruction::And) {
7114 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7115 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7116 } else if (BO->getOpcode() == Instruction::Or) {
7118 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7119 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7123 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
7124 if (!ICI) return false;
7126 // Now that we found a conditional branch that dominates the loop or controls
7127 // the loop latch. Check to see if it is the comparison we are looking for.
7128 ICmpInst::Predicate FoundPred;
7130 FoundPred = ICI->getInversePredicate();
7132 FoundPred = ICI->getPredicate();
7134 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
7135 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
7137 // Balance the types.
7138 if (getTypeSizeInBits(LHS->getType()) <
7139 getTypeSizeInBits(FoundLHS->getType())) {
7140 if (CmpInst::isSigned(Pred)) {
7141 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
7142 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
7144 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
7145 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
7147 } else if (getTypeSizeInBits(LHS->getType()) >
7148 getTypeSizeInBits(FoundLHS->getType())) {
7149 if (CmpInst::isSigned(FoundPred)) {
7150 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
7151 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
7153 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
7154 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
7158 // Canonicalize the query to match the way instcombine will have
7159 // canonicalized the comparison.
7160 if (SimplifyICmpOperands(Pred, LHS, RHS))
7162 return CmpInst::isTrueWhenEqual(Pred);
7163 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
7164 if (FoundLHS == FoundRHS)
7165 return CmpInst::isFalseWhenEqual(FoundPred);
7167 // Check to see if we can make the LHS or RHS match.
7168 if (LHS == FoundRHS || RHS == FoundLHS) {
7169 if (isa<SCEVConstant>(RHS)) {
7170 std::swap(FoundLHS, FoundRHS);
7171 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
7173 std::swap(LHS, RHS);
7174 Pred = ICmpInst::getSwappedPredicate(Pred);
7178 // Check whether the found predicate is the same as the desired predicate.
7179 if (FoundPred == Pred)
7180 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7182 // Check whether swapping the found predicate makes it the same as the
7183 // desired predicate.
7184 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
7185 if (isa<SCEVConstant>(RHS))
7186 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
7188 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
7189 RHS, LHS, FoundLHS, FoundRHS);
7192 // Check if we can make progress by sharpening ranges.
7193 if (FoundPred == ICmpInst::ICMP_NE &&
7194 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
7196 const SCEVConstant *C = nullptr;
7197 const SCEV *V = nullptr;
7199 if (isa<SCEVConstant>(FoundLHS)) {
7200 C = cast<SCEVConstant>(FoundLHS);
7203 C = cast<SCEVConstant>(FoundRHS);
7207 // The guarding predicate tells us that C != V. If the known range
7208 // of V is [C, t), we can sharpen the range to [C + 1, t). The
7209 // range we consider has to correspond to same signedness as the
7210 // predicate we're interested in folding.
7212 APInt Min = ICmpInst::isSigned(Pred) ?
7213 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7215 if (Min == C->getValue()->getValue()) {
7216 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7217 // This is true even if (Min + 1) wraps around -- in case of
7218 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7220 APInt SharperMin = Min + 1;
7223 case ICmpInst::ICMP_SGE:
7224 case ICmpInst::ICMP_UGE:
7225 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7227 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7228 getConstant(SharperMin)))
7231 case ICmpInst::ICMP_SGT:
7232 case ICmpInst::ICMP_UGT:
7233 // We know from the range information that (V `Pred` Min ||
7234 // V == Min). We know from the guarding condition that !(V
7235 // == Min). This gives us
7237 // V `Pred` Min || V == Min && !(V == Min)
7240 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7242 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7252 // Check whether the actual condition is beyond sufficient.
7253 if (FoundPred == ICmpInst::ICMP_EQ)
7254 if (ICmpInst::isTrueWhenEqual(Pred))
7255 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7257 if (Pred == ICmpInst::ICMP_NE)
7258 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7259 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7262 // Otherwise assume the worst.
7266 /// isImpliedCondOperands - Test whether the condition described by Pred,
7267 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7268 /// and FoundRHS is true.
7269 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7270 const SCEV *LHS, const SCEV *RHS,
7271 const SCEV *FoundLHS,
7272 const SCEV *FoundRHS) {
7273 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7276 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7277 FoundLHS, FoundRHS) ||
7278 // ~x < ~y --> x > y
7279 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7280 getNotSCEV(FoundRHS),
7281 getNotSCEV(FoundLHS));
7285 /// If Expr computes ~A, return A else return nullptr
7286 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7287 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7288 if (!Add || Add->getNumOperands() != 2) return nullptr;
7290 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
7291 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
7294 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7295 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
7297 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
7298 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
7301 return AddRHS->getOperand(1);
7305 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7306 template<typename MaxExprType>
7307 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7308 const SCEV *Candidate) {
7309 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7310 if (!MaxExpr) return false;
7312 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7313 return It != MaxExpr->op_end();
7317 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7318 template<typename MaxExprType>
7319 static bool IsMinConsistingOf(ScalarEvolution &SE,
7320 const SCEV *MaybeMinExpr,
7321 const SCEV *Candidate) {
7322 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7326 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7329 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
7330 ICmpInst::Predicate Pred,
7331 const SCEV *LHS, const SCEV *RHS) {
7333 // If both sides are affine addrecs for the same loop, with equal
7334 // steps, and we know the recurrences don't wrap, then we only
7335 // need to check the predicate on the starting values.
7337 if (!ICmpInst::isRelational(Pred))
7340 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7343 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7346 if (LAR->getLoop() != RAR->getLoop())
7348 if (!LAR->isAffine() || !RAR->isAffine())
7351 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
7354 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
7355 SCEV::FlagNSW : SCEV::FlagNUW;
7356 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
7359 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
7362 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7364 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7365 ICmpInst::Predicate Pred,
7366 const SCEV *LHS, const SCEV *RHS) {
7371 case ICmpInst::ICMP_SGE:
7372 std::swap(LHS, RHS);
7374 case ICmpInst::ICMP_SLE:
7377 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7379 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7381 case ICmpInst::ICMP_UGE:
7382 std::swap(LHS, RHS);
7384 case ICmpInst::ICMP_ULE:
7387 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7389 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7392 llvm_unreachable("covered switch fell through?!");
7395 /// isImpliedCondOperandsHelper - Test whether the condition described by
7396 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7397 /// FoundLHS, and FoundRHS is true.
7399 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7400 const SCEV *LHS, const SCEV *RHS,
7401 const SCEV *FoundLHS,
7402 const SCEV *FoundRHS) {
7403 auto IsKnownPredicateFull =
7404 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7405 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7406 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
7407 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS);
7411 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7412 case ICmpInst::ICMP_EQ:
7413 case ICmpInst::ICMP_NE:
7414 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7417 case ICmpInst::ICMP_SLT:
7418 case ICmpInst::ICMP_SLE:
7419 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7420 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7423 case ICmpInst::ICMP_SGT:
7424 case ICmpInst::ICMP_SGE:
7425 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7426 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7429 case ICmpInst::ICMP_ULT:
7430 case ICmpInst::ICMP_ULE:
7431 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7432 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7435 case ICmpInst::ICMP_UGT:
7436 case ICmpInst::ICMP_UGE:
7437 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7438 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7446 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
7447 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
7448 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
7451 const SCEV *FoundLHS,
7452 const SCEV *FoundRHS) {
7453 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
7454 // The restriction on `FoundRHS` be lifted easily -- it exists only to
7455 // reduce the compile time impact of this optimization.
7458 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
7459 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
7460 !isa<SCEVConstant>(AddLHS->getOperand(0)))
7463 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
7465 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
7466 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
7467 ConstantRange FoundLHSRange =
7468 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
7470 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
7473 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
7474 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
7476 // We can also compute the range of values for `LHS` that satisfy the
7477 // consequent, "`LHS` `Pred` `RHS`":
7478 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
7479 ConstantRange SatisfyingLHSRange =
7480 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
7482 // The antecedent implies the consequent if every value of `LHS` that
7483 // satisfies the antecedent also satisfies the consequent.
7484 return SatisfyingLHSRange.contains(LHSRange);
7487 // Verify if an linear IV with positive stride can overflow when in a
7488 // less-than comparison, knowing the invariant term of the comparison, the
7489 // stride and the knowledge of NSW/NUW flags on the recurrence.
7490 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7491 bool IsSigned, bool NoWrap) {
7492 if (NoWrap) return false;
7494 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7495 const SCEV *One = getConstant(Stride->getType(), 1);
7498 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7499 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7500 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7503 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7504 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7507 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7508 APInt MaxValue = APInt::getMaxValue(BitWidth);
7509 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7512 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7513 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7516 // Verify if an linear IV with negative stride can overflow when in a
7517 // greater-than comparison, knowing the invariant term of the comparison,
7518 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7519 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7520 bool IsSigned, bool NoWrap) {
7521 if (NoWrap) return false;
7523 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7524 const SCEV *One = getConstant(Stride->getType(), 1);
7527 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7528 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7529 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7532 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7533 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7536 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7537 APInt MinValue = APInt::getMinValue(BitWidth);
7538 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7541 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7542 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7545 // Compute the backedge taken count knowing the interval difference, the
7546 // stride and presence of the equality in the comparison.
7547 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7549 const SCEV *One = getConstant(Step->getType(), 1);
7550 Delta = Equality ? getAddExpr(Delta, Step)
7551 : getAddExpr(Delta, getMinusSCEV(Step, One));
7552 return getUDivExpr(Delta, Step);
7555 /// HowManyLessThans - Return the number of times a backedge containing the
7556 /// specified less-than comparison will execute. If not computable, return
7557 /// CouldNotCompute.
7559 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7560 /// the branch (loops exits only if condition is true). In this case, we can use
7561 /// NoWrapFlags to skip overflow checks.
7562 ScalarEvolution::ExitLimit
7563 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7564 const Loop *L, bool IsSigned,
7565 bool ControlsExit) {
7566 // We handle only IV < Invariant
7567 if (!isLoopInvariant(RHS, L))
7568 return getCouldNotCompute();
7570 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7572 // Avoid weird loops
7573 if (!IV || IV->getLoop() != L || !IV->isAffine())
7574 return getCouldNotCompute();
7576 bool NoWrap = ControlsExit &&
7577 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7579 const SCEV *Stride = IV->getStepRecurrence(*this);
7581 // Avoid negative or zero stride values
7582 if (!isKnownPositive(Stride))
7583 return getCouldNotCompute();
7585 // Avoid proven overflow cases: this will ensure that the backedge taken count
7586 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7587 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7588 // behaviors like the case of C language.
7589 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7590 return getCouldNotCompute();
7592 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7593 : ICmpInst::ICMP_ULT;
7594 const SCEV *Start = IV->getStart();
7595 const SCEV *End = RHS;
7596 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7597 const SCEV *Diff = getMinusSCEV(RHS, Start);
7598 // If we have NoWrap set, then we can assume that the increment won't
7599 // overflow, in which case if RHS - Start is a constant, we don't need to
7600 // do a max operation since we can just figure it out statically
7601 if (NoWrap && isa<SCEVConstant>(Diff)) {
7602 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7606 End = IsSigned ? getSMaxExpr(RHS, Start)
7607 : getUMaxExpr(RHS, Start);
7610 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7612 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7613 : getUnsignedRange(Start).getUnsignedMin();
7615 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7616 : getUnsignedRange(Stride).getUnsignedMin();
7618 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7619 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7620 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7622 // Although End can be a MAX expression we estimate MaxEnd considering only
7623 // the case End = RHS. This is safe because in the other case (End - Start)
7624 // is zero, leading to a zero maximum backedge taken count.
7626 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7627 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7629 const SCEV *MaxBECount;
7630 if (isa<SCEVConstant>(BECount))
7631 MaxBECount = BECount;
7633 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7634 getConstant(MinStride), false);
7636 if (isa<SCEVCouldNotCompute>(MaxBECount))
7637 MaxBECount = BECount;
7639 return ExitLimit(BECount, MaxBECount);
7642 ScalarEvolution::ExitLimit
7643 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7644 const Loop *L, bool IsSigned,
7645 bool ControlsExit) {
7646 // We handle only IV > Invariant
7647 if (!isLoopInvariant(RHS, L))
7648 return getCouldNotCompute();
7650 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7652 // Avoid weird loops
7653 if (!IV || IV->getLoop() != L || !IV->isAffine())
7654 return getCouldNotCompute();
7656 bool NoWrap = ControlsExit &&
7657 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7659 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7661 // Avoid negative or zero stride values
7662 if (!isKnownPositive(Stride))
7663 return getCouldNotCompute();
7665 // Avoid proven overflow cases: this will ensure that the backedge taken count
7666 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7667 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7668 // behaviors like the case of C language.
7669 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7670 return getCouldNotCompute();
7672 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7673 : ICmpInst::ICMP_UGT;
7675 const SCEV *Start = IV->getStart();
7676 const SCEV *End = RHS;
7677 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7678 const SCEV *Diff = getMinusSCEV(RHS, Start);
7679 // If we have NoWrap set, then we can assume that the increment won't
7680 // overflow, in which case if RHS - Start is a constant, we don't need to
7681 // do a max operation since we can just figure it out statically
7682 if (NoWrap && isa<SCEVConstant>(Diff)) {
7683 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7684 if (!D.isNegative())
7687 End = IsSigned ? getSMinExpr(RHS, Start)
7688 : getUMinExpr(RHS, Start);
7691 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7693 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7694 : getUnsignedRange(Start).getUnsignedMax();
7696 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7697 : getUnsignedRange(Stride).getUnsignedMin();
7699 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7700 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7701 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7703 // Although End can be a MIN expression we estimate MinEnd considering only
7704 // the case End = RHS. This is safe because in the other case (Start - End)
7705 // is zero, leading to a zero maximum backedge taken count.
7707 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7708 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7711 const SCEV *MaxBECount = getCouldNotCompute();
7712 if (isa<SCEVConstant>(BECount))
7713 MaxBECount = BECount;
7715 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7716 getConstant(MinStride), false);
7718 if (isa<SCEVCouldNotCompute>(MaxBECount))
7719 MaxBECount = BECount;
7721 return ExitLimit(BECount, MaxBECount);
7724 /// getNumIterationsInRange - Return the number of iterations of this loop that
7725 /// produce values in the specified constant range. Another way of looking at
7726 /// this is that it returns the first iteration number where the value is not in
7727 /// the condition, thus computing the exit count. If the iteration count can't
7728 /// be computed, an instance of SCEVCouldNotCompute is returned.
7729 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7730 ScalarEvolution &SE) const {
7731 if (Range.isFullSet()) // Infinite loop.
7732 return SE.getCouldNotCompute();
7734 // If the start is a non-zero constant, shift the range to simplify things.
7735 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7736 if (!SC->getValue()->isZero()) {
7737 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7738 Operands[0] = SE.getConstant(SC->getType(), 0);
7739 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7740 getNoWrapFlags(FlagNW));
7741 if (const SCEVAddRecExpr *ShiftedAddRec =
7742 dyn_cast<SCEVAddRecExpr>(Shifted))
7743 return ShiftedAddRec->getNumIterationsInRange(
7744 Range.subtract(SC->getValue()->getValue()), SE);
7745 // This is strange and shouldn't happen.
7746 return SE.getCouldNotCompute();
7749 // The only time we can solve this is when we have all constant indices.
7750 // Otherwise, we cannot determine the overflow conditions.
7751 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7752 if (!isa<SCEVConstant>(getOperand(i)))
7753 return SE.getCouldNotCompute();
7756 // Okay at this point we know that all elements of the chrec are constants and
7757 // that the start element is zero.
7759 // First check to see if the range contains zero. If not, the first
7761 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7762 if (!Range.contains(APInt(BitWidth, 0)))
7763 return SE.getConstant(getType(), 0);
7766 // If this is an affine expression then we have this situation:
7767 // Solve {0,+,A} in Range === Ax in Range
7769 // We know that zero is in the range. If A is positive then we know that
7770 // the upper value of the range must be the first possible exit value.
7771 // If A is negative then the lower of the range is the last possible loop
7772 // value. Also note that we already checked for a full range.
7773 APInt One(BitWidth,1);
7774 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7775 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7777 // The exit value should be (End+A)/A.
7778 APInt ExitVal = (End + A).udiv(A);
7779 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7781 // Evaluate at the exit value. If we really did fall out of the valid
7782 // range, then we computed our trip count, otherwise wrap around or other
7783 // things must have happened.
7784 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7785 if (Range.contains(Val->getValue()))
7786 return SE.getCouldNotCompute(); // Something strange happened
7788 // Ensure that the previous value is in the range. This is a sanity check.
7789 assert(Range.contains(
7790 EvaluateConstantChrecAtConstant(this,
7791 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7792 "Linear scev computation is off in a bad way!");
7793 return SE.getConstant(ExitValue);
7794 } else if (isQuadratic()) {
7795 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7796 // quadratic equation to solve it. To do this, we must frame our problem in
7797 // terms of figuring out when zero is crossed, instead of when
7798 // Range.getUpper() is crossed.
7799 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7800 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7801 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7802 // getNoWrapFlags(FlagNW)
7805 // Next, solve the constructed addrec
7806 std::pair<const SCEV *,const SCEV *> Roots =
7807 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7808 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7809 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7811 // Pick the smallest positive root value.
7812 if (ConstantInt *CB =
7813 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7814 R1->getValue(), R2->getValue()))) {
7815 if (!CB->getZExtValue())
7816 std::swap(R1, R2); // R1 is the minimum root now.
7818 // Make sure the root is not off by one. The returned iteration should
7819 // not be in the range, but the previous one should be. When solving
7820 // for "X*X < 5", for example, we should not return a root of 2.
7821 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7824 if (Range.contains(R1Val->getValue())) {
7825 // The next iteration must be out of the range...
7826 ConstantInt *NextVal =
7827 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7829 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7830 if (!Range.contains(R1Val->getValue()))
7831 return SE.getConstant(NextVal);
7832 return SE.getCouldNotCompute(); // Something strange happened
7835 // If R1 was not in the range, then it is a good return value. Make
7836 // sure that R1-1 WAS in the range though, just in case.
7837 ConstantInt *NextVal =
7838 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7839 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7840 if (Range.contains(R1Val->getValue()))
7842 return SE.getCouldNotCompute(); // Something strange happened
7847 return SE.getCouldNotCompute();
7853 FindUndefs() : Found(false) {}
7855 bool follow(const SCEV *S) {
7856 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7857 if (isa<UndefValue>(C->getValue()))
7859 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7860 if (isa<UndefValue>(C->getValue()))
7864 // Keep looking if we haven't found it yet.
7867 bool isDone() const {
7868 // Stop recursion if we have found an undef.
7874 // Return true when S contains at least an undef value.
7876 containsUndefs(const SCEV *S) {
7878 SCEVTraversal<FindUndefs> ST(F);
7885 // Collect all steps of SCEV expressions.
7886 struct SCEVCollectStrides {
7887 ScalarEvolution &SE;
7888 SmallVectorImpl<const SCEV *> &Strides;
7890 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7891 : SE(SE), Strides(S) {}
7893 bool follow(const SCEV *S) {
7894 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7895 Strides.push_back(AR->getStepRecurrence(SE));
7898 bool isDone() const { return false; }
7901 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7902 struct SCEVCollectTerms {
7903 SmallVectorImpl<const SCEV *> &Terms;
7905 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7908 bool follow(const SCEV *S) {
7909 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7910 if (!containsUndefs(S))
7913 // Stop recursion: once we collected a term, do not walk its operands.
7920 bool isDone() const { return false; }
7924 /// Find parametric terms in this SCEVAddRecExpr.
7925 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
7926 SmallVectorImpl<const SCEV *> &Terms) {
7927 SmallVector<const SCEV *, 4> Strides;
7928 SCEVCollectStrides StrideCollector(*this, Strides);
7929 visitAll(Expr, StrideCollector);
7932 dbgs() << "Strides:\n";
7933 for (const SCEV *S : Strides)
7934 dbgs() << *S << "\n";
7937 for (const SCEV *S : Strides) {
7938 SCEVCollectTerms TermCollector(Terms);
7939 visitAll(S, TermCollector);
7943 dbgs() << "Terms:\n";
7944 for (const SCEV *T : Terms)
7945 dbgs() << *T << "\n";
7949 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7950 SmallVectorImpl<const SCEV *> &Terms,
7951 SmallVectorImpl<const SCEV *> &Sizes) {
7952 int Last = Terms.size() - 1;
7953 const SCEV *Step = Terms[Last];
7955 // End of recursion.
7957 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7958 SmallVector<const SCEV *, 2> Qs;
7959 for (const SCEV *Op : M->operands())
7960 if (!isa<SCEVConstant>(Op))
7963 Step = SE.getMulExpr(Qs);
7966 Sizes.push_back(Step);
7970 for (const SCEV *&Term : Terms) {
7971 // Normalize the terms before the next call to findArrayDimensionsRec.
7973 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7975 // Bail out when GCD does not evenly divide one of the terms.
7982 // Remove all SCEVConstants.
7983 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7984 return isa<SCEVConstant>(E);
7988 if (Terms.size() > 0)
7989 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7992 Sizes.push_back(Step);
7997 struct FindParameter {
7998 bool FoundParameter;
7999 FindParameter() : FoundParameter(false) {}
8001 bool follow(const SCEV *S) {
8002 if (isa<SCEVUnknown>(S)) {
8003 FoundParameter = true;
8004 // Stop recursion: we found a parameter.
8010 bool isDone() const {
8011 // Stop recursion if we have found a parameter.
8012 return FoundParameter;
8017 // Returns true when S contains at least a SCEVUnknown parameter.
8019 containsParameters(const SCEV *S) {
8021 SCEVTraversal<FindParameter> ST(F);
8024 return F.FoundParameter;
8027 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
8029 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
8030 for (const SCEV *T : Terms)
8031 if (containsParameters(T))
8036 // Return the number of product terms in S.
8037 static inline int numberOfTerms(const SCEV *S) {
8038 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
8039 return Expr->getNumOperands();
8043 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
8044 if (isa<SCEVConstant>(T))
8047 if (isa<SCEVUnknown>(T))
8050 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
8051 SmallVector<const SCEV *, 2> Factors;
8052 for (const SCEV *Op : M->operands())
8053 if (!isa<SCEVConstant>(Op))
8054 Factors.push_back(Op);
8056 return SE.getMulExpr(Factors);
8062 /// Return the size of an element read or written by Inst.
8063 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
8065 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
8066 Ty = Store->getValueOperand()->getType();
8067 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
8068 Ty = Load->getType();
8072 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
8073 return getSizeOfExpr(ETy, Ty);
8076 /// Second step of delinearization: compute the array dimensions Sizes from the
8077 /// set of Terms extracted from the memory access function of this SCEVAddRec.
8078 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
8079 SmallVectorImpl<const SCEV *> &Sizes,
8080 const SCEV *ElementSize) const {
8082 if (Terms.size() < 1 || !ElementSize)
8085 // Early return when Terms do not contain parameters: we do not delinearize
8086 // non parametric SCEVs.
8087 if (!containsParameters(Terms))
8091 dbgs() << "Terms:\n";
8092 for (const SCEV *T : Terms)
8093 dbgs() << *T << "\n";
8096 // Remove duplicates.
8097 std::sort(Terms.begin(), Terms.end());
8098 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
8100 // Put larger terms first.
8101 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
8102 return numberOfTerms(LHS) > numberOfTerms(RHS);
8105 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8107 // Divide all terms by the element size.
8108 for (const SCEV *&Term : Terms) {
8110 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
8114 SmallVector<const SCEV *, 4> NewTerms;
8116 // Remove constant factors.
8117 for (const SCEV *T : Terms)
8118 if (const SCEV *NewT = removeConstantFactors(SE, T))
8119 NewTerms.push_back(NewT);
8122 dbgs() << "Terms after sorting:\n";
8123 for (const SCEV *T : NewTerms)
8124 dbgs() << *T << "\n";
8127 if (NewTerms.empty() ||
8128 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
8133 // The last element to be pushed into Sizes is the size of an element.
8134 Sizes.push_back(ElementSize);
8137 dbgs() << "Sizes:\n";
8138 for (const SCEV *S : Sizes)
8139 dbgs() << *S << "\n";
8143 /// Third step of delinearization: compute the access functions for the
8144 /// Subscripts based on the dimensions in Sizes.
8145 void ScalarEvolution::computeAccessFunctions(
8146 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
8147 SmallVectorImpl<const SCEV *> &Sizes) {
8149 // Early exit in case this SCEV is not an affine multivariate function.
8153 if (auto AR = dyn_cast<SCEVAddRecExpr>(Expr))
8154 if (!AR->isAffine())
8157 const SCEV *Res = Expr;
8158 int Last = Sizes.size() - 1;
8159 for (int i = Last; i >= 0; i--) {
8161 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
8164 dbgs() << "Res: " << *Res << "\n";
8165 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
8166 dbgs() << "Res divided by Sizes[i]:\n";
8167 dbgs() << "Quotient: " << *Q << "\n";
8168 dbgs() << "Remainder: " << *R << "\n";
8173 // Do not record the last subscript corresponding to the size of elements in
8177 // Bail out if the remainder is too complex.
8178 if (isa<SCEVAddRecExpr>(R)) {
8187 // Record the access function for the current subscript.
8188 Subscripts.push_back(R);
8191 // Also push in last position the remainder of the last division: it will be
8192 // the access function of the innermost dimension.
8193 Subscripts.push_back(Res);
8195 std::reverse(Subscripts.begin(), Subscripts.end());
8198 dbgs() << "Subscripts:\n";
8199 for (const SCEV *S : Subscripts)
8200 dbgs() << *S << "\n";
8204 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
8205 /// sizes of an array access. Returns the remainder of the delinearization that
8206 /// is the offset start of the array. The SCEV->delinearize algorithm computes
8207 /// the multiples of SCEV coefficients: that is a pattern matching of sub
8208 /// expressions in the stride and base of a SCEV corresponding to the
8209 /// computation of a GCD (greatest common divisor) of base and stride. When
8210 /// SCEV->delinearize fails, it returns the SCEV unchanged.
8212 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
8214 /// void foo(long n, long m, long o, double A[n][m][o]) {
8216 /// for (long i = 0; i < n; i++)
8217 /// for (long j = 0; j < m; j++)
8218 /// for (long k = 0; k < o; k++)
8219 /// A[i][j][k] = 1.0;
8222 /// the delinearization input is the following AddRec SCEV:
8224 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
8226 /// From this SCEV, we are able to say that the base offset of the access is %A
8227 /// because it appears as an offset that does not divide any of the strides in
8230 /// CHECK: Base offset: %A
8232 /// and then SCEV->delinearize determines the size of some of the dimensions of
8233 /// the array as these are the multiples by which the strides are happening:
8235 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
8237 /// Note that the outermost dimension remains of UnknownSize because there are
8238 /// no strides that would help identifying the size of the last dimension: when
8239 /// the array has been statically allocated, one could compute the size of that
8240 /// dimension by dividing the overall size of the array by the size of the known
8241 /// dimensions: %m * %o * 8.
8243 /// Finally delinearize provides the access functions for the array reference
8244 /// that does correspond to A[i][j][k] of the above C testcase:
8246 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
8248 /// The testcases are checking the output of a function pass:
8249 /// DelinearizationPass that walks through all loads and stores of a function
8250 /// asking for the SCEV of the memory access with respect to all enclosing
8251 /// loops, calling SCEV->delinearize on that and printing the results.
8253 void ScalarEvolution::delinearize(const SCEV *Expr,
8254 SmallVectorImpl<const SCEV *> &Subscripts,
8255 SmallVectorImpl<const SCEV *> &Sizes,
8256 const SCEV *ElementSize) {
8257 // First step: collect parametric terms.
8258 SmallVector<const SCEV *, 4> Terms;
8259 collectParametricTerms(Expr, Terms);
8264 // Second step: find subscript sizes.
8265 findArrayDimensions(Terms, Sizes, ElementSize);
8270 // Third step: compute the access functions for each subscript.
8271 computeAccessFunctions(Expr, Subscripts, Sizes);
8273 if (Subscripts.empty())
8277 dbgs() << "succeeded to delinearize " << *Expr << "\n";
8278 dbgs() << "ArrayDecl[UnknownSize]";
8279 for (const SCEV *S : Sizes)
8280 dbgs() << "[" << *S << "]";
8282 dbgs() << "\nArrayRef";
8283 for (const SCEV *S : Subscripts)
8284 dbgs() << "[" << *S << "]";
8289 //===----------------------------------------------------------------------===//
8290 // SCEVCallbackVH Class Implementation
8291 //===----------------------------------------------------------------------===//
8293 void ScalarEvolution::SCEVCallbackVH::deleted() {
8294 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8295 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
8296 SE->ConstantEvolutionLoopExitValue.erase(PN);
8297 SE->ValueExprMap.erase(getValPtr());
8298 // this now dangles!
8301 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
8302 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8304 // Forget all the expressions associated with users of the old value,
8305 // so that future queries will recompute the expressions using the new
8307 Value *Old = getValPtr();
8308 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
8309 SmallPtrSet<User *, 8> Visited;
8310 while (!Worklist.empty()) {
8311 User *U = Worklist.pop_back_val();
8312 // Deleting the Old value will cause this to dangle. Postpone
8313 // that until everything else is done.
8316 if (!Visited.insert(U).second)
8318 if (PHINode *PN = dyn_cast<PHINode>(U))
8319 SE->ConstantEvolutionLoopExitValue.erase(PN);
8320 SE->ValueExprMap.erase(U);
8321 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
8323 // Delete the Old value.
8324 if (PHINode *PN = dyn_cast<PHINode>(Old))
8325 SE->ConstantEvolutionLoopExitValue.erase(PN);
8326 SE->ValueExprMap.erase(Old);
8327 // this now dangles!
8330 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
8331 : CallbackVH(V), SE(se) {}
8333 //===----------------------------------------------------------------------===//
8334 // ScalarEvolution Class Implementation
8335 //===----------------------------------------------------------------------===//
8337 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
8338 AssumptionCache &AC, DominatorTree &DT,
8340 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
8341 CouldNotCompute(new SCEVCouldNotCompute()),
8342 WalkingBEDominatingConds(false), ValuesAtScopes(64), LoopDispositions(64),
8343 BlockDispositions(64), FirstUnknown(nullptr) {}
8345 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
8346 : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
8347 CouldNotCompute(std::move(Arg.CouldNotCompute)),
8348 ValueExprMap(std::move(Arg.ValueExprMap)),
8349 WalkingBEDominatingConds(false),
8350 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
8351 ConstantEvolutionLoopExitValue(
8352 std::move(Arg.ConstantEvolutionLoopExitValue)),
8353 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
8354 LoopDispositions(std::move(Arg.LoopDispositions)),
8355 BlockDispositions(std::move(Arg.BlockDispositions)),
8356 UnsignedRanges(std::move(Arg.UnsignedRanges)),
8357 SignedRanges(std::move(Arg.SignedRanges)),
8358 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
8359 SCEVAllocator(std::move(Arg.SCEVAllocator)),
8360 FirstUnknown(Arg.FirstUnknown) {
8361 Arg.FirstUnknown = nullptr;
8364 ScalarEvolution::~ScalarEvolution() {
8365 // Iterate through all the SCEVUnknown instances and call their
8366 // destructors, so that they release their references to their values.
8367 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
8369 FirstUnknown = nullptr;
8371 ValueExprMap.clear();
8373 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
8374 // that a loop had multiple computable exits.
8375 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8376 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
8381 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
8382 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
8385 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8386 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8389 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8391 // Print all inner loops first
8392 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8393 PrintLoopInfo(OS, SE, *I);
8396 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8399 SmallVector<BasicBlock *, 8> ExitBlocks;
8400 L->getExitBlocks(ExitBlocks);
8401 if (ExitBlocks.size() != 1)
8402 OS << "<multiple exits> ";
8404 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8405 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8407 OS << "Unpredictable backedge-taken count. ";
8412 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8415 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8416 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8418 OS << "Unpredictable max backedge-taken count. ";
8424 void ScalarEvolution::print(raw_ostream &OS) const {
8425 // ScalarEvolution's implementation of the print method is to print
8426 // out SCEV values of all instructions that are interesting. Doing
8427 // this potentially causes it to create new SCEV objects though,
8428 // which technically conflicts with the const qualifier. This isn't
8429 // observable from outside the class though, so casting away the
8430 // const isn't dangerous.
8431 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8433 OS << "Classifying expressions for: ";
8434 F.printAsOperand(OS, /*PrintType=*/false);
8436 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
8437 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
8440 const SCEV *SV = SE.getSCEV(&*I);
8442 if (!isa<SCEVCouldNotCompute>(SV)) {
8444 SE.getUnsignedRange(SV).print(OS);
8446 SE.getSignedRange(SV).print(OS);
8449 const Loop *L = LI.getLoopFor((*I).getParent());
8451 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8455 if (!isa<SCEVCouldNotCompute>(AtUse)) {
8457 SE.getUnsignedRange(AtUse).print(OS);
8459 SE.getSignedRange(AtUse).print(OS);
8464 OS << "\t\t" "Exits: ";
8465 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8466 if (!SE.isLoopInvariant(ExitValue, L)) {
8467 OS << "<<Unknown>>";
8476 OS << "Determining loop execution counts for: ";
8477 F.printAsOperand(OS, /*PrintType=*/false);
8479 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
8480 PrintLoopInfo(OS, &SE, *I);
8483 ScalarEvolution::LoopDisposition
8484 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8485 auto &Values = LoopDispositions[S];
8486 for (auto &V : Values) {
8487 if (V.getPointer() == L)
8490 Values.emplace_back(L, LoopVariant);
8491 LoopDisposition D = computeLoopDisposition(S, L);
8492 auto &Values2 = LoopDispositions[S];
8493 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8494 if (V.getPointer() == L) {
8502 ScalarEvolution::LoopDisposition
8503 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8504 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8506 return LoopInvariant;
8510 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8511 case scAddRecExpr: {
8512 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8514 // If L is the addrec's loop, it's computable.
8515 if (AR->getLoop() == L)
8516 return LoopComputable;
8518 // Add recurrences are never invariant in the function-body (null loop).
8522 // This recurrence is variant w.r.t. L if L contains AR's loop.
8523 if (L->contains(AR->getLoop()))
8526 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8527 if (AR->getLoop()->contains(L))
8528 return LoopInvariant;
8530 // This recurrence is variant w.r.t. L if any of its operands
8532 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8534 if (!isLoopInvariant(*I, L))
8537 // Otherwise it's loop-invariant.
8538 return LoopInvariant;
8544 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8545 bool HasVarying = false;
8546 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8548 LoopDisposition D = getLoopDisposition(*I, L);
8549 if (D == LoopVariant)
8551 if (D == LoopComputable)
8554 return HasVarying ? LoopComputable : LoopInvariant;
8557 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8558 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8559 if (LD == LoopVariant)
8561 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8562 if (RD == LoopVariant)
8564 return (LD == LoopInvariant && RD == LoopInvariant) ?
8565 LoopInvariant : LoopComputable;
8568 // All non-instruction values are loop invariant. All instructions are loop
8569 // invariant if they are not contained in the specified loop.
8570 // Instructions are never considered invariant in the function body
8571 // (null loop) because they are defined within the "loop".
8572 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8573 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8574 return LoopInvariant;
8575 case scCouldNotCompute:
8576 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8578 llvm_unreachable("Unknown SCEV kind!");
8581 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8582 return getLoopDisposition(S, L) == LoopInvariant;
8585 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8586 return getLoopDisposition(S, L) == LoopComputable;
8589 ScalarEvolution::BlockDisposition
8590 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8591 auto &Values = BlockDispositions[S];
8592 for (auto &V : Values) {
8593 if (V.getPointer() == BB)
8596 Values.emplace_back(BB, DoesNotDominateBlock);
8597 BlockDisposition D = computeBlockDisposition(S, BB);
8598 auto &Values2 = BlockDispositions[S];
8599 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8600 if (V.getPointer() == BB) {
8608 ScalarEvolution::BlockDisposition
8609 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8610 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8612 return ProperlyDominatesBlock;
8616 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8617 case scAddRecExpr: {
8618 // This uses a "dominates" query instead of "properly dominates" query
8619 // to test for proper dominance too, because the instruction which
8620 // produces the addrec's value is a PHI, and a PHI effectively properly
8621 // dominates its entire containing block.
8622 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8623 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
8624 return DoesNotDominateBlock;
8626 // FALL THROUGH into SCEVNAryExpr handling.
8631 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8633 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8635 BlockDisposition D = getBlockDisposition(*I, BB);
8636 if (D == DoesNotDominateBlock)
8637 return DoesNotDominateBlock;
8638 if (D == DominatesBlock)
8641 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8644 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8645 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8646 BlockDisposition LD = getBlockDisposition(LHS, BB);
8647 if (LD == DoesNotDominateBlock)
8648 return DoesNotDominateBlock;
8649 BlockDisposition RD = getBlockDisposition(RHS, BB);
8650 if (RD == DoesNotDominateBlock)
8651 return DoesNotDominateBlock;
8652 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8653 ProperlyDominatesBlock : DominatesBlock;
8656 if (Instruction *I =
8657 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8658 if (I->getParent() == BB)
8659 return DominatesBlock;
8660 if (DT.properlyDominates(I->getParent(), BB))
8661 return ProperlyDominatesBlock;
8662 return DoesNotDominateBlock;
8664 return ProperlyDominatesBlock;
8665 case scCouldNotCompute:
8666 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8668 llvm_unreachable("Unknown SCEV kind!");
8671 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8672 return getBlockDisposition(S, BB) >= DominatesBlock;
8675 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8676 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8680 // Search for a SCEV expression node within an expression tree.
8681 // Implements SCEVTraversal::Visitor.
8686 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8688 bool follow(const SCEV *S) {
8689 IsFound |= (S == Node);
8692 bool isDone() const { return IsFound; }
8696 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8697 SCEVSearch Search(Op);
8698 visitAll(S, Search);
8699 return Search.IsFound;
8702 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8703 ValuesAtScopes.erase(S);
8704 LoopDispositions.erase(S);
8705 BlockDispositions.erase(S);
8706 UnsignedRanges.erase(S);
8707 SignedRanges.erase(S);
8709 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8710 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8711 BackedgeTakenInfo &BEInfo = I->second;
8712 if (BEInfo.hasOperand(S, this)) {
8714 BackedgeTakenCounts.erase(I++);
8721 typedef DenseMap<const Loop *, std::string> VerifyMap;
8723 /// replaceSubString - Replaces all occurrences of From in Str with To.
8724 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8726 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8727 Str.replace(Pos, From.size(), To.data(), To.size());
8732 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8734 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8735 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8736 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8738 std::string &S = Map[L];
8740 raw_string_ostream OS(S);
8741 SE.getBackedgeTakenCount(L)->print(OS);
8743 // false and 0 are semantically equivalent. This can happen in dead loops.
8744 replaceSubString(OS.str(), "false", "0");
8745 // Remove wrap flags, their use in SCEV is highly fragile.
8746 // FIXME: Remove this when SCEV gets smarter about them.
8747 replaceSubString(OS.str(), "<nw>", "");
8748 replaceSubString(OS.str(), "<nsw>", "");
8749 replaceSubString(OS.str(), "<nuw>", "");
8754 void ScalarEvolution::verify() const {
8755 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8757 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8758 // FIXME: It would be much better to store actual values instead of strings,
8759 // but SCEV pointers will change if we drop the caches.
8760 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8761 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
8762 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8764 // Gather stringified backedge taken counts for all loops using a fresh
8765 // ScalarEvolution object.
8766 ScalarEvolution SE2(F, TLI, AC, DT, LI);
8767 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
8768 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
8770 // Now compare whether they're the same with and without caches. This allows
8771 // verifying that no pass changed the cache.
8772 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8773 "New loops suddenly appeared!");
8775 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8776 OldE = BackedgeDumpsOld.end(),
8777 NewI = BackedgeDumpsNew.begin();
8778 OldI != OldE; ++OldI, ++NewI) {
8779 assert(OldI->first == NewI->first && "Loop order changed!");
8781 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8783 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8784 // means that a pass is buggy or SCEV has to learn a new pattern but is
8785 // usually not harmful.
8786 if (OldI->second != NewI->second &&
8787 OldI->second.find("undef") == std::string::npos &&
8788 NewI->second.find("undef") == std::string::npos &&
8789 OldI->second != "***COULDNOTCOMPUTE***" &&
8790 NewI->second != "***COULDNOTCOMPUTE***") {
8791 dbgs() << "SCEVValidator: SCEV for loop '"
8792 << OldI->first->getHeader()->getName()
8793 << "' changed from '" << OldI->second
8794 << "' to '" << NewI->second << "'!\n";
8799 // TODO: Verify more things.
8802 char ScalarEvolutionAnalysis::PassID;
8804 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
8805 AnalysisManager<Function> *AM) {
8806 return ScalarEvolution(F, AM->getResult<TargetLibraryAnalysis>(F),
8807 AM->getResult<AssumptionAnalysis>(F),
8808 AM->getResult<DominatorTreeAnalysis>(F),
8809 AM->getResult<LoopAnalysis>(F));
8813 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> *AM) {
8814 AM->getResult<ScalarEvolutionAnalysis>(F).print(OS);
8815 return PreservedAnalyses::all();
8818 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
8819 "Scalar Evolution Analysis", false, true)
8820 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
8821 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
8822 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
8823 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
8824 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
8825 "Scalar Evolution Analysis", false, true)
8826 char ScalarEvolutionWrapperPass::ID = 0;
8828 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
8829 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
8832 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
8833 SE.reset(new ScalarEvolution(
8834 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
8835 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
8836 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
8837 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
8841 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
8843 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
8847 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
8854 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
8855 AU.setPreservesAll();
8856 AU.addRequiredTransitive<AssumptionCacheTracker>();
8857 AU.addRequiredTransitive<LoopInfoWrapperPass>();
8858 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
8859 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();