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 if (!Numerator->isAffine())
786 return cannotDivide(Numerator);
787 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
788 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
789 // Bail out if the types do not match.
790 Type *Ty = Denominator->getType();
791 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
792 Ty != StepQ->getType() || Ty != StepR->getType())
793 return cannotDivide(Numerator);
794 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
795 Numerator->getNoWrapFlags());
796 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
797 Numerator->getNoWrapFlags());
800 void visitAddExpr(const SCEVAddExpr *Numerator) {
801 SmallVector<const SCEV *, 2> Qs, Rs;
802 Type *Ty = Denominator->getType();
804 for (const SCEV *Op : Numerator->operands()) {
806 divide(SE, Op, Denominator, &Q, &R);
808 // Bail out if types do not match.
809 if (Ty != Q->getType() || Ty != R->getType())
810 return cannotDivide(Numerator);
816 if (Qs.size() == 1) {
822 Quotient = SE.getAddExpr(Qs);
823 Remainder = SE.getAddExpr(Rs);
826 void visitMulExpr(const SCEVMulExpr *Numerator) {
827 SmallVector<const SCEV *, 2> Qs;
828 Type *Ty = Denominator->getType();
830 bool FoundDenominatorTerm = false;
831 for (const SCEV *Op : Numerator->operands()) {
832 // Bail out if types do not match.
833 if (Ty != Op->getType())
834 return cannotDivide(Numerator);
836 if (FoundDenominatorTerm) {
841 // Check whether Denominator divides one of the product operands.
843 divide(SE, Op, Denominator, &Q, &R);
849 // Bail out if types do not match.
850 if (Ty != Q->getType())
851 return cannotDivide(Numerator);
853 FoundDenominatorTerm = true;
857 if (FoundDenominatorTerm) {
862 Quotient = SE.getMulExpr(Qs);
866 if (!isa<SCEVUnknown>(Denominator))
867 return cannotDivide(Numerator);
869 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
870 ValueToValueMap RewriteMap;
871 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
872 cast<SCEVConstant>(Zero)->getValue();
873 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
875 if (Remainder->isZero()) {
876 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
877 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
878 cast<SCEVConstant>(One)->getValue();
880 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
884 // Quotient is (Numerator - Remainder) divided by Denominator.
886 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
887 // This SCEV does not seem to simplify: fail the division here.
888 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
889 return cannotDivide(Numerator);
890 divide(SE, Diff, Denominator, &Q, &R);
892 return cannotDivide(Numerator);
897 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
898 const SCEV *Denominator)
899 : SE(S), Denominator(Denominator) {
900 Zero = SE.getConstant(Denominator->getType(), 0);
901 One = SE.getConstant(Denominator->getType(), 1);
903 // We generally do not know how to divide Expr by Denominator. We
904 // initialize the division to a "cannot divide" state to simplify the rest
906 cannotDivide(Numerator);
909 // Convenience function for giving up on the division. We set the quotient to
910 // be equal to zero and the remainder to be equal to the numerator.
911 void cannotDivide(const SCEV *Numerator) {
913 Remainder = Numerator;
917 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
922 //===----------------------------------------------------------------------===//
923 // Simple SCEV method implementations
924 //===----------------------------------------------------------------------===//
926 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
928 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
931 // Handle the simplest case efficiently.
933 return SE.getTruncateOrZeroExtend(It, ResultTy);
935 // We are using the following formula for BC(It, K):
937 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
939 // Suppose, W is the bitwidth of the return value. We must be prepared for
940 // overflow. Hence, we must assure that the result of our computation is
941 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
942 // safe in modular arithmetic.
944 // However, this code doesn't use exactly that formula; the formula it uses
945 // is something like the following, where T is the number of factors of 2 in
946 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
949 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
951 // This formula is trivially equivalent to the previous formula. However,
952 // this formula can be implemented much more efficiently. The trick is that
953 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
954 // arithmetic. To do exact division in modular arithmetic, all we have
955 // to do is multiply by the inverse. Therefore, this step can be done at
958 // The next issue is how to safely do the division by 2^T. The way this
959 // is done is by doing the multiplication step at a width of at least W + T
960 // bits. This way, the bottom W+T bits of the product are accurate. Then,
961 // when we perform the division by 2^T (which is equivalent to a right shift
962 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
963 // truncated out after the division by 2^T.
965 // In comparison to just directly using the first formula, this technique
966 // is much more efficient; using the first formula requires W * K bits,
967 // but this formula less than W + K bits. Also, the first formula requires
968 // a division step, whereas this formula only requires multiplies and shifts.
970 // It doesn't matter whether the subtraction step is done in the calculation
971 // width or the input iteration count's width; if the subtraction overflows,
972 // the result must be zero anyway. We prefer here to do it in the width of
973 // the induction variable because it helps a lot for certain cases; CodeGen
974 // isn't smart enough to ignore the overflow, which leads to much less
975 // efficient code if the width of the subtraction is wider than the native
978 // (It's possible to not widen at all by pulling out factors of 2 before
979 // the multiplication; for example, K=2 can be calculated as
980 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
981 // extra arithmetic, so it's not an obvious win, and it gets
982 // much more complicated for K > 3.)
984 // Protection from insane SCEVs; this bound is conservative,
985 // but it probably doesn't matter.
987 return SE.getCouldNotCompute();
989 unsigned W = SE.getTypeSizeInBits(ResultTy);
991 // Calculate K! / 2^T and T; we divide out the factors of two before
992 // multiplying for calculating K! / 2^T to avoid overflow.
993 // Other overflow doesn't matter because we only care about the bottom
994 // W bits of the result.
995 APInt OddFactorial(W, 1);
997 for (unsigned i = 3; i <= K; ++i) {
999 unsigned TwoFactors = Mult.countTrailingZeros();
1001 Mult = Mult.lshr(TwoFactors);
1002 OddFactorial *= Mult;
1005 // We need at least W + T bits for the multiplication step
1006 unsigned CalculationBits = W + T;
1008 // Calculate 2^T, at width T+W.
1009 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1011 // Calculate the multiplicative inverse of K! / 2^T;
1012 // this multiplication factor will perform the exact division by
1014 APInt Mod = APInt::getSignedMinValue(W+1);
1015 APInt MultiplyFactor = OddFactorial.zext(W+1);
1016 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1017 MultiplyFactor = MultiplyFactor.trunc(W);
1019 // Calculate the product, at width T+W
1020 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1022 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1023 for (unsigned i = 1; i != K; ++i) {
1024 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1025 Dividend = SE.getMulExpr(Dividend,
1026 SE.getTruncateOrZeroExtend(S, CalculationTy));
1030 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1032 // Truncate the result, and divide by K! / 2^T.
1034 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1035 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1038 /// evaluateAtIteration - Return the value of this chain of recurrences at
1039 /// the specified iteration number. We can evaluate this recurrence by
1040 /// multiplying each element in the chain by the binomial coefficient
1041 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1043 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1045 /// where BC(It, k) stands for binomial coefficient.
1047 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1048 ScalarEvolution &SE) const {
1049 const SCEV *Result = getStart();
1050 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1051 // The computation is correct in the face of overflow provided that the
1052 // multiplication is performed _after_ the evaluation of the binomial
1054 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1055 if (isa<SCEVCouldNotCompute>(Coeff))
1058 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1063 //===----------------------------------------------------------------------===//
1064 // SCEV Expression folder implementations
1065 //===----------------------------------------------------------------------===//
1067 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1069 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1070 "This is not a truncating conversion!");
1071 assert(isSCEVable(Ty) &&
1072 "This is not a conversion to a SCEVable type!");
1073 Ty = getEffectiveSCEVType(Ty);
1075 FoldingSetNodeID ID;
1076 ID.AddInteger(scTruncate);
1080 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1082 // Fold if the operand is constant.
1083 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1085 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1087 // trunc(trunc(x)) --> trunc(x)
1088 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1089 return getTruncateExpr(ST->getOperand(), Ty);
1091 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1092 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1093 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1095 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1096 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1097 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1099 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1100 // eliminate all the truncates, or we replace other casts with truncates.
1101 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1102 SmallVector<const SCEV *, 4> Operands;
1103 bool hasTrunc = false;
1104 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1105 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1106 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1107 hasTrunc = isa<SCEVTruncateExpr>(S);
1108 Operands.push_back(S);
1111 return getAddExpr(Operands);
1112 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1115 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1116 // eliminate all the truncates, or we replace other casts with truncates.
1117 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1118 SmallVector<const SCEV *, 4> Operands;
1119 bool hasTrunc = false;
1120 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1121 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1122 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1123 hasTrunc = isa<SCEVTruncateExpr>(S);
1124 Operands.push_back(S);
1127 return getMulExpr(Operands);
1128 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1131 // If the input value is a chrec scev, truncate the chrec's operands.
1132 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1133 SmallVector<const SCEV *, 4> Operands;
1134 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1135 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
1136 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1139 // The cast wasn't folded; create an explicit cast node. We can reuse
1140 // the existing insert position since if we get here, we won't have
1141 // made any changes which would invalidate it.
1142 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1144 UniqueSCEVs.InsertNode(S, IP);
1148 // Get the limit of a recurrence such that incrementing by Step cannot cause
1149 // signed overflow as long as the value of the recurrence within the
1150 // loop does not exceed this limit before incrementing.
1151 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1152 ICmpInst::Predicate *Pred,
1153 ScalarEvolution *SE) {
1154 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1155 if (SE->isKnownPositive(Step)) {
1156 *Pred = ICmpInst::ICMP_SLT;
1157 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1158 SE->getSignedRange(Step).getSignedMax());
1160 if (SE->isKnownNegative(Step)) {
1161 *Pred = ICmpInst::ICMP_SGT;
1162 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1163 SE->getSignedRange(Step).getSignedMin());
1168 // Get the limit of a recurrence such that incrementing by Step cannot cause
1169 // unsigned overflow as long as the value of the recurrence within the loop does
1170 // not exceed this limit before incrementing.
1171 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1172 ICmpInst::Predicate *Pred,
1173 ScalarEvolution *SE) {
1174 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1175 *Pred = ICmpInst::ICMP_ULT;
1177 return SE->getConstant(APInt::getMinValue(BitWidth) -
1178 SE->getUnsignedRange(Step).getUnsignedMax());
1183 struct ExtendOpTraitsBase {
1184 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1187 // Used to make code generic over signed and unsigned overflow.
1188 template <typename ExtendOp> struct ExtendOpTraits {
1191 // static const SCEV::NoWrapFlags WrapType;
1193 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1195 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1196 // ICmpInst::Predicate *Pred,
1197 // ScalarEvolution *SE);
1201 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1202 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1204 static const GetExtendExprTy GetExtendExpr;
1206 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1207 ICmpInst::Predicate *Pred,
1208 ScalarEvolution *SE) {
1209 return getSignedOverflowLimitForStep(Step, Pred, SE);
1213 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1214 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1217 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1218 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1220 static const GetExtendExprTy GetExtendExpr;
1222 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1223 ICmpInst::Predicate *Pred,
1224 ScalarEvolution *SE) {
1225 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1229 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1230 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1233 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1234 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1235 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1236 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1237 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1238 // expression "Step + sext/zext(PreIncAR)" is congruent with
1239 // "sext/zext(PostIncAR)"
1240 template <typename ExtendOpTy>
1241 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1242 ScalarEvolution *SE) {
1243 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1244 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1246 const Loop *L = AR->getLoop();
1247 const SCEV *Start = AR->getStart();
1248 const SCEV *Step = AR->getStepRecurrence(*SE);
1250 // Check for a simple looking step prior to loop entry.
1251 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1255 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1256 // subtraction is expensive. For this purpose, perform a quick and dirty
1257 // difference, by checking for Step in the operand list.
1258 SmallVector<const SCEV *, 4> DiffOps;
1259 for (const SCEV *Op : SA->operands())
1261 DiffOps.push_back(Op);
1263 if (DiffOps.size() == SA->getNumOperands())
1266 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1269 // 1. NSW/NUW flags on the step increment.
1270 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1271 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1272 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1274 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1275 // "S+X does not sign/unsign-overflow".
1278 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1279 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1280 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1283 // 2. Direct overflow check on the step operation's expression.
1284 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1285 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1286 const SCEV *OperandExtendedStart =
1287 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1288 (SE->*GetExtendExpr)(Step, WideTy));
1289 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1290 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1291 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1292 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1293 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1294 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1299 // 3. Loop precondition.
1300 ICmpInst::Predicate Pred;
1301 const SCEV *OverflowLimit =
1302 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1304 if (OverflowLimit &&
1305 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1311 // Get the normalized zero or sign extended expression for this AddRec's Start.
1312 template <typename ExtendOpTy>
1313 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1314 ScalarEvolution *SE) {
1315 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1317 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1319 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1321 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1322 (SE->*GetExtendExpr)(PreStart, Ty));
1325 // Try to prove away overflow by looking at "nearby" add recurrences. A
1326 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1327 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1331 // {S,+,X} == {S-T,+,X} + T
1332 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1334 // If ({S-T,+,X} + T) does not overflow ... (1)
1336 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1338 // If {S-T,+,X} does not overflow ... (2)
1340 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1341 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1343 // If (S-T)+T does not overflow ... (3)
1345 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1346 // == {Ext(S),+,Ext(X)} == LHS
1348 // Thus, if (1), (2) and (3) are true for some T, then
1349 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1351 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1352 // does not overflow" restricted to the 0th iteration. Therefore we only need
1353 // to check for (1) and (2).
1355 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1356 // is `Delta` (defined below).
1358 template <typename ExtendOpTy>
1359 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1362 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1364 // We restrict `Start` to a constant to prevent SCEV from spending too much
1365 // time here. It is correct (but more expensive) to continue with a
1366 // non-constant `Start` and do a general SCEV subtraction to compute
1367 // `PreStart` below.
1369 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1373 APInt StartAI = StartC->getValue()->getValue();
1375 for (unsigned Delta : {-2, -1, 1, 2}) {
1376 const SCEV *PreStart = getConstant(StartAI - Delta);
1378 // Give up if we don't already have the add recurrence we need because
1379 // actually constructing an add recurrence is relatively expensive.
1380 const SCEVAddRecExpr *PreAR = [&]() {
1381 FoldingSetNodeID ID;
1382 ID.AddInteger(scAddRecExpr);
1383 ID.AddPointer(PreStart);
1384 ID.AddPointer(Step);
1387 return static_cast<SCEVAddRecExpr *>(
1388 this->UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1391 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1392 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1393 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1394 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1395 DeltaS, &Pred, this);
1396 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1404 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1406 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1407 "This is not an extending conversion!");
1408 assert(isSCEVable(Ty) &&
1409 "This is not a conversion to a SCEVable type!");
1410 Ty = getEffectiveSCEVType(Ty);
1412 // Fold if the operand is constant.
1413 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1415 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1417 // zext(zext(x)) --> zext(x)
1418 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1419 return getZeroExtendExpr(SZ->getOperand(), Ty);
1421 // Before doing any expensive analysis, check to see if we've already
1422 // computed a SCEV for this Op and Ty.
1423 FoldingSetNodeID ID;
1424 ID.AddInteger(scZeroExtend);
1428 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1430 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1431 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1432 // It's possible the bits taken off by the truncate were all zero bits. If
1433 // so, we should be able to simplify this further.
1434 const SCEV *X = ST->getOperand();
1435 ConstantRange CR = getUnsignedRange(X);
1436 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1437 unsigned NewBits = getTypeSizeInBits(Ty);
1438 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1439 CR.zextOrTrunc(NewBits)))
1440 return getTruncateOrZeroExtend(X, Ty);
1443 // If the input value is a chrec scev, and we can prove that the value
1444 // did not overflow the old, smaller, value, we can zero extend all of the
1445 // operands (often constants). This allows analysis of something like
1446 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1447 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1448 if (AR->isAffine()) {
1449 const SCEV *Start = AR->getStart();
1450 const SCEV *Step = AR->getStepRecurrence(*this);
1451 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1452 const Loop *L = AR->getLoop();
1454 // If we have special knowledge that this addrec won't overflow,
1455 // we don't need to do any further analysis.
1456 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1457 return getAddRecExpr(
1458 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1459 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1461 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1462 // Note that this serves two purposes: It filters out loops that are
1463 // simply not analyzable, and it covers the case where this code is
1464 // being called from within backedge-taken count analysis, such that
1465 // attempting to ask for the backedge-taken count would likely result
1466 // in infinite recursion. In the later case, the analysis code will
1467 // cope with a conservative value, and it will take care to purge
1468 // that value once it has finished.
1469 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1470 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1471 // Manually compute the final value for AR, checking for
1474 // Check whether the backedge-taken count can be losslessly casted to
1475 // the addrec's type. The count is always unsigned.
1476 const SCEV *CastedMaxBECount =
1477 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1478 const SCEV *RecastedMaxBECount =
1479 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1480 if (MaxBECount == RecastedMaxBECount) {
1481 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1482 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1483 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1484 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1485 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1486 const SCEV *WideMaxBECount =
1487 getZeroExtendExpr(CastedMaxBECount, WideTy);
1488 const SCEV *OperandExtendedAdd =
1489 getAddExpr(WideStart,
1490 getMulExpr(WideMaxBECount,
1491 getZeroExtendExpr(Step, WideTy)));
1492 if (ZAdd == OperandExtendedAdd) {
1493 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1494 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1495 // Return the expression with the addrec on the outside.
1496 return getAddRecExpr(
1497 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1498 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1500 // Similar to above, only this time treat the step value as signed.
1501 // This covers loops that count down.
1502 OperandExtendedAdd =
1503 getAddExpr(WideStart,
1504 getMulExpr(WideMaxBECount,
1505 getSignExtendExpr(Step, WideTy)));
1506 if (ZAdd == OperandExtendedAdd) {
1507 // Cache knowledge of AR NW, which is propagated to this AddRec.
1508 // Negative step causes unsigned wrap, but it still can't self-wrap.
1509 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1510 // Return the expression with the addrec on the outside.
1511 return getAddRecExpr(
1512 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1513 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1517 // If the backedge is guarded by a comparison with the pre-inc value
1518 // the addrec is safe. Also, if the entry is guarded by a comparison
1519 // with the start value and the backedge is guarded by a comparison
1520 // with the post-inc value, the addrec is safe.
1521 if (isKnownPositive(Step)) {
1522 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1523 getUnsignedRange(Step).getUnsignedMax());
1524 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1525 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1526 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1527 AR->getPostIncExpr(*this), N))) {
1528 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1529 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1530 // Return the expression with the addrec on the outside.
1531 return getAddRecExpr(
1532 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1533 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1535 } else if (isKnownNegative(Step)) {
1536 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1537 getSignedRange(Step).getSignedMin());
1538 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1539 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1540 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1541 AR->getPostIncExpr(*this), N))) {
1542 // Cache knowledge of AR NW, which is propagated to this AddRec.
1543 // Negative step causes unsigned wrap, but it still can't self-wrap.
1544 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1545 // Return the expression with the addrec on the outside.
1546 return getAddRecExpr(
1547 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1548 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1553 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1554 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1555 return getAddRecExpr(
1556 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1557 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1561 // The cast wasn't folded; create an explicit cast node.
1562 // Recompute the insert position, as it may have been invalidated.
1563 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1564 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1566 UniqueSCEVs.InsertNode(S, IP);
1570 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1572 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1573 "This is not an extending conversion!");
1574 assert(isSCEVable(Ty) &&
1575 "This is not a conversion to a SCEVable type!");
1576 Ty = getEffectiveSCEVType(Ty);
1578 // Fold if the operand is constant.
1579 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1581 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1583 // sext(sext(x)) --> sext(x)
1584 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1585 return getSignExtendExpr(SS->getOperand(), Ty);
1587 // sext(zext(x)) --> zext(x)
1588 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1589 return getZeroExtendExpr(SZ->getOperand(), Ty);
1591 // Before doing any expensive analysis, check to see if we've already
1592 // computed a SCEV for this Op and Ty.
1593 FoldingSetNodeID ID;
1594 ID.AddInteger(scSignExtend);
1598 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1600 // If the input value is provably positive, build a zext instead.
1601 if (isKnownNonNegative(Op))
1602 return getZeroExtendExpr(Op, Ty);
1604 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1605 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1606 // It's possible the bits taken off by the truncate were all sign bits. If
1607 // so, we should be able to simplify this further.
1608 const SCEV *X = ST->getOperand();
1609 ConstantRange CR = getSignedRange(X);
1610 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1611 unsigned NewBits = getTypeSizeInBits(Ty);
1612 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1613 CR.sextOrTrunc(NewBits)))
1614 return getTruncateOrSignExtend(X, Ty);
1617 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1618 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1619 if (SA->getNumOperands() == 2) {
1620 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1621 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1623 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1624 const APInt &C1 = SC1->getValue()->getValue();
1625 const APInt &C2 = SC2->getValue()->getValue();
1626 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1627 C2.ugt(C1) && C2.isPowerOf2())
1628 return getAddExpr(getSignExtendExpr(SC1, Ty),
1629 getSignExtendExpr(SMul, Ty));
1634 // If the input value is a chrec scev, and we can prove that the value
1635 // did not overflow the old, smaller, value, we can sign extend all of the
1636 // operands (often constants). This allows analysis of something like
1637 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1638 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1639 if (AR->isAffine()) {
1640 const SCEV *Start = AR->getStart();
1641 const SCEV *Step = AR->getStepRecurrence(*this);
1642 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1643 const Loop *L = AR->getLoop();
1645 // If we have special knowledge that this addrec won't overflow,
1646 // we don't need to do any further analysis.
1647 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1648 return getAddRecExpr(
1649 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1650 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1652 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1653 // Note that this serves two purposes: It filters out loops that are
1654 // simply not analyzable, and it covers the case where this code is
1655 // being called from within backedge-taken count analysis, such that
1656 // attempting to ask for the backedge-taken count would likely result
1657 // in infinite recursion. In the later case, the analysis code will
1658 // cope with a conservative value, and it will take care to purge
1659 // that value once it has finished.
1660 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1661 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1662 // Manually compute the final value for AR, checking for
1665 // Check whether the backedge-taken count can be losslessly casted to
1666 // the addrec's type. The count is always unsigned.
1667 const SCEV *CastedMaxBECount =
1668 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1669 const SCEV *RecastedMaxBECount =
1670 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1671 if (MaxBECount == RecastedMaxBECount) {
1672 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1673 // Check whether Start+Step*MaxBECount has no signed overflow.
1674 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1675 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1676 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1677 const SCEV *WideMaxBECount =
1678 getZeroExtendExpr(CastedMaxBECount, WideTy);
1679 const SCEV *OperandExtendedAdd =
1680 getAddExpr(WideStart,
1681 getMulExpr(WideMaxBECount,
1682 getSignExtendExpr(Step, WideTy)));
1683 if (SAdd == OperandExtendedAdd) {
1684 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1685 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1686 // Return the expression with the addrec on the outside.
1687 return getAddRecExpr(
1688 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1689 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1691 // Similar to above, only this time treat the step value as unsigned.
1692 // This covers loops that count up with an unsigned step.
1693 OperandExtendedAdd =
1694 getAddExpr(WideStart,
1695 getMulExpr(WideMaxBECount,
1696 getZeroExtendExpr(Step, WideTy)));
1697 if (SAdd == OperandExtendedAdd) {
1698 // If AR wraps around then
1700 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1701 // => SAdd != OperandExtendedAdd
1703 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1704 // (SAdd == OperandExtendedAdd => AR is NW)
1706 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1708 // Return the expression with the addrec on the outside.
1709 return getAddRecExpr(
1710 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1711 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1715 // If the backedge is guarded by a comparison with the pre-inc value
1716 // the addrec is safe. Also, if the entry is guarded by a comparison
1717 // with the start value and the backedge is guarded by a comparison
1718 // with the post-inc value, the addrec is safe.
1719 ICmpInst::Predicate Pred;
1720 const SCEV *OverflowLimit =
1721 getSignedOverflowLimitForStep(Step, &Pred, this);
1722 if (OverflowLimit &&
1723 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1724 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1725 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1727 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1728 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1729 return getAddRecExpr(
1730 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1731 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1734 // If Start and Step are constants, check if we can apply this
1736 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1737 auto SC1 = dyn_cast<SCEVConstant>(Start);
1738 auto SC2 = dyn_cast<SCEVConstant>(Step);
1740 const APInt &C1 = SC1->getValue()->getValue();
1741 const APInt &C2 = SC2->getValue()->getValue();
1742 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1744 Start = getSignExtendExpr(Start, Ty);
1745 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1746 L, AR->getNoWrapFlags());
1747 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1751 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1752 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1753 return getAddRecExpr(
1754 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1755 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1759 // The cast wasn't folded; create an explicit cast node.
1760 // Recompute the insert position, as it may have been invalidated.
1761 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1762 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1764 UniqueSCEVs.InsertNode(S, IP);
1768 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1769 /// unspecified bits out to the given type.
1771 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1773 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1774 "This is not an extending conversion!");
1775 assert(isSCEVable(Ty) &&
1776 "This is not a conversion to a SCEVable type!");
1777 Ty = getEffectiveSCEVType(Ty);
1779 // Sign-extend negative constants.
1780 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1781 if (SC->getValue()->getValue().isNegative())
1782 return getSignExtendExpr(Op, Ty);
1784 // Peel off a truncate cast.
1785 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1786 const SCEV *NewOp = T->getOperand();
1787 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1788 return getAnyExtendExpr(NewOp, Ty);
1789 return getTruncateOrNoop(NewOp, Ty);
1792 // Next try a zext cast. If the cast is folded, use it.
1793 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1794 if (!isa<SCEVZeroExtendExpr>(ZExt))
1797 // Next try a sext cast. If the cast is folded, use it.
1798 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1799 if (!isa<SCEVSignExtendExpr>(SExt))
1802 // Force the cast to be folded into the operands of an addrec.
1803 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1804 SmallVector<const SCEV *, 4> Ops;
1805 for (const SCEV *Op : AR->operands())
1806 Ops.push_back(getAnyExtendExpr(Op, Ty));
1807 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1810 // If the expression is obviously signed, use the sext cast value.
1811 if (isa<SCEVSMaxExpr>(Op))
1814 // Absent any other information, use the zext cast value.
1818 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1819 /// a list of operands to be added under the given scale, update the given
1820 /// map. This is a helper function for getAddRecExpr. As an example of
1821 /// what it does, given a sequence of operands that would form an add
1822 /// expression like this:
1824 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1826 /// where A and B are constants, update the map with these values:
1828 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1830 /// and add 13 + A*B*29 to AccumulatedConstant.
1831 /// This will allow getAddRecExpr to produce this:
1833 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1835 /// This form often exposes folding opportunities that are hidden in
1836 /// the original operand list.
1838 /// Return true iff it appears that any interesting folding opportunities
1839 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1840 /// the common case where no interesting opportunities are present, and
1841 /// is also used as a check to avoid infinite recursion.
1844 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1845 SmallVectorImpl<const SCEV *> &NewOps,
1846 APInt &AccumulatedConstant,
1847 const SCEV *const *Ops, size_t NumOperands,
1849 ScalarEvolution &SE) {
1850 bool Interesting = false;
1852 // Iterate over the add operands. They are sorted, with constants first.
1854 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1856 // Pull a buried constant out to the outside.
1857 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1859 AccumulatedConstant += Scale * C->getValue()->getValue();
1862 // Next comes everything else. We're especially interested in multiplies
1863 // here, but they're in the middle, so just visit the rest with one loop.
1864 for (; i != NumOperands; ++i) {
1865 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1866 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1868 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1869 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1870 // A multiplication of a constant with another add; recurse.
1871 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1873 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1874 Add->op_begin(), Add->getNumOperands(),
1877 // A multiplication of a constant with some other value. Update
1879 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1880 const SCEV *Key = SE.getMulExpr(MulOps);
1881 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1882 M.insert(std::make_pair(Key, NewScale));
1884 NewOps.push_back(Pair.first->first);
1886 Pair.first->second += NewScale;
1887 // The map already had an entry for this value, which may indicate
1888 // a folding opportunity.
1893 // An ordinary operand. Update the map.
1894 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1895 M.insert(std::make_pair(Ops[i], Scale));
1897 NewOps.push_back(Pair.first->first);
1899 Pair.first->second += Scale;
1900 // The map already had an entry for this value, which may indicate
1901 // a folding opportunity.
1911 struct APIntCompare {
1912 bool operator()(const APInt &LHS, const APInt &RHS) const {
1913 return LHS.ult(RHS);
1918 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1919 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1920 // can't-overflow flags for the operation if possible.
1921 static SCEV::NoWrapFlags
1922 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1923 const SmallVectorImpl<const SCEV *> &Ops,
1924 SCEV::NoWrapFlags OldFlags) {
1925 using namespace std::placeholders;
1928 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1930 assert(CanAnalyze && "don't call from other places!");
1932 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1933 SCEV::NoWrapFlags SignOrUnsignWrap =
1934 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1936 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1937 auto IsKnownNonNegative =
1938 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1940 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1941 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1942 return ScalarEvolution::setFlags(OldFlags,
1943 (SCEV::NoWrapFlags)SignOrUnsignMask);
1948 /// getAddExpr - Get a canonical add expression, or something simpler if
1950 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1951 SCEV::NoWrapFlags Flags) {
1952 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1953 "only nuw or nsw allowed");
1954 assert(!Ops.empty() && "Cannot get empty add!");
1955 if (Ops.size() == 1) return Ops[0];
1957 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1958 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1959 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1960 "SCEVAddExpr operand types don't match!");
1963 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1965 // Sort by complexity, this groups all similar expression types together.
1966 GroupByComplexity(Ops, &LI);
1968 // If there are any constants, fold them together.
1970 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1972 assert(Idx < Ops.size());
1973 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1974 // We found two constants, fold them together!
1975 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1976 RHSC->getValue()->getValue());
1977 if (Ops.size() == 2) return Ops[0];
1978 Ops.erase(Ops.begin()+1); // Erase the folded element
1979 LHSC = cast<SCEVConstant>(Ops[0]);
1982 // If we are left with a constant zero being added, strip it off.
1983 if (LHSC->getValue()->isZero()) {
1984 Ops.erase(Ops.begin());
1988 if (Ops.size() == 1) return Ops[0];
1991 // Okay, check to see if the same value occurs in the operand list more than
1992 // once. If so, merge them together into an multiply expression. Since we
1993 // sorted the list, these values are required to be adjacent.
1994 Type *Ty = Ops[0]->getType();
1995 bool FoundMatch = false;
1996 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1997 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1998 // Scan ahead to count how many equal operands there are.
2000 while (i+Count != e && Ops[i+Count] == Ops[i])
2002 // Merge the values into a multiply.
2003 const SCEV *Scale = getConstant(Ty, Count);
2004 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2005 if (Ops.size() == Count)
2008 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2009 --i; e -= Count - 1;
2013 return getAddExpr(Ops, Flags);
2015 // Check for truncates. If all the operands are truncated from the same
2016 // type, see if factoring out the truncate would permit the result to be
2017 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2018 // if the contents of the resulting outer trunc fold to something simple.
2019 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2020 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2021 Type *DstType = Trunc->getType();
2022 Type *SrcType = Trunc->getOperand()->getType();
2023 SmallVector<const SCEV *, 8> LargeOps;
2025 // Check all the operands to see if they can be represented in the
2026 // source type of the truncate.
2027 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2028 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2029 if (T->getOperand()->getType() != SrcType) {
2033 LargeOps.push_back(T->getOperand());
2034 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2035 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2036 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2037 SmallVector<const SCEV *, 8> LargeMulOps;
2038 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2039 if (const SCEVTruncateExpr *T =
2040 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2041 if (T->getOperand()->getType() != SrcType) {
2045 LargeMulOps.push_back(T->getOperand());
2046 } else if (const SCEVConstant *C =
2047 dyn_cast<SCEVConstant>(M->getOperand(j))) {
2048 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2055 LargeOps.push_back(getMulExpr(LargeMulOps));
2062 // Evaluate the expression in the larger type.
2063 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2064 // If it folds to something simple, use it. Otherwise, don't.
2065 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2066 return getTruncateExpr(Fold, DstType);
2070 // Skip past any other cast SCEVs.
2071 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2074 // If there are add operands they would be next.
2075 if (Idx < Ops.size()) {
2076 bool DeletedAdd = false;
2077 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2078 // If we have an add, expand the add operands onto the end of the operands
2080 Ops.erase(Ops.begin()+Idx);
2081 Ops.append(Add->op_begin(), Add->op_end());
2085 // If we deleted at least one add, we added operands to the end of the list,
2086 // and they are not necessarily sorted. Recurse to resort and resimplify
2087 // any operands we just acquired.
2089 return getAddExpr(Ops);
2092 // Skip over the add expression until we get to a multiply.
2093 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2096 // Check to see if there are any folding opportunities present with
2097 // operands multiplied by constant values.
2098 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2099 uint64_t BitWidth = getTypeSizeInBits(Ty);
2100 DenseMap<const SCEV *, APInt> M;
2101 SmallVector<const SCEV *, 8> NewOps;
2102 APInt AccumulatedConstant(BitWidth, 0);
2103 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2104 Ops.data(), Ops.size(),
2105 APInt(BitWidth, 1), *this)) {
2106 // Some interesting folding opportunity is present, so its worthwhile to
2107 // re-generate the operands list. Group the operands by constant scale,
2108 // to avoid multiplying by the same constant scale multiple times.
2109 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2110 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
2111 E = NewOps.end(); I != E; ++I)
2112 MulOpLists[M.find(*I)->second].push_back(*I);
2113 // Re-generate the operands list.
2115 if (AccumulatedConstant != 0)
2116 Ops.push_back(getConstant(AccumulatedConstant));
2117 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
2118 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
2120 Ops.push_back(getMulExpr(getConstant(I->first),
2121 getAddExpr(I->second)));
2123 return getConstant(Ty, 0);
2124 if (Ops.size() == 1)
2126 return getAddExpr(Ops);
2130 // If we are adding something to a multiply expression, make sure the
2131 // something is not already an operand of the multiply. If so, merge it into
2133 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2134 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2135 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2136 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2137 if (isa<SCEVConstant>(MulOpSCEV))
2139 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2140 if (MulOpSCEV == Ops[AddOp]) {
2141 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2142 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2143 if (Mul->getNumOperands() != 2) {
2144 // If the multiply has more than two operands, we must get the
2146 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2147 Mul->op_begin()+MulOp);
2148 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2149 InnerMul = getMulExpr(MulOps);
2151 const SCEV *One = getConstant(Ty, 1);
2152 const SCEV *AddOne = getAddExpr(One, InnerMul);
2153 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2154 if (Ops.size() == 2) return OuterMul;
2156 Ops.erase(Ops.begin()+AddOp);
2157 Ops.erase(Ops.begin()+Idx-1);
2159 Ops.erase(Ops.begin()+Idx);
2160 Ops.erase(Ops.begin()+AddOp-1);
2162 Ops.push_back(OuterMul);
2163 return getAddExpr(Ops);
2166 // Check this multiply against other multiplies being added together.
2167 for (unsigned OtherMulIdx = Idx+1;
2168 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2170 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2171 // If MulOp occurs in OtherMul, we can fold the two multiplies
2173 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2174 OMulOp != e; ++OMulOp)
2175 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2176 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2177 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2178 if (Mul->getNumOperands() != 2) {
2179 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2180 Mul->op_begin()+MulOp);
2181 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2182 InnerMul1 = getMulExpr(MulOps);
2184 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2185 if (OtherMul->getNumOperands() != 2) {
2186 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2187 OtherMul->op_begin()+OMulOp);
2188 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2189 InnerMul2 = getMulExpr(MulOps);
2191 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2192 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2193 if (Ops.size() == 2) return OuterMul;
2194 Ops.erase(Ops.begin()+Idx);
2195 Ops.erase(Ops.begin()+OtherMulIdx-1);
2196 Ops.push_back(OuterMul);
2197 return getAddExpr(Ops);
2203 // If there are any add recurrences in the operands list, see if any other
2204 // added values are loop invariant. If so, we can fold them into the
2206 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2209 // Scan over all recurrences, trying to fold loop invariants into them.
2210 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2211 // Scan all of the other operands to this add and add them to the vector if
2212 // they are loop invariant w.r.t. the recurrence.
2213 SmallVector<const SCEV *, 8> LIOps;
2214 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2215 const Loop *AddRecLoop = AddRec->getLoop();
2216 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2217 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2218 LIOps.push_back(Ops[i]);
2219 Ops.erase(Ops.begin()+i);
2223 // If we found some loop invariants, fold them into the recurrence.
2224 if (!LIOps.empty()) {
2225 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2226 LIOps.push_back(AddRec->getStart());
2228 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2230 AddRecOps[0] = getAddExpr(LIOps);
2232 // Build the new addrec. Propagate the NUW and NSW flags if both the
2233 // outer add and the inner addrec are guaranteed to have no overflow.
2234 // Always propagate NW.
2235 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2236 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2238 // If all of the other operands were loop invariant, we are done.
2239 if (Ops.size() == 1) return NewRec;
2241 // Otherwise, add the folded AddRec by the non-invariant parts.
2242 for (unsigned i = 0;; ++i)
2243 if (Ops[i] == AddRec) {
2247 return getAddExpr(Ops);
2250 // Okay, if there weren't any loop invariants to be folded, check to see if
2251 // there are multiple AddRec's with the same loop induction variable being
2252 // added together. If so, we can fold them.
2253 for (unsigned OtherIdx = Idx+1;
2254 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2256 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2257 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2258 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2260 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2262 if (const SCEVAddRecExpr *OtherAddRec =
2263 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2264 if (OtherAddRec->getLoop() == AddRecLoop) {
2265 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2267 if (i >= AddRecOps.size()) {
2268 AddRecOps.append(OtherAddRec->op_begin()+i,
2269 OtherAddRec->op_end());
2272 AddRecOps[i] = getAddExpr(AddRecOps[i],
2273 OtherAddRec->getOperand(i));
2275 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2277 // Step size has changed, so we cannot guarantee no self-wraparound.
2278 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2279 return getAddExpr(Ops);
2282 // Otherwise couldn't fold anything into this recurrence. Move onto the
2286 // Okay, it looks like we really DO need an add expr. Check to see if we
2287 // already have one, otherwise create a new one.
2288 FoldingSetNodeID ID;
2289 ID.AddInteger(scAddExpr);
2290 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2291 ID.AddPointer(Ops[i]);
2294 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2296 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2297 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2298 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2300 UniqueSCEVs.InsertNode(S, IP);
2302 S->setNoWrapFlags(Flags);
2306 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2308 if (j > 1 && k / j != i) Overflow = true;
2312 /// Compute the result of "n choose k", the binomial coefficient. If an
2313 /// intermediate computation overflows, Overflow will be set and the return will
2314 /// be garbage. Overflow is not cleared on absence of overflow.
2315 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2316 // We use the multiplicative formula:
2317 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2318 // At each iteration, we take the n-th term of the numeral and divide by the
2319 // (k-n)th term of the denominator. This division will always produce an
2320 // integral result, and helps reduce the chance of overflow in the
2321 // intermediate computations. However, we can still overflow even when the
2322 // final result would fit.
2324 if (n == 0 || n == k) return 1;
2325 if (k > n) return 0;
2331 for (uint64_t i = 1; i <= k; ++i) {
2332 r = umul_ov(r, n-(i-1), Overflow);
2338 /// Determine if any of the operands in this SCEV are a constant or if
2339 /// any of the add or multiply expressions in this SCEV contain a constant.
2340 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2341 SmallVector<const SCEV *, 4> Ops;
2342 Ops.push_back(StartExpr);
2343 while (!Ops.empty()) {
2344 const SCEV *CurrentExpr = Ops.pop_back_val();
2345 if (isa<SCEVConstant>(*CurrentExpr))
2348 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2349 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2350 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2356 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2358 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2359 SCEV::NoWrapFlags Flags) {
2360 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2361 "only nuw or nsw allowed");
2362 assert(!Ops.empty() && "Cannot get empty mul!");
2363 if (Ops.size() == 1) return Ops[0];
2365 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2366 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2367 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2368 "SCEVMulExpr operand types don't match!");
2371 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2373 // Sort by complexity, this groups all similar expression types together.
2374 GroupByComplexity(Ops, &LI);
2376 // If there are any constants, fold them together.
2378 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2380 // C1*(C2+V) -> C1*C2 + C1*V
2381 if (Ops.size() == 2)
2382 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2383 // If any of Add's ops are Adds or Muls with a constant,
2384 // apply this transformation as well.
2385 if (Add->getNumOperands() == 2)
2386 if (containsConstantSomewhere(Add))
2387 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2388 getMulExpr(LHSC, Add->getOperand(1)));
2391 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2392 // We found two constants, fold them together!
2393 ConstantInt *Fold = ConstantInt::get(getContext(),
2394 LHSC->getValue()->getValue() *
2395 RHSC->getValue()->getValue());
2396 Ops[0] = getConstant(Fold);
2397 Ops.erase(Ops.begin()+1); // Erase the folded element
2398 if (Ops.size() == 1) return Ops[0];
2399 LHSC = cast<SCEVConstant>(Ops[0]);
2402 // If we are left with a constant one being multiplied, strip it off.
2403 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2404 Ops.erase(Ops.begin());
2406 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2407 // If we have a multiply of zero, it will always be zero.
2409 } else if (Ops[0]->isAllOnesValue()) {
2410 // If we have a mul by -1 of an add, try distributing the -1 among the
2412 if (Ops.size() == 2) {
2413 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2414 SmallVector<const SCEV *, 4> NewOps;
2415 bool AnyFolded = false;
2416 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2417 E = Add->op_end(); I != E; ++I) {
2418 const SCEV *Mul = getMulExpr(Ops[0], *I);
2419 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2420 NewOps.push_back(Mul);
2423 return getAddExpr(NewOps);
2425 else if (const SCEVAddRecExpr *
2426 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2427 // Negation preserves a recurrence's no self-wrap property.
2428 SmallVector<const SCEV *, 4> Operands;
2429 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2430 E = AddRec->op_end(); I != E; ++I) {
2431 Operands.push_back(getMulExpr(Ops[0], *I));
2433 return getAddRecExpr(Operands, AddRec->getLoop(),
2434 AddRec->getNoWrapFlags(SCEV::FlagNW));
2439 if (Ops.size() == 1)
2443 // Skip over the add expression until we get to a multiply.
2444 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2447 // If there are mul operands inline them all into this expression.
2448 if (Idx < Ops.size()) {
2449 bool DeletedMul = false;
2450 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2451 // If we have an mul, expand the mul operands onto the end of the operands
2453 Ops.erase(Ops.begin()+Idx);
2454 Ops.append(Mul->op_begin(), Mul->op_end());
2458 // If we deleted at least one mul, we added operands to the end of the list,
2459 // and they are not necessarily sorted. Recurse to resort and resimplify
2460 // any operands we just acquired.
2462 return getMulExpr(Ops);
2465 // If there are any add recurrences in the operands list, see if any other
2466 // added values are loop invariant. If so, we can fold them into the
2468 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2471 // Scan over all recurrences, trying to fold loop invariants into them.
2472 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2473 // Scan all of the other operands to this mul and add them to the vector if
2474 // they are loop invariant w.r.t. the recurrence.
2475 SmallVector<const SCEV *, 8> LIOps;
2476 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2477 const Loop *AddRecLoop = AddRec->getLoop();
2478 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2479 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2480 LIOps.push_back(Ops[i]);
2481 Ops.erase(Ops.begin()+i);
2485 // If we found some loop invariants, fold them into the recurrence.
2486 if (!LIOps.empty()) {
2487 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2488 SmallVector<const SCEV *, 4> NewOps;
2489 NewOps.reserve(AddRec->getNumOperands());
2490 const SCEV *Scale = getMulExpr(LIOps);
2491 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2492 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2494 // Build the new addrec. Propagate the NUW and NSW flags if both the
2495 // outer mul and the inner addrec are guaranteed to have no overflow.
2497 // No self-wrap cannot be guaranteed after changing the step size, but
2498 // will be inferred if either NUW or NSW is true.
2499 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2500 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2502 // If all of the other operands were loop invariant, we are done.
2503 if (Ops.size() == 1) return NewRec;
2505 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2506 for (unsigned i = 0;; ++i)
2507 if (Ops[i] == AddRec) {
2511 return getMulExpr(Ops);
2514 // Okay, if there weren't any loop invariants to be folded, check to see if
2515 // there are multiple AddRec's with the same loop induction variable being
2516 // multiplied together. If so, we can fold them.
2518 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2519 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2520 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2521 // ]]],+,...up to x=2n}.
2522 // Note that the arguments to choose() are always integers with values
2523 // known at compile time, never SCEV objects.
2525 // The implementation avoids pointless extra computations when the two
2526 // addrec's are of different length (mathematically, it's equivalent to
2527 // an infinite stream of zeros on the right).
2528 bool OpsModified = false;
2529 for (unsigned OtherIdx = Idx+1;
2530 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2532 const SCEVAddRecExpr *OtherAddRec =
2533 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2534 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2537 bool Overflow = false;
2538 Type *Ty = AddRec->getType();
2539 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2540 SmallVector<const SCEV*, 7> AddRecOps;
2541 for (int x = 0, xe = AddRec->getNumOperands() +
2542 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2543 const SCEV *Term = getConstant(Ty, 0);
2544 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2545 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2546 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2547 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2548 z < ze && !Overflow; ++z) {
2549 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2551 if (LargerThan64Bits)
2552 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2554 Coeff = Coeff1*Coeff2;
2555 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2556 const SCEV *Term1 = AddRec->getOperand(y-z);
2557 const SCEV *Term2 = OtherAddRec->getOperand(z);
2558 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2561 AddRecOps.push_back(Term);
2564 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2566 if (Ops.size() == 2) return NewAddRec;
2567 Ops[Idx] = NewAddRec;
2568 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2570 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2576 return getMulExpr(Ops);
2578 // Otherwise couldn't fold anything into this recurrence. Move onto the
2582 // Okay, it looks like we really DO need an mul expr. Check to see if we
2583 // already have one, otherwise create a new one.
2584 FoldingSetNodeID ID;
2585 ID.AddInteger(scMulExpr);
2586 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2587 ID.AddPointer(Ops[i]);
2590 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2592 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2593 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2594 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2596 UniqueSCEVs.InsertNode(S, IP);
2598 S->setNoWrapFlags(Flags);
2602 /// getUDivExpr - Get a canonical unsigned division expression, or something
2603 /// simpler if possible.
2604 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2606 assert(getEffectiveSCEVType(LHS->getType()) ==
2607 getEffectiveSCEVType(RHS->getType()) &&
2608 "SCEVUDivExpr operand types don't match!");
2610 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2611 if (RHSC->getValue()->equalsInt(1))
2612 return LHS; // X udiv 1 --> x
2613 // If the denominator is zero, the result of the udiv is undefined. Don't
2614 // try to analyze it, because the resolution chosen here may differ from
2615 // the resolution chosen in other parts of the compiler.
2616 if (!RHSC->getValue()->isZero()) {
2617 // Determine if the division can be folded into the operands of
2619 // TODO: Generalize this to non-constants by using known-bits information.
2620 Type *Ty = LHS->getType();
2621 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2622 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2623 // For non-power-of-two values, effectively round the value up to the
2624 // nearest power of two.
2625 if (!RHSC->getValue()->getValue().isPowerOf2())
2627 IntegerType *ExtTy =
2628 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2629 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2630 if (const SCEVConstant *Step =
2631 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2632 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2633 const APInt &StepInt = Step->getValue()->getValue();
2634 const APInt &DivInt = RHSC->getValue()->getValue();
2635 if (!StepInt.urem(DivInt) &&
2636 getZeroExtendExpr(AR, ExtTy) ==
2637 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2638 getZeroExtendExpr(Step, ExtTy),
2639 AR->getLoop(), SCEV::FlagAnyWrap)) {
2640 SmallVector<const SCEV *, 4> Operands;
2641 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2642 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2643 return getAddRecExpr(Operands, AR->getLoop(),
2646 /// Get a canonical UDivExpr for a recurrence.
2647 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2648 // We can currently only fold X%N if X is constant.
2649 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2650 if (StartC && !DivInt.urem(StepInt) &&
2651 getZeroExtendExpr(AR, ExtTy) ==
2652 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2653 getZeroExtendExpr(Step, ExtTy),
2654 AR->getLoop(), SCEV::FlagAnyWrap)) {
2655 const APInt &StartInt = StartC->getValue()->getValue();
2656 const APInt &StartRem = StartInt.urem(StepInt);
2658 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2659 AR->getLoop(), SCEV::FlagNW);
2662 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2663 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2664 SmallVector<const SCEV *, 4> Operands;
2665 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2666 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2667 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2668 // Find an operand that's safely divisible.
2669 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2670 const SCEV *Op = M->getOperand(i);
2671 const SCEV *Div = getUDivExpr(Op, RHSC);
2672 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2673 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2676 return getMulExpr(Operands);
2680 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2681 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2682 SmallVector<const SCEV *, 4> Operands;
2683 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2684 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2685 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2687 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2688 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2689 if (isa<SCEVUDivExpr>(Op) ||
2690 getMulExpr(Op, RHS) != A->getOperand(i))
2692 Operands.push_back(Op);
2694 if (Operands.size() == A->getNumOperands())
2695 return getAddExpr(Operands);
2699 // Fold if both operands are constant.
2700 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2701 Constant *LHSCV = LHSC->getValue();
2702 Constant *RHSCV = RHSC->getValue();
2703 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2709 FoldingSetNodeID ID;
2710 ID.AddInteger(scUDivExpr);
2714 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2715 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2717 UniqueSCEVs.InsertNode(S, IP);
2721 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2722 APInt A = C1->getValue()->getValue().abs();
2723 APInt B = C2->getValue()->getValue().abs();
2724 uint32_t ABW = A.getBitWidth();
2725 uint32_t BBW = B.getBitWidth();
2732 return APIntOps::GreatestCommonDivisor(A, B);
2735 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2736 /// something simpler if possible. There is no representation for an exact udiv
2737 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2738 /// We can't do this when it's not exact because the udiv may be clearing bits.
2739 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2741 // TODO: we could try to find factors in all sorts of things, but for now we
2742 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2743 // end of this file for inspiration.
2745 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2747 return getUDivExpr(LHS, RHS);
2749 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2750 // If the mulexpr multiplies by a constant, then that constant must be the
2751 // first element of the mulexpr.
2752 if (const SCEVConstant *LHSCst =
2753 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2754 if (LHSCst == RHSCst) {
2755 SmallVector<const SCEV *, 2> Operands;
2756 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2757 return getMulExpr(Operands);
2760 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2761 // that there's a factor provided by one of the other terms. We need to
2763 APInt Factor = gcd(LHSCst, RHSCst);
2764 if (!Factor.isIntN(1)) {
2765 LHSCst = cast<SCEVConstant>(
2766 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2767 RHSCst = cast<SCEVConstant>(
2768 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2769 SmallVector<const SCEV *, 2> Operands;
2770 Operands.push_back(LHSCst);
2771 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2772 LHS = getMulExpr(Operands);
2774 Mul = dyn_cast<SCEVMulExpr>(LHS);
2776 return getUDivExactExpr(LHS, RHS);
2781 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2782 if (Mul->getOperand(i) == RHS) {
2783 SmallVector<const SCEV *, 2> Operands;
2784 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2785 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2786 return getMulExpr(Operands);
2790 return getUDivExpr(LHS, RHS);
2793 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2794 /// Simplify the expression as much as possible.
2795 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2797 SCEV::NoWrapFlags Flags) {
2798 SmallVector<const SCEV *, 4> Operands;
2799 Operands.push_back(Start);
2800 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2801 if (StepChrec->getLoop() == L) {
2802 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2803 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2806 Operands.push_back(Step);
2807 return getAddRecExpr(Operands, L, Flags);
2810 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2811 /// Simplify the expression as much as possible.
2813 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2814 const Loop *L, SCEV::NoWrapFlags Flags) {
2815 if (Operands.size() == 1) return Operands[0];
2817 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2818 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2819 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2820 "SCEVAddRecExpr operand types don't match!");
2821 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2822 assert(isLoopInvariant(Operands[i], L) &&
2823 "SCEVAddRecExpr operand is not loop-invariant!");
2826 if (Operands.back()->isZero()) {
2827 Operands.pop_back();
2828 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2831 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2832 // use that information to infer NUW and NSW flags. However, computing a
2833 // BE count requires calling getAddRecExpr, so we may not yet have a
2834 // meaningful BE count at this point (and if we don't, we'd be stuck
2835 // with a SCEVCouldNotCompute as the cached BE count).
2837 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2839 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2840 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2841 const Loop *NestedLoop = NestedAR->getLoop();
2842 if (L->contains(NestedLoop)
2843 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2844 : (!NestedLoop->contains(L) &&
2845 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2846 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2847 NestedAR->op_end());
2848 Operands[0] = NestedAR->getStart();
2849 // AddRecs require their operands be loop-invariant with respect to their
2850 // loops. Don't perform this transformation if it would break this
2852 bool AllInvariant = true;
2853 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2854 if (!isLoopInvariant(Operands[i], L)) {
2855 AllInvariant = false;
2859 // Create a recurrence for the outer loop with the same step size.
2861 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2862 // inner recurrence has the same property.
2863 SCEV::NoWrapFlags OuterFlags =
2864 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2866 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2867 AllInvariant = true;
2868 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2869 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2870 AllInvariant = false;
2874 // Ok, both add recurrences are valid after the transformation.
2876 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2877 // the outer recurrence has the same property.
2878 SCEV::NoWrapFlags InnerFlags =
2879 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2880 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2883 // Reset Operands to its original state.
2884 Operands[0] = NestedAR;
2888 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2889 // already have one, otherwise create a new one.
2890 FoldingSetNodeID ID;
2891 ID.AddInteger(scAddRecExpr);
2892 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2893 ID.AddPointer(Operands[i]);
2897 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2899 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2900 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2901 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2902 O, Operands.size(), L);
2903 UniqueSCEVs.InsertNode(S, IP);
2905 S->setNoWrapFlags(Flags);
2910 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2911 const SmallVectorImpl<const SCEV *> &IndexExprs,
2913 // getSCEV(Base)->getType() has the same address space as Base->getType()
2914 // because SCEV::getType() preserves the address space.
2915 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2916 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2917 // instruction to its SCEV, because the Instruction may be guarded by control
2918 // flow and the no-overflow bits may not be valid for the expression in any
2919 // context. This can be fixed similarly to how these flags are handled for
2921 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2923 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2924 // The address space is unimportant. The first thing we do on CurTy is getting
2925 // its element type.
2926 Type *CurTy = PointerType::getUnqual(PointeeType);
2927 for (const SCEV *IndexExpr : IndexExprs) {
2928 // Compute the (potentially symbolic) offset in bytes for this index.
2929 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2930 // For a struct, add the member offset.
2931 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2932 unsigned FieldNo = Index->getZExtValue();
2933 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2935 // Add the field offset to the running total offset.
2936 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2938 // Update CurTy to the type of the field at Index.
2939 CurTy = STy->getTypeAtIndex(Index);
2941 // Update CurTy to its element type.
2942 CurTy = cast<SequentialType>(CurTy)->getElementType();
2943 // For an array, add the element offset, explicitly scaled.
2944 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2945 // Getelementptr indices are signed.
2946 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2948 // Multiply the index by the element size to compute the element offset.
2949 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2951 // Add the element offset to the running total offset.
2952 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2956 // Add the total offset from all the GEP indices to the base.
2957 return getAddExpr(BaseExpr, TotalOffset, Wrap);
2960 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2962 SmallVector<const SCEV *, 2> Ops;
2965 return getSMaxExpr(Ops);
2969 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2970 assert(!Ops.empty() && "Cannot get empty smax!");
2971 if (Ops.size() == 1) return Ops[0];
2973 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2974 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2975 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2976 "SCEVSMaxExpr operand types don't match!");
2979 // Sort by complexity, this groups all similar expression types together.
2980 GroupByComplexity(Ops, &LI);
2982 // If there are any constants, fold them together.
2984 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2986 assert(Idx < Ops.size());
2987 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2988 // We found two constants, fold them together!
2989 ConstantInt *Fold = ConstantInt::get(getContext(),
2990 APIntOps::smax(LHSC->getValue()->getValue(),
2991 RHSC->getValue()->getValue()));
2992 Ops[0] = getConstant(Fold);
2993 Ops.erase(Ops.begin()+1); // Erase the folded element
2994 if (Ops.size() == 1) return Ops[0];
2995 LHSC = cast<SCEVConstant>(Ops[0]);
2998 // If we are left with a constant minimum-int, strip it off.
2999 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3000 Ops.erase(Ops.begin());
3002 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3003 // If we have an smax with a constant maximum-int, it will always be
3008 if (Ops.size() == 1) return Ops[0];
3011 // Find the first SMax
3012 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3015 // Check to see if one of the operands is an SMax. If so, expand its operands
3016 // onto our operand list, and recurse to simplify.
3017 if (Idx < Ops.size()) {
3018 bool DeletedSMax = false;
3019 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3020 Ops.erase(Ops.begin()+Idx);
3021 Ops.append(SMax->op_begin(), SMax->op_end());
3026 return getSMaxExpr(Ops);
3029 // Okay, check to see if the same value occurs in the operand list twice. If
3030 // so, delete one. Since we sorted the list, these values are required to
3032 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3033 // X smax Y smax Y --> X smax Y
3034 // X smax Y --> X, if X is always greater than Y
3035 if (Ops[i] == Ops[i+1] ||
3036 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3037 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3039 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3040 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3044 if (Ops.size() == 1) return Ops[0];
3046 assert(!Ops.empty() && "Reduced smax down to nothing!");
3048 // Okay, it looks like we really DO need an smax expr. Check to see if we
3049 // already have one, otherwise create a new one.
3050 FoldingSetNodeID ID;
3051 ID.AddInteger(scSMaxExpr);
3052 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3053 ID.AddPointer(Ops[i]);
3055 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3056 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3057 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3058 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3060 UniqueSCEVs.InsertNode(S, IP);
3064 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3066 SmallVector<const SCEV *, 2> Ops;
3069 return getUMaxExpr(Ops);
3073 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3074 assert(!Ops.empty() && "Cannot get empty umax!");
3075 if (Ops.size() == 1) return Ops[0];
3077 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3078 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3079 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3080 "SCEVUMaxExpr operand types don't match!");
3083 // Sort by complexity, this groups all similar expression types together.
3084 GroupByComplexity(Ops, &LI);
3086 // If there are any constants, fold them together.
3088 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3090 assert(Idx < Ops.size());
3091 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3092 // We found two constants, fold them together!
3093 ConstantInt *Fold = ConstantInt::get(getContext(),
3094 APIntOps::umax(LHSC->getValue()->getValue(),
3095 RHSC->getValue()->getValue()));
3096 Ops[0] = getConstant(Fold);
3097 Ops.erase(Ops.begin()+1); // Erase the folded element
3098 if (Ops.size() == 1) return Ops[0];
3099 LHSC = cast<SCEVConstant>(Ops[0]);
3102 // If we are left with a constant minimum-int, strip it off.
3103 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3104 Ops.erase(Ops.begin());
3106 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3107 // If we have an umax with a constant maximum-int, it will always be
3112 if (Ops.size() == 1) return Ops[0];
3115 // Find the first UMax
3116 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3119 // Check to see if one of the operands is a UMax. If so, expand its operands
3120 // onto our operand list, and recurse to simplify.
3121 if (Idx < Ops.size()) {
3122 bool DeletedUMax = false;
3123 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3124 Ops.erase(Ops.begin()+Idx);
3125 Ops.append(UMax->op_begin(), UMax->op_end());
3130 return getUMaxExpr(Ops);
3133 // Okay, check to see if the same value occurs in the operand list twice. If
3134 // so, delete one. Since we sorted the list, these values are required to
3136 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3137 // X umax Y umax Y --> X umax Y
3138 // X umax Y --> X, if X is always greater than Y
3139 if (Ops[i] == Ops[i+1] ||
3140 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3141 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3143 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3144 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3148 if (Ops.size() == 1) return Ops[0];
3150 assert(!Ops.empty() && "Reduced umax down to nothing!");
3152 // Okay, it looks like we really DO need a umax expr. Check to see if we
3153 // already have one, otherwise create a new one.
3154 FoldingSetNodeID ID;
3155 ID.AddInteger(scUMaxExpr);
3156 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3157 ID.AddPointer(Ops[i]);
3159 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3160 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3161 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3162 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3164 UniqueSCEVs.InsertNode(S, IP);
3168 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3170 // ~smax(~x, ~y) == smin(x, y).
3171 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3174 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3176 // ~umax(~x, ~y) == umin(x, y)
3177 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3180 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3181 // We can bypass creating a target-independent
3182 // constant expression and then folding it back into a ConstantInt.
3183 // This is just a compile-time optimization.
3184 return getConstant(IntTy,
3185 F.getParent()->getDataLayout().getTypeAllocSize(AllocTy));
3188 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
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.
3196 F.getParent()->getDataLayout().getStructLayout(STy)->getElementOffset(
3200 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3201 // Don't attempt to do anything other than create a SCEVUnknown object
3202 // here. createSCEV only calls getUnknown after checking for all other
3203 // interesting possibilities, and any other code that calls getUnknown
3204 // is doing so in order to hide a value from SCEV canonicalization.
3206 FoldingSetNodeID ID;
3207 ID.AddInteger(scUnknown);
3210 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3211 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3212 "Stale SCEVUnknown in uniquing map!");
3215 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3217 FirstUnknown = cast<SCEVUnknown>(S);
3218 UniqueSCEVs.InsertNode(S, IP);
3222 //===----------------------------------------------------------------------===//
3223 // Basic SCEV Analysis and PHI Idiom Recognition Code
3226 /// isSCEVable - Test if values of the given type are analyzable within
3227 /// the SCEV framework. This primarily includes integer types, and it
3228 /// can optionally include pointer types if the ScalarEvolution class
3229 /// has access to target-specific information.
3230 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3231 // Integers and pointers are always SCEVable.
3232 return Ty->isIntegerTy() || Ty->isPointerTy();
3235 /// getTypeSizeInBits - Return the size in bits of the specified type,
3236 /// for which isSCEVable must return true.
3237 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3238 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3239 return F.getParent()->getDataLayout().getTypeSizeInBits(Ty);
3242 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3243 /// the given type and which represents how SCEV will treat the given
3244 /// type, for which isSCEVable must return true. For pointer types,
3245 /// this is the pointer-sized integer type.
3246 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3247 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3249 if (Ty->isIntegerTy()) {
3253 // The only other support type is pointer.
3254 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3255 return F.getParent()->getDataLayout().getIntPtrType(Ty);
3258 const SCEV *ScalarEvolution::getCouldNotCompute() {
3259 return CouldNotCompute.get();
3263 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3264 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3265 // is set iff if find such SCEVUnknown.
3267 struct FindInvalidSCEVUnknown {
3269 FindInvalidSCEVUnknown() { FindOne = false; }
3270 bool follow(const SCEV *S) {
3271 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3275 if (!cast<SCEVUnknown>(S)->getValue())
3282 bool isDone() const { return FindOne; }
3286 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3287 FindInvalidSCEVUnknown F;
3288 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3294 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3295 /// expression and create a new one.
3296 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3297 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3299 const SCEV *S = getExistingSCEV(V);
3302 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3307 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3308 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3310 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3311 if (I != ValueExprMap.end()) {
3312 const SCEV *S = I->second;
3313 if (checkValidity(S))
3315 ValueExprMap.erase(I);
3320 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3322 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3323 SCEV::NoWrapFlags Flags) {
3324 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3326 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3328 Type *Ty = V->getType();
3329 Ty = getEffectiveSCEVType(Ty);
3331 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3334 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3335 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3336 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3338 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3340 Type *Ty = V->getType();
3341 Ty = getEffectiveSCEVType(Ty);
3342 const SCEV *AllOnes =
3343 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3344 return getMinusSCEV(AllOnes, V);
3347 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3348 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3349 SCEV::NoWrapFlags Flags) {
3350 // Fast path: X - X --> 0.
3352 return getConstant(LHS->getType(), 0);
3354 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3355 // makes it so that we cannot make much use of NUW.
3356 auto AddFlags = SCEV::FlagAnyWrap;
3357 const bool RHSIsNotMinSigned =
3358 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3359 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3360 // Let M be the minimum representable signed value. Then (-1)*RHS
3361 // signed-wraps if and only if RHS is M. That can happen even for
3362 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3363 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3364 // (-1)*RHS, we need to prove that RHS != M.
3366 // If LHS is non-negative and we know that LHS - RHS does not
3367 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3368 // either by proving that RHS > M or that LHS >= 0.
3369 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3370 AddFlags = SCEV::FlagNSW;
3374 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3375 // RHS is NSW and LHS >= 0.
3377 // The difficulty here is that the NSW flag may have been proven
3378 // relative to a loop that is to be found in a recurrence in LHS and
3379 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3380 // larger scope than intended.
3381 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3383 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3386 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3387 /// input value to the specified type. If the type must be extended, it is zero
3390 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3391 Type *SrcTy = V->getType();
3392 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3393 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3394 "Cannot truncate or zero extend with non-integer arguments!");
3395 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3396 return V; // No conversion
3397 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3398 return getTruncateExpr(V, Ty);
3399 return getZeroExtendExpr(V, Ty);
3402 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3403 /// input value to the specified type. If the type must be extended, it is sign
3406 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3408 Type *SrcTy = V->getType();
3409 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3410 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3411 "Cannot truncate or zero extend with non-integer arguments!");
3412 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3413 return V; // No conversion
3414 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3415 return getTruncateExpr(V, Ty);
3416 return getSignExtendExpr(V, Ty);
3419 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3420 /// input value to the specified type. If the type must be extended, it is zero
3421 /// extended. The conversion must not be narrowing.
3423 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3424 Type *SrcTy = V->getType();
3425 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3426 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3427 "Cannot noop or zero extend with non-integer arguments!");
3428 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3429 "getNoopOrZeroExtend cannot truncate!");
3430 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3431 return V; // No conversion
3432 return getZeroExtendExpr(V, Ty);
3435 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3436 /// input value to the specified type. If the type must be extended, it is sign
3437 /// extended. The conversion must not be narrowing.
3439 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3440 Type *SrcTy = V->getType();
3441 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3442 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3443 "Cannot noop or sign extend with non-integer arguments!");
3444 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3445 "getNoopOrSignExtend cannot truncate!");
3446 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3447 return V; // No conversion
3448 return getSignExtendExpr(V, Ty);
3451 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3452 /// the input value to the specified type. If the type must be extended,
3453 /// it is extended with unspecified bits. The conversion must not be
3456 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3457 Type *SrcTy = V->getType();
3458 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3459 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3460 "Cannot noop or any extend with non-integer arguments!");
3461 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3462 "getNoopOrAnyExtend cannot truncate!");
3463 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3464 return V; // No conversion
3465 return getAnyExtendExpr(V, Ty);
3468 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3469 /// input value to the specified type. The conversion must not be widening.
3471 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3472 Type *SrcTy = V->getType();
3473 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3474 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3475 "Cannot truncate or noop with non-integer arguments!");
3476 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3477 "getTruncateOrNoop cannot extend!");
3478 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3479 return V; // No conversion
3480 return getTruncateExpr(V, Ty);
3483 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3484 /// the types using zero-extension, and then perform a umax operation
3486 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3488 const SCEV *PromotedLHS = LHS;
3489 const SCEV *PromotedRHS = RHS;
3491 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3492 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3494 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3496 return getUMaxExpr(PromotedLHS, PromotedRHS);
3499 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3500 /// the types using zero-extension, and then perform a umin operation
3502 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3504 const SCEV *PromotedLHS = LHS;
3505 const SCEV *PromotedRHS = RHS;
3507 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3508 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3510 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3512 return getUMinExpr(PromotedLHS, PromotedRHS);
3515 /// getPointerBase - Transitively follow the chain of pointer-type operands
3516 /// until reaching a SCEV that does not have a single pointer operand. This
3517 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3518 /// but corner cases do exist.
3519 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3520 // A pointer operand may evaluate to a nonpointer expression, such as null.
3521 if (!V->getType()->isPointerTy())
3524 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3525 return getPointerBase(Cast->getOperand());
3527 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3528 const SCEV *PtrOp = nullptr;
3529 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3531 if ((*I)->getType()->isPointerTy()) {
3532 // Cannot find the base of an expression with multiple pointer operands.
3540 return getPointerBase(PtrOp);
3545 /// PushDefUseChildren - Push users of the given Instruction
3546 /// onto the given Worklist.
3548 PushDefUseChildren(Instruction *I,
3549 SmallVectorImpl<Instruction *> &Worklist) {
3550 // Push the def-use children onto the Worklist stack.
3551 for (User *U : I->users())
3552 Worklist.push_back(cast<Instruction>(U));
3555 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3556 /// instructions that depend on the given instruction and removes them from
3557 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3560 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3561 SmallVector<Instruction *, 16> Worklist;
3562 PushDefUseChildren(PN, Worklist);
3564 SmallPtrSet<Instruction *, 8> Visited;
3566 while (!Worklist.empty()) {
3567 Instruction *I = Worklist.pop_back_val();
3568 if (!Visited.insert(I).second)
3571 ValueExprMapType::iterator It =
3572 ValueExprMap.find_as(static_cast<Value *>(I));
3573 if (It != ValueExprMap.end()) {
3574 const SCEV *Old = It->second;
3576 // Short-circuit the def-use traversal if the symbolic name
3577 // ceases to appear in expressions.
3578 if (Old != SymName && !hasOperand(Old, SymName))
3581 // SCEVUnknown for a PHI either means that it has an unrecognized
3582 // structure, it's a PHI that's in the progress of being computed
3583 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3584 // additional loop trip count information isn't going to change anything.
3585 // In the second case, createNodeForPHI will perform the necessary
3586 // updates on its own when it gets to that point. In the third, we do
3587 // want to forget the SCEVUnknown.
3588 if (!isa<PHINode>(I) ||
3589 !isa<SCEVUnknown>(Old) ||
3590 (I != PN && Old == SymName)) {
3591 forgetMemoizedResults(Old);
3592 ValueExprMap.erase(It);
3596 PushDefUseChildren(I, Worklist);
3600 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3601 /// a loop header, making it a potential recurrence, or it doesn't.
3603 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3604 if (const Loop *L = LI.getLoopFor(PN->getParent()))
3605 if (L->getHeader() == PN->getParent()) {
3606 // The loop may have multiple entrances or multiple exits; we can analyze
3607 // this phi as an addrec if it has a unique entry value and a unique
3609 Value *BEValueV = nullptr, *StartValueV = nullptr;
3610 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3611 Value *V = PN->getIncomingValue(i);
3612 if (L->contains(PN->getIncomingBlock(i))) {
3615 } else if (BEValueV != V) {
3619 } else if (!StartValueV) {
3621 } else if (StartValueV != V) {
3622 StartValueV = nullptr;
3626 if (BEValueV && StartValueV) {
3627 // While we are analyzing this PHI node, handle its value symbolically.
3628 const SCEV *SymbolicName = getUnknown(PN);
3629 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3630 "PHI node already processed?");
3631 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3633 // Using this symbolic name for the PHI, analyze the value coming around
3635 const SCEV *BEValue = getSCEV(BEValueV);
3637 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3638 // has a special value for the first iteration of the loop.
3640 // If the value coming around the backedge is an add with the symbolic
3641 // value we just inserted, then we found a simple induction variable!
3642 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3643 // If there is a single occurrence of the symbolic value, replace it
3644 // with a recurrence.
3645 unsigned FoundIndex = Add->getNumOperands();
3646 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3647 if (Add->getOperand(i) == SymbolicName)
3648 if (FoundIndex == e) {
3653 if (FoundIndex != Add->getNumOperands()) {
3654 // Create an add with everything but the specified operand.
3655 SmallVector<const SCEV *, 8> Ops;
3656 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3657 if (i != FoundIndex)
3658 Ops.push_back(Add->getOperand(i));
3659 const SCEV *Accum = getAddExpr(Ops);
3661 // This is not a valid addrec if the step amount is varying each
3662 // loop iteration, but is not itself an addrec in this loop.
3663 if (isLoopInvariant(Accum, L) ||
3664 (isa<SCEVAddRecExpr>(Accum) &&
3665 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3666 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3668 // If the increment doesn't overflow, then neither the addrec nor
3669 // the post-increment will overflow.
3670 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3671 if (OBO->getOperand(0) == PN) {
3672 if (OBO->hasNoUnsignedWrap())
3673 Flags = setFlags(Flags, SCEV::FlagNUW);
3674 if (OBO->hasNoSignedWrap())
3675 Flags = setFlags(Flags, SCEV::FlagNSW);
3677 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3678 // If the increment is an inbounds GEP, then we know the address
3679 // space cannot be wrapped around. We cannot make any guarantee
3680 // about signed or unsigned overflow because pointers are
3681 // unsigned but we may have a negative index from the base
3682 // pointer. We can guarantee that no unsigned wrap occurs if the
3683 // indices form a positive value.
3684 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3685 Flags = setFlags(Flags, SCEV::FlagNW);
3687 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3688 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3689 Flags = setFlags(Flags, SCEV::FlagNUW);
3692 // We cannot transfer nuw and nsw flags from subtraction
3693 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3697 const SCEV *StartVal = getSCEV(StartValueV);
3698 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3700 // Since the no-wrap flags are on the increment, they apply to the
3701 // post-incremented value as well.
3702 if (isLoopInvariant(Accum, L))
3703 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3706 // Okay, for the entire analysis of this edge we assumed the PHI
3707 // to be symbolic. We now need to go back and purge all of the
3708 // entries for the scalars that use the symbolic expression.
3709 ForgetSymbolicName(PN, SymbolicName);
3710 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3714 } else if (const SCEVAddRecExpr *AddRec =
3715 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3716 // Otherwise, this could be a loop like this:
3717 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3718 // In this case, j = {1,+,1} and BEValue is j.
3719 // Because the other in-value of i (0) fits the evolution of BEValue
3720 // i really is an addrec evolution.
3721 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3722 const SCEV *StartVal = getSCEV(StartValueV);
3724 // If StartVal = j.start - j.stride, we can use StartVal as the
3725 // initial step of the addrec evolution.
3726 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3727 AddRec->getOperand(1))) {
3728 // FIXME: For constant StartVal, we should be able to infer
3730 const SCEV *PHISCEV =
3731 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3734 // Okay, for the entire analysis of this edge we assumed the PHI
3735 // to be symbolic. We now need to go back and purge all of the
3736 // entries for the scalars that use the symbolic expression.
3737 ForgetSymbolicName(PN, SymbolicName);
3738 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3746 // If the PHI has a single incoming value, follow that value, unless the
3747 // PHI's incoming blocks are in a different loop, in which case doing so
3748 // risks breaking LCSSA form. Instcombine would normally zap these, but
3749 // it doesn't have DominatorTree information, so it may miss cases.
3750 if (Value *V = SimplifyInstruction(PN, F.getParent()->getDataLayout(), &TLI,
3752 if (LI.replacementPreservesLCSSAForm(PN, V))
3755 // If it's not a loop phi, we can't handle it yet.
3756 return getUnknown(PN);
3759 /// createNodeForGEP - Expand GEP instructions into add and multiply
3760 /// operations. This allows them to be analyzed by regular SCEV code.
3762 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3763 Value *Base = GEP->getOperand(0);
3764 // Don't attempt to analyze GEPs over unsized objects.
3765 if (!Base->getType()->getPointerElementType()->isSized())
3766 return getUnknown(GEP);
3768 SmallVector<const SCEV *, 4> IndexExprs;
3769 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
3770 IndexExprs.push_back(getSCEV(*Index));
3771 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
3775 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3776 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3777 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3778 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3780 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3781 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3782 return C->getValue()->getValue().countTrailingZeros();
3784 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3785 return std::min(GetMinTrailingZeros(T->getOperand()),
3786 (uint32_t)getTypeSizeInBits(T->getType()));
3788 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3789 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3790 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3791 getTypeSizeInBits(E->getType()) : OpRes;
3794 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3795 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3796 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3797 getTypeSizeInBits(E->getType()) : OpRes;
3800 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3801 // The result is the min of all operands results.
3802 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3803 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3804 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3808 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3809 // The result is the sum of all operands results.
3810 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3811 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3812 for (unsigned i = 1, e = M->getNumOperands();
3813 SumOpRes != BitWidth && i != e; ++i)
3814 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3819 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3820 // The result is the min of all operands results.
3821 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3822 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3823 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3827 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3828 // The result is the min of all operands results.
3829 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3830 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3831 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3835 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3836 // The result is the min of all operands results.
3837 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3838 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3839 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3843 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3844 // For a SCEVUnknown, ask ValueTracking.
3845 unsigned BitWidth = getTypeSizeInBits(U->getType());
3846 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3847 computeKnownBits(U->getValue(), Zeros, Ones, F.getParent()->getDataLayout(),
3848 0, &AC, nullptr, &DT);
3849 return Zeros.countTrailingOnes();
3856 /// GetRangeFromMetadata - Helper method to assign a range to V from
3857 /// metadata present in the IR.
3858 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3859 if (Instruction *I = dyn_cast<Instruction>(V)) {
3860 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3861 ConstantRange TotalRange(
3862 cast<IntegerType>(I->getType())->getBitWidth(), false);
3864 unsigned NumRanges = MD->getNumOperands() / 2;
3865 assert(NumRanges >= 1);
3867 for (unsigned i = 0; i < NumRanges; ++i) {
3868 ConstantInt *Lower =
3869 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3870 ConstantInt *Upper =
3871 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3872 ConstantRange Range(Lower->getValue(), Upper->getValue());
3873 TotalRange = TotalRange.unionWith(Range);
3883 /// getRange - Determine the range for a particular SCEV. If SignHint is
3884 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
3885 /// with a "cleaner" unsigned (resp. signed) representation.
3888 ScalarEvolution::getRange(const SCEV *S,
3889 ScalarEvolution::RangeSignHint SignHint) {
3890 DenseMap<const SCEV *, ConstantRange> &Cache =
3891 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
3894 // See if we've computed this range already.
3895 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
3896 if (I != Cache.end())
3899 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3900 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
3902 unsigned BitWidth = getTypeSizeInBits(S->getType());
3903 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3905 // If the value has known zeros, the maximum value will have those known zeros
3907 uint32_t TZ = GetMinTrailingZeros(S);
3909 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
3910 ConservativeResult =
3911 ConstantRange(APInt::getMinValue(BitWidth),
3912 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3914 ConservativeResult = ConstantRange(
3915 APInt::getSignedMinValue(BitWidth),
3916 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3919 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3920 ConstantRange X = getRange(Add->getOperand(0), SignHint);
3921 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3922 X = X.add(getRange(Add->getOperand(i), SignHint));
3923 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
3926 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3927 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
3928 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3929 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
3930 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
3933 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3934 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
3935 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3936 X = X.smax(getRange(SMax->getOperand(i), SignHint));
3937 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
3940 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3941 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
3942 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3943 X = X.umax(getRange(UMax->getOperand(i), SignHint));
3944 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
3947 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3948 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
3949 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
3950 return setRange(UDiv, SignHint,
3951 ConservativeResult.intersectWith(X.udiv(Y)));
3954 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3955 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
3956 return setRange(ZExt, SignHint,
3957 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3960 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3961 ConstantRange X = getRange(SExt->getOperand(), SignHint);
3962 return setRange(SExt, SignHint,
3963 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3966 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3967 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
3968 return setRange(Trunc, SignHint,
3969 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3972 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3973 // If there's no unsigned wrap, the value will never be less than its
3975 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3976 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3977 if (!C->getValue()->isZero())
3978 ConservativeResult =
3979 ConservativeResult.intersectWith(
3980 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3982 // If there's no signed wrap, and all the operands have the same sign or
3983 // zero, the value won't ever change sign.
3984 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3985 bool AllNonNeg = true;
3986 bool AllNonPos = true;
3987 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3988 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3989 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3992 ConservativeResult = ConservativeResult.intersectWith(
3993 ConstantRange(APInt(BitWidth, 0),
3994 APInt::getSignedMinValue(BitWidth)));
3996 ConservativeResult = ConservativeResult.intersectWith(
3997 ConstantRange(APInt::getSignedMinValue(BitWidth),
3998 APInt(BitWidth, 1)));
4001 // TODO: non-affine addrec
4002 if (AddRec->isAffine()) {
4003 Type *Ty = AddRec->getType();
4004 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4005 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4006 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4008 // Check for overflow. This must be done with ConstantRange arithmetic
4009 // because we could be called from within the ScalarEvolution overflow
4012 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4013 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4014 ConstantRange ZExtMaxBECountRange =
4015 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4017 const SCEV *Start = AddRec->getStart();
4018 const SCEV *Step = AddRec->getStepRecurrence(*this);
4019 ConstantRange StepSRange = getSignedRange(Step);
4020 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4022 ConstantRange StartURange = getUnsignedRange(Start);
4023 ConstantRange EndURange =
4024 StartURange.add(MaxBECountRange.multiply(StepSRange));
4026 // Check for unsigned overflow.
4027 ConstantRange ZExtStartURange =
4028 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4029 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4030 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4032 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4033 EndURange.getUnsignedMin());
4034 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4035 EndURange.getUnsignedMax());
4036 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4038 ConservativeResult =
4039 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4042 ConstantRange StartSRange = getSignedRange(Start);
4043 ConstantRange EndSRange =
4044 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4046 // Check for signed overflow. This must be done with ConstantRange
4047 // arithmetic because we could be called from within the ScalarEvolution
4048 // overflow checking code.
4049 ConstantRange SExtStartSRange =
4050 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4051 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4052 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4054 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4055 EndSRange.getSignedMin());
4056 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4057 EndSRange.getSignedMax());
4058 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4060 ConservativeResult =
4061 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4066 return setRange(AddRec, SignHint, ConservativeResult);
4069 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4070 // Check if the IR explicitly contains !range metadata.
4071 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4072 if (MDRange.hasValue())
4073 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4075 // Split here to avoid paying the compile-time cost of calling both
4076 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4078 const DataLayout &DL = F.getParent()->getDataLayout();
4079 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4080 // For a SCEVUnknown, ask ValueTracking.
4081 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4082 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4083 if (Ones != ~Zeros + 1)
4084 ConservativeResult =
4085 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4087 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4088 "generalize as needed!");
4089 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4091 ConservativeResult = ConservativeResult.intersectWith(
4092 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4093 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4096 return setRange(U, SignHint, ConservativeResult);
4099 return setRange(S, SignHint, ConservativeResult);
4102 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4103 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4104 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4106 // Return early if there are no flags to propagate to the SCEV.
4107 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4108 if (BinOp->hasNoUnsignedWrap())
4109 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4110 if (BinOp->hasNoSignedWrap())
4111 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4112 if (Flags == SCEV::FlagAnyWrap) {
4113 return SCEV::FlagAnyWrap;
4116 // Here we check that BinOp is in the header of the innermost loop
4117 // containing BinOp, since we only deal with instructions in the loop
4118 // header. The actual loop we need to check later will come from an add
4119 // recurrence, but getting that requires computing the SCEV of the operands,
4120 // which can be expensive. This check we can do cheaply to rule out some
4122 Loop *innermostContainingLoop = LI.getLoopFor(BinOp->getParent());
4123 if (innermostContainingLoop == nullptr ||
4124 innermostContainingLoop->getHeader() != BinOp->getParent())
4125 return SCEV::FlagAnyWrap;
4127 // Only proceed if we can prove that BinOp does not yield poison.
4128 if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
4130 // At this point we know that if V is executed, then it does not wrap
4131 // according to at least one of NSW or NUW. If V is not executed, then we do
4132 // not know if the calculation that V represents would wrap. Multiple
4133 // instructions can map to the same SCEV. If we apply NSW or NUW from V to
4134 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4135 // derived from other instructions that map to the same SCEV. We cannot make
4136 // that guarantee for cases where V is not executed. So we need to find the
4137 // loop that V is considered in relation to and prove that V is executed for
4138 // every iteration of that loop. That implies that the value that V
4139 // calculates does not wrap anywhere in the loop, so then we can apply the
4140 // flags to the SCEV.
4142 // We check isLoopInvariant to disambiguate in case we are adding two
4143 // recurrences from different loops, so that we know which loop to prove
4144 // that V is executed in.
4145 for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
4146 const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
4147 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4148 const int OtherOpIndex = 1 - OpIndex;
4149 const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
4150 if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
4151 isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
4155 return SCEV::FlagAnyWrap;
4158 /// createSCEV - We know that there is no SCEV for the specified value. Analyze
4161 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4162 if (!isSCEVable(V->getType()))
4163 return getUnknown(V);
4165 unsigned Opcode = Instruction::UserOp1;
4166 if (Instruction *I = dyn_cast<Instruction>(V)) {
4167 Opcode = I->getOpcode();
4169 // Don't attempt to analyze instructions in blocks that aren't
4170 // reachable. Such instructions don't matter, and they aren't required
4171 // to obey basic rules for definitions dominating uses which this
4172 // analysis depends on.
4173 if (!DT.isReachableFromEntry(I->getParent()))
4174 return getUnknown(V);
4175 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4176 Opcode = CE->getOpcode();
4177 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4178 return getConstant(CI);
4179 else if (isa<ConstantPointerNull>(V))
4180 return getConstant(V->getType(), 0);
4181 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4182 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4184 return getUnknown(V);
4186 Operator *U = cast<Operator>(V);
4188 case Instruction::Add: {
4189 // The simple thing to do would be to just call getSCEV on both operands
4190 // and call getAddExpr with the result. However if we're looking at a
4191 // bunch of things all added together, this can be quite inefficient,
4192 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4193 // Instead, gather up all the operands and make a single getAddExpr call.
4194 // LLVM IR canonical form means we need only traverse the left operands.
4195 SmallVector<const SCEV *, 4> AddOps;
4196 for (Value *Op = U;; Op = U->getOperand(0)) {
4197 U = dyn_cast<Operator>(Op);
4198 unsigned Opcode = U ? U->getOpcode() : 0;
4199 if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
4200 assert(Op != V && "V should be an add");
4201 AddOps.push_back(getSCEV(Op));
4205 if (auto *OpSCEV = getExistingSCEV(U)) {
4206 AddOps.push_back(OpSCEV);
4210 // If a NUW or NSW flag can be applied to the SCEV for this
4211 // addition, then compute the SCEV for this addition by itself
4212 // with a separate call to getAddExpr. We need to do that
4213 // instead of pushing the operands of the addition onto AddOps,
4214 // since the flags are only known to apply to this particular
4215 // addition - they may not apply to other additions that can be
4216 // formed with operands from AddOps.
4217 const SCEV *RHS = getSCEV(U->getOperand(1));
4218 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4219 if (Flags != SCEV::FlagAnyWrap) {
4220 const SCEV *LHS = getSCEV(U->getOperand(0));
4221 if (Opcode == Instruction::Sub)
4222 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4224 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4228 if (Opcode == Instruction::Sub)
4229 AddOps.push_back(getNegativeSCEV(RHS));
4231 AddOps.push_back(RHS);
4233 return getAddExpr(AddOps);
4236 case Instruction::Mul: {
4237 SmallVector<const SCEV *, 4> MulOps;
4238 for (Value *Op = U;; Op = U->getOperand(0)) {
4239 U = dyn_cast<Operator>(Op);
4240 if (!U || U->getOpcode() != Instruction::Mul) {
4241 assert(Op != V && "V should be a mul");
4242 MulOps.push_back(getSCEV(Op));
4246 if (auto *OpSCEV = getExistingSCEV(U)) {
4247 MulOps.push_back(OpSCEV);
4251 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4252 if (Flags != SCEV::FlagAnyWrap) {
4253 MulOps.push_back(getMulExpr(getSCEV(U->getOperand(0)),
4254 getSCEV(U->getOperand(1)), Flags));
4258 MulOps.push_back(getSCEV(U->getOperand(1)));
4260 return getMulExpr(MulOps);
4262 case Instruction::UDiv:
4263 return getUDivExpr(getSCEV(U->getOperand(0)),
4264 getSCEV(U->getOperand(1)));
4265 case Instruction::Sub:
4266 return getMinusSCEV(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)),
4267 getNoWrapFlagsFromUB(U));
4268 case Instruction::And:
4269 // For an expression like x&255 that merely masks off the high bits,
4270 // use zext(trunc(x)) as the SCEV expression.
4271 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4272 if (CI->isNullValue())
4273 return getSCEV(U->getOperand(1));
4274 if (CI->isAllOnesValue())
4275 return getSCEV(U->getOperand(0));
4276 const APInt &A = CI->getValue();
4278 // Instcombine's ShrinkDemandedConstant may strip bits out of
4279 // constants, obscuring what would otherwise be a low-bits mask.
4280 // Use computeKnownBits to compute what ShrinkDemandedConstant
4281 // knew about to reconstruct a low-bits mask value.
4282 unsigned LZ = A.countLeadingZeros();
4283 unsigned TZ = A.countTrailingZeros();
4284 unsigned BitWidth = A.getBitWidth();
4285 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4286 computeKnownBits(U->getOperand(0), KnownZero, KnownOne,
4287 F.getParent()->getDataLayout(), 0, &AC, nullptr, &DT);
4289 APInt EffectiveMask =
4290 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4291 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4292 const SCEV *MulCount = getConstant(
4293 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4297 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4298 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4305 case Instruction::Or:
4306 // If the RHS of the Or is a constant, we may have something like:
4307 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4308 // optimizations will transparently handle this case.
4310 // In order for this transformation to be safe, the LHS must be of the
4311 // form X*(2^n) and the Or constant must be less than 2^n.
4312 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4313 const SCEV *LHS = getSCEV(U->getOperand(0));
4314 const APInt &CIVal = CI->getValue();
4315 if (GetMinTrailingZeros(LHS) >=
4316 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4317 // Build a plain add SCEV.
4318 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4319 // If the LHS of the add was an addrec and it has no-wrap flags,
4320 // transfer the no-wrap flags, since an or won't introduce a wrap.
4321 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4322 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4323 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4324 OldAR->getNoWrapFlags());
4330 case Instruction::Xor:
4331 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4332 // If the RHS of the xor is a signbit, then this is just an add.
4333 // Instcombine turns add of signbit into xor as a strength reduction step.
4334 if (CI->getValue().isSignBit())
4335 return getAddExpr(getSCEV(U->getOperand(0)),
4336 getSCEV(U->getOperand(1)));
4338 // If the RHS of xor is -1, then this is a not operation.
4339 if (CI->isAllOnesValue())
4340 return getNotSCEV(getSCEV(U->getOperand(0)));
4342 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4343 // This is a variant of the check for xor with -1, and it handles
4344 // the case where instcombine has trimmed non-demanded bits out
4345 // of an xor with -1.
4346 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4347 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4348 if (BO->getOpcode() == Instruction::And &&
4349 LCI->getValue() == CI->getValue())
4350 if (const SCEVZeroExtendExpr *Z =
4351 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4352 Type *UTy = U->getType();
4353 const SCEV *Z0 = Z->getOperand();
4354 Type *Z0Ty = Z0->getType();
4355 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4357 // If C is a low-bits mask, the zero extend is serving to
4358 // mask off the high bits. Complement the operand and
4359 // re-apply the zext.
4360 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4361 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4363 // If C is a single bit, it may be in the sign-bit position
4364 // before the zero-extend. In this case, represent the xor
4365 // using an add, which is equivalent, and re-apply the zext.
4366 APInt Trunc = CI->getValue().trunc(Z0TySize);
4367 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4369 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4375 case Instruction::Shl:
4376 // Turn shift left of a constant amount into a multiply.
4377 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4378 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4380 // If the shift count is not less than the bitwidth, the result of
4381 // the shift is undefined. Don't try to analyze it, because the
4382 // resolution chosen here may differ from the resolution chosen in
4383 // other parts of the compiler.
4384 if (SA->getValue().uge(BitWidth))
4387 // It is currently not resolved how to interpret NSW for left
4388 // shift by BitWidth - 1, so we avoid applying flags in that
4389 // case. Remove this check (or this comment) once the situation
4391 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
4392 // and http://reviews.llvm.org/D8890 .
4393 auto Flags = SCEV::FlagAnyWrap;
4394 if (SA->getValue().ult(BitWidth - 1)) Flags = getNoWrapFlagsFromUB(U);
4396 Constant *X = ConstantInt::get(getContext(),
4397 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4398 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X), Flags);
4402 case Instruction::LShr:
4403 // Turn logical shift right of a constant into a unsigned divide.
4404 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4405 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4407 // If the shift count is not less than the bitwidth, the result of
4408 // the shift is undefined. Don't try to analyze it, because the
4409 // resolution chosen here may differ from the resolution chosen in
4410 // other parts of the compiler.
4411 if (SA->getValue().uge(BitWidth))
4414 Constant *X = ConstantInt::get(getContext(),
4415 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4416 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4420 case Instruction::AShr:
4421 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4422 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4423 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4424 if (L->getOpcode() == Instruction::Shl &&
4425 L->getOperand(1) == U->getOperand(1)) {
4426 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4428 // If the shift count is not less than the bitwidth, the result of
4429 // the shift is undefined. Don't try to analyze it, because the
4430 // resolution chosen here may differ from the resolution chosen in
4431 // other parts of the compiler.
4432 if (CI->getValue().uge(BitWidth))
4435 uint64_t Amt = BitWidth - CI->getZExtValue();
4436 if (Amt == BitWidth)
4437 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4439 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4440 IntegerType::get(getContext(),
4446 case Instruction::Trunc:
4447 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4449 case Instruction::ZExt:
4450 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4452 case Instruction::SExt:
4453 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4455 case Instruction::BitCast:
4456 // BitCasts are no-op casts so we just eliminate the cast.
4457 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4458 return getSCEV(U->getOperand(0));
4461 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4462 // lead to pointer expressions which cannot safely be expanded to GEPs,
4463 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4464 // simplifying integer expressions.
4466 case Instruction::GetElementPtr:
4467 return createNodeForGEP(cast<GEPOperator>(U));
4469 case Instruction::PHI:
4470 return createNodeForPHI(cast<PHINode>(U));
4472 case Instruction::Select:
4473 // This could be a smax or umax that was lowered earlier.
4474 // Try to recover it.
4475 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4476 Value *LHS = ICI->getOperand(0);
4477 Value *RHS = ICI->getOperand(1);
4478 switch (ICI->getPredicate()) {
4479 case ICmpInst::ICMP_SLT:
4480 case ICmpInst::ICMP_SLE:
4481 std::swap(LHS, RHS);
4483 case ICmpInst::ICMP_SGT:
4484 case ICmpInst::ICMP_SGE:
4485 // a >s b ? a+x : b+x -> smax(a, b)+x
4486 // a >s b ? b+x : a+x -> smin(a, b)+x
4487 if (getTypeSizeInBits(LHS->getType()) <=
4488 getTypeSizeInBits(U->getType())) {
4489 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType());
4490 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType());
4491 const SCEV *LA = getSCEV(U->getOperand(1));
4492 const SCEV *RA = getSCEV(U->getOperand(2));
4493 const SCEV *LDiff = getMinusSCEV(LA, LS);
4494 const SCEV *RDiff = getMinusSCEV(RA, RS);
4496 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4497 LDiff = getMinusSCEV(LA, RS);
4498 RDiff = getMinusSCEV(RA, LS);
4500 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4503 case ICmpInst::ICMP_ULT:
4504 case ICmpInst::ICMP_ULE:
4505 std::swap(LHS, RHS);
4507 case ICmpInst::ICMP_UGT:
4508 case ICmpInst::ICMP_UGE:
4509 // a >u b ? a+x : b+x -> umax(a, b)+x
4510 // a >u b ? b+x : a+x -> umin(a, b)+x
4511 if (getTypeSizeInBits(LHS->getType()) <=
4512 getTypeSizeInBits(U->getType())) {
4513 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4514 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType());
4515 const SCEV *LA = getSCEV(U->getOperand(1));
4516 const SCEV *RA = getSCEV(U->getOperand(2));
4517 const SCEV *LDiff = getMinusSCEV(LA, LS);
4518 const SCEV *RDiff = getMinusSCEV(RA, RS);
4520 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4521 LDiff = getMinusSCEV(LA, RS);
4522 RDiff = getMinusSCEV(RA, LS);
4524 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4527 case ICmpInst::ICMP_NE:
4528 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4529 if (getTypeSizeInBits(LHS->getType()) <=
4530 getTypeSizeInBits(U->getType()) &&
4531 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4532 const SCEV *One = getConstant(U->getType(), 1);
4533 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4534 const SCEV *LA = getSCEV(U->getOperand(1));
4535 const SCEV *RA = getSCEV(U->getOperand(2));
4536 const SCEV *LDiff = getMinusSCEV(LA, LS);
4537 const SCEV *RDiff = getMinusSCEV(RA, One);
4539 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4542 case ICmpInst::ICMP_EQ:
4543 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4544 if (getTypeSizeInBits(LHS->getType()) <=
4545 getTypeSizeInBits(U->getType()) &&
4546 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4547 const SCEV *One = getConstant(U->getType(), 1);
4548 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4549 const SCEV *LA = getSCEV(U->getOperand(1));
4550 const SCEV *RA = getSCEV(U->getOperand(2));
4551 const SCEV *LDiff = getMinusSCEV(LA, One);
4552 const SCEV *RDiff = getMinusSCEV(RA, LS);
4554 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4562 default: // We cannot analyze this expression.
4566 return getUnknown(V);
4571 //===----------------------------------------------------------------------===//
4572 // Iteration Count Computation Code
4575 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4576 if (BasicBlock *ExitingBB = L->getExitingBlock())
4577 return getSmallConstantTripCount(L, ExitingBB);
4579 // No trip count information for multiple exits.
4583 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4584 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4585 /// constant. Will also return 0 if the maximum trip count is very large (>=
4588 /// This "trip count" assumes that control exits via ExitingBlock. More
4589 /// precisely, it is the number of times that control may reach ExitingBlock
4590 /// before taking the branch. For loops with multiple exits, it may not be the
4591 /// number times that the loop header executes because the loop may exit
4592 /// prematurely via another branch.
4593 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4594 BasicBlock *ExitingBlock) {
4595 assert(ExitingBlock && "Must pass a non-null exiting block!");
4596 assert(L->isLoopExiting(ExitingBlock) &&
4597 "Exiting block must actually branch out of the loop!");
4598 const SCEVConstant *ExitCount =
4599 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4603 ConstantInt *ExitConst = ExitCount->getValue();
4605 // Guard against huge trip counts.
4606 if (ExitConst->getValue().getActiveBits() > 32)
4609 // In case of integer overflow, this returns 0, which is correct.
4610 return ((unsigned)ExitConst->getZExtValue()) + 1;
4613 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4614 if (BasicBlock *ExitingBB = L->getExitingBlock())
4615 return getSmallConstantTripMultiple(L, ExitingBB);
4617 // No trip multiple information for multiple exits.
4621 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4622 /// trip count of this loop as a normal unsigned value, if possible. This
4623 /// means that the actual trip count is always a multiple of the returned
4624 /// value (don't forget the trip count could very well be zero as well!).
4626 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4627 /// multiple of a constant (which is also the case if the trip count is simply
4628 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4629 /// if the trip count is very large (>= 2^32).
4631 /// As explained in the comments for getSmallConstantTripCount, this assumes
4632 /// that control exits the loop via ExitingBlock.
4634 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4635 BasicBlock *ExitingBlock) {
4636 assert(ExitingBlock && "Must pass a non-null exiting block!");
4637 assert(L->isLoopExiting(ExitingBlock) &&
4638 "Exiting block must actually branch out of the loop!");
4639 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4640 if (ExitCount == getCouldNotCompute())
4643 // Get the trip count from the BE count by adding 1.
4644 const SCEV *TCMul = getAddExpr(ExitCount,
4645 getConstant(ExitCount->getType(), 1));
4646 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4647 // to factor simple cases.
4648 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4649 TCMul = Mul->getOperand(0);
4651 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4655 ConstantInt *Result = MulC->getValue();
4657 // Guard against huge trip counts (this requires checking
4658 // for zero to handle the case where the trip count == -1 and the
4660 if (!Result || Result->getValue().getActiveBits() > 32 ||
4661 Result->getValue().getActiveBits() == 0)
4664 return (unsigned)Result->getZExtValue();
4667 // getExitCount - Get the expression for the number of loop iterations for which
4668 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4669 // SCEVCouldNotCompute.
4670 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4671 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4674 /// getBackedgeTakenCount - If the specified loop has a predictable
4675 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4676 /// object. The backedge-taken count is the number of times the loop header
4677 /// will be branched to from within the loop. This is one less than the
4678 /// trip count of the loop, since it doesn't count the first iteration,
4679 /// when the header is branched to from outside the loop.
4681 /// Note that it is not valid to call this method on a loop without a
4682 /// loop-invariant backedge-taken count (see
4683 /// hasLoopInvariantBackedgeTakenCount).
4685 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4686 return getBackedgeTakenInfo(L).getExact(this);
4689 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4690 /// return the least SCEV value that is known never to be less than the
4691 /// actual backedge taken count.
4692 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4693 return getBackedgeTakenInfo(L).getMax(this);
4696 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4697 /// onto the given Worklist.
4699 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4700 BasicBlock *Header = L->getHeader();
4702 // Push all Loop-header PHIs onto the Worklist stack.
4703 for (BasicBlock::iterator I = Header->begin();
4704 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4705 Worklist.push_back(PN);
4708 const ScalarEvolution::BackedgeTakenInfo &
4709 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4710 // Initially insert an invalid entry for this loop. If the insertion
4711 // succeeds, proceed to actually compute a backedge-taken count and
4712 // update the value. The temporary CouldNotCompute value tells SCEV
4713 // code elsewhere that it shouldn't attempt to request a new
4714 // backedge-taken count, which could result in infinite recursion.
4715 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4716 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4718 return Pair.first->second;
4720 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4721 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4722 // must be cleared in this scope.
4723 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4725 if (Result.getExact(this) != getCouldNotCompute()) {
4726 assert(isLoopInvariant(Result.getExact(this), L) &&
4727 isLoopInvariant(Result.getMax(this), L) &&
4728 "Computed backedge-taken count isn't loop invariant for loop!");
4729 ++NumTripCountsComputed;
4731 else if (Result.getMax(this) == getCouldNotCompute() &&
4732 isa<PHINode>(L->getHeader()->begin())) {
4733 // Only count loops that have phi nodes as not being computable.
4734 ++NumTripCountsNotComputed;
4737 // Now that we know more about the trip count for this loop, forget any
4738 // existing SCEV values for PHI nodes in this loop since they are only
4739 // conservative estimates made without the benefit of trip count
4740 // information. This is similar to the code in forgetLoop, except that
4741 // it handles SCEVUnknown PHI nodes specially.
4742 if (Result.hasAnyInfo()) {
4743 SmallVector<Instruction *, 16> Worklist;
4744 PushLoopPHIs(L, Worklist);
4746 SmallPtrSet<Instruction *, 8> Visited;
4747 while (!Worklist.empty()) {
4748 Instruction *I = Worklist.pop_back_val();
4749 if (!Visited.insert(I).second)
4752 ValueExprMapType::iterator It =
4753 ValueExprMap.find_as(static_cast<Value *>(I));
4754 if (It != ValueExprMap.end()) {
4755 const SCEV *Old = It->second;
4757 // SCEVUnknown for a PHI either means that it has an unrecognized
4758 // structure, or it's a PHI that's in the progress of being computed
4759 // by createNodeForPHI. In the former case, additional loop trip
4760 // count information isn't going to change anything. In the later
4761 // case, createNodeForPHI will perform the necessary updates on its
4762 // own when it gets to that point.
4763 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4764 forgetMemoizedResults(Old);
4765 ValueExprMap.erase(It);
4767 if (PHINode *PN = dyn_cast<PHINode>(I))
4768 ConstantEvolutionLoopExitValue.erase(PN);
4771 PushDefUseChildren(I, Worklist);
4775 // Re-lookup the insert position, since the call to
4776 // ComputeBackedgeTakenCount above could result in a
4777 // recusive call to getBackedgeTakenInfo (on a different
4778 // loop), which would invalidate the iterator computed
4780 return BackedgeTakenCounts.find(L)->second = Result;
4783 /// forgetLoop - This method should be called by the client when it has
4784 /// changed a loop in a way that may effect ScalarEvolution's ability to
4785 /// compute a trip count, or if the loop is deleted.
4786 void ScalarEvolution::forgetLoop(const Loop *L) {
4787 // Drop any stored trip count value.
4788 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4789 BackedgeTakenCounts.find(L);
4790 if (BTCPos != BackedgeTakenCounts.end()) {
4791 BTCPos->second.clear();
4792 BackedgeTakenCounts.erase(BTCPos);
4795 // Drop information about expressions based on loop-header PHIs.
4796 SmallVector<Instruction *, 16> Worklist;
4797 PushLoopPHIs(L, Worklist);
4799 SmallPtrSet<Instruction *, 8> Visited;
4800 while (!Worklist.empty()) {
4801 Instruction *I = Worklist.pop_back_val();
4802 if (!Visited.insert(I).second)
4805 ValueExprMapType::iterator It =
4806 ValueExprMap.find_as(static_cast<Value *>(I));
4807 if (It != ValueExprMap.end()) {
4808 forgetMemoizedResults(It->second);
4809 ValueExprMap.erase(It);
4810 if (PHINode *PN = dyn_cast<PHINode>(I))
4811 ConstantEvolutionLoopExitValue.erase(PN);
4814 PushDefUseChildren(I, Worklist);
4817 // Forget all contained loops too, to avoid dangling entries in the
4818 // ValuesAtScopes map.
4819 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4823 /// forgetValue - This method should be called by the client when it has
4824 /// changed a value in a way that may effect its value, or which may
4825 /// disconnect it from a def-use chain linking it to a loop.
4826 void ScalarEvolution::forgetValue(Value *V) {
4827 Instruction *I = dyn_cast<Instruction>(V);
4830 // Drop information about expressions based on loop-header PHIs.
4831 SmallVector<Instruction *, 16> Worklist;
4832 Worklist.push_back(I);
4834 SmallPtrSet<Instruction *, 8> Visited;
4835 while (!Worklist.empty()) {
4836 I = Worklist.pop_back_val();
4837 if (!Visited.insert(I).second)
4840 ValueExprMapType::iterator It =
4841 ValueExprMap.find_as(static_cast<Value *>(I));
4842 if (It != ValueExprMap.end()) {
4843 forgetMemoizedResults(It->second);
4844 ValueExprMap.erase(It);
4845 if (PHINode *PN = dyn_cast<PHINode>(I))
4846 ConstantEvolutionLoopExitValue.erase(PN);
4849 PushDefUseChildren(I, Worklist);
4853 /// getExact - Get the exact loop backedge taken count considering all loop
4854 /// exits. A computable result can only be returned for loops with a single
4855 /// exit. Returning the minimum taken count among all exits is incorrect
4856 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
4857 /// assumes that the limit of each loop test is never skipped. This is a valid
4858 /// assumption as long as the loop exits via that test. For precise results, it
4859 /// is the caller's responsibility to specify the relevant loop exit using
4860 /// getExact(ExitingBlock, SE).
4862 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4863 // If any exits were not computable, the loop is not computable.
4864 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4866 // We need exactly one computable exit.
4867 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4868 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4870 const SCEV *BECount = nullptr;
4871 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4872 ENT != nullptr; ENT = ENT->getNextExit()) {
4874 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4877 BECount = ENT->ExactNotTaken;
4878 else if (BECount != ENT->ExactNotTaken)
4879 return SE->getCouldNotCompute();
4881 assert(BECount && "Invalid not taken count for loop exit");
4885 /// getExact - Get the exact not taken count for this loop exit.
4887 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4888 ScalarEvolution *SE) const {
4889 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4890 ENT != nullptr; ENT = ENT->getNextExit()) {
4892 if (ENT->ExitingBlock == ExitingBlock)
4893 return ENT->ExactNotTaken;
4895 return SE->getCouldNotCompute();
4898 /// getMax - Get the max backedge taken count for the loop.
4900 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4901 return Max ? Max : SE->getCouldNotCompute();
4904 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4905 ScalarEvolution *SE) const {
4906 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4909 if (!ExitNotTaken.ExitingBlock)
4912 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4913 ENT != nullptr; ENT = ENT->getNextExit()) {
4915 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4916 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4923 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4924 /// computable exit into a persistent ExitNotTakenInfo array.
4925 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4926 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4927 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4930 ExitNotTaken.setIncomplete();
4932 unsigned NumExits = ExitCounts.size();
4933 if (NumExits == 0) return;
4935 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4936 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4937 if (NumExits == 1) return;
4939 // Handle the rare case of multiple computable exits.
4940 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4942 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4943 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4944 PrevENT->setNextExit(ENT);
4945 ENT->ExitingBlock = ExitCounts[i].first;
4946 ENT->ExactNotTaken = ExitCounts[i].second;
4950 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4951 void ScalarEvolution::BackedgeTakenInfo::clear() {
4952 ExitNotTaken.ExitingBlock = nullptr;
4953 ExitNotTaken.ExactNotTaken = nullptr;
4954 delete[] ExitNotTaken.getNextExit();
4957 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4958 /// of the specified loop will execute.
4959 ScalarEvolution::BackedgeTakenInfo
4960 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4961 SmallVector<BasicBlock *, 8> ExitingBlocks;
4962 L->getExitingBlocks(ExitingBlocks);
4964 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4965 bool CouldComputeBECount = true;
4966 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4967 const SCEV *MustExitMaxBECount = nullptr;
4968 const SCEV *MayExitMaxBECount = nullptr;
4970 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4971 // and compute maxBECount.
4972 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4973 BasicBlock *ExitBB = ExitingBlocks[i];
4974 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4976 // 1. For each exit that can be computed, add an entry to ExitCounts.
4977 // CouldComputeBECount is true only if all exits can be computed.
4978 if (EL.Exact == getCouldNotCompute())
4979 // We couldn't compute an exact value for this exit, so
4980 // we won't be able to compute an exact value for the loop.
4981 CouldComputeBECount = false;
4983 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4985 // 2. Derive the loop's MaxBECount from each exit's max number of
4986 // non-exiting iterations. Partition the loop exits into two kinds:
4987 // LoopMustExits and LoopMayExits.
4989 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4990 // is a LoopMayExit. If any computable LoopMustExit is found, then
4991 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4992 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4993 // considered greater than any computable EL.Max.
4994 if (EL.Max != getCouldNotCompute() && Latch &&
4995 DT.dominates(ExitBB, Latch)) {
4996 if (!MustExitMaxBECount)
4997 MustExitMaxBECount = EL.Max;
4999 MustExitMaxBECount =
5000 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5002 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5003 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5004 MayExitMaxBECount = EL.Max;
5007 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5011 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5012 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5013 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5016 /// ComputeExitLimit - Compute the number of times the backedge of the specified
5017 /// loop will execute if it exits via the specified block.
5018 ScalarEvolution::ExitLimit
5019 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
5021 // Okay, we've chosen an exiting block. See what condition causes us to
5022 // exit at this block and remember the exit block and whether all other targets
5023 // lead to the loop header.
5024 bool MustExecuteLoopHeader = true;
5025 BasicBlock *Exit = nullptr;
5026 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5028 if (!L->contains(*SI)) {
5029 if (Exit) // Multiple exit successors.
5030 return getCouldNotCompute();
5032 } else if (*SI != L->getHeader()) {
5033 MustExecuteLoopHeader = false;
5036 // At this point, we know we have a conditional branch that determines whether
5037 // the loop is exited. However, we don't know if the branch is executed each
5038 // time through the loop. If not, then the execution count of the branch will
5039 // not be equal to the trip count of the loop.
5041 // Currently we check for this by checking to see if the Exit branch goes to
5042 // the loop header. If so, we know it will always execute the same number of
5043 // times as the loop. We also handle the case where the exit block *is* the
5044 // loop header. This is common for un-rotated loops.
5046 // If both of those tests fail, walk up the unique predecessor chain to the
5047 // header, stopping if there is an edge that doesn't exit the loop. If the
5048 // header is reached, the execution count of the branch will be equal to the
5049 // trip count of the loop.
5051 // More extensive analysis could be done to handle more cases here.
5053 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5054 // The simple checks failed, try climbing the unique predecessor chain
5055 // up to the header.
5057 for (BasicBlock *BB = ExitingBlock; BB; ) {
5058 BasicBlock *Pred = BB->getUniquePredecessor();
5060 return getCouldNotCompute();
5061 TerminatorInst *PredTerm = Pred->getTerminator();
5062 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5065 // If the predecessor has a successor that isn't BB and isn't
5066 // outside the loop, assume the worst.
5067 if (L->contains(PredSucc))
5068 return getCouldNotCompute();
5070 if (Pred == L->getHeader()) {
5077 return getCouldNotCompute();
5080 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5081 TerminatorInst *Term = ExitingBlock->getTerminator();
5082 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5083 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5084 // Proceed to the next level to examine the exit condition expression.
5085 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5086 BI->getSuccessor(1),
5087 /*ControlsExit=*/IsOnlyExit);
5090 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5091 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
5092 /*ControlsExit=*/IsOnlyExit);
5094 return getCouldNotCompute();
5097 /// ComputeExitLimitFromCond - Compute the number of times the
5098 /// backedge of the specified loop will execute if its exit condition
5099 /// were a conditional branch of ExitCond, TBB, and FBB.
5101 /// @param ControlsExit is true if ExitCond directly controls the exit
5102 /// branch. In this case, we can assume that the loop exits only if the
5103 /// condition is true and can infer that failing to meet the condition prior to
5104 /// integer wraparound results in undefined behavior.
5105 ScalarEvolution::ExitLimit
5106 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
5110 bool ControlsExit) {
5111 // Check if the controlling expression for this loop is an And or Or.
5112 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5113 if (BO->getOpcode() == Instruction::And) {
5114 // Recurse on the operands of the and.
5115 bool EitherMayExit = L->contains(TBB);
5116 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5117 ControlsExit && !EitherMayExit);
5118 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5119 ControlsExit && !EitherMayExit);
5120 const SCEV *BECount = getCouldNotCompute();
5121 const SCEV *MaxBECount = getCouldNotCompute();
5122 if (EitherMayExit) {
5123 // Both conditions must be true for the loop to continue executing.
5124 // Choose the less conservative count.
5125 if (EL0.Exact == getCouldNotCompute() ||
5126 EL1.Exact == getCouldNotCompute())
5127 BECount = getCouldNotCompute();
5129 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5130 if (EL0.Max == getCouldNotCompute())
5131 MaxBECount = EL1.Max;
5132 else if (EL1.Max == getCouldNotCompute())
5133 MaxBECount = EL0.Max;
5135 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5137 // Both conditions must be true at the same time for the loop to exit.
5138 // For now, be conservative.
5139 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5140 if (EL0.Max == EL1.Max)
5141 MaxBECount = EL0.Max;
5142 if (EL0.Exact == EL1.Exact)
5143 BECount = EL0.Exact;
5146 return ExitLimit(BECount, MaxBECount);
5148 if (BO->getOpcode() == Instruction::Or) {
5149 // Recurse on the operands of the or.
5150 bool EitherMayExit = L->contains(FBB);
5151 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5152 ControlsExit && !EitherMayExit);
5153 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5154 ControlsExit && !EitherMayExit);
5155 const SCEV *BECount = getCouldNotCompute();
5156 const SCEV *MaxBECount = getCouldNotCompute();
5157 if (EitherMayExit) {
5158 // Both conditions must be false for the loop to continue executing.
5159 // Choose the less conservative count.
5160 if (EL0.Exact == getCouldNotCompute() ||
5161 EL1.Exact == getCouldNotCompute())
5162 BECount = getCouldNotCompute();
5164 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5165 if (EL0.Max == getCouldNotCompute())
5166 MaxBECount = EL1.Max;
5167 else if (EL1.Max == getCouldNotCompute())
5168 MaxBECount = EL0.Max;
5170 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5172 // Both conditions must be false at the same time for the loop to exit.
5173 // For now, be conservative.
5174 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5175 if (EL0.Max == EL1.Max)
5176 MaxBECount = EL0.Max;
5177 if (EL0.Exact == EL1.Exact)
5178 BECount = EL0.Exact;
5181 return ExitLimit(BECount, MaxBECount);
5185 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5186 // Proceed to the next level to examine the icmp.
5187 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5188 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5190 // Check for a constant condition. These are normally stripped out by
5191 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5192 // preserve the CFG and is temporarily leaving constant conditions
5194 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5195 if (L->contains(FBB) == !CI->getZExtValue())
5196 // The backedge is always taken.
5197 return getCouldNotCompute();
5199 // The backedge is never taken.
5200 return getConstant(CI->getType(), 0);
5203 // If it's not an integer or pointer comparison then compute it the hard way.
5204 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5207 /// ComputeExitLimitFromICmp - Compute the number of times the
5208 /// backedge of the specified loop will execute if its exit condition
5209 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5210 ScalarEvolution::ExitLimit
5211 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5215 bool ControlsExit) {
5217 // If the condition was exit on true, convert the condition to exit on false
5218 ICmpInst::Predicate Cond;
5219 if (!L->contains(FBB))
5220 Cond = ExitCond->getPredicate();
5222 Cond = ExitCond->getInversePredicate();
5224 // Handle common loops like: for (X = "string"; *X; ++X)
5225 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5226 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5228 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5229 if (ItCnt.hasAnyInfo())
5233 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5234 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5236 // Try to evaluate any dependencies out of the loop.
5237 LHS = getSCEVAtScope(LHS, L);
5238 RHS = getSCEVAtScope(RHS, L);
5240 // At this point, we would like to compute how many iterations of the
5241 // loop the predicate will return true for these inputs.
5242 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5243 // If there is a loop-invariant, force it into the RHS.
5244 std::swap(LHS, RHS);
5245 Cond = ICmpInst::getSwappedPredicate(Cond);
5248 // Simplify the operands before analyzing them.
5249 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5251 // If we have a comparison of a chrec against a constant, try to use value
5252 // ranges to answer this query.
5253 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5254 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5255 if (AddRec->getLoop() == L) {
5256 // Form the constant range.
5257 ConstantRange CompRange(
5258 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5260 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5261 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5265 case ICmpInst::ICMP_NE: { // while (X != Y)
5266 // Convert to: while (X-Y != 0)
5267 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5268 if (EL.hasAnyInfo()) return EL;
5271 case ICmpInst::ICMP_EQ: { // while (X == Y)
5272 // Convert to: while (X-Y == 0)
5273 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5274 if (EL.hasAnyInfo()) return EL;
5277 case ICmpInst::ICMP_SLT:
5278 case ICmpInst::ICMP_ULT: { // while (X < Y)
5279 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5280 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5281 if (EL.hasAnyInfo()) return EL;
5284 case ICmpInst::ICMP_SGT:
5285 case ICmpInst::ICMP_UGT: { // while (X > Y)
5286 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5287 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5288 if (EL.hasAnyInfo()) return EL;
5293 dbgs() << "ComputeBackedgeTakenCount ";
5294 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5295 dbgs() << "[unsigned] ";
5296 dbgs() << *LHS << " "
5297 << Instruction::getOpcodeName(Instruction::ICmp)
5298 << " " << *RHS << "\n";
5302 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5305 ScalarEvolution::ExitLimit
5306 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5308 BasicBlock *ExitingBlock,
5309 bool ControlsExit) {
5310 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5312 // Give up if the exit is the default dest of a switch.
5313 if (Switch->getDefaultDest() == ExitingBlock)
5314 return getCouldNotCompute();
5316 assert(L->contains(Switch->getDefaultDest()) &&
5317 "Default case must not exit the loop!");
5318 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5319 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5321 // while (X != Y) --> while (X-Y != 0)
5322 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5323 if (EL.hasAnyInfo())
5326 return getCouldNotCompute();
5329 static ConstantInt *
5330 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5331 ScalarEvolution &SE) {
5332 const SCEV *InVal = SE.getConstant(C);
5333 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5334 assert(isa<SCEVConstant>(Val) &&
5335 "Evaluation of SCEV at constant didn't fold correctly?");
5336 return cast<SCEVConstant>(Val)->getValue();
5339 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5340 /// 'icmp op load X, cst', try to see if we can compute the backedge
5341 /// execution count.
5342 ScalarEvolution::ExitLimit
5343 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5347 ICmpInst::Predicate predicate) {
5349 if (LI->isVolatile()) return getCouldNotCompute();
5351 // Check to see if the loaded pointer is a getelementptr of a global.
5352 // TODO: Use SCEV instead of manually grubbing with GEPs.
5353 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5354 if (!GEP) return getCouldNotCompute();
5356 // Make sure that it is really a constant global we are gepping, with an
5357 // initializer, and make sure the first IDX is really 0.
5358 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5359 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5360 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5361 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5362 return getCouldNotCompute();
5364 // Okay, we allow one non-constant index into the GEP instruction.
5365 Value *VarIdx = nullptr;
5366 std::vector<Constant*> Indexes;
5367 unsigned VarIdxNum = 0;
5368 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5369 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5370 Indexes.push_back(CI);
5371 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5372 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5373 VarIdx = GEP->getOperand(i);
5375 Indexes.push_back(nullptr);
5378 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5380 return getCouldNotCompute();
5382 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5383 // Check to see if X is a loop variant variable value now.
5384 const SCEV *Idx = getSCEV(VarIdx);
5385 Idx = getSCEVAtScope(Idx, L);
5387 // We can only recognize very limited forms of loop index expressions, in
5388 // particular, only affine AddRec's like {C1,+,C2}.
5389 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5390 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5391 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5392 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5393 return getCouldNotCompute();
5395 unsigned MaxSteps = MaxBruteForceIterations;
5396 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5397 ConstantInt *ItCst = ConstantInt::get(
5398 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5399 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5401 // Form the GEP offset.
5402 Indexes[VarIdxNum] = Val;
5404 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5406 if (!Result) break; // Cannot compute!
5408 // Evaluate the condition for this iteration.
5409 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5410 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5411 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5413 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5414 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5417 ++NumArrayLenItCounts;
5418 return getConstant(ItCst); // Found terminating iteration!
5421 return getCouldNotCompute();
5425 /// CanConstantFold - Return true if we can constant fold an instruction of the
5426 /// specified type, assuming that all operands were constants.
5427 static bool CanConstantFold(const Instruction *I) {
5428 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5429 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5433 if (const CallInst *CI = dyn_cast<CallInst>(I))
5434 if (const Function *F = CI->getCalledFunction())
5435 return canConstantFoldCallTo(F);
5439 /// Determine whether this instruction can constant evolve within this loop
5440 /// assuming its operands can all constant evolve.
5441 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5442 // An instruction outside of the loop can't be derived from a loop PHI.
5443 if (!L->contains(I)) return false;
5445 if (isa<PHINode>(I)) {
5446 // We don't currently keep track of the control flow needed to evaluate
5447 // PHIs, so we cannot handle PHIs inside of loops.
5448 return L->getHeader() == I->getParent();
5451 // If we won't be able to constant fold this expression even if the operands
5452 // are constants, bail early.
5453 return CanConstantFold(I);
5456 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5457 /// recursing through each instruction operand until reaching a loop header phi.
5459 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5460 DenseMap<Instruction *, PHINode *> &PHIMap) {
5462 // Otherwise, we can evaluate this instruction if all of its operands are
5463 // constant or derived from a PHI node themselves.
5464 PHINode *PHI = nullptr;
5465 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5466 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5468 if (isa<Constant>(*OpI)) continue;
5470 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5471 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5473 PHINode *P = dyn_cast<PHINode>(OpInst);
5475 // If this operand is already visited, reuse the prior result.
5476 // We may have P != PHI if this is the deepest point at which the
5477 // inconsistent paths meet.
5478 P = PHIMap.lookup(OpInst);
5480 // Recurse and memoize the results, whether a phi is found or not.
5481 // This recursive call invalidates pointers into PHIMap.
5482 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5486 return nullptr; // Not evolving from PHI
5487 if (PHI && PHI != P)
5488 return nullptr; // Evolving from multiple different PHIs.
5491 // This is a expression evolving from a constant PHI!
5495 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5496 /// in the loop that V is derived from. We allow arbitrary operations along the
5497 /// way, but the operands of an operation must either be constants or a value
5498 /// derived from a constant PHI. If this expression does not fit with these
5499 /// constraints, return null.
5500 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5501 Instruction *I = dyn_cast<Instruction>(V);
5502 if (!I || !canConstantEvolve(I, L)) return nullptr;
5504 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5508 // Record non-constant instructions contained by the loop.
5509 DenseMap<Instruction *, PHINode *> PHIMap;
5510 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5513 /// EvaluateExpression - Given an expression that passes the
5514 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5515 /// in the loop has the value PHIVal. If we can't fold this expression for some
5516 /// reason, return null.
5517 static Constant *EvaluateExpression(Value *V, const Loop *L,
5518 DenseMap<Instruction *, Constant *> &Vals,
5519 const DataLayout &DL,
5520 const TargetLibraryInfo *TLI) {
5521 // Convenient constant check, but redundant for recursive calls.
5522 if (Constant *C = dyn_cast<Constant>(V)) return C;
5523 Instruction *I = dyn_cast<Instruction>(V);
5524 if (!I) return nullptr;
5526 if (Constant *C = Vals.lookup(I)) return C;
5528 // An instruction inside the loop depends on a value outside the loop that we
5529 // weren't given a mapping for, or a value such as a call inside the loop.
5530 if (!canConstantEvolve(I, L)) return nullptr;
5532 // An unmapped PHI can be due to a branch or another loop inside this loop,
5533 // or due to this not being the initial iteration through a loop where we
5534 // couldn't compute the evolution of this particular PHI last time.
5535 if (isa<PHINode>(I)) return nullptr;
5537 std::vector<Constant*> Operands(I->getNumOperands());
5539 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5540 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5542 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5543 if (!Operands[i]) return nullptr;
5546 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5548 if (!C) return nullptr;
5552 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5553 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5554 Operands[1], DL, TLI);
5555 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5556 if (!LI->isVolatile())
5557 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5559 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5563 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5564 /// in the header of its containing loop, we know the loop executes a
5565 /// constant number of times, and the PHI node is just a recurrence
5566 /// involving constants, fold it.
5568 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5571 DenseMap<PHINode*, Constant*>::const_iterator I =
5572 ConstantEvolutionLoopExitValue.find(PN);
5573 if (I != ConstantEvolutionLoopExitValue.end())
5576 if (BEs.ugt(MaxBruteForceIterations))
5577 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5579 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5581 DenseMap<Instruction *, Constant *> CurrentIterVals;
5582 BasicBlock *Header = L->getHeader();
5583 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5585 // Since the loop is canonicalized, the PHI node must have two entries. One
5586 // entry must be a constant (coming in from outside of the loop), and the
5587 // second must be derived from the same PHI.
5588 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5589 PHINode *PHI = nullptr;
5590 for (BasicBlock::iterator I = Header->begin();
5591 (PHI = dyn_cast<PHINode>(I)); ++I) {
5592 Constant *StartCST =
5593 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5594 if (!StartCST) continue;
5595 CurrentIterVals[PHI] = StartCST;
5597 if (!CurrentIterVals.count(PN))
5598 return RetVal = nullptr;
5600 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5602 // Execute the loop symbolically to determine the exit value.
5603 if (BEs.getActiveBits() >= 32)
5604 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5606 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5607 unsigned IterationNum = 0;
5608 const DataLayout &DL = F.getParent()->getDataLayout();
5609 for (; ; ++IterationNum) {
5610 if (IterationNum == NumIterations)
5611 return RetVal = CurrentIterVals[PN]; // Got exit value!
5613 // Compute the value of the PHIs for the next iteration.
5614 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5615 DenseMap<Instruction *, Constant *> NextIterVals;
5617 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5619 return nullptr; // Couldn't evaluate!
5620 NextIterVals[PN] = NextPHI;
5622 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5624 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5625 // cease to be able to evaluate one of them or if they stop evolving,
5626 // because that doesn't necessarily prevent us from computing PN.
5627 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5628 for (DenseMap<Instruction *, Constant *>::const_iterator
5629 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5630 PHINode *PHI = dyn_cast<PHINode>(I->first);
5631 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5632 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5634 // We use two distinct loops because EvaluateExpression may invalidate any
5635 // iterators into CurrentIterVals.
5636 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5637 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5638 PHINode *PHI = I->first;
5639 Constant *&NextPHI = NextIterVals[PHI];
5640 if (!NextPHI) { // Not already computed.
5641 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5642 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5644 if (NextPHI != I->second)
5645 StoppedEvolving = false;
5648 // If all entries in CurrentIterVals == NextIterVals then we can stop
5649 // iterating, the loop can't continue to change.
5650 if (StoppedEvolving)
5651 return RetVal = CurrentIterVals[PN];
5653 CurrentIterVals.swap(NextIterVals);
5657 /// ComputeExitCountExhaustively - If the loop is known to execute a
5658 /// constant number of times (the condition evolves only from constants),
5659 /// try to evaluate a few iterations of the loop until we get the exit
5660 /// condition gets a value of ExitWhen (true or false). If we cannot
5661 /// evaluate the trip count of the loop, return getCouldNotCompute().
5662 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5665 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5666 if (!PN) return getCouldNotCompute();
5668 // If the loop is canonicalized, the PHI will have exactly two entries.
5669 // That's the only form we support here.
5670 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5672 DenseMap<Instruction *, Constant *> CurrentIterVals;
5673 BasicBlock *Header = L->getHeader();
5674 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5676 // One entry must be a constant (coming in from outside of the loop), and the
5677 // second must be derived from the same PHI.
5678 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5679 PHINode *PHI = nullptr;
5680 for (BasicBlock::iterator I = Header->begin();
5681 (PHI = dyn_cast<PHINode>(I)); ++I) {
5682 Constant *StartCST =
5683 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5684 if (!StartCST) continue;
5685 CurrentIterVals[PHI] = StartCST;
5687 if (!CurrentIterVals.count(PN))
5688 return getCouldNotCompute();
5690 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5691 // the loop symbolically to determine when the condition gets a value of
5693 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5694 const DataLayout &DL = F.getParent()->getDataLayout();
5695 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5696 ConstantInt *CondVal = dyn_cast_or_null<ConstantInt>(
5697 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
5699 // Couldn't symbolically evaluate.
5700 if (!CondVal) return getCouldNotCompute();
5702 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5703 ++NumBruteForceTripCountsComputed;
5704 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5707 // Update all the PHI nodes for the next iteration.
5708 DenseMap<Instruction *, Constant *> NextIterVals;
5710 // Create a list of which PHIs we need to compute. We want to do this before
5711 // calling EvaluateExpression on them because that may invalidate iterators
5712 // into CurrentIterVals.
5713 SmallVector<PHINode *, 8> PHIsToCompute;
5714 for (DenseMap<Instruction *, Constant *>::const_iterator
5715 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5716 PHINode *PHI = dyn_cast<PHINode>(I->first);
5717 if (!PHI || PHI->getParent() != Header) continue;
5718 PHIsToCompute.push_back(PHI);
5720 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5721 E = PHIsToCompute.end(); I != E; ++I) {
5723 Constant *&NextPHI = NextIterVals[PHI];
5724 if (NextPHI) continue; // Already computed!
5726 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5727 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5729 CurrentIterVals.swap(NextIterVals);
5732 // Too many iterations were needed to evaluate.
5733 return getCouldNotCompute();
5736 /// getSCEVAtScope - Return a SCEV expression for the specified value
5737 /// at the specified scope in the program. The L value specifies a loop
5738 /// nest to evaluate the expression at, where null is the top-level or a
5739 /// specified loop is immediately inside of the loop.
5741 /// This method can be used to compute the exit value for a variable defined
5742 /// in a loop by querying what the value will hold in the parent loop.
5744 /// In the case that a relevant loop exit value cannot be computed, the
5745 /// original value V is returned.
5746 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5747 // Check to see if we've folded this expression at this loop before.
5748 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5749 for (unsigned u = 0; u < Values.size(); u++) {
5750 if (Values[u].first == L)
5751 return Values[u].second ? Values[u].second : V;
5753 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5754 // Otherwise compute it.
5755 const SCEV *C = computeSCEVAtScope(V, L);
5756 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5757 for (unsigned u = Values2.size(); u > 0; u--) {
5758 if (Values2[u - 1].first == L) {
5759 Values2[u - 1].second = C;
5766 /// This builds up a Constant using the ConstantExpr interface. That way, we
5767 /// will return Constants for objects which aren't represented by a
5768 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5769 /// Returns NULL if the SCEV isn't representable as a Constant.
5770 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5771 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5772 case scCouldNotCompute:
5776 return cast<SCEVConstant>(V)->getValue();
5778 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5779 case scSignExtend: {
5780 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5781 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5782 return ConstantExpr::getSExt(CastOp, SS->getType());
5785 case scZeroExtend: {
5786 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5787 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5788 return ConstantExpr::getZExt(CastOp, SZ->getType());
5792 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5793 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5794 return ConstantExpr::getTrunc(CastOp, ST->getType());
5798 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5799 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5800 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5801 unsigned AS = PTy->getAddressSpace();
5802 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5803 C = ConstantExpr::getBitCast(C, DestPtrTy);
5805 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5806 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5807 if (!C2) return nullptr;
5810 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5811 unsigned AS = C2->getType()->getPointerAddressSpace();
5813 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5814 // The offsets have been converted to bytes. We can add bytes to an
5815 // i8* by GEP with the byte count in the first index.
5816 C = ConstantExpr::getBitCast(C, DestPtrTy);
5819 // Don't bother trying to sum two pointers. We probably can't
5820 // statically compute a load that results from it anyway.
5821 if (C2->getType()->isPointerTy())
5824 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5825 if (PTy->getElementType()->isStructTy())
5826 C2 = ConstantExpr::getIntegerCast(
5827 C2, Type::getInt32Ty(C->getContext()), true);
5828 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
5830 C = ConstantExpr::getAdd(C, C2);
5837 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5838 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5839 // Don't bother with pointers at all.
5840 if (C->getType()->isPointerTy()) return nullptr;
5841 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5842 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5843 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5844 C = ConstantExpr::getMul(C, C2);
5851 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5852 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5853 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5854 if (LHS->getType() == RHS->getType())
5855 return ConstantExpr::getUDiv(LHS, RHS);
5860 break; // TODO: smax, umax.
5865 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5866 if (isa<SCEVConstant>(V)) return V;
5868 // If this instruction is evolved from a constant-evolving PHI, compute the
5869 // exit value from the loop without using SCEVs.
5870 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5871 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5872 const Loop *LI = this->LI[I->getParent()];
5873 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5874 if (PHINode *PN = dyn_cast<PHINode>(I))
5875 if (PN->getParent() == LI->getHeader()) {
5876 // Okay, there is no closed form solution for the PHI node. Check
5877 // to see if the loop that contains it has a known backedge-taken
5878 // count. If so, we may be able to force computation of the exit
5880 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5881 if (const SCEVConstant *BTCC =
5882 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5883 // Okay, we know how many times the containing loop executes. If
5884 // this is a constant evolving PHI node, get the final value at
5885 // the specified iteration number.
5886 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5887 BTCC->getValue()->getValue(),
5889 if (RV) return getSCEV(RV);
5893 // Okay, this is an expression that we cannot symbolically evaluate
5894 // into a SCEV. Check to see if it's possible to symbolically evaluate
5895 // the arguments into constants, and if so, try to constant propagate the
5896 // result. This is particularly useful for computing loop exit values.
5897 if (CanConstantFold(I)) {
5898 SmallVector<Constant *, 4> Operands;
5899 bool MadeImprovement = false;
5900 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5901 Value *Op = I->getOperand(i);
5902 if (Constant *C = dyn_cast<Constant>(Op)) {
5903 Operands.push_back(C);
5907 // If any of the operands is non-constant and if they are
5908 // non-integer and non-pointer, don't even try to analyze them
5909 // with scev techniques.
5910 if (!isSCEVable(Op->getType()))
5913 const SCEV *OrigV = getSCEV(Op);
5914 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5915 MadeImprovement |= OrigV != OpV;
5917 Constant *C = BuildConstantFromSCEV(OpV);
5919 if (C->getType() != Op->getType())
5920 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5924 Operands.push_back(C);
5927 // Check to see if getSCEVAtScope actually made an improvement.
5928 if (MadeImprovement) {
5929 Constant *C = nullptr;
5930 const DataLayout &DL = F.getParent()->getDataLayout();
5931 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5932 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5933 Operands[1], DL, &TLI);
5934 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5935 if (!LI->isVolatile())
5936 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5938 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
5946 // This is some other type of SCEVUnknown, just return it.
5950 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5951 // Avoid performing the look-up in the common case where the specified
5952 // expression has no loop-variant portions.
5953 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5954 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5955 if (OpAtScope != Comm->getOperand(i)) {
5956 // Okay, at least one of these operands is loop variant but might be
5957 // foldable. Build a new instance of the folded commutative expression.
5958 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5959 Comm->op_begin()+i);
5960 NewOps.push_back(OpAtScope);
5962 for (++i; i != e; ++i) {
5963 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5964 NewOps.push_back(OpAtScope);
5966 if (isa<SCEVAddExpr>(Comm))
5967 return getAddExpr(NewOps);
5968 if (isa<SCEVMulExpr>(Comm))
5969 return getMulExpr(NewOps);
5970 if (isa<SCEVSMaxExpr>(Comm))
5971 return getSMaxExpr(NewOps);
5972 if (isa<SCEVUMaxExpr>(Comm))
5973 return getUMaxExpr(NewOps);
5974 llvm_unreachable("Unknown commutative SCEV type!");
5977 // If we got here, all operands are loop invariant.
5981 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5982 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5983 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5984 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5985 return Div; // must be loop invariant
5986 return getUDivExpr(LHS, RHS);
5989 // If this is a loop recurrence for a loop that does not contain L, then we
5990 // are dealing with the final value computed by the loop.
5991 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5992 // First, attempt to evaluate each operand.
5993 // Avoid performing the look-up in the common case where the specified
5994 // expression has no loop-variant portions.
5995 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5996 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5997 if (OpAtScope == AddRec->getOperand(i))
6000 // Okay, at least one of these operands is loop variant but might be
6001 // foldable. Build a new instance of the folded commutative expression.
6002 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6003 AddRec->op_begin()+i);
6004 NewOps.push_back(OpAtScope);
6005 for (++i; i != e; ++i)
6006 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6008 const SCEV *FoldedRec =
6009 getAddRecExpr(NewOps, AddRec->getLoop(),
6010 AddRec->getNoWrapFlags(SCEV::FlagNW));
6011 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6012 // The addrec may be folded to a nonrecurrence, for example, if the
6013 // induction variable is multiplied by zero after constant folding. Go
6014 // ahead and return the folded value.
6020 // If the scope is outside the addrec's loop, evaluate it by using the
6021 // loop exit value of the addrec.
6022 if (!AddRec->getLoop()->contains(L)) {
6023 // To evaluate this recurrence, we need to know how many times the AddRec
6024 // loop iterates. Compute this now.
6025 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6026 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6028 // Then, evaluate the AddRec.
6029 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6035 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6036 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6037 if (Op == Cast->getOperand())
6038 return Cast; // must be loop invariant
6039 return getZeroExtendExpr(Op, Cast->getType());
6042 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6043 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6044 if (Op == Cast->getOperand())
6045 return Cast; // must be loop invariant
6046 return getSignExtendExpr(Op, Cast->getType());
6049 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6050 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6051 if (Op == Cast->getOperand())
6052 return Cast; // must be loop invariant
6053 return getTruncateExpr(Op, Cast->getType());
6056 llvm_unreachable("Unknown SCEV type!");
6059 /// getSCEVAtScope - This is a convenience function which does
6060 /// getSCEVAtScope(getSCEV(V), L).
6061 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6062 return getSCEVAtScope(getSCEV(V), L);
6065 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6066 /// following equation:
6068 /// A * X = B (mod N)
6070 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6071 /// A and B isn't important.
6073 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6074 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6075 ScalarEvolution &SE) {
6076 uint32_t BW = A.getBitWidth();
6077 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6078 assert(A != 0 && "A must be non-zero.");
6082 // The gcd of A and N may have only one prime factor: 2. The number of
6083 // trailing zeros in A is its multiplicity
6084 uint32_t Mult2 = A.countTrailingZeros();
6087 // 2. Check if B is divisible by D.
6089 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6090 // is not less than multiplicity of this prime factor for D.
6091 if (B.countTrailingZeros() < Mult2)
6092 return SE.getCouldNotCompute();
6094 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6097 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6098 // bit width during computations.
6099 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6100 APInt Mod(BW + 1, 0);
6101 Mod.setBit(BW - Mult2); // Mod = N / D
6102 APInt I = AD.multiplicativeInverse(Mod);
6104 // 4. Compute the minimum unsigned root of the equation:
6105 // I * (B / D) mod (N / D)
6106 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6108 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6110 return SE.getConstant(Result.trunc(BW));
6113 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6114 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6115 /// might be the same) or two SCEVCouldNotCompute objects.
6117 static std::pair<const SCEV *,const SCEV *>
6118 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6119 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6120 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6121 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6122 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6124 // We currently can only solve this if the coefficients are constants.
6125 if (!LC || !MC || !NC) {
6126 const SCEV *CNC = SE.getCouldNotCompute();
6127 return std::make_pair(CNC, CNC);
6130 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6131 const APInt &L = LC->getValue()->getValue();
6132 const APInt &M = MC->getValue()->getValue();
6133 const APInt &N = NC->getValue()->getValue();
6134 APInt Two(BitWidth, 2);
6135 APInt Four(BitWidth, 4);
6138 using namespace APIntOps;
6140 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6141 // The B coefficient is M-N/2
6145 // The A coefficient is N/2
6146 APInt A(N.sdiv(Two));
6148 // Compute the B^2-4ac term.
6151 SqrtTerm -= Four * (A * C);
6153 if (SqrtTerm.isNegative()) {
6154 // The loop is provably infinite.
6155 const SCEV *CNC = SE.getCouldNotCompute();
6156 return std::make_pair(CNC, CNC);
6159 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6160 // integer value or else APInt::sqrt() will assert.
6161 APInt SqrtVal(SqrtTerm.sqrt());
6163 // Compute the two solutions for the quadratic formula.
6164 // The divisions must be performed as signed divisions.
6167 if (TwoA.isMinValue()) {
6168 const SCEV *CNC = SE.getCouldNotCompute();
6169 return std::make_pair(CNC, CNC);
6172 LLVMContext &Context = SE.getContext();
6174 ConstantInt *Solution1 =
6175 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6176 ConstantInt *Solution2 =
6177 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6179 return std::make_pair(SE.getConstant(Solution1),
6180 SE.getConstant(Solution2));
6181 } // end APIntOps namespace
6184 /// HowFarToZero - Return the number of times a backedge comparing the specified
6185 /// value to zero will execute. If not computable, return CouldNotCompute.
6187 /// This is only used for loops with a "x != y" exit test. The exit condition is
6188 /// now expressed as a single expression, V = x-y. So the exit test is
6189 /// effectively V != 0. We know and take advantage of the fact that this
6190 /// expression only being used in a comparison by zero context.
6191 ScalarEvolution::ExitLimit
6192 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6193 // If the value is a constant
6194 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6195 // If the value is already zero, the branch will execute zero times.
6196 if (C->getValue()->isZero()) return C;
6197 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6200 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6201 if (!AddRec || AddRec->getLoop() != L)
6202 return getCouldNotCompute();
6204 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6205 // the quadratic equation to solve it.
6206 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6207 std::pair<const SCEV *,const SCEV *> Roots =
6208 SolveQuadraticEquation(AddRec, *this);
6209 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6210 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6213 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6214 << " sol#2: " << *R2 << "\n";
6216 // Pick the smallest positive root value.
6217 if (ConstantInt *CB =
6218 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6221 if (!CB->getZExtValue())
6222 std::swap(R1, R2); // R1 is the minimum root now.
6224 // We can only use this value if the chrec ends up with an exact zero
6225 // value at this index. When solving for "X*X != 5", for example, we
6226 // should not accept a root of 2.
6227 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6229 return R1; // We found a quadratic root!
6232 return getCouldNotCompute();
6235 // Otherwise we can only handle this if it is affine.
6236 if (!AddRec->isAffine())
6237 return getCouldNotCompute();
6239 // If this is an affine expression, the execution count of this branch is
6240 // the minimum unsigned root of the following equation:
6242 // Start + Step*N = 0 (mod 2^BW)
6246 // Step*N = -Start (mod 2^BW)
6248 // where BW is the common bit width of Start and Step.
6250 // Get the initial value for the loop.
6251 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6252 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6254 // For now we handle only constant steps.
6256 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6257 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6258 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6259 // We have not yet seen any such cases.
6260 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6261 if (!StepC || StepC->getValue()->equalsInt(0))
6262 return getCouldNotCompute();
6264 // For positive steps (counting up until unsigned overflow):
6265 // N = -Start/Step (as unsigned)
6266 // For negative steps (counting down to zero):
6268 // First compute the unsigned distance from zero in the direction of Step.
6269 bool CountDown = StepC->getValue()->getValue().isNegative();
6270 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6272 // Handle unitary steps, which cannot wraparound.
6273 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6274 // N = Distance (as unsigned)
6275 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6276 ConstantRange CR = getUnsignedRange(Start);
6277 const SCEV *MaxBECount;
6278 if (!CountDown && CR.getUnsignedMin().isMinValue())
6279 // When counting up, the worst starting value is 1, not 0.
6280 MaxBECount = CR.getUnsignedMax().isMinValue()
6281 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6282 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6284 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6285 : -CR.getUnsignedMin());
6286 return ExitLimit(Distance, MaxBECount);
6289 // As a special case, handle the instance where Step is a positive power of
6290 // two. In this case, determining whether Step divides Distance evenly can be
6291 // done by counting and comparing the number of trailing zeros of Step and
6294 const APInt &StepV = StepC->getValue()->getValue();
6295 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6296 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6297 // case is not handled as this code is guarded by !CountDown.
6298 if (StepV.isPowerOf2() &&
6299 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
6300 // Here we've constrained the equation to be of the form
6302 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
6304 // where we're operating on a W bit wide integer domain and k is
6305 // non-negative. The smallest unsigned solution for X is the trip count.
6307 // (0) is equivalent to:
6309 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
6310 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
6311 // <=> 2^k * Distance' - X = L * 2^(W - N)
6312 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
6314 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
6317 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
6319 // E.g. say we're solving
6321 // 2 * Val = 2 * X (in i8) ... (3)
6323 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
6325 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
6326 // necessarily the smallest unsigned value of X that satisfies (3).
6327 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
6328 // is i8 1, not i8 -127
6330 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
6332 // Since SCEV does not have a URem node, we construct one using a truncate
6333 // and a zero extend.
6335 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
6336 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
6337 auto *WideTy = Distance->getType();
6339 return getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
6343 // If the condition controls loop exit (the loop exits only if the expression
6344 // is true) and the addition is no-wrap we can use unsigned divide to
6345 // compute the backedge count. In this case, the step may not divide the
6346 // distance, but we don't care because if the condition is "missed" the loop
6347 // will have undefined behavior due to wrapping.
6348 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6350 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6351 return ExitLimit(Exact, Exact);
6354 // Then, try to solve the above equation provided that Start is constant.
6355 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6356 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6357 -StartC->getValue()->getValue(),
6359 return getCouldNotCompute();
6362 /// HowFarToNonZero - Return the number of times a backedge checking the
6363 /// specified value for nonzero will execute. If not computable, return
6365 ScalarEvolution::ExitLimit
6366 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6367 // Loops that look like: while (X == 0) are very strange indeed. We don't
6368 // handle them yet except for the trivial case. This could be expanded in the
6369 // future as needed.
6371 // If the value is a constant, check to see if it is known to be non-zero
6372 // already. If so, the backedge will execute zero times.
6373 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6374 if (!C->getValue()->isNullValue())
6375 return getConstant(C->getType(), 0);
6376 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6379 // We could implement others, but I really doubt anyone writes loops like
6380 // this, and if they did, they would already be constant folded.
6381 return getCouldNotCompute();
6384 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6385 /// (which may not be an immediate predecessor) which has exactly one
6386 /// successor from which BB is reachable, or null if no such block is
6389 std::pair<BasicBlock *, BasicBlock *>
6390 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6391 // If the block has a unique predecessor, then there is no path from the
6392 // predecessor to the block that does not go through the direct edge
6393 // from the predecessor to the block.
6394 if (BasicBlock *Pred = BB->getSinglePredecessor())
6395 return std::make_pair(Pred, BB);
6397 // A loop's header is defined to be a block that dominates the loop.
6398 // If the header has a unique predecessor outside the loop, it must be
6399 // a block that has exactly one successor that can reach the loop.
6400 if (Loop *L = LI.getLoopFor(BB))
6401 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6403 return std::pair<BasicBlock *, BasicBlock *>();
6406 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6407 /// testing whether two expressions are equal, however for the purposes of
6408 /// looking for a condition guarding a loop, it can be useful to be a little
6409 /// more general, since a front-end may have replicated the controlling
6412 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6413 // Quick check to see if they are the same SCEV.
6414 if (A == B) return true;
6416 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6417 // two different instructions with the same value. Check for this case.
6418 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6419 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6420 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6421 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6422 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6425 // Otherwise assume they may have a different value.
6429 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6430 /// predicate Pred. Return true iff any changes were made.
6432 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6433 const SCEV *&LHS, const SCEV *&RHS,
6435 bool Changed = false;
6437 // If we hit the max recursion limit bail out.
6441 // Canonicalize a constant to the right side.
6442 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6443 // Check for both operands constant.
6444 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6445 if (ConstantExpr::getICmp(Pred,
6447 RHSC->getValue())->isNullValue())
6448 goto trivially_false;
6450 goto trivially_true;
6452 // Otherwise swap the operands to put the constant on the right.
6453 std::swap(LHS, RHS);
6454 Pred = ICmpInst::getSwappedPredicate(Pred);
6458 // If we're comparing an addrec with a value which is loop-invariant in the
6459 // addrec's loop, put the addrec on the left. Also make a dominance check,
6460 // as both operands could be addrecs loop-invariant in each other's loop.
6461 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6462 const Loop *L = AR->getLoop();
6463 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6464 std::swap(LHS, RHS);
6465 Pred = ICmpInst::getSwappedPredicate(Pred);
6470 // If there's a constant operand, canonicalize comparisons with boundary
6471 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6472 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6473 const APInt &RA = RC->getValue()->getValue();
6475 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6476 case ICmpInst::ICMP_EQ:
6477 case ICmpInst::ICMP_NE:
6478 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6480 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6481 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6482 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6483 ME->getOperand(0)->isAllOnesValue()) {
6484 RHS = AE->getOperand(1);
6485 LHS = ME->getOperand(1);
6489 case ICmpInst::ICMP_UGE:
6490 if ((RA - 1).isMinValue()) {
6491 Pred = ICmpInst::ICMP_NE;
6492 RHS = getConstant(RA - 1);
6496 if (RA.isMaxValue()) {
6497 Pred = ICmpInst::ICMP_EQ;
6501 if (RA.isMinValue()) goto trivially_true;
6503 Pred = ICmpInst::ICMP_UGT;
6504 RHS = getConstant(RA - 1);
6507 case ICmpInst::ICMP_ULE:
6508 if ((RA + 1).isMaxValue()) {
6509 Pred = ICmpInst::ICMP_NE;
6510 RHS = getConstant(RA + 1);
6514 if (RA.isMinValue()) {
6515 Pred = ICmpInst::ICMP_EQ;
6519 if (RA.isMaxValue()) goto trivially_true;
6521 Pred = ICmpInst::ICMP_ULT;
6522 RHS = getConstant(RA + 1);
6525 case ICmpInst::ICMP_SGE:
6526 if ((RA - 1).isMinSignedValue()) {
6527 Pred = ICmpInst::ICMP_NE;
6528 RHS = getConstant(RA - 1);
6532 if (RA.isMaxSignedValue()) {
6533 Pred = ICmpInst::ICMP_EQ;
6537 if (RA.isMinSignedValue()) goto trivially_true;
6539 Pred = ICmpInst::ICMP_SGT;
6540 RHS = getConstant(RA - 1);
6543 case ICmpInst::ICMP_SLE:
6544 if ((RA + 1).isMaxSignedValue()) {
6545 Pred = ICmpInst::ICMP_NE;
6546 RHS = getConstant(RA + 1);
6550 if (RA.isMinSignedValue()) {
6551 Pred = ICmpInst::ICMP_EQ;
6555 if (RA.isMaxSignedValue()) goto trivially_true;
6557 Pred = ICmpInst::ICMP_SLT;
6558 RHS = getConstant(RA + 1);
6561 case ICmpInst::ICMP_UGT:
6562 if (RA.isMinValue()) {
6563 Pred = ICmpInst::ICMP_NE;
6567 if ((RA + 1).isMaxValue()) {
6568 Pred = ICmpInst::ICMP_EQ;
6569 RHS = getConstant(RA + 1);
6573 if (RA.isMaxValue()) goto trivially_false;
6575 case ICmpInst::ICMP_ULT:
6576 if (RA.isMaxValue()) {
6577 Pred = ICmpInst::ICMP_NE;
6581 if ((RA - 1).isMinValue()) {
6582 Pred = ICmpInst::ICMP_EQ;
6583 RHS = getConstant(RA - 1);
6587 if (RA.isMinValue()) goto trivially_false;
6589 case ICmpInst::ICMP_SGT:
6590 if (RA.isMinSignedValue()) {
6591 Pred = ICmpInst::ICMP_NE;
6595 if ((RA + 1).isMaxSignedValue()) {
6596 Pred = ICmpInst::ICMP_EQ;
6597 RHS = getConstant(RA + 1);
6601 if (RA.isMaxSignedValue()) goto trivially_false;
6603 case ICmpInst::ICMP_SLT:
6604 if (RA.isMaxSignedValue()) {
6605 Pred = ICmpInst::ICMP_NE;
6609 if ((RA - 1).isMinSignedValue()) {
6610 Pred = ICmpInst::ICMP_EQ;
6611 RHS = getConstant(RA - 1);
6615 if (RA.isMinSignedValue()) goto trivially_false;
6620 // Check for obvious equality.
6621 if (HasSameValue(LHS, RHS)) {
6622 if (ICmpInst::isTrueWhenEqual(Pred))
6623 goto trivially_true;
6624 if (ICmpInst::isFalseWhenEqual(Pred))
6625 goto trivially_false;
6628 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6629 // adding or subtracting 1 from one of the operands.
6631 case ICmpInst::ICMP_SLE:
6632 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6633 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6635 Pred = ICmpInst::ICMP_SLT;
6637 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6638 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6640 Pred = ICmpInst::ICMP_SLT;
6644 case ICmpInst::ICMP_SGE:
6645 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6646 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6648 Pred = ICmpInst::ICMP_SGT;
6650 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6651 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6653 Pred = ICmpInst::ICMP_SGT;
6657 case ICmpInst::ICMP_ULE:
6658 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6659 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6661 Pred = ICmpInst::ICMP_ULT;
6663 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6664 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6666 Pred = ICmpInst::ICMP_ULT;
6670 case ICmpInst::ICMP_UGE:
6671 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6672 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6674 Pred = ICmpInst::ICMP_UGT;
6676 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6677 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6679 Pred = ICmpInst::ICMP_UGT;
6687 // TODO: More simplifications are possible here.
6689 // Recursively simplify until we either hit a recursion limit or nothing
6692 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6698 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6699 Pred = ICmpInst::ICMP_EQ;
6704 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6705 Pred = ICmpInst::ICMP_NE;
6709 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6710 return getSignedRange(S).getSignedMax().isNegative();
6713 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6714 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6717 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6718 return !getSignedRange(S).getSignedMin().isNegative();
6721 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6722 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6725 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6726 return isKnownNegative(S) || isKnownPositive(S);
6729 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6730 const SCEV *LHS, const SCEV *RHS) {
6731 // Canonicalize the inputs first.
6732 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6734 // If LHS or RHS is an addrec, check to see if the condition is true in
6735 // every iteration of the loop.
6736 // If LHS and RHS are both addrec, both conditions must be true in
6737 // every iteration of the loop.
6738 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6739 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6740 bool LeftGuarded = false;
6741 bool RightGuarded = false;
6743 const Loop *L = LAR->getLoop();
6744 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6745 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6746 if (!RAR) return true;
6751 const Loop *L = RAR->getLoop();
6752 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6753 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6754 if (!LAR) return true;
6755 RightGuarded = true;
6758 if (LeftGuarded && RightGuarded)
6761 // Otherwise see what can be done with known constant ranges.
6762 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6765 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
6766 ICmpInst::Predicate Pred,
6768 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
6771 // Verify an invariant: inverting the predicate should turn a monotonically
6772 // increasing change to a monotonically decreasing one, and vice versa.
6773 bool IncreasingSwapped;
6774 bool ResultSwapped = isMonotonicPredicateImpl(
6775 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
6777 assert(Result == ResultSwapped && "should be able to analyze both!");
6779 assert(Increasing == !IncreasingSwapped &&
6780 "monotonicity should flip as we flip the predicate");
6786 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
6787 ICmpInst::Predicate Pred,
6790 // A zero step value for LHS means the induction variable is essentially a
6791 // loop invariant value. We don't really depend on the predicate actually
6792 // flipping from false to true (for increasing predicates, and the other way
6793 // around for decreasing predicates), all we care about is that *if* the
6794 // predicate changes then it only changes from false to true.
6796 // A zero step value in itself is not very useful, but there may be places
6797 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
6798 // as general as possible.
6802 return false; // Conservative answer
6804 case ICmpInst::ICMP_UGT:
6805 case ICmpInst::ICMP_UGE:
6806 case ICmpInst::ICMP_ULT:
6807 case ICmpInst::ICMP_ULE:
6808 if (!LHS->getNoWrapFlags(SCEV::FlagNUW))
6811 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
6814 case ICmpInst::ICMP_SGT:
6815 case ICmpInst::ICMP_SGE:
6816 case ICmpInst::ICMP_SLT:
6817 case ICmpInst::ICMP_SLE: {
6818 if (!LHS->getNoWrapFlags(SCEV::FlagNSW))
6821 const SCEV *Step = LHS->getStepRecurrence(*this);
6823 if (isKnownNonNegative(Step)) {
6824 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
6828 if (isKnownNonPositive(Step)) {
6829 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
6838 llvm_unreachable("switch has default clause!");
6841 bool ScalarEvolution::isLoopInvariantPredicate(
6842 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
6843 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
6844 const SCEV *&InvariantRHS) {
6846 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
6847 if (!isLoopInvariant(RHS, L)) {
6848 if (!isLoopInvariant(LHS, L))
6851 std::swap(LHS, RHS);
6852 Pred = ICmpInst::getSwappedPredicate(Pred);
6855 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
6856 if (!ArLHS || ArLHS->getLoop() != L)
6860 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
6863 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
6864 // true as the loop iterates, and the backedge is control dependent on
6865 // "ArLHS `Pred` RHS" == true then we can reason as follows:
6867 // * if the predicate was false in the first iteration then the predicate
6868 // is never evaluated again, since the loop exits without taking the
6870 // * if the predicate was true in the first iteration then it will
6871 // continue to be true for all future iterations since it is
6872 // monotonically increasing.
6874 // For both the above possibilities, we can replace the loop varying
6875 // predicate with its value on the first iteration of the loop (which is
6878 // A similar reasoning applies for a monotonically decreasing predicate, by
6879 // replacing true with false and false with true in the above two bullets.
6881 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
6883 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
6886 InvariantPred = Pred;
6887 InvariantLHS = ArLHS->getStart();
6893 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6894 const SCEV *LHS, const SCEV *RHS) {
6895 if (HasSameValue(LHS, RHS))
6896 return ICmpInst::isTrueWhenEqual(Pred);
6898 // This code is split out from isKnownPredicate because it is called from
6899 // within isLoopEntryGuardedByCond.
6902 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6903 case ICmpInst::ICMP_SGT:
6904 std::swap(LHS, RHS);
6905 case ICmpInst::ICMP_SLT: {
6906 ConstantRange LHSRange = getSignedRange(LHS);
6907 ConstantRange RHSRange = getSignedRange(RHS);
6908 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6910 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6914 case ICmpInst::ICMP_SGE:
6915 std::swap(LHS, RHS);
6916 case ICmpInst::ICMP_SLE: {
6917 ConstantRange LHSRange = getSignedRange(LHS);
6918 ConstantRange RHSRange = getSignedRange(RHS);
6919 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6921 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6925 case ICmpInst::ICMP_UGT:
6926 std::swap(LHS, RHS);
6927 case ICmpInst::ICMP_ULT: {
6928 ConstantRange LHSRange = getUnsignedRange(LHS);
6929 ConstantRange RHSRange = getUnsignedRange(RHS);
6930 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6932 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6936 case ICmpInst::ICMP_UGE:
6937 std::swap(LHS, RHS);
6938 case ICmpInst::ICMP_ULE: {
6939 ConstantRange LHSRange = getUnsignedRange(LHS);
6940 ConstantRange RHSRange = getUnsignedRange(RHS);
6941 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6943 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6947 case ICmpInst::ICMP_NE: {
6948 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6950 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6953 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6954 if (isKnownNonZero(Diff))
6958 case ICmpInst::ICMP_EQ:
6959 // The check at the top of the function catches the case where
6960 // the values are known to be equal.
6966 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6967 /// protected by a conditional between LHS and RHS. This is used to
6968 /// to eliminate casts.
6970 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6971 ICmpInst::Predicate Pred,
6972 const SCEV *LHS, const SCEV *RHS) {
6973 // Interpret a null as meaning no loop, where there is obviously no guard
6974 // (interprocedural conditions notwithstanding).
6975 if (!L) return true;
6977 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6979 BasicBlock *Latch = L->getLoopLatch();
6983 BranchInst *LoopContinuePredicate =
6984 dyn_cast<BranchInst>(Latch->getTerminator());
6985 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6986 isImpliedCond(Pred, LHS, RHS,
6987 LoopContinuePredicate->getCondition(),
6988 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6991 struct ClearWalkingBEDominatingCondsOnExit {
6992 ScalarEvolution &SE;
6994 explicit ClearWalkingBEDominatingCondsOnExit(ScalarEvolution &SE)
6997 ~ClearWalkingBEDominatingCondsOnExit() {
6998 SE.WalkingBEDominatingConds = false;
7002 // We don't want more than one activation of the following loops on the stack
7003 // -- that can lead to O(n!) time complexity.
7004 if (WalkingBEDominatingConds)
7007 WalkingBEDominatingConds = true;
7008 ClearWalkingBEDominatingCondsOnExit ClearOnExit(*this);
7010 // Check conditions due to any @llvm.assume intrinsics.
7011 for (auto &AssumeVH : AC.assumptions()) {
7014 auto *CI = cast<CallInst>(AssumeVH);
7015 if (!DT.dominates(CI, Latch->getTerminator()))
7018 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7022 // If the loop is not reachable from the entry block, we risk running into an
7023 // infinite loop as we walk up into the dom tree. These loops do not matter
7024 // anyway, so we just return a conservative answer when we see them.
7025 if (!DT.isReachableFromEntry(L->getHeader()))
7028 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7029 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7031 assert(DTN && "should reach the loop header before reaching the root!");
7033 BasicBlock *BB = DTN->getBlock();
7034 BasicBlock *PBB = BB->getSinglePredecessor();
7038 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7039 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7042 Value *Condition = ContinuePredicate->getCondition();
7044 // If we have an edge `E` within the loop body that dominates the only
7045 // latch, the condition guarding `E` also guards the backedge. This
7046 // reasoning works only for loops with a single latch.
7048 BasicBlockEdge DominatingEdge(PBB, BB);
7049 if (DominatingEdge.isSingleEdge()) {
7050 // We're constructively (and conservatively) enumerating edges within the
7051 // loop body that dominate the latch. The dominator tree better agree
7053 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7055 if (isImpliedCond(Pred, LHS, RHS, Condition,
7056 BB != ContinuePredicate->getSuccessor(0)))
7064 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7065 /// by a conditional between LHS and RHS. This is used to help avoid max
7066 /// expressions in loop trip counts, and to eliminate casts.
7068 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7069 ICmpInst::Predicate Pred,
7070 const SCEV *LHS, const SCEV *RHS) {
7071 // Interpret a null as meaning no loop, where there is obviously no guard
7072 // (interprocedural conditions notwithstanding).
7073 if (!L) return false;
7075 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7077 // Starting at the loop predecessor, climb up the predecessor chain, as long
7078 // as there are predecessors that can be found that have unique successors
7079 // leading to the original header.
7080 for (std::pair<BasicBlock *, BasicBlock *>
7081 Pair(L->getLoopPredecessor(), L->getHeader());
7083 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7085 BranchInst *LoopEntryPredicate =
7086 dyn_cast<BranchInst>(Pair.first->getTerminator());
7087 if (!LoopEntryPredicate ||
7088 LoopEntryPredicate->isUnconditional())
7091 if (isImpliedCond(Pred, LHS, RHS,
7092 LoopEntryPredicate->getCondition(),
7093 LoopEntryPredicate->getSuccessor(0) != Pair.second))
7097 // Check conditions due to any @llvm.assume intrinsics.
7098 for (auto &AssumeVH : AC.assumptions()) {
7101 auto *CI = cast<CallInst>(AssumeVH);
7102 if (!DT.dominates(CI, L->getHeader()))
7105 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7112 /// RAII wrapper to prevent recursive application of isImpliedCond.
7113 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7114 /// currently evaluating isImpliedCond.
7115 struct MarkPendingLoopPredicate {
7117 DenseSet<Value*> &LoopPreds;
7120 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7121 : Cond(C), LoopPreds(LP) {
7122 Pending = !LoopPreds.insert(Cond).second;
7124 ~MarkPendingLoopPredicate() {
7126 LoopPreds.erase(Cond);
7130 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7131 /// and RHS is true whenever the given Cond value evaluates to true.
7132 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7133 const SCEV *LHS, const SCEV *RHS,
7134 Value *FoundCondValue,
7136 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7140 // Recursively handle And and Or conditions.
7141 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7142 if (BO->getOpcode() == Instruction::And) {
7144 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7145 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7146 } else if (BO->getOpcode() == Instruction::Or) {
7148 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7149 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7153 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
7154 if (!ICI) return false;
7156 // Now that we found a conditional branch that dominates the loop or controls
7157 // the loop latch. Check to see if it is the comparison we are looking for.
7158 ICmpInst::Predicate FoundPred;
7160 FoundPred = ICI->getInversePredicate();
7162 FoundPred = ICI->getPredicate();
7164 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
7165 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
7167 // Balance the types.
7168 if (getTypeSizeInBits(LHS->getType()) <
7169 getTypeSizeInBits(FoundLHS->getType())) {
7170 if (CmpInst::isSigned(Pred)) {
7171 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
7172 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
7174 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
7175 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
7177 } else if (getTypeSizeInBits(LHS->getType()) >
7178 getTypeSizeInBits(FoundLHS->getType())) {
7179 if (CmpInst::isSigned(FoundPred)) {
7180 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
7181 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
7183 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
7184 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
7188 // Canonicalize the query to match the way instcombine will have
7189 // canonicalized the comparison.
7190 if (SimplifyICmpOperands(Pred, LHS, RHS))
7192 return CmpInst::isTrueWhenEqual(Pred);
7193 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
7194 if (FoundLHS == FoundRHS)
7195 return CmpInst::isFalseWhenEqual(FoundPred);
7197 // Check to see if we can make the LHS or RHS match.
7198 if (LHS == FoundRHS || RHS == FoundLHS) {
7199 if (isa<SCEVConstant>(RHS)) {
7200 std::swap(FoundLHS, FoundRHS);
7201 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
7203 std::swap(LHS, RHS);
7204 Pred = ICmpInst::getSwappedPredicate(Pred);
7208 // Check whether the found predicate is the same as the desired predicate.
7209 if (FoundPred == Pred)
7210 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7212 // Check whether swapping the found predicate makes it the same as the
7213 // desired predicate.
7214 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
7215 if (isa<SCEVConstant>(RHS))
7216 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
7218 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
7219 RHS, LHS, FoundLHS, FoundRHS);
7222 // Check if we can make progress by sharpening ranges.
7223 if (FoundPred == ICmpInst::ICMP_NE &&
7224 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
7226 const SCEVConstant *C = nullptr;
7227 const SCEV *V = nullptr;
7229 if (isa<SCEVConstant>(FoundLHS)) {
7230 C = cast<SCEVConstant>(FoundLHS);
7233 C = cast<SCEVConstant>(FoundRHS);
7237 // The guarding predicate tells us that C != V. If the known range
7238 // of V is [C, t), we can sharpen the range to [C + 1, t). The
7239 // range we consider has to correspond to same signedness as the
7240 // predicate we're interested in folding.
7242 APInt Min = ICmpInst::isSigned(Pred) ?
7243 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7245 if (Min == C->getValue()->getValue()) {
7246 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7247 // This is true even if (Min + 1) wraps around -- in case of
7248 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7250 APInt SharperMin = Min + 1;
7253 case ICmpInst::ICMP_SGE:
7254 case ICmpInst::ICMP_UGE:
7255 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7257 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7258 getConstant(SharperMin)))
7261 case ICmpInst::ICMP_SGT:
7262 case ICmpInst::ICMP_UGT:
7263 // We know from the range information that (V `Pred` Min ||
7264 // V == Min). We know from the guarding condition that !(V
7265 // == Min). This gives us
7267 // V `Pred` Min || V == Min && !(V == Min)
7270 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7272 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7282 // Check whether the actual condition is beyond sufficient.
7283 if (FoundPred == ICmpInst::ICMP_EQ)
7284 if (ICmpInst::isTrueWhenEqual(Pred))
7285 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7287 if (Pred == ICmpInst::ICMP_NE)
7288 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7289 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7292 // Otherwise assume the worst.
7296 /// isImpliedCondOperands - Test whether the condition described by Pred,
7297 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7298 /// and FoundRHS is true.
7299 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7300 const SCEV *LHS, const SCEV *RHS,
7301 const SCEV *FoundLHS,
7302 const SCEV *FoundRHS) {
7303 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7306 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7307 FoundLHS, FoundRHS) ||
7308 // ~x < ~y --> x > y
7309 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7310 getNotSCEV(FoundRHS),
7311 getNotSCEV(FoundLHS));
7315 /// If Expr computes ~A, return A else return nullptr
7316 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7317 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7318 if (!Add || Add->getNumOperands() != 2) return nullptr;
7320 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
7321 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
7324 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7325 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
7327 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
7328 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
7331 return AddRHS->getOperand(1);
7335 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7336 template<typename MaxExprType>
7337 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7338 const SCEV *Candidate) {
7339 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7340 if (!MaxExpr) return false;
7342 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7343 return It != MaxExpr->op_end();
7347 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7348 template<typename MaxExprType>
7349 static bool IsMinConsistingOf(ScalarEvolution &SE,
7350 const SCEV *MaybeMinExpr,
7351 const SCEV *Candidate) {
7352 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7356 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7359 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
7360 ICmpInst::Predicate Pred,
7361 const SCEV *LHS, const SCEV *RHS) {
7363 // If both sides are affine addrecs for the same loop, with equal
7364 // steps, and we know the recurrences don't wrap, then we only
7365 // need to check the predicate on the starting values.
7367 if (!ICmpInst::isRelational(Pred))
7370 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7373 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7376 if (LAR->getLoop() != RAR->getLoop())
7378 if (!LAR->isAffine() || !RAR->isAffine())
7381 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
7384 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
7385 SCEV::FlagNSW : SCEV::FlagNUW;
7386 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
7389 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
7392 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7394 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7395 ICmpInst::Predicate Pred,
7396 const SCEV *LHS, const SCEV *RHS) {
7401 case ICmpInst::ICMP_SGE:
7402 std::swap(LHS, RHS);
7404 case ICmpInst::ICMP_SLE:
7407 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7409 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7411 case ICmpInst::ICMP_UGE:
7412 std::swap(LHS, RHS);
7414 case ICmpInst::ICMP_ULE:
7417 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7419 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7422 llvm_unreachable("covered switch fell through?!");
7425 /// isImpliedCondOperandsHelper - Test whether the condition described by
7426 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7427 /// FoundLHS, and FoundRHS is true.
7429 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7430 const SCEV *LHS, const SCEV *RHS,
7431 const SCEV *FoundLHS,
7432 const SCEV *FoundRHS) {
7433 auto IsKnownPredicateFull =
7434 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7435 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7436 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
7437 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS);
7441 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7442 case ICmpInst::ICMP_EQ:
7443 case ICmpInst::ICMP_NE:
7444 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7447 case ICmpInst::ICMP_SLT:
7448 case ICmpInst::ICMP_SLE:
7449 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7450 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7453 case ICmpInst::ICMP_SGT:
7454 case ICmpInst::ICMP_SGE:
7455 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7456 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7459 case ICmpInst::ICMP_ULT:
7460 case ICmpInst::ICMP_ULE:
7461 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7462 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7465 case ICmpInst::ICMP_UGT:
7466 case ICmpInst::ICMP_UGE:
7467 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7468 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7476 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
7477 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
7478 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
7481 const SCEV *FoundLHS,
7482 const SCEV *FoundRHS) {
7483 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
7484 // The restriction on `FoundRHS` be lifted easily -- it exists only to
7485 // reduce the compile time impact of this optimization.
7488 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
7489 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
7490 !isa<SCEVConstant>(AddLHS->getOperand(0)))
7493 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
7495 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
7496 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
7497 ConstantRange FoundLHSRange =
7498 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
7500 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
7503 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
7504 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
7506 // We can also compute the range of values for `LHS` that satisfy the
7507 // consequent, "`LHS` `Pred` `RHS`":
7508 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
7509 ConstantRange SatisfyingLHSRange =
7510 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
7512 // The antecedent implies the consequent if every value of `LHS` that
7513 // satisfies the antecedent also satisfies the consequent.
7514 return SatisfyingLHSRange.contains(LHSRange);
7517 // Verify if an linear IV with positive stride can overflow when in a
7518 // less-than comparison, knowing the invariant term of the comparison, the
7519 // stride and the knowledge of NSW/NUW flags on the recurrence.
7520 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7521 bool IsSigned, bool NoWrap) {
7522 if (NoWrap) return false;
7524 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7525 const SCEV *One = getConstant(Stride->getType(), 1);
7528 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7529 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7530 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7533 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7534 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7537 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7538 APInt MaxValue = APInt::getMaxValue(BitWidth);
7539 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7542 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7543 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7546 // Verify if an linear IV with negative stride can overflow when in a
7547 // greater-than comparison, knowing the invariant term of the comparison,
7548 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7549 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7550 bool IsSigned, bool NoWrap) {
7551 if (NoWrap) return false;
7553 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7554 const SCEV *One = getConstant(Stride->getType(), 1);
7557 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7558 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7559 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7562 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7563 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7566 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7567 APInt MinValue = APInt::getMinValue(BitWidth);
7568 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7571 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7572 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7575 // Compute the backedge taken count knowing the interval difference, the
7576 // stride and presence of the equality in the comparison.
7577 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7579 const SCEV *One = getConstant(Step->getType(), 1);
7580 Delta = Equality ? getAddExpr(Delta, Step)
7581 : getAddExpr(Delta, getMinusSCEV(Step, One));
7582 return getUDivExpr(Delta, Step);
7585 /// HowManyLessThans - Return the number of times a backedge containing the
7586 /// specified less-than comparison will execute. If not computable, return
7587 /// CouldNotCompute.
7589 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7590 /// the branch (loops exits only if condition is true). In this case, we can use
7591 /// NoWrapFlags to skip overflow checks.
7592 ScalarEvolution::ExitLimit
7593 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7594 const Loop *L, bool IsSigned,
7595 bool ControlsExit) {
7596 // We handle only IV < Invariant
7597 if (!isLoopInvariant(RHS, L))
7598 return getCouldNotCompute();
7600 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7602 // Avoid weird loops
7603 if (!IV || IV->getLoop() != L || !IV->isAffine())
7604 return getCouldNotCompute();
7606 bool NoWrap = ControlsExit &&
7607 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7609 const SCEV *Stride = IV->getStepRecurrence(*this);
7611 // Avoid negative or zero stride values
7612 if (!isKnownPositive(Stride))
7613 return getCouldNotCompute();
7615 // Avoid proven overflow cases: this will ensure that the backedge taken count
7616 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7617 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7618 // behaviors like the case of C language.
7619 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7620 return getCouldNotCompute();
7622 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7623 : ICmpInst::ICMP_ULT;
7624 const SCEV *Start = IV->getStart();
7625 const SCEV *End = RHS;
7626 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7627 const SCEV *Diff = getMinusSCEV(RHS, Start);
7628 // If we have NoWrap set, then we can assume that the increment won't
7629 // overflow, in which case if RHS - Start is a constant, we don't need to
7630 // do a max operation since we can just figure it out statically
7631 if (NoWrap && isa<SCEVConstant>(Diff)) {
7632 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7636 End = IsSigned ? getSMaxExpr(RHS, Start)
7637 : getUMaxExpr(RHS, Start);
7640 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7642 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7643 : getUnsignedRange(Start).getUnsignedMin();
7645 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7646 : getUnsignedRange(Stride).getUnsignedMin();
7648 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7649 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7650 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7652 // Although End can be a MAX expression we estimate MaxEnd considering only
7653 // the case End = RHS. This is safe because in the other case (End - Start)
7654 // is zero, leading to a zero maximum backedge taken count.
7656 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7657 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7659 const SCEV *MaxBECount;
7660 if (isa<SCEVConstant>(BECount))
7661 MaxBECount = BECount;
7663 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7664 getConstant(MinStride), false);
7666 if (isa<SCEVCouldNotCompute>(MaxBECount))
7667 MaxBECount = BECount;
7669 return ExitLimit(BECount, MaxBECount);
7672 ScalarEvolution::ExitLimit
7673 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7674 const Loop *L, bool IsSigned,
7675 bool ControlsExit) {
7676 // We handle only IV > Invariant
7677 if (!isLoopInvariant(RHS, L))
7678 return getCouldNotCompute();
7680 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7682 // Avoid weird loops
7683 if (!IV || IV->getLoop() != L || !IV->isAffine())
7684 return getCouldNotCompute();
7686 bool NoWrap = ControlsExit &&
7687 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7689 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7691 // Avoid negative or zero stride values
7692 if (!isKnownPositive(Stride))
7693 return getCouldNotCompute();
7695 // Avoid proven overflow cases: this will ensure that the backedge taken count
7696 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7697 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7698 // behaviors like the case of C language.
7699 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7700 return getCouldNotCompute();
7702 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7703 : ICmpInst::ICMP_UGT;
7705 const SCEV *Start = IV->getStart();
7706 const SCEV *End = RHS;
7707 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7708 const SCEV *Diff = getMinusSCEV(RHS, Start);
7709 // If we have NoWrap set, then we can assume that the increment won't
7710 // overflow, in which case if RHS - Start is a constant, we don't need to
7711 // do a max operation since we can just figure it out statically
7712 if (NoWrap && isa<SCEVConstant>(Diff)) {
7713 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7714 if (!D.isNegative())
7717 End = IsSigned ? getSMinExpr(RHS, Start)
7718 : getUMinExpr(RHS, Start);
7721 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7723 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7724 : getUnsignedRange(Start).getUnsignedMax();
7726 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7727 : getUnsignedRange(Stride).getUnsignedMin();
7729 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7730 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7731 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7733 // Although End can be a MIN expression we estimate MinEnd considering only
7734 // the case End = RHS. This is safe because in the other case (Start - End)
7735 // is zero, leading to a zero maximum backedge taken count.
7737 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7738 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7741 const SCEV *MaxBECount = getCouldNotCompute();
7742 if (isa<SCEVConstant>(BECount))
7743 MaxBECount = BECount;
7745 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7746 getConstant(MinStride), false);
7748 if (isa<SCEVCouldNotCompute>(MaxBECount))
7749 MaxBECount = BECount;
7751 return ExitLimit(BECount, MaxBECount);
7754 /// getNumIterationsInRange - Return the number of iterations of this loop that
7755 /// produce values in the specified constant range. Another way of looking at
7756 /// this is that it returns the first iteration number where the value is not in
7757 /// the condition, thus computing the exit count. If the iteration count can't
7758 /// be computed, an instance of SCEVCouldNotCompute is returned.
7759 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7760 ScalarEvolution &SE) const {
7761 if (Range.isFullSet()) // Infinite loop.
7762 return SE.getCouldNotCompute();
7764 // If the start is a non-zero constant, shift the range to simplify things.
7765 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7766 if (!SC->getValue()->isZero()) {
7767 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7768 Operands[0] = SE.getConstant(SC->getType(), 0);
7769 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7770 getNoWrapFlags(FlagNW));
7771 if (const SCEVAddRecExpr *ShiftedAddRec =
7772 dyn_cast<SCEVAddRecExpr>(Shifted))
7773 return ShiftedAddRec->getNumIterationsInRange(
7774 Range.subtract(SC->getValue()->getValue()), SE);
7775 // This is strange and shouldn't happen.
7776 return SE.getCouldNotCompute();
7779 // The only time we can solve this is when we have all constant indices.
7780 // Otherwise, we cannot determine the overflow conditions.
7781 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7782 if (!isa<SCEVConstant>(getOperand(i)))
7783 return SE.getCouldNotCompute();
7786 // Okay at this point we know that all elements of the chrec are constants and
7787 // that the start element is zero.
7789 // First check to see if the range contains zero. If not, the first
7791 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7792 if (!Range.contains(APInt(BitWidth, 0)))
7793 return SE.getConstant(getType(), 0);
7796 // If this is an affine expression then we have this situation:
7797 // Solve {0,+,A} in Range === Ax in Range
7799 // We know that zero is in the range. If A is positive then we know that
7800 // the upper value of the range must be the first possible exit value.
7801 // If A is negative then the lower of the range is the last possible loop
7802 // value. Also note that we already checked for a full range.
7803 APInt One(BitWidth,1);
7804 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7805 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7807 // The exit value should be (End+A)/A.
7808 APInt ExitVal = (End + A).udiv(A);
7809 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7811 // Evaluate at the exit value. If we really did fall out of the valid
7812 // range, then we computed our trip count, otherwise wrap around or other
7813 // things must have happened.
7814 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7815 if (Range.contains(Val->getValue()))
7816 return SE.getCouldNotCompute(); // Something strange happened
7818 // Ensure that the previous value is in the range. This is a sanity check.
7819 assert(Range.contains(
7820 EvaluateConstantChrecAtConstant(this,
7821 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7822 "Linear scev computation is off in a bad way!");
7823 return SE.getConstant(ExitValue);
7824 } else if (isQuadratic()) {
7825 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7826 // quadratic equation to solve it. To do this, we must frame our problem in
7827 // terms of figuring out when zero is crossed, instead of when
7828 // Range.getUpper() is crossed.
7829 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7830 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7831 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7832 // getNoWrapFlags(FlagNW)
7835 // Next, solve the constructed addrec
7836 std::pair<const SCEV *,const SCEV *> Roots =
7837 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7838 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7839 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7841 // Pick the smallest positive root value.
7842 if (ConstantInt *CB =
7843 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7844 R1->getValue(), R2->getValue()))) {
7845 if (!CB->getZExtValue())
7846 std::swap(R1, R2); // R1 is the minimum root now.
7848 // Make sure the root is not off by one. The returned iteration should
7849 // not be in the range, but the previous one should be. When solving
7850 // for "X*X < 5", for example, we should not return a root of 2.
7851 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7854 if (Range.contains(R1Val->getValue())) {
7855 // The next iteration must be out of the range...
7856 ConstantInt *NextVal =
7857 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7859 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7860 if (!Range.contains(R1Val->getValue()))
7861 return SE.getConstant(NextVal);
7862 return SE.getCouldNotCompute(); // Something strange happened
7865 // If R1 was not in the range, then it is a good return value. Make
7866 // sure that R1-1 WAS in the range though, just in case.
7867 ConstantInt *NextVal =
7868 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7869 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7870 if (Range.contains(R1Val->getValue()))
7872 return SE.getCouldNotCompute(); // Something strange happened
7877 return SE.getCouldNotCompute();
7883 FindUndefs() : Found(false) {}
7885 bool follow(const SCEV *S) {
7886 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7887 if (isa<UndefValue>(C->getValue()))
7889 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7890 if (isa<UndefValue>(C->getValue()))
7894 // Keep looking if we haven't found it yet.
7897 bool isDone() const {
7898 // Stop recursion if we have found an undef.
7904 // Return true when S contains at least an undef value.
7906 containsUndefs(const SCEV *S) {
7908 SCEVTraversal<FindUndefs> ST(F);
7915 // Collect all steps of SCEV expressions.
7916 struct SCEVCollectStrides {
7917 ScalarEvolution &SE;
7918 SmallVectorImpl<const SCEV *> &Strides;
7920 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7921 : SE(SE), Strides(S) {}
7923 bool follow(const SCEV *S) {
7924 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7925 Strides.push_back(AR->getStepRecurrence(SE));
7928 bool isDone() const { return false; }
7931 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7932 struct SCEVCollectTerms {
7933 SmallVectorImpl<const SCEV *> &Terms;
7935 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7938 bool follow(const SCEV *S) {
7939 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7940 if (!containsUndefs(S))
7943 // Stop recursion: once we collected a term, do not walk its operands.
7950 bool isDone() const { return false; }
7954 /// Find parametric terms in this SCEVAddRecExpr.
7955 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
7956 SmallVectorImpl<const SCEV *> &Terms) {
7957 SmallVector<const SCEV *, 4> Strides;
7958 SCEVCollectStrides StrideCollector(*this, Strides);
7959 visitAll(Expr, StrideCollector);
7962 dbgs() << "Strides:\n";
7963 for (const SCEV *S : Strides)
7964 dbgs() << *S << "\n";
7967 for (const SCEV *S : Strides) {
7968 SCEVCollectTerms TermCollector(Terms);
7969 visitAll(S, TermCollector);
7973 dbgs() << "Terms:\n";
7974 for (const SCEV *T : Terms)
7975 dbgs() << *T << "\n";
7979 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7980 SmallVectorImpl<const SCEV *> &Terms,
7981 SmallVectorImpl<const SCEV *> &Sizes) {
7982 int Last = Terms.size() - 1;
7983 const SCEV *Step = Terms[Last];
7985 // End of recursion.
7987 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7988 SmallVector<const SCEV *, 2> Qs;
7989 for (const SCEV *Op : M->operands())
7990 if (!isa<SCEVConstant>(Op))
7993 Step = SE.getMulExpr(Qs);
7996 Sizes.push_back(Step);
8000 for (const SCEV *&Term : Terms) {
8001 // Normalize the terms before the next call to findArrayDimensionsRec.
8003 SCEVDivision::divide(SE, Term, Step, &Q, &R);
8005 // Bail out when GCD does not evenly divide one of the terms.
8012 // Remove all SCEVConstants.
8013 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
8014 return isa<SCEVConstant>(E);
8018 if (Terms.size() > 0)
8019 if (!findArrayDimensionsRec(SE, Terms, Sizes))
8022 Sizes.push_back(Step);
8027 struct FindParameter {
8028 bool FoundParameter;
8029 FindParameter() : FoundParameter(false) {}
8031 bool follow(const SCEV *S) {
8032 if (isa<SCEVUnknown>(S)) {
8033 FoundParameter = true;
8034 // Stop recursion: we found a parameter.
8040 bool isDone() const {
8041 // Stop recursion if we have found a parameter.
8042 return FoundParameter;
8047 // Returns true when S contains at least a SCEVUnknown parameter.
8049 containsParameters(const SCEV *S) {
8051 SCEVTraversal<FindParameter> ST(F);
8054 return F.FoundParameter;
8057 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
8059 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
8060 for (const SCEV *T : Terms)
8061 if (containsParameters(T))
8066 // Return the number of product terms in S.
8067 static inline int numberOfTerms(const SCEV *S) {
8068 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
8069 return Expr->getNumOperands();
8073 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
8074 if (isa<SCEVConstant>(T))
8077 if (isa<SCEVUnknown>(T))
8080 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
8081 SmallVector<const SCEV *, 2> Factors;
8082 for (const SCEV *Op : M->operands())
8083 if (!isa<SCEVConstant>(Op))
8084 Factors.push_back(Op);
8086 return SE.getMulExpr(Factors);
8092 /// Return the size of an element read or written by Inst.
8093 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
8095 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
8096 Ty = Store->getValueOperand()->getType();
8097 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
8098 Ty = Load->getType();
8102 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
8103 return getSizeOfExpr(ETy, Ty);
8106 /// Second step of delinearization: compute the array dimensions Sizes from the
8107 /// set of Terms extracted from the memory access function of this SCEVAddRec.
8108 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
8109 SmallVectorImpl<const SCEV *> &Sizes,
8110 const SCEV *ElementSize) const {
8112 if (Terms.size() < 1 || !ElementSize)
8115 // Early return when Terms do not contain parameters: we do not delinearize
8116 // non parametric SCEVs.
8117 if (!containsParameters(Terms))
8121 dbgs() << "Terms:\n";
8122 for (const SCEV *T : Terms)
8123 dbgs() << *T << "\n";
8126 // Remove duplicates.
8127 std::sort(Terms.begin(), Terms.end());
8128 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
8130 // Put larger terms first.
8131 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
8132 return numberOfTerms(LHS) > numberOfTerms(RHS);
8135 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8137 // Divide all terms by the element size.
8138 for (const SCEV *&Term : Terms) {
8140 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
8144 SmallVector<const SCEV *, 4> NewTerms;
8146 // Remove constant factors.
8147 for (const SCEV *T : Terms)
8148 if (const SCEV *NewT = removeConstantFactors(SE, T))
8149 NewTerms.push_back(NewT);
8152 dbgs() << "Terms after sorting:\n";
8153 for (const SCEV *T : NewTerms)
8154 dbgs() << *T << "\n";
8157 if (NewTerms.empty() ||
8158 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
8163 // The last element to be pushed into Sizes is the size of an element.
8164 Sizes.push_back(ElementSize);
8167 dbgs() << "Sizes:\n";
8168 for (const SCEV *S : Sizes)
8169 dbgs() << *S << "\n";
8173 /// Third step of delinearization: compute the access functions for the
8174 /// Subscripts based on the dimensions in Sizes.
8175 void ScalarEvolution::computeAccessFunctions(
8176 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
8177 SmallVectorImpl<const SCEV *> &Sizes) {
8179 // Early exit in case this SCEV is not an affine multivariate function.
8183 if (auto AR = dyn_cast<SCEVAddRecExpr>(Expr))
8184 if (!AR->isAffine())
8187 const SCEV *Res = Expr;
8188 int Last = Sizes.size() - 1;
8189 for (int i = Last; i >= 0; i--) {
8191 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
8194 dbgs() << "Res: " << *Res << "\n";
8195 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
8196 dbgs() << "Res divided by Sizes[i]:\n";
8197 dbgs() << "Quotient: " << *Q << "\n";
8198 dbgs() << "Remainder: " << *R << "\n";
8203 // Do not record the last subscript corresponding to the size of elements in
8207 // Bail out if the remainder is too complex.
8208 if (isa<SCEVAddRecExpr>(R)) {
8217 // Record the access function for the current subscript.
8218 Subscripts.push_back(R);
8221 // Also push in last position the remainder of the last division: it will be
8222 // the access function of the innermost dimension.
8223 Subscripts.push_back(Res);
8225 std::reverse(Subscripts.begin(), Subscripts.end());
8228 dbgs() << "Subscripts:\n";
8229 for (const SCEV *S : Subscripts)
8230 dbgs() << *S << "\n";
8234 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
8235 /// sizes of an array access. Returns the remainder of the delinearization that
8236 /// is the offset start of the array. The SCEV->delinearize algorithm computes
8237 /// the multiples of SCEV coefficients: that is a pattern matching of sub
8238 /// expressions in the stride and base of a SCEV corresponding to the
8239 /// computation of a GCD (greatest common divisor) of base and stride. When
8240 /// SCEV->delinearize fails, it returns the SCEV unchanged.
8242 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
8244 /// void foo(long n, long m, long o, double A[n][m][o]) {
8246 /// for (long i = 0; i < n; i++)
8247 /// for (long j = 0; j < m; j++)
8248 /// for (long k = 0; k < o; k++)
8249 /// A[i][j][k] = 1.0;
8252 /// the delinearization input is the following AddRec SCEV:
8254 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
8256 /// From this SCEV, we are able to say that the base offset of the access is %A
8257 /// because it appears as an offset that does not divide any of the strides in
8260 /// CHECK: Base offset: %A
8262 /// and then SCEV->delinearize determines the size of some of the dimensions of
8263 /// the array as these are the multiples by which the strides are happening:
8265 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
8267 /// Note that the outermost dimension remains of UnknownSize because there are
8268 /// no strides that would help identifying the size of the last dimension: when
8269 /// the array has been statically allocated, one could compute the size of that
8270 /// dimension by dividing the overall size of the array by the size of the known
8271 /// dimensions: %m * %o * 8.
8273 /// Finally delinearize provides the access functions for the array reference
8274 /// that does correspond to A[i][j][k] of the above C testcase:
8276 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
8278 /// The testcases are checking the output of a function pass:
8279 /// DelinearizationPass that walks through all loads and stores of a function
8280 /// asking for the SCEV of the memory access with respect to all enclosing
8281 /// loops, calling SCEV->delinearize on that and printing the results.
8283 void ScalarEvolution::delinearize(const SCEV *Expr,
8284 SmallVectorImpl<const SCEV *> &Subscripts,
8285 SmallVectorImpl<const SCEV *> &Sizes,
8286 const SCEV *ElementSize) {
8287 // First step: collect parametric terms.
8288 SmallVector<const SCEV *, 4> Terms;
8289 collectParametricTerms(Expr, Terms);
8294 // Second step: find subscript sizes.
8295 findArrayDimensions(Terms, Sizes, ElementSize);
8300 // Third step: compute the access functions for each subscript.
8301 computeAccessFunctions(Expr, Subscripts, Sizes);
8303 if (Subscripts.empty())
8307 dbgs() << "succeeded to delinearize " << *Expr << "\n";
8308 dbgs() << "ArrayDecl[UnknownSize]";
8309 for (const SCEV *S : Sizes)
8310 dbgs() << "[" << *S << "]";
8312 dbgs() << "\nArrayRef";
8313 for (const SCEV *S : Subscripts)
8314 dbgs() << "[" << *S << "]";
8319 //===----------------------------------------------------------------------===//
8320 // SCEVCallbackVH Class Implementation
8321 //===----------------------------------------------------------------------===//
8323 void ScalarEvolution::SCEVCallbackVH::deleted() {
8324 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8325 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
8326 SE->ConstantEvolutionLoopExitValue.erase(PN);
8327 SE->ValueExprMap.erase(getValPtr());
8328 // this now dangles!
8331 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
8332 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8334 // Forget all the expressions associated with users of the old value,
8335 // so that future queries will recompute the expressions using the new
8337 Value *Old = getValPtr();
8338 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
8339 SmallPtrSet<User *, 8> Visited;
8340 while (!Worklist.empty()) {
8341 User *U = Worklist.pop_back_val();
8342 // Deleting the Old value will cause this to dangle. Postpone
8343 // that until everything else is done.
8346 if (!Visited.insert(U).second)
8348 if (PHINode *PN = dyn_cast<PHINode>(U))
8349 SE->ConstantEvolutionLoopExitValue.erase(PN);
8350 SE->ValueExprMap.erase(U);
8351 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
8353 // Delete the Old value.
8354 if (PHINode *PN = dyn_cast<PHINode>(Old))
8355 SE->ConstantEvolutionLoopExitValue.erase(PN);
8356 SE->ValueExprMap.erase(Old);
8357 // this now dangles!
8360 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
8361 : CallbackVH(V), SE(se) {}
8363 //===----------------------------------------------------------------------===//
8364 // ScalarEvolution Class Implementation
8365 //===----------------------------------------------------------------------===//
8367 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
8368 AssumptionCache &AC, DominatorTree &DT,
8370 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
8371 CouldNotCompute(new SCEVCouldNotCompute()),
8372 WalkingBEDominatingConds(false), ValuesAtScopes(64), LoopDispositions(64),
8373 BlockDispositions(64), FirstUnknown(nullptr) {}
8375 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
8376 : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
8377 CouldNotCompute(std::move(Arg.CouldNotCompute)),
8378 ValueExprMap(std::move(Arg.ValueExprMap)),
8379 WalkingBEDominatingConds(false),
8380 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
8381 ConstantEvolutionLoopExitValue(
8382 std::move(Arg.ConstantEvolutionLoopExitValue)),
8383 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
8384 LoopDispositions(std::move(Arg.LoopDispositions)),
8385 BlockDispositions(std::move(Arg.BlockDispositions)),
8386 UnsignedRanges(std::move(Arg.UnsignedRanges)),
8387 SignedRanges(std::move(Arg.SignedRanges)),
8388 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
8389 SCEVAllocator(std::move(Arg.SCEVAllocator)),
8390 FirstUnknown(Arg.FirstUnknown) {
8391 Arg.FirstUnknown = nullptr;
8394 ScalarEvolution::~ScalarEvolution() {
8395 // Iterate through all the SCEVUnknown instances and call their
8396 // destructors, so that they release their references to their values.
8397 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
8399 FirstUnknown = nullptr;
8401 ValueExprMap.clear();
8403 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
8404 // that a loop had multiple computable exits.
8405 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8406 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
8411 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
8412 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
8415 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8416 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8419 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8421 // Print all inner loops first
8422 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8423 PrintLoopInfo(OS, SE, *I);
8426 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8429 SmallVector<BasicBlock *, 8> ExitBlocks;
8430 L->getExitBlocks(ExitBlocks);
8431 if (ExitBlocks.size() != 1)
8432 OS << "<multiple exits> ";
8434 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8435 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8437 OS << "Unpredictable backedge-taken count. ";
8442 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8445 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8446 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8448 OS << "Unpredictable max backedge-taken count. ";
8454 void ScalarEvolution::print(raw_ostream &OS) const {
8455 // ScalarEvolution's implementation of the print method is to print
8456 // out SCEV values of all instructions that are interesting. Doing
8457 // this potentially causes it to create new SCEV objects though,
8458 // which technically conflicts with the const qualifier. This isn't
8459 // observable from outside the class though, so casting away the
8460 // const isn't dangerous.
8461 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8463 OS << "Classifying expressions for: ";
8464 F.printAsOperand(OS, /*PrintType=*/false);
8466 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
8467 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
8470 const SCEV *SV = SE.getSCEV(&*I);
8472 if (!isa<SCEVCouldNotCompute>(SV)) {
8474 SE.getUnsignedRange(SV).print(OS);
8476 SE.getSignedRange(SV).print(OS);
8479 const Loop *L = LI.getLoopFor((*I).getParent());
8481 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8485 if (!isa<SCEVCouldNotCompute>(AtUse)) {
8487 SE.getUnsignedRange(AtUse).print(OS);
8489 SE.getSignedRange(AtUse).print(OS);
8494 OS << "\t\t" "Exits: ";
8495 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8496 if (!SE.isLoopInvariant(ExitValue, L)) {
8497 OS << "<<Unknown>>";
8506 OS << "Determining loop execution counts for: ";
8507 F.printAsOperand(OS, /*PrintType=*/false);
8509 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
8510 PrintLoopInfo(OS, &SE, *I);
8513 ScalarEvolution::LoopDisposition
8514 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8515 auto &Values = LoopDispositions[S];
8516 for (auto &V : Values) {
8517 if (V.getPointer() == L)
8520 Values.emplace_back(L, LoopVariant);
8521 LoopDisposition D = computeLoopDisposition(S, L);
8522 auto &Values2 = LoopDispositions[S];
8523 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8524 if (V.getPointer() == L) {
8532 ScalarEvolution::LoopDisposition
8533 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8534 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8536 return LoopInvariant;
8540 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8541 case scAddRecExpr: {
8542 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8544 // If L is the addrec's loop, it's computable.
8545 if (AR->getLoop() == L)
8546 return LoopComputable;
8548 // Add recurrences are never invariant in the function-body (null loop).
8552 // This recurrence is variant w.r.t. L if L contains AR's loop.
8553 if (L->contains(AR->getLoop()))
8556 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8557 if (AR->getLoop()->contains(L))
8558 return LoopInvariant;
8560 // This recurrence is variant w.r.t. L if any of its operands
8562 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8564 if (!isLoopInvariant(*I, L))
8567 // Otherwise it's loop-invariant.
8568 return LoopInvariant;
8574 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8575 bool HasVarying = false;
8576 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8578 LoopDisposition D = getLoopDisposition(*I, L);
8579 if (D == LoopVariant)
8581 if (D == LoopComputable)
8584 return HasVarying ? LoopComputable : LoopInvariant;
8587 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8588 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8589 if (LD == LoopVariant)
8591 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8592 if (RD == LoopVariant)
8594 return (LD == LoopInvariant && RD == LoopInvariant) ?
8595 LoopInvariant : LoopComputable;
8598 // All non-instruction values are loop invariant. All instructions are loop
8599 // invariant if they are not contained in the specified loop.
8600 // Instructions are never considered invariant in the function body
8601 // (null loop) because they are defined within the "loop".
8602 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8603 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8604 return LoopInvariant;
8605 case scCouldNotCompute:
8606 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8608 llvm_unreachable("Unknown SCEV kind!");
8611 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8612 return getLoopDisposition(S, L) == LoopInvariant;
8615 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8616 return getLoopDisposition(S, L) == LoopComputable;
8619 ScalarEvolution::BlockDisposition
8620 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8621 auto &Values = BlockDispositions[S];
8622 for (auto &V : Values) {
8623 if (V.getPointer() == BB)
8626 Values.emplace_back(BB, DoesNotDominateBlock);
8627 BlockDisposition D = computeBlockDisposition(S, BB);
8628 auto &Values2 = BlockDispositions[S];
8629 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8630 if (V.getPointer() == BB) {
8638 ScalarEvolution::BlockDisposition
8639 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8640 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8642 return ProperlyDominatesBlock;
8646 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8647 case scAddRecExpr: {
8648 // This uses a "dominates" query instead of "properly dominates" query
8649 // to test for proper dominance too, because the instruction which
8650 // produces the addrec's value is a PHI, and a PHI effectively properly
8651 // dominates its entire containing block.
8652 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8653 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
8654 return DoesNotDominateBlock;
8656 // FALL THROUGH into SCEVNAryExpr handling.
8661 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8663 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8665 BlockDisposition D = getBlockDisposition(*I, BB);
8666 if (D == DoesNotDominateBlock)
8667 return DoesNotDominateBlock;
8668 if (D == DominatesBlock)
8671 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8674 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8675 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8676 BlockDisposition LD = getBlockDisposition(LHS, BB);
8677 if (LD == DoesNotDominateBlock)
8678 return DoesNotDominateBlock;
8679 BlockDisposition RD = getBlockDisposition(RHS, BB);
8680 if (RD == DoesNotDominateBlock)
8681 return DoesNotDominateBlock;
8682 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8683 ProperlyDominatesBlock : DominatesBlock;
8686 if (Instruction *I =
8687 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8688 if (I->getParent() == BB)
8689 return DominatesBlock;
8690 if (DT.properlyDominates(I->getParent(), BB))
8691 return ProperlyDominatesBlock;
8692 return DoesNotDominateBlock;
8694 return ProperlyDominatesBlock;
8695 case scCouldNotCompute:
8696 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8698 llvm_unreachable("Unknown SCEV kind!");
8701 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8702 return getBlockDisposition(S, BB) >= DominatesBlock;
8705 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8706 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8710 // Search for a SCEV expression node within an expression tree.
8711 // Implements SCEVTraversal::Visitor.
8716 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8718 bool follow(const SCEV *S) {
8719 IsFound |= (S == Node);
8722 bool isDone() const { return IsFound; }
8726 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8727 SCEVSearch Search(Op);
8728 visitAll(S, Search);
8729 return Search.IsFound;
8732 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8733 ValuesAtScopes.erase(S);
8734 LoopDispositions.erase(S);
8735 BlockDispositions.erase(S);
8736 UnsignedRanges.erase(S);
8737 SignedRanges.erase(S);
8739 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8740 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8741 BackedgeTakenInfo &BEInfo = I->second;
8742 if (BEInfo.hasOperand(S, this)) {
8744 BackedgeTakenCounts.erase(I++);
8751 typedef DenseMap<const Loop *, std::string> VerifyMap;
8753 /// replaceSubString - Replaces all occurrences of From in Str with To.
8754 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8756 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8757 Str.replace(Pos, From.size(), To.data(), To.size());
8762 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8764 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8765 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8766 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8768 std::string &S = Map[L];
8770 raw_string_ostream OS(S);
8771 SE.getBackedgeTakenCount(L)->print(OS);
8773 // false and 0 are semantically equivalent. This can happen in dead loops.
8774 replaceSubString(OS.str(), "false", "0");
8775 // Remove wrap flags, their use in SCEV is highly fragile.
8776 // FIXME: Remove this when SCEV gets smarter about them.
8777 replaceSubString(OS.str(), "<nw>", "");
8778 replaceSubString(OS.str(), "<nsw>", "");
8779 replaceSubString(OS.str(), "<nuw>", "");
8784 void ScalarEvolution::verify() const {
8785 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8787 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8788 // FIXME: It would be much better to store actual values instead of strings,
8789 // but SCEV pointers will change if we drop the caches.
8790 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8791 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
8792 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8794 // Gather stringified backedge taken counts for all loops using a fresh
8795 // ScalarEvolution object.
8796 ScalarEvolution SE2(F, TLI, AC, DT, LI);
8797 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
8798 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
8800 // Now compare whether they're the same with and without caches. This allows
8801 // verifying that no pass changed the cache.
8802 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8803 "New loops suddenly appeared!");
8805 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8806 OldE = BackedgeDumpsOld.end(),
8807 NewI = BackedgeDumpsNew.begin();
8808 OldI != OldE; ++OldI, ++NewI) {
8809 assert(OldI->first == NewI->first && "Loop order changed!");
8811 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8813 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8814 // means that a pass is buggy or SCEV has to learn a new pattern but is
8815 // usually not harmful.
8816 if (OldI->second != NewI->second &&
8817 OldI->second.find("undef") == std::string::npos &&
8818 NewI->second.find("undef") == std::string::npos &&
8819 OldI->second != "***COULDNOTCOMPUTE***" &&
8820 NewI->second != "***COULDNOTCOMPUTE***") {
8821 dbgs() << "SCEVValidator: SCEV for loop '"
8822 << OldI->first->getHeader()->getName()
8823 << "' changed from '" << OldI->second
8824 << "' to '" << NewI->second << "'!\n";
8829 // TODO: Verify more things.
8832 char ScalarEvolutionAnalysis::PassID;
8834 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
8835 AnalysisManager<Function> *AM) {
8836 return ScalarEvolution(F, AM->getResult<TargetLibraryAnalysis>(F),
8837 AM->getResult<AssumptionAnalysis>(F),
8838 AM->getResult<DominatorTreeAnalysis>(F),
8839 AM->getResult<LoopAnalysis>(F));
8843 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> *AM) {
8844 AM->getResult<ScalarEvolutionAnalysis>(F).print(OS);
8845 return PreservedAnalyses::all();
8848 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
8849 "Scalar Evolution Analysis", false, true)
8850 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
8851 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
8852 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
8853 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
8854 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
8855 "Scalar Evolution Analysis", false, true)
8856 char ScalarEvolutionWrapperPass::ID = 0;
8858 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
8859 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
8862 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
8863 SE.reset(new ScalarEvolution(
8864 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
8865 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
8866 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
8867 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
8871 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
8873 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
8877 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
8884 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
8885 AU.setPreservesAll();
8886 AU.addRequiredTransitive<AssumptionCacheTracker>();
8887 AU.addRequiredTransitive<LoopInfoWrapperPass>();
8888 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
8889 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();