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"
91 #include "llvm/Support/SaveAndRestore.h"
95 #define DEBUG_TYPE "scalar-evolution"
97 STATISTIC(NumArrayLenItCounts,
98 "Number of trip counts computed with array length");
99 STATISTIC(NumTripCountsComputed,
100 "Number of loops with predictable loop counts");
101 STATISTIC(NumTripCountsNotComputed,
102 "Number of loops without predictable loop counts");
103 STATISTIC(NumBruteForceTripCountsComputed,
104 "Number of loops with trip counts computed by force");
106 static cl::opt<unsigned>
107 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
108 cl::desc("Maximum number of iterations SCEV will "
109 "symbolically execute a constant "
113 // FIXME: Enable this with XDEBUG when the test suite is clean.
115 VerifySCEV("verify-scev",
116 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
118 //===----------------------------------------------------------------------===//
119 // SCEV class definitions
120 //===----------------------------------------------------------------------===//
122 //===----------------------------------------------------------------------===//
123 // Implementation of the SCEV class.
127 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.getZero(Denominator->getType());
901 One = SE.getOne(Denominator->getType());
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 (const SCEV *Op : AddRec->operands())
1135 Operands.push_back(getTruncateExpr(Op, 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 auto PreStartFlags =
1271 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1272 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1273 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1274 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1276 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1277 // "S+X does not sign/unsign-overflow".
1280 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1281 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1282 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1285 // 2. Direct overflow check on the step operation's expression.
1286 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1287 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1288 const SCEV *OperandExtendedStart =
1289 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1290 (SE->*GetExtendExpr)(Step, WideTy));
1291 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1292 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1293 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1294 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1295 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1296 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1301 // 3. Loop precondition.
1302 ICmpInst::Predicate Pred;
1303 const SCEV *OverflowLimit =
1304 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1306 if (OverflowLimit &&
1307 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1313 // Get the normalized zero or sign extended expression for this AddRec's Start.
1314 template <typename ExtendOpTy>
1315 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1316 ScalarEvolution *SE) {
1317 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1319 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1321 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1323 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1324 (SE->*GetExtendExpr)(PreStart, Ty));
1327 // Try to prove away overflow by looking at "nearby" add recurrences. A
1328 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1329 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1333 // {S,+,X} == {S-T,+,X} + T
1334 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1336 // If ({S-T,+,X} + T) does not overflow ... (1)
1338 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1340 // If {S-T,+,X} does not overflow ... (2)
1342 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1343 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1345 // If (S-T)+T does not overflow ... (3)
1347 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1348 // == {Ext(S),+,Ext(X)} == LHS
1350 // Thus, if (1), (2) and (3) are true for some T, then
1351 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1353 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1354 // does not overflow" restricted to the 0th iteration. Therefore we only need
1355 // to check for (1) and (2).
1357 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1358 // is `Delta` (defined below).
1360 template <typename ExtendOpTy>
1361 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1364 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1366 // We restrict `Start` to a constant to prevent SCEV from spending too much
1367 // time here. It is correct (but more expensive) to continue with a
1368 // non-constant `Start` and do a general SCEV subtraction to compute
1369 // `PreStart` below.
1371 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1375 APInt StartAI = StartC->getValue()->getValue();
1377 for (unsigned Delta : {-2, -1, 1, 2}) {
1378 const SCEV *PreStart = getConstant(StartAI - Delta);
1380 FoldingSetNodeID ID;
1381 ID.AddInteger(scAddRecExpr);
1382 ID.AddPointer(PreStart);
1383 ID.AddPointer(Step);
1387 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1389 // Give up if we don't already have the add recurrence we need because
1390 // actually constructing an add recurrence is relatively expensive.
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 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1562 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1563 if (SA->getNoWrapFlags(SCEV::FlagNUW)) {
1564 // If the addition does not unsign overflow then we can, by definition,
1565 // commute the zero extension with the addition operation.
1566 SmallVector<const SCEV *, 4> Ops;
1567 for (const auto *Op : SA->operands())
1568 Ops.push_back(getZeroExtendExpr(Op, Ty));
1569 return getAddExpr(Ops, SCEV::FlagNUW);
1573 // The cast wasn't folded; create an explicit cast node.
1574 // Recompute the insert position, as it may have been invalidated.
1575 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1576 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1578 UniqueSCEVs.InsertNode(S, IP);
1582 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1584 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1585 "This is not an extending conversion!");
1586 assert(isSCEVable(Ty) &&
1587 "This is not a conversion to a SCEVable type!");
1588 Ty = getEffectiveSCEVType(Ty);
1590 // Fold if the operand is constant.
1591 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1593 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1595 // sext(sext(x)) --> sext(x)
1596 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1597 return getSignExtendExpr(SS->getOperand(), Ty);
1599 // sext(zext(x)) --> zext(x)
1600 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1601 return getZeroExtendExpr(SZ->getOperand(), Ty);
1603 // Before doing any expensive analysis, check to see if we've already
1604 // computed a SCEV for this Op and Ty.
1605 FoldingSetNodeID ID;
1606 ID.AddInteger(scSignExtend);
1610 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1612 // If the input value is provably positive, build a zext instead.
1613 if (isKnownNonNegative(Op))
1614 return getZeroExtendExpr(Op, Ty);
1616 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1617 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1618 // It's possible the bits taken off by the truncate were all sign bits. If
1619 // so, we should be able to simplify this further.
1620 const SCEV *X = ST->getOperand();
1621 ConstantRange CR = getSignedRange(X);
1622 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1623 unsigned NewBits = getTypeSizeInBits(Ty);
1624 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1625 CR.sextOrTrunc(NewBits)))
1626 return getTruncateOrSignExtend(X, Ty);
1629 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1630 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1631 if (SA->getNumOperands() == 2) {
1632 auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1633 auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1635 if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1636 const APInt &C1 = SC1->getValue()->getValue();
1637 const APInt &C2 = SC2->getValue()->getValue();
1638 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1639 C2.ugt(C1) && C2.isPowerOf2())
1640 return getAddExpr(getSignExtendExpr(SC1, Ty),
1641 getSignExtendExpr(SMul, Ty));
1646 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1647 if (SA->getNoWrapFlags(SCEV::FlagNSW)) {
1648 // If the addition does not sign overflow then we can, by definition,
1649 // commute the sign extension with the addition operation.
1650 SmallVector<const SCEV *, 4> Ops;
1651 for (const auto *Op : SA->operands())
1652 Ops.push_back(getSignExtendExpr(Op, Ty));
1653 return getAddExpr(Ops, SCEV::FlagNSW);
1656 // If the input value is a chrec scev, and we can prove that the value
1657 // did not overflow the old, smaller, value, we can sign extend all of the
1658 // operands (often constants). This allows analysis of something like
1659 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1660 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1661 if (AR->isAffine()) {
1662 const SCEV *Start = AR->getStart();
1663 const SCEV *Step = AR->getStepRecurrence(*this);
1664 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1665 const Loop *L = AR->getLoop();
1667 // If we have special knowledge that this addrec won't overflow,
1668 // we don't need to do any further analysis.
1669 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1670 return getAddRecExpr(
1671 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1672 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1674 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1675 // Note that this serves two purposes: It filters out loops that are
1676 // simply not analyzable, and it covers the case where this code is
1677 // being called from within backedge-taken count analysis, such that
1678 // attempting to ask for the backedge-taken count would likely result
1679 // in infinite recursion. In the later case, the analysis code will
1680 // cope with a conservative value, and it will take care to purge
1681 // that value once it has finished.
1682 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1683 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1684 // Manually compute the final value for AR, checking for
1687 // Check whether the backedge-taken count can be losslessly casted to
1688 // the addrec's type. The count is always unsigned.
1689 const SCEV *CastedMaxBECount =
1690 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1691 const SCEV *RecastedMaxBECount =
1692 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1693 if (MaxBECount == RecastedMaxBECount) {
1694 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1695 // Check whether Start+Step*MaxBECount has no signed overflow.
1696 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1697 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1698 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1699 const SCEV *WideMaxBECount =
1700 getZeroExtendExpr(CastedMaxBECount, WideTy);
1701 const SCEV *OperandExtendedAdd =
1702 getAddExpr(WideStart,
1703 getMulExpr(WideMaxBECount,
1704 getSignExtendExpr(Step, WideTy)));
1705 if (SAdd == OperandExtendedAdd) {
1706 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1707 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1708 // Return the expression with the addrec on the outside.
1709 return getAddRecExpr(
1710 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1711 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1713 // Similar to above, only this time treat the step value as unsigned.
1714 // This covers loops that count up with an unsigned step.
1715 OperandExtendedAdd =
1716 getAddExpr(WideStart,
1717 getMulExpr(WideMaxBECount,
1718 getZeroExtendExpr(Step, WideTy)));
1719 if (SAdd == OperandExtendedAdd) {
1720 // If AR wraps around then
1722 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1723 // => SAdd != OperandExtendedAdd
1725 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1726 // (SAdd == OperandExtendedAdd => AR is NW)
1728 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1730 // Return the expression with the addrec on the outside.
1731 return getAddRecExpr(
1732 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1733 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1737 // If the backedge is guarded by a comparison with the pre-inc value
1738 // the addrec is safe. Also, if the entry is guarded by a comparison
1739 // with the start value and the backedge is guarded by a comparison
1740 // with the post-inc value, the addrec is safe.
1741 ICmpInst::Predicate Pred;
1742 const SCEV *OverflowLimit =
1743 getSignedOverflowLimitForStep(Step, &Pred, this);
1744 if (OverflowLimit &&
1745 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1746 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1747 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1749 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1750 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1751 return getAddRecExpr(
1752 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1753 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1756 // If Start and Step are constants, check if we can apply this
1758 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1759 auto *SC1 = dyn_cast<SCEVConstant>(Start);
1760 auto *SC2 = dyn_cast<SCEVConstant>(Step);
1762 const APInt &C1 = SC1->getValue()->getValue();
1763 const APInt &C2 = SC2->getValue()->getValue();
1764 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1766 Start = getSignExtendExpr(Start, Ty);
1767 const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1768 AR->getNoWrapFlags());
1769 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1773 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1774 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1775 return getAddRecExpr(
1776 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1777 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1781 // The cast wasn't folded; create an explicit cast node.
1782 // Recompute the insert position, as it may have been invalidated.
1783 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1784 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1786 UniqueSCEVs.InsertNode(S, IP);
1790 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1791 /// unspecified bits out to the given type.
1793 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1795 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1796 "This is not an extending conversion!");
1797 assert(isSCEVable(Ty) &&
1798 "This is not a conversion to a SCEVable type!");
1799 Ty = getEffectiveSCEVType(Ty);
1801 // Sign-extend negative constants.
1802 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1803 if (SC->getValue()->getValue().isNegative())
1804 return getSignExtendExpr(Op, Ty);
1806 // Peel off a truncate cast.
1807 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1808 const SCEV *NewOp = T->getOperand();
1809 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1810 return getAnyExtendExpr(NewOp, Ty);
1811 return getTruncateOrNoop(NewOp, Ty);
1814 // Next try a zext cast. If the cast is folded, use it.
1815 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1816 if (!isa<SCEVZeroExtendExpr>(ZExt))
1819 // Next try a sext cast. If the cast is folded, use it.
1820 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1821 if (!isa<SCEVSignExtendExpr>(SExt))
1824 // Force the cast to be folded into the operands of an addrec.
1825 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1826 SmallVector<const SCEV *, 4> Ops;
1827 for (const SCEV *Op : AR->operands())
1828 Ops.push_back(getAnyExtendExpr(Op, Ty));
1829 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1832 // If the expression is obviously signed, use the sext cast value.
1833 if (isa<SCEVSMaxExpr>(Op))
1836 // Absent any other information, use the zext cast value.
1840 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1841 /// a list of operands to be added under the given scale, update the given
1842 /// map. This is a helper function for getAddRecExpr. As an example of
1843 /// what it does, given a sequence of operands that would form an add
1844 /// expression like this:
1846 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1848 /// where A and B are constants, update the map with these values:
1850 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1852 /// and add 13 + A*B*29 to AccumulatedConstant.
1853 /// This will allow getAddRecExpr to produce this:
1855 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1857 /// This form often exposes folding opportunities that are hidden in
1858 /// the original operand list.
1860 /// Return true iff it appears that any interesting folding opportunities
1861 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1862 /// the common case where no interesting opportunities are present, and
1863 /// is also used as a check to avoid infinite recursion.
1866 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1867 SmallVectorImpl<const SCEV *> &NewOps,
1868 APInt &AccumulatedConstant,
1869 const SCEV *const *Ops, size_t NumOperands,
1871 ScalarEvolution &SE) {
1872 bool Interesting = false;
1874 // Iterate over the add operands. They are sorted, with constants first.
1876 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1878 // Pull a buried constant out to the outside.
1879 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1881 AccumulatedConstant += Scale * C->getValue()->getValue();
1884 // Next comes everything else. We're especially interested in multiplies
1885 // here, but they're in the middle, so just visit the rest with one loop.
1886 for (; i != NumOperands; ++i) {
1887 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1888 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1890 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1891 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1892 // A multiplication of a constant with another add; recurse.
1893 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1895 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1896 Add->op_begin(), Add->getNumOperands(),
1899 // A multiplication of a constant with some other value. Update
1901 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1902 const SCEV *Key = SE.getMulExpr(MulOps);
1903 auto Pair = M.insert(std::make_pair(Key, NewScale));
1905 NewOps.push_back(Pair.first->first);
1907 Pair.first->second += NewScale;
1908 // The map already had an entry for this value, which may indicate
1909 // a folding opportunity.
1914 // An ordinary operand. Update the map.
1915 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1916 M.insert(std::make_pair(Ops[i], Scale));
1918 NewOps.push_back(Pair.first->first);
1920 Pair.first->second += Scale;
1921 // The map already had an entry for this value, which may indicate
1922 // a folding opportunity.
1932 struct APIntCompare {
1933 bool operator()(const APInt &LHS, const APInt &RHS) const {
1934 return LHS.ult(RHS);
1939 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1940 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1941 // can't-overflow flags for the operation if possible.
1942 static SCEV::NoWrapFlags
1943 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1944 const SmallVectorImpl<const SCEV *> &Ops,
1945 SCEV::NoWrapFlags Flags) {
1946 using namespace std::placeholders;
1947 typedef OverflowingBinaryOperator OBO;
1950 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1952 assert(CanAnalyze && "don't call from other places!");
1954 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1955 SCEV::NoWrapFlags SignOrUnsignWrap =
1956 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1958 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1959 auto IsKnownNonNegative =
1960 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1962 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1963 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1965 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1967 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1969 if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
1970 Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
1972 // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
1973 // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
1975 const APInt &C = cast<SCEVConstant>(Ops[0])->getValue()->getValue();
1976 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
1978 ConstantRange::makeNoWrapRegion(Instruction::Add, C, OBO::NoSignedWrap);
1979 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
1980 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
1982 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
1984 ConstantRange::makeNoWrapRegion(Instruction::Add, C,
1985 OBO::NoUnsignedWrap);
1986 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
1987 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
1994 /// getAddExpr - Get a canonical add expression, or something simpler if
1996 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1997 SCEV::NoWrapFlags Flags) {
1998 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1999 "only nuw or nsw allowed");
2000 assert(!Ops.empty() && "Cannot get empty add!");
2001 if (Ops.size() == 1) return Ops[0];
2003 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2004 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2005 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2006 "SCEVAddExpr operand types don't match!");
2009 // Sort by complexity, this groups all similar expression types together.
2010 GroupByComplexity(Ops, &LI);
2012 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2014 // If there are any constants, fold them together.
2016 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2018 assert(Idx < Ops.size());
2019 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2020 // We found two constants, fold them together!
2021 Ops[0] = getConstant(LHSC->getValue()->getValue() +
2022 RHSC->getValue()->getValue());
2023 if (Ops.size() == 2) return Ops[0];
2024 Ops.erase(Ops.begin()+1); // Erase the folded element
2025 LHSC = cast<SCEVConstant>(Ops[0]);
2028 // If we are left with a constant zero being added, strip it off.
2029 if (LHSC->getValue()->isZero()) {
2030 Ops.erase(Ops.begin());
2034 if (Ops.size() == 1) return Ops[0];
2037 // Okay, check to see if the same value occurs in the operand list more than
2038 // once. If so, merge them together into an multiply expression. Since we
2039 // sorted the list, these values are required to be adjacent.
2040 Type *Ty = Ops[0]->getType();
2041 bool FoundMatch = false;
2042 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2043 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2044 // Scan ahead to count how many equal operands there are.
2046 while (i+Count != e && Ops[i+Count] == Ops[i])
2048 // Merge the values into a multiply.
2049 const SCEV *Scale = getConstant(Ty, Count);
2050 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2051 if (Ops.size() == Count)
2054 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2055 --i; e -= Count - 1;
2059 return getAddExpr(Ops, Flags);
2061 // Check for truncates. If all the operands are truncated from the same
2062 // type, see if factoring out the truncate would permit the result to be
2063 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2064 // if the contents of the resulting outer trunc fold to something simple.
2065 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2066 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2067 Type *DstType = Trunc->getType();
2068 Type *SrcType = Trunc->getOperand()->getType();
2069 SmallVector<const SCEV *, 8> LargeOps;
2071 // Check all the operands to see if they can be represented in the
2072 // source type of the truncate.
2073 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2074 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2075 if (T->getOperand()->getType() != SrcType) {
2079 LargeOps.push_back(T->getOperand());
2080 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2081 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2082 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2083 SmallVector<const SCEV *, 8> LargeMulOps;
2084 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2085 if (const SCEVTruncateExpr *T =
2086 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2087 if (T->getOperand()->getType() != SrcType) {
2091 LargeMulOps.push_back(T->getOperand());
2092 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2093 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2100 LargeOps.push_back(getMulExpr(LargeMulOps));
2107 // Evaluate the expression in the larger type.
2108 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2109 // If it folds to something simple, use it. Otherwise, don't.
2110 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2111 return getTruncateExpr(Fold, DstType);
2115 // Skip past any other cast SCEVs.
2116 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2119 // If there are add operands they would be next.
2120 if (Idx < Ops.size()) {
2121 bool DeletedAdd = false;
2122 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2123 // If we have an add, expand the add operands onto the end of the operands
2125 Ops.erase(Ops.begin()+Idx);
2126 Ops.append(Add->op_begin(), Add->op_end());
2130 // If we deleted at least one add, we added operands to the end of the list,
2131 // and they are not necessarily sorted. Recurse to resort and resimplify
2132 // any operands we just acquired.
2134 return getAddExpr(Ops);
2137 // Skip over the add expression until we get to a multiply.
2138 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2141 // Check to see if there are any folding opportunities present with
2142 // operands multiplied by constant values.
2143 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2144 uint64_t BitWidth = getTypeSizeInBits(Ty);
2145 DenseMap<const SCEV *, APInt> M;
2146 SmallVector<const SCEV *, 8> NewOps;
2147 APInt AccumulatedConstant(BitWidth, 0);
2148 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2149 Ops.data(), Ops.size(),
2150 APInt(BitWidth, 1), *this)) {
2151 // Some interesting folding opportunity is present, so its worthwhile to
2152 // re-generate the operands list. Group the operands by constant scale,
2153 // to avoid multiplying by the same constant scale multiple times.
2154 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2155 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
2156 E = NewOps.end(); I != E; ++I)
2157 MulOpLists[M.find(*I)->second].push_back(*I);
2158 // Re-generate the operands list.
2160 if (AccumulatedConstant != 0)
2161 Ops.push_back(getConstant(AccumulatedConstant));
2162 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
2163 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
2165 Ops.push_back(getMulExpr(getConstant(I->first),
2166 getAddExpr(I->second)));
2169 if (Ops.size() == 1)
2171 return getAddExpr(Ops);
2175 // If we are adding something to a multiply expression, make sure the
2176 // something is not already an operand of the multiply. If so, merge it into
2178 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2179 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2180 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2181 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2182 if (isa<SCEVConstant>(MulOpSCEV))
2184 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2185 if (MulOpSCEV == Ops[AddOp]) {
2186 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2187 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2188 if (Mul->getNumOperands() != 2) {
2189 // If the multiply has more than two operands, we must get the
2191 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2192 Mul->op_begin()+MulOp);
2193 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2194 InnerMul = getMulExpr(MulOps);
2196 const SCEV *One = getOne(Ty);
2197 const SCEV *AddOne = getAddExpr(One, InnerMul);
2198 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2199 if (Ops.size() == 2) return OuterMul;
2201 Ops.erase(Ops.begin()+AddOp);
2202 Ops.erase(Ops.begin()+Idx-1);
2204 Ops.erase(Ops.begin()+Idx);
2205 Ops.erase(Ops.begin()+AddOp-1);
2207 Ops.push_back(OuterMul);
2208 return getAddExpr(Ops);
2211 // Check this multiply against other multiplies being added together.
2212 for (unsigned OtherMulIdx = Idx+1;
2213 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2215 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2216 // If MulOp occurs in OtherMul, we can fold the two multiplies
2218 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2219 OMulOp != e; ++OMulOp)
2220 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2221 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2222 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2223 if (Mul->getNumOperands() != 2) {
2224 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2225 Mul->op_begin()+MulOp);
2226 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2227 InnerMul1 = getMulExpr(MulOps);
2229 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2230 if (OtherMul->getNumOperands() != 2) {
2231 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2232 OtherMul->op_begin()+OMulOp);
2233 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2234 InnerMul2 = getMulExpr(MulOps);
2236 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2237 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2238 if (Ops.size() == 2) return OuterMul;
2239 Ops.erase(Ops.begin()+Idx);
2240 Ops.erase(Ops.begin()+OtherMulIdx-1);
2241 Ops.push_back(OuterMul);
2242 return getAddExpr(Ops);
2248 // If there are any add recurrences in the operands list, see if any other
2249 // added values are loop invariant. If so, we can fold them into the
2251 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2254 // Scan over all recurrences, trying to fold loop invariants into them.
2255 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2256 // Scan all of the other operands to this add and add them to the vector if
2257 // they are loop invariant w.r.t. the recurrence.
2258 SmallVector<const SCEV *, 8> LIOps;
2259 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2260 const Loop *AddRecLoop = AddRec->getLoop();
2261 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2262 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2263 LIOps.push_back(Ops[i]);
2264 Ops.erase(Ops.begin()+i);
2268 // If we found some loop invariants, fold them into the recurrence.
2269 if (!LIOps.empty()) {
2270 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2271 LIOps.push_back(AddRec->getStart());
2273 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2275 AddRecOps[0] = getAddExpr(LIOps);
2277 // Build the new addrec. Propagate the NUW and NSW flags if both the
2278 // outer add and the inner addrec are guaranteed to have no overflow.
2279 // Always propagate NW.
2280 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2281 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2283 // If all of the other operands were loop invariant, we are done.
2284 if (Ops.size() == 1) return NewRec;
2286 // Otherwise, add the folded AddRec by the non-invariant parts.
2287 for (unsigned i = 0;; ++i)
2288 if (Ops[i] == AddRec) {
2292 return getAddExpr(Ops);
2295 // Okay, if there weren't any loop invariants to be folded, check to see if
2296 // there are multiple AddRec's with the same loop induction variable being
2297 // added together. If so, we can fold them.
2298 for (unsigned OtherIdx = Idx+1;
2299 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2301 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2302 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2303 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2305 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2307 if (const SCEVAddRecExpr *OtherAddRec =
2308 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2309 if (OtherAddRec->getLoop() == AddRecLoop) {
2310 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2312 if (i >= AddRecOps.size()) {
2313 AddRecOps.append(OtherAddRec->op_begin()+i,
2314 OtherAddRec->op_end());
2317 AddRecOps[i] = getAddExpr(AddRecOps[i],
2318 OtherAddRec->getOperand(i));
2320 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2322 // Step size has changed, so we cannot guarantee no self-wraparound.
2323 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2324 return getAddExpr(Ops);
2327 // Otherwise couldn't fold anything into this recurrence. Move onto the
2331 // Okay, it looks like we really DO need an add expr. Check to see if we
2332 // already have one, otherwise create a new one.
2333 FoldingSetNodeID ID;
2334 ID.AddInteger(scAddExpr);
2335 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2336 ID.AddPointer(Ops[i]);
2339 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2341 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2342 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2343 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2345 UniqueSCEVs.InsertNode(S, IP);
2347 S->setNoWrapFlags(Flags);
2351 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2353 if (j > 1 && k / j != i) Overflow = true;
2357 /// Compute the result of "n choose k", the binomial coefficient. If an
2358 /// intermediate computation overflows, Overflow will be set and the return will
2359 /// be garbage. Overflow is not cleared on absence of overflow.
2360 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2361 // We use the multiplicative formula:
2362 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2363 // At each iteration, we take the n-th term of the numeral and divide by the
2364 // (k-n)th term of the denominator. This division will always produce an
2365 // integral result, and helps reduce the chance of overflow in the
2366 // intermediate computations. However, we can still overflow even when the
2367 // final result would fit.
2369 if (n == 0 || n == k) return 1;
2370 if (k > n) return 0;
2376 for (uint64_t i = 1; i <= k; ++i) {
2377 r = umul_ov(r, n-(i-1), Overflow);
2383 /// Determine if any of the operands in this SCEV are a constant or if
2384 /// any of the add or multiply expressions in this SCEV contain a constant.
2385 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2386 SmallVector<const SCEV *, 4> Ops;
2387 Ops.push_back(StartExpr);
2388 while (!Ops.empty()) {
2389 const SCEV *CurrentExpr = Ops.pop_back_val();
2390 if (isa<SCEVConstant>(*CurrentExpr))
2393 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2394 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2395 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2401 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2403 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2404 SCEV::NoWrapFlags Flags) {
2405 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2406 "only nuw or nsw allowed");
2407 assert(!Ops.empty() && "Cannot get empty mul!");
2408 if (Ops.size() == 1) return Ops[0];
2410 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2411 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2412 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2413 "SCEVMulExpr operand types don't match!");
2416 // Sort by complexity, this groups all similar expression types together.
2417 GroupByComplexity(Ops, &LI);
2419 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2421 // If there are any constants, fold them together.
2423 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2425 // C1*(C2+V) -> C1*C2 + C1*V
2426 if (Ops.size() == 2)
2427 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2428 // If any of Add's ops are Adds or Muls with a constant,
2429 // apply this transformation as well.
2430 if (Add->getNumOperands() == 2)
2431 if (containsConstantSomewhere(Add))
2432 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2433 getMulExpr(LHSC, Add->getOperand(1)));
2436 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2437 // We found two constants, fold them together!
2438 ConstantInt *Fold = ConstantInt::get(getContext(),
2439 LHSC->getValue()->getValue() *
2440 RHSC->getValue()->getValue());
2441 Ops[0] = getConstant(Fold);
2442 Ops.erase(Ops.begin()+1); // Erase the folded element
2443 if (Ops.size() == 1) return Ops[0];
2444 LHSC = cast<SCEVConstant>(Ops[0]);
2447 // If we are left with a constant one being multiplied, strip it off.
2448 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2449 Ops.erase(Ops.begin());
2451 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2452 // If we have a multiply of zero, it will always be zero.
2454 } else if (Ops[0]->isAllOnesValue()) {
2455 // If we have a mul by -1 of an add, try distributing the -1 among the
2457 if (Ops.size() == 2) {
2458 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2459 SmallVector<const SCEV *, 4> NewOps;
2460 bool AnyFolded = false;
2461 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2462 E = Add->op_end(); I != E; ++I) {
2463 const SCEV *Mul = getMulExpr(Ops[0], *I);
2464 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2465 NewOps.push_back(Mul);
2468 return getAddExpr(NewOps);
2469 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2470 // Negation preserves a recurrence's no self-wrap property.
2471 SmallVector<const SCEV *, 4> Operands;
2472 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2473 E = AddRec->op_end(); I != E; ++I) {
2474 Operands.push_back(getMulExpr(Ops[0], *I));
2476 return getAddRecExpr(Operands, AddRec->getLoop(),
2477 AddRec->getNoWrapFlags(SCEV::FlagNW));
2482 if (Ops.size() == 1)
2486 // Skip over the add expression until we get to a multiply.
2487 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2490 // If there are mul operands inline them all into this expression.
2491 if (Idx < Ops.size()) {
2492 bool DeletedMul = false;
2493 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2494 // If we have an mul, expand the mul operands onto the end of the operands
2496 Ops.erase(Ops.begin()+Idx);
2497 Ops.append(Mul->op_begin(), Mul->op_end());
2501 // If we deleted at least one mul, we added operands to the end of the list,
2502 // and they are not necessarily sorted. Recurse to resort and resimplify
2503 // any operands we just acquired.
2505 return getMulExpr(Ops);
2508 // If there are any add recurrences in the operands list, see if any other
2509 // added values are loop invariant. If so, we can fold them into the
2511 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2514 // Scan over all recurrences, trying to fold loop invariants into them.
2515 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2516 // Scan all of the other operands to this mul and add them to the vector if
2517 // they are loop invariant w.r.t. the recurrence.
2518 SmallVector<const SCEV *, 8> LIOps;
2519 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2520 const Loop *AddRecLoop = AddRec->getLoop();
2521 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2522 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2523 LIOps.push_back(Ops[i]);
2524 Ops.erase(Ops.begin()+i);
2528 // If we found some loop invariants, fold them into the recurrence.
2529 if (!LIOps.empty()) {
2530 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2531 SmallVector<const SCEV *, 4> NewOps;
2532 NewOps.reserve(AddRec->getNumOperands());
2533 const SCEV *Scale = getMulExpr(LIOps);
2534 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2535 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2537 // Build the new addrec. Propagate the NUW and NSW flags if both the
2538 // outer mul and the inner addrec are guaranteed to have no overflow.
2540 // No self-wrap cannot be guaranteed after changing the step size, but
2541 // will be inferred if either NUW or NSW is true.
2542 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2543 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2545 // If all of the other operands were loop invariant, we are done.
2546 if (Ops.size() == 1) return NewRec;
2548 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2549 for (unsigned i = 0;; ++i)
2550 if (Ops[i] == AddRec) {
2554 return getMulExpr(Ops);
2557 // Okay, if there weren't any loop invariants to be folded, check to see if
2558 // there are multiple AddRec's with the same loop induction variable being
2559 // multiplied together. If so, we can fold them.
2561 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2562 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2563 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2564 // ]]],+,...up to x=2n}.
2565 // Note that the arguments to choose() are always integers with values
2566 // known at compile time, never SCEV objects.
2568 // The implementation avoids pointless extra computations when the two
2569 // addrec's are of different length (mathematically, it's equivalent to
2570 // an infinite stream of zeros on the right).
2571 bool OpsModified = false;
2572 for (unsigned OtherIdx = Idx+1;
2573 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2575 const SCEVAddRecExpr *OtherAddRec =
2576 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2577 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2580 bool Overflow = false;
2581 Type *Ty = AddRec->getType();
2582 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2583 SmallVector<const SCEV*, 7> AddRecOps;
2584 for (int x = 0, xe = AddRec->getNumOperands() +
2585 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2586 const SCEV *Term = getZero(Ty);
2587 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2588 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2589 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2590 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2591 z < ze && !Overflow; ++z) {
2592 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2594 if (LargerThan64Bits)
2595 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2597 Coeff = Coeff1*Coeff2;
2598 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2599 const SCEV *Term1 = AddRec->getOperand(y-z);
2600 const SCEV *Term2 = OtherAddRec->getOperand(z);
2601 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2604 AddRecOps.push_back(Term);
2607 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2609 if (Ops.size() == 2) return NewAddRec;
2610 Ops[Idx] = NewAddRec;
2611 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2613 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2619 return getMulExpr(Ops);
2621 // Otherwise couldn't fold anything into this recurrence. Move onto the
2625 // Okay, it looks like we really DO need an mul expr. Check to see if we
2626 // already have one, otherwise create a new one.
2627 FoldingSetNodeID ID;
2628 ID.AddInteger(scMulExpr);
2629 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2630 ID.AddPointer(Ops[i]);
2633 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2635 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2636 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2637 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2639 UniqueSCEVs.InsertNode(S, IP);
2641 S->setNoWrapFlags(Flags);
2645 /// getUDivExpr - Get a canonical unsigned division expression, or something
2646 /// simpler if possible.
2647 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2649 assert(getEffectiveSCEVType(LHS->getType()) ==
2650 getEffectiveSCEVType(RHS->getType()) &&
2651 "SCEVUDivExpr operand types don't match!");
2653 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2654 if (RHSC->getValue()->equalsInt(1))
2655 return LHS; // X udiv 1 --> x
2656 // If the denominator is zero, the result of the udiv is undefined. Don't
2657 // try to analyze it, because the resolution chosen here may differ from
2658 // the resolution chosen in other parts of the compiler.
2659 if (!RHSC->getValue()->isZero()) {
2660 // Determine if the division can be folded into the operands of
2662 // TODO: Generalize this to non-constants by using known-bits information.
2663 Type *Ty = LHS->getType();
2664 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2665 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2666 // For non-power-of-two values, effectively round the value up to the
2667 // nearest power of two.
2668 if (!RHSC->getValue()->getValue().isPowerOf2())
2670 IntegerType *ExtTy =
2671 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2672 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2673 if (const SCEVConstant *Step =
2674 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2675 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2676 const APInt &StepInt = Step->getValue()->getValue();
2677 const APInt &DivInt = RHSC->getValue()->getValue();
2678 if (!StepInt.urem(DivInt) &&
2679 getZeroExtendExpr(AR, ExtTy) ==
2680 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2681 getZeroExtendExpr(Step, ExtTy),
2682 AR->getLoop(), SCEV::FlagAnyWrap)) {
2683 SmallVector<const SCEV *, 4> Operands;
2684 for (const SCEV *Op : AR->operands())
2685 Operands.push_back(getUDivExpr(Op, RHS));
2686 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
2688 /// Get a canonical UDivExpr for a recurrence.
2689 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2690 // We can currently only fold X%N if X is constant.
2691 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2692 if (StartC && !DivInt.urem(StepInt) &&
2693 getZeroExtendExpr(AR, ExtTy) ==
2694 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2695 getZeroExtendExpr(Step, ExtTy),
2696 AR->getLoop(), SCEV::FlagAnyWrap)) {
2697 const APInt &StartInt = StartC->getValue()->getValue();
2698 const APInt &StartRem = StartInt.urem(StepInt);
2700 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2701 AR->getLoop(), SCEV::FlagNW);
2704 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2705 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2706 SmallVector<const SCEV *, 4> Operands;
2707 for (const SCEV *Op : M->operands())
2708 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2709 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2710 // Find an operand that's safely divisible.
2711 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2712 const SCEV *Op = M->getOperand(i);
2713 const SCEV *Div = getUDivExpr(Op, RHSC);
2714 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2715 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2718 return getMulExpr(Operands);
2722 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2723 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2724 SmallVector<const SCEV *, 4> Operands;
2725 for (const SCEV *Op : A->operands())
2726 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2727 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2729 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2730 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2731 if (isa<SCEVUDivExpr>(Op) ||
2732 getMulExpr(Op, RHS) != A->getOperand(i))
2734 Operands.push_back(Op);
2736 if (Operands.size() == A->getNumOperands())
2737 return getAddExpr(Operands);
2741 // Fold if both operands are constant.
2742 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2743 Constant *LHSCV = LHSC->getValue();
2744 Constant *RHSCV = RHSC->getValue();
2745 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2751 FoldingSetNodeID ID;
2752 ID.AddInteger(scUDivExpr);
2756 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2757 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2759 UniqueSCEVs.InsertNode(S, IP);
2763 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2764 APInt A = C1->getValue()->getValue().abs();
2765 APInt B = C2->getValue()->getValue().abs();
2766 uint32_t ABW = A.getBitWidth();
2767 uint32_t BBW = B.getBitWidth();
2774 return APIntOps::GreatestCommonDivisor(A, B);
2777 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2778 /// something simpler if possible. There is no representation for an exact udiv
2779 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2780 /// We can't do this when it's not exact because the udiv may be clearing bits.
2781 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2783 // TODO: we could try to find factors in all sorts of things, but for now we
2784 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2785 // end of this file for inspiration.
2787 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2789 return getUDivExpr(LHS, RHS);
2791 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2792 // If the mulexpr multiplies by a constant, then that constant must be the
2793 // first element of the mulexpr.
2794 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2795 if (LHSCst == RHSCst) {
2796 SmallVector<const SCEV *, 2> Operands;
2797 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2798 return getMulExpr(Operands);
2801 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2802 // that there's a factor provided by one of the other terms. We need to
2804 APInt Factor = gcd(LHSCst, RHSCst);
2805 if (!Factor.isIntN(1)) {
2806 LHSCst = cast<SCEVConstant>(
2807 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2808 RHSCst = cast<SCEVConstant>(
2809 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2810 SmallVector<const SCEV *, 2> Operands;
2811 Operands.push_back(LHSCst);
2812 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2813 LHS = getMulExpr(Operands);
2815 Mul = dyn_cast<SCEVMulExpr>(LHS);
2817 return getUDivExactExpr(LHS, RHS);
2822 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2823 if (Mul->getOperand(i) == RHS) {
2824 SmallVector<const SCEV *, 2> Operands;
2825 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2826 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2827 return getMulExpr(Operands);
2831 return getUDivExpr(LHS, RHS);
2834 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2835 /// Simplify the expression as much as possible.
2836 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2838 SCEV::NoWrapFlags Flags) {
2839 SmallVector<const SCEV *, 4> Operands;
2840 Operands.push_back(Start);
2841 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2842 if (StepChrec->getLoop() == L) {
2843 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2844 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2847 Operands.push_back(Step);
2848 return getAddRecExpr(Operands, L, Flags);
2851 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2852 /// Simplify the expression as much as possible.
2854 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2855 const Loop *L, SCEV::NoWrapFlags Flags) {
2856 if (Operands.size() == 1) return Operands[0];
2858 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2859 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2860 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2861 "SCEVAddRecExpr operand types don't match!");
2862 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2863 assert(isLoopInvariant(Operands[i], L) &&
2864 "SCEVAddRecExpr operand is not loop-invariant!");
2867 if (Operands.back()->isZero()) {
2868 Operands.pop_back();
2869 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2872 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2873 // use that information to infer NUW and NSW flags. However, computing a
2874 // BE count requires calling getAddRecExpr, so we may not yet have a
2875 // meaningful BE count at this point (and if we don't, we'd be stuck
2876 // with a SCEVCouldNotCompute as the cached BE count).
2878 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2880 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2881 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2882 const Loop *NestedLoop = NestedAR->getLoop();
2883 if (L->contains(NestedLoop)
2884 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2885 : (!NestedLoop->contains(L) &&
2886 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2887 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2888 NestedAR->op_end());
2889 Operands[0] = NestedAR->getStart();
2890 // AddRecs require their operands be loop-invariant with respect to their
2891 // loops. Don't perform this transformation if it would break this
2894 std::all_of(Operands.begin(), Operands.end(),
2895 [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
2898 // Create a recurrence for the outer loop with the same step size.
2900 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2901 // inner recurrence has the same property.
2902 SCEV::NoWrapFlags OuterFlags =
2903 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2905 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2906 AllInvariant = std::all_of(
2907 NestedOperands.begin(), NestedOperands.end(),
2908 [&](const SCEV *Op) { return isLoopInvariant(Op, NestedLoop); });
2911 // Ok, both add recurrences are valid after the transformation.
2913 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2914 // the outer recurrence has the same property.
2915 SCEV::NoWrapFlags InnerFlags =
2916 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2917 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2920 // Reset Operands to its original state.
2921 Operands[0] = NestedAR;
2925 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2926 // already have one, otherwise create a new one.
2927 FoldingSetNodeID ID;
2928 ID.AddInteger(scAddRecExpr);
2929 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2930 ID.AddPointer(Operands[i]);
2934 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2936 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2937 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2938 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2939 O, Operands.size(), L);
2940 UniqueSCEVs.InsertNode(S, IP);
2942 S->setNoWrapFlags(Flags);
2947 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2948 const SmallVectorImpl<const SCEV *> &IndexExprs,
2950 // getSCEV(Base)->getType() has the same address space as Base->getType()
2951 // because SCEV::getType() preserves the address space.
2952 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2953 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2954 // instruction to its SCEV, because the Instruction may be guarded by control
2955 // flow and the no-overflow bits may not be valid for the expression in any
2956 // context. This can be fixed similarly to how these flags are handled for
2958 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2960 const SCEV *TotalOffset = getZero(IntPtrTy);
2961 // The address space is unimportant. The first thing we do on CurTy is getting
2962 // its element type.
2963 Type *CurTy = PointerType::getUnqual(PointeeType);
2964 for (const SCEV *IndexExpr : IndexExprs) {
2965 // Compute the (potentially symbolic) offset in bytes for this index.
2966 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2967 // For a struct, add the member offset.
2968 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2969 unsigned FieldNo = Index->getZExtValue();
2970 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2972 // Add the field offset to the running total offset.
2973 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2975 // Update CurTy to the type of the field at Index.
2976 CurTy = STy->getTypeAtIndex(Index);
2978 // Update CurTy to its element type.
2979 CurTy = cast<SequentialType>(CurTy)->getElementType();
2980 // For an array, add the element offset, explicitly scaled.
2981 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2982 // Getelementptr indices are signed.
2983 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2985 // Multiply the index by the element size to compute the element offset.
2986 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2988 // Add the element offset to the running total offset.
2989 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2993 // Add the total offset from all the GEP indices to the base.
2994 return getAddExpr(BaseExpr, TotalOffset, Wrap);
2997 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2999 SmallVector<const SCEV *, 2> Ops;
3002 return getSMaxExpr(Ops);
3006 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3007 assert(!Ops.empty() && "Cannot get empty smax!");
3008 if (Ops.size() == 1) return Ops[0];
3010 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3011 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3012 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3013 "SCEVSMaxExpr operand types don't match!");
3016 // Sort by complexity, this groups all similar expression types together.
3017 GroupByComplexity(Ops, &LI);
3019 // If there are any constants, fold them together.
3021 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3023 assert(Idx < Ops.size());
3024 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3025 // We found two constants, fold them together!
3026 ConstantInt *Fold = ConstantInt::get(getContext(),
3027 APIntOps::smax(LHSC->getValue()->getValue(),
3028 RHSC->getValue()->getValue()));
3029 Ops[0] = getConstant(Fold);
3030 Ops.erase(Ops.begin()+1); // Erase the folded element
3031 if (Ops.size() == 1) return Ops[0];
3032 LHSC = cast<SCEVConstant>(Ops[0]);
3035 // If we are left with a constant minimum-int, strip it off.
3036 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3037 Ops.erase(Ops.begin());
3039 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3040 // If we have an smax with a constant maximum-int, it will always be
3045 if (Ops.size() == 1) return Ops[0];
3048 // Find the first SMax
3049 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3052 // Check to see if one of the operands is an SMax. If so, expand its operands
3053 // onto our operand list, and recurse to simplify.
3054 if (Idx < Ops.size()) {
3055 bool DeletedSMax = false;
3056 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3057 Ops.erase(Ops.begin()+Idx);
3058 Ops.append(SMax->op_begin(), SMax->op_end());
3063 return getSMaxExpr(Ops);
3066 // Okay, check to see if the same value occurs in the operand list twice. If
3067 // so, delete one. Since we sorted the list, these values are required to
3069 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3070 // X smax Y smax Y --> X smax Y
3071 // X smax Y --> X, if X is always greater than Y
3072 if (Ops[i] == Ops[i+1] ||
3073 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3074 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3076 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3077 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3081 if (Ops.size() == 1) return Ops[0];
3083 assert(!Ops.empty() && "Reduced smax down to nothing!");
3085 // Okay, it looks like we really DO need an smax expr. Check to see if we
3086 // already have one, otherwise create a new one.
3087 FoldingSetNodeID ID;
3088 ID.AddInteger(scSMaxExpr);
3089 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3090 ID.AddPointer(Ops[i]);
3092 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3093 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3094 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3095 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3097 UniqueSCEVs.InsertNode(S, IP);
3101 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3103 SmallVector<const SCEV *, 2> Ops;
3106 return getUMaxExpr(Ops);
3110 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3111 assert(!Ops.empty() && "Cannot get empty umax!");
3112 if (Ops.size() == 1) return Ops[0];
3114 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3115 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3116 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3117 "SCEVUMaxExpr operand types don't match!");
3120 // Sort by complexity, this groups all similar expression types together.
3121 GroupByComplexity(Ops, &LI);
3123 // If there are any constants, fold them together.
3125 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3127 assert(Idx < Ops.size());
3128 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3129 // We found two constants, fold them together!
3130 ConstantInt *Fold = ConstantInt::get(getContext(),
3131 APIntOps::umax(LHSC->getValue()->getValue(),
3132 RHSC->getValue()->getValue()));
3133 Ops[0] = getConstant(Fold);
3134 Ops.erase(Ops.begin()+1); // Erase the folded element
3135 if (Ops.size() == 1) return Ops[0];
3136 LHSC = cast<SCEVConstant>(Ops[0]);
3139 // If we are left with a constant minimum-int, strip it off.
3140 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3141 Ops.erase(Ops.begin());
3143 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3144 // If we have an umax with a constant maximum-int, it will always be
3149 if (Ops.size() == 1) return Ops[0];
3152 // Find the first UMax
3153 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3156 // Check to see if one of the operands is a UMax. If so, expand its operands
3157 // onto our operand list, and recurse to simplify.
3158 if (Idx < Ops.size()) {
3159 bool DeletedUMax = false;
3160 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3161 Ops.erase(Ops.begin()+Idx);
3162 Ops.append(UMax->op_begin(), UMax->op_end());
3167 return getUMaxExpr(Ops);
3170 // Okay, check to see if the same value occurs in the operand list twice. If
3171 // so, delete one. Since we sorted the list, these values are required to
3173 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3174 // X umax Y umax Y --> X umax Y
3175 // X umax Y --> X, if X is always greater than Y
3176 if (Ops[i] == Ops[i+1] ||
3177 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3178 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3180 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3181 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3185 if (Ops.size() == 1) return Ops[0];
3187 assert(!Ops.empty() && "Reduced umax down to nothing!");
3189 // Okay, it looks like we really DO need a umax expr. Check to see if we
3190 // already have one, otherwise create a new one.
3191 FoldingSetNodeID ID;
3192 ID.AddInteger(scUMaxExpr);
3193 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3194 ID.AddPointer(Ops[i]);
3196 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3197 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3198 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3199 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3201 UniqueSCEVs.InsertNode(S, IP);
3205 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3207 // ~smax(~x, ~y) == smin(x, y).
3208 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3211 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3213 // ~umax(~x, ~y) == umin(x, y)
3214 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3217 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3218 // We can bypass creating a target-independent
3219 // constant expression and then folding it back into a ConstantInt.
3220 // This is just a compile-time optimization.
3221 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3224 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3227 // We can bypass creating a target-independent
3228 // constant expression and then folding it back into a ConstantInt.
3229 // This is just a compile-time optimization.
3231 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3234 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3235 // Don't attempt to do anything other than create a SCEVUnknown object
3236 // here. createSCEV only calls getUnknown after checking for all other
3237 // interesting possibilities, and any other code that calls getUnknown
3238 // is doing so in order to hide a value from SCEV canonicalization.
3240 FoldingSetNodeID ID;
3241 ID.AddInteger(scUnknown);
3244 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3245 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3246 "Stale SCEVUnknown in uniquing map!");
3249 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3251 FirstUnknown = cast<SCEVUnknown>(S);
3252 UniqueSCEVs.InsertNode(S, IP);
3256 //===----------------------------------------------------------------------===//
3257 // Basic SCEV Analysis and PHI Idiom Recognition Code
3260 /// isSCEVable - Test if values of the given type are analyzable within
3261 /// the SCEV framework. This primarily includes integer types, and it
3262 /// can optionally include pointer types if the ScalarEvolution class
3263 /// has access to target-specific information.
3264 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3265 // Integers and pointers are always SCEVable.
3266 return Ty->isIntegerTy() || Ty->isPointerTy();
3269 /// getTypeSizeInBits - Return the size in bits of the specified type,
3270 /// for which isSCEVable must return true.
3271 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3272 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3273 return getDataLayout().getTypeSizeInBits(Ty);
3276 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3277 /// the given type and which represents how SCEV will treat the given
3278 /// type, for which isSCEVable must return true. For pointer types,
3279 /// this is the pointer-sized integer type.
3280 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3281 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3283 if (Ty->isIntegerTy())
3286 // The only other support type is pointer.
3287 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3288 return getDataLayout().getIntPtrType(Ty);
3291 const SCEV *ScalarEvolution::getCouldNotCompute() {
3292 return CouldNotCompute.get();
3296 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3297 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3298 // is set iff if find such SCEVUnknown.
3300 struct FindInvalidSCEVUnknown {
3302 FindInvalidSCEVUnknown() { FindOne = false; }
3303 bool follow(const SCEV *S) {
3304 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3308 if (!cast<SCEVUnknown>(S)->getValue())
3315 bool isDone() const { return FindOne; }
3319 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3320 FindInvalidSCEVUnknown F;
3321 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3327 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3328 /// expression and create a new one.
3329 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3330 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3332 const SCEV *S = getExistingSCEV(V);
3335 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3340 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3341 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3343 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3344 if (I != ValueExprMap.end()) {
3345 const SCEV *S = I->second;
3346 if (checkValidity(S))
3348 ValueExprMap.erase(I);
3353 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3355 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3356 SCEV::NoWrapFlags Flags) {
3357 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3359 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3361 Type *Ty = V->getType();
3362 Ty = getEffectiveSCEVType(Ty);
3364 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3367 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3368 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3369 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3371 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3373 Type *Ty = V->getType();
3374 Ty = getEffectiveSCEVType(Ty);
3375 const SCEV *AllOnes =
3376 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3377 return getMinusSCEV(AllOnes, V);
3380 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3381 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3382 SCEV::NoWrapFlags Flags) {
3383 // Fast path: X - X --> 0.
3385 return getZero(LHS->getType());
3387 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3388 // makes it so that we cannot make much use of NUW.
3389 auto AddFlags = SCEV::FlagAnyWrap;
3390 const bool RHSIsNotMinSigned =
3391 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3392 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3393 // Let M be the minimum representable signed value. Then (-1)*RHS
3394 // signed-wraps if and only if RHS is M. That can happen even for
3395 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3396 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3397 // (-1)*RHS, we need to prove that RHS != M.
3399 // If LHS is non-negative and we know that LHS - RHS does not
3400 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3401 // either by proving that RHS > M or that LHS >= 0.
3402 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3403 AddFlags = SCEV::FlagNSW;
3407 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3408 // RHS is NSW and LHS >= 0.
3410 // The difficulty here is that the NSW flag may have been proven
3411 // relative to a loop that is to be found in a recurrence in LHS and
3412 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3413 // larger scope than intended.
3414 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3416 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3419 /// getTruncateOrZeroExtend - 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
3423 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3424 Type *SrcTy = V->getType();
3425 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3426 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3427 "Cannot truncate or zero extend with non-integer arguments!");
3428 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3429 return V; // No conversion
3430 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3431 return getTruncateExpr(V, Ty);
3432 return getZeroExtendExpr(V, Ty);
3435 /// getTruncateOrSignExtend - 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
3439 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3441 Type *SrcTy = V->getType();
3442 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3443 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3444 "Cannot truncate or zero extend with non-integer arguments!");
3445 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3446 return V; // No conversion
3447 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3448 return getTruncateExpr(V, Ty);
3449 return getSignExtendExpr(V, Ty);
3452 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3453 /// input value to the specified type. If the type must be extended, it is zero
3454 /// extended. The conversion must not be narrowing.
3456 ScalarEvolution::getNoopOrZeroExtend(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 zero extend with non-integer arguments!");
3461 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3462 "getNoopOrZeroExtend cannot truncate!");
3463 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3464 return V; // No conversion
3465 return getZeroExtendExpr(V, Ty);
3468 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3469 /// input value to the specified type. If the type must be extended, it is sign
3470 /// extended. The conversion must not be narrowing.
3472 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3473 Type *SrcTy = V->getType();
3474 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3475 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3476 "Cannot noop or sign extend with non-integer arguments!");
3477 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3478 "getNoopOrSignExtend cannot truncate!");
3479 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3480 return V; // No conversion
3481 return getSignExtendExpr(V, Ty);
3484 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3485 /// the input value to the specified type. If the type must be extended,
3486 /// it is extended with unspecified bits. The conversion must not be
3489 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3490 Type *SrcTy = V->getType();
3491 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3492 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3493 "Cannot noop or any extend with non-integer arguments!");
3494 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3495 "getNoopOrAnyExtend cannot truncate!");
3496 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3497 return V; // No conversion
3498 return getAnyExtendExpr(V, Ty);
3501 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3502 /// input value to the specified type. The conversion must not be widening.
3504 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3505 Type *SrcTy = V->getType();
3506 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3507 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3508 "Cannot truncate or noop with non-integer arguments!");
3509 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3510 "getTruncateOrNoop cannot extend!");
3511 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3512 return V; // No conversion
3513 return getTruncateExpr(V, Ty);
3516 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3517 /// the types using zero-extension, and then perform a umax operation
3519 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3521 const SCEV *PromotedLHS = LHS;
3522 const SCEV *PromotedRHS = RHS;
3524 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3525 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3527 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3529 return getUMaxExpr(PromotedLHS, PromotedRHS);
3532 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3533 /// the types using zero-extension, and then perform a umin operation
3535 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3537 const SCEV *PromotedLHS = LHS;
3538 const SCEV *PromotedRHS = RHS;
3540 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3541 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3543 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3545 return getUMinExpr(PromotedLHS, PromotedRHS);
3548 /// getPointerBase - Transitively follow the chain of pointer-type operands
3549 /// until reaching a SCEV that does not have a single pointer operand. This
3550 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3551 /// but corner cases do exist.
3552 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3553 // A pointer operand may evaluate to a nonpointer expression, such as null.
3554 if (!V->getType()->isPointerTy())
3557 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3558 return getPointerBase(Cast->getOperand());
3559 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3560 const SCEV *PtrOp = nullptr;
3561 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3563 if ((*I)->getType()->isPointerTy()) {
3564 // Cannot find the base of an expression with multiple pointer operands.
3572 return getPointerBase(PtrOp);
3577 /// PushDefUseChildren - Push users of the given Instruction
3578 /// onto the given Worklist.
3580 PushDefUseChildren(Instruction *I,
3581 SmallVectorImpl<Instruction *> &Worklist) {
3582 // Push the def-use children onto the Worklist stack.
3583 for (User *U : I->users())
3584 Worklist.push_back(cast<Instruction>(U));
3587 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3588 /// instructions that depend on the given instruction and removes them from
3589 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3592 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3593 SmallVector<Instruction *, 16> Worklist;
3594 PushDefUseChildren(PN, Worklist);
3596 SmallPtrSet<Instruction *, 8> Visited;
3598 while (!Worklist.empty()) {
3599 Instruction *I = Worklist.pop_back_val();
3600 if (!Visited.insert(I).second)
3603 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
3604 if (It != ValueExprMap.end()) {
3605 const SCEV *Old = It->second;
3607 // Short-circuit the def-use traversal if the symbolic name
3608 // ceases to appear in expressions.
3609 if (Old != SymName && !hasOperand(Old, SymName))
3612 // SCEVUnknown for a PHI either means that it has an unrecognized
3613 // structure, it's a PHI that's in the progress of being computed
3614 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3615 // additional loop trip count information isn't going to change anything.
3616 // In the second case, createNodeForPHI will perform the necessary
3617 // updates on its own when it gets to that point. In the third, we do
3618 // want to forget the SCEVUnknown.
3619 if (!isa<PHINode>(I) ||
3620 !isa<SCEVUnknown>(Old) ||
3621 (I != PN && Old == SymName)) {
3622 forgetMemoizedResults(Old);
3623 ValueExprMap.erase(It);
3627 PushDefUseChildren(I, Worklist);
3631 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
3632 const Loop *L = LI.getLoopFor(PN->getParent());
3633 if (!L || L->getHeader() != PN->getParent())
3636 // The loop may have multiple entrances or multiple exits; we can analyze
3637 // this phi as an addrec if it has a unique entry value and a unique
3639 Value *BEValueV = nullptr, *StartValueV = nullptr;
3640 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3641 Value *V = PN->getIncomingValue(i);
3642 if (L->contains(PN->getIncomingBlock(i))) {
3645 } else if (BEValueV != V) {
3649 } else if (!StartValueV) {
3651 } else if (StartValueV != V) {
3652 StartValueV = nullptr;
3656 if (BEValueV && StartValueV) {
3657 // While we are analyzing this PHI node, handle its value symbolically.
3658 const SCEV *SymbolicName = getUnknown(PN);
3659 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3660 "PHI node already processed?");
3661 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3663 // Using this symbolic name for the PHI, analyze the value coming around
3665 const SCEV *BEValue = getSCEV(BEValueV);
3667 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3668 // has a special value for the first iteration of the loop.
3670 // If the value coming around the backedge is an add with the symbolic
3671 // value we just inserted, then we found a simple induction variable!
3672 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3673 // If there is a single occurrence of the symbolic value, replace it
3674 // with a recurrence.
3675 unsigned FoundIndex = Add->getNumOperands();
3676 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3677 if (Add->getOperand(i) == SymbolicName)
3678 if (FoundIndex == e) {
3683 if (FoundIndex != Add->getNumOperands()) {
3684 // Create an add with everything but the specified operand.
3685 SmallVector<const SCEV *, 8> Ops;
3686 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3687 if (i != FoundIndex)
3688 Ops.push_back(Add->getOperand(i));
3689 const SCEV *Accum = getAddExpr(Ops);
3691 // This is not a valid addrec if the step amount is varying each
3692 // loop iteration, but is not itself an addrec in this loop.
3693 if (isLoopInvariant(Accum, L) ||
3694 (isa<SCEVAddRecExpr>(Accum) &&
3695 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3696 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3698 // If the increment doesn't overflow, then neither the addrec nor
3699 // the post-increment will overflow.
3700 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3701 if (OBO->getOperand(0) == PN) {
3702 if (OBO->hasNoUnsignedWrap())
3703 Flags = setFlags(Flags, SCEV::FlagNUW);
3704 if (OBO->hasNoSignedWrap())
3705 Flags = setFlags(Flags, SCEV::FlagNSW);
3707 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3708 // If the increment is an inbounds GEP, then we know the address
3709 // space cannot be wrapped around. We cannot make any guarantee
3710 // about signed or unsigned overflow because pointers are
3711 // unsigned but we may have a negative index from the base
3712 // pointer. We can guarantee that no unsigned wrap occurs if the
3713 // indices form a positive value.
3714 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3715 Flags = setFlags(Flags, SCEV::FlagNW);
3717 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3718 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3719 Flags = setFlags(Flags, SCEV::FlagNUW);
3722 // We cannot transfer nuw and nsw flags from subtraction
3723 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3727 const SCEV *StartVal = getSCEV(StartValueV);
3728 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3730 // Since the no-wrap flags are on the increment, they apply to the
3731 // post-incremented value as well.
3732 if (isLoopInvariant(Accum, L))
3733 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
3735 // Okay, for the entire analysis of this edge we assumed the PHI
3736 // to be symbolic. We now need to go back and purge all of the
3737 // entries for the scalars that use the symbolic expression.
3738 ForgetSymbolicName(PN, SymbolicName);
3739 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3743 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
3744 // Otherwise, this could be a loop like this:
3745 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3746 // In this case, j = {1,+,1} and BEValue is j.
3747 // Because the other in-value of i (0) fits the evolution of BEValue
3748 // i really is an addrec evolution.
3749 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3750 const SCEV *StartVal = getSCEV(StartValueV);
3752 // If StartVal = j.start - j.stride, we can use StartVal as the
3753 // initial step of the addrec evolution.
3755 getMinusSCEV(AddRec->getOperand(0), AddRec->getOperand(1))) {
3756 // FIXME: For constant StartVal, we should be able to infer
3758 const SCEV *PHISCEV = getAddRecExpr(StartVal, AddRec->getOperand(1),
3759 L, SCEV::FlagAnyWrap);
3761 // Okay, for the entire analysis of this edge we assumed the PHI
3762 // to be symbolic. We now need to go back and purge all of the
3763 // entries for the scalars that use the symbolic expression.
3764 ForgetSymbolicName(PN, SymbolicName);
3765 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3775 // Checks if the SCEV S is available at BB. S is considered available at BB
3776 // if S can be materialized at BB without introducing a fault.
3777 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
3779 struct CheckAvailable {
3780 bool TraversalDone = false;
3781 bool Available = true;
3783 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
3784 BasicBlock *BB = nullptr;
3787 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
3788 : L(L), BB(BB), DT(DT) {}
3790 bool setUnavailable() {
3791 TraversalDone = true;
3796 bool follow(const SCEV *S) {
3797 switch (S->getSCEVType()) {
3798 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
3799 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
3800 // These expressions are available if their operand(s) is/are.
3803 case scAddRecExpr: {
3804 // We allow add recurrences that are on the loop BB is in, or some
3805 // outer loop. This guarantees availability because the value of the
3806 // add recurrence at BB is simply the "current" value of the induction
3807 // variable. We can relax this in the future; for instance an add
3808 // recurrence on a sibling dominating loop is also available at BB.
3809 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
3810 if (L && (ARLoop == L || ARLoop->contains(L)))
3813 return setUnavailable();
3817 // For SCEVUnknown, we check for simple dominance.
3818 const auto *SU = cast<SCEVUnknown>(S);
3819 Value *V = SU->getValue();
3821 if (isa<Argument>(V))
3824 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
3827 return setUnavailable();
3831 case scCouldNotCompute:
3832 // We do not try to smart about these at all.
3833 return setUnavailable();
3835 llvm_unreachable("switch should be fully covered!");
3838 bool isDone() { return TraversalDone; }
3841 CheckAvailable CA(L, BB, DT);
3842 SCEVTraversal<CheckAvailable> ST(CA);
3845 return CA.Available;
3848 // Try to match a control flow sequence that branches out at BI and merges back
3849 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
3851 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
3852 Value *&C, Value *&LHS, Value *&RHS) {
3853 C = BI->getCondition();
3855 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
3856 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
3858 if (!LeftEdge.isSingleEdge())
3861 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
3863 Use &LeftUse = Merge->getOperandUse(0);
3864 Use &RightUse = Merge->getOperandUse(1);
3866 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
3872 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
3881 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
3882 if (PN->getNumIncomingValues() == 2) {
3883 const Loop *L = LI.getLoopFor(PN->getParent());
3887 // br %cond, label %left, label %right
3893 // V = phi [ %x, %left ], [ %y, %right ]
3895 // as "select %cond, %x, %y"
3897 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
3898 assert(IDom && "At least the entry block should dominate PN");
3900 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
3901 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
3903 if (BI && BI->isConditional() &&
3904 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
3905 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
3906 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
3907 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
3913 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3914 if (const SCEV *S = createAddRecFromPHI(PN))
3917 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
3920 // If the PHI has a single incoming value, follow that value, unless the
3921 // PHI's incoming blocks are in a different loop, in which case doing so
3922 // risks breaking LCSSA form. Instcombine would normally zap these, but
3923 // it doesn't have DominatorTree information, so it may miss cases.
3924 if (Value *V = SimplifyInstruction(PN, getDataLayout(), &TLI, &DT, &AC))
3925 if (LI.replacementPreservesLCSSAForm(PN, V))
3928 // If it's not a loop phi, we can't handle it yet.
3929 return getUnknown(PN);
3932 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
3936 // Handle "constant" branch or select. This can occur for instance when a
3937 // loop pass transforms an inner loop and moves on to process the outer loop.
3938 if (auto *CI = dyn_cast<ConstantInt>(Cond))
3939 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
3941 // Try to match some simple smax or umax patterns.
3942 auto *ICI = dyn_cast<ICmpInst>(Cond);
3944 return getUnknown(I);
3946 Value *LHS = ICI->getOperand(0);
3947 Value *RHS = ICI->getOperand(1);
3949 switch (ICI->getPredicate()) {
3950 case ICmpInst::ICMP_SLT:
3951 case ICmpInst::ICMP_SLE:
3952 std::swap(LHS, RHS);
3954 case ICmpInst::ICMP_SGT:
3955 case ICmpInst::ICMP_SGE:
3956 // a >s b ? a+x : b+x -> smax(a, b)+x
3957 // a >s b ? b+x : a+x -> smin(a, b)+x
3958 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
3959 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
3960 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
3961 const SCEV *LA = getSCEV(TrueVal);
3962 const SCEV *RA = getSCEV(FalseVal);
3963 const SCEV *LDiff = getMinusSCEV(LA, LS);
3964 const SCEV *RDiff = getMinusSCEV(RA, RS);
3966 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3967 LDiff = getMinusSCEV(LA, RS);
3968 RDiff = getMinusSCEV(RA, LS);
3970 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3973 case ICmpInst::ICMP_ULT:
3974 case ICmpInst::ICMP_ULE:
3975 std::swap(LHS, RHS);
3977 case ICmpInst::ICMP_UGT:
3978 case ICmpInst::ICMP_UGE:
3979 // a >u b ? a+x : b+x -> umax(a, b)+x
3980 // a >u b ? b+x : a+x -> umin(a, b)+x
3981 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
3982 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
3983 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
3984 const SCEV *LA = getSCEV(TrueVal);
3985 const SCEV *RA = getSCEV(FalseVal);
3986 const SCEV *LDiff = getMinusSCEV(LA, LS);
3987 const SCEV *RDiff = getMinusSCEV(RA, RS);
3989 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3990 LDiff = getMinusSCEV(LA, RS);
3991 RDiff = getMinusSCEV(RA, LS);
3993 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3996 case ICmpInst::ICMP_NE:
3997 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3998 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
3999 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4000 const SCEV *One = getOne(I->getType());
4001 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4002 const SCEV *LA = getSCEV(TrueVal);
4003 const SCEV *RA = getSCEV(FalseVal);
4004 const SCEV *LDiff = getMinusSCEV(LA, LS);
4005 const SCEV *RDiff = getMinusSCEV(RA, One);
4007 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4010 case ICmpInst::ICMP_EQ:
4011 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4012 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4013 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4014 const SCEV *One = getOne(I->getType());
4015 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4016 const SCEV *LA = getSCEV(TrueVal);
4017 const SCEV *RA = getSCEV(FalseVal);
4018 const SCEV *LDiff = getMinusSCEV(LA, One);
4019 const SCEV *RDiff = getMinusSCEV(RA, LS);
4021 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4028 return getUnknown(I);
4031 /// createNodeForGEP - Expand GEP instructions into add and multiply
4032 /// operations. This allows them to be analyzed by regular SCEV code.
4034 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
4035 Value *Base = GEP->getOperand(0);
4036 // Don't attempt to analyze GEPs over unsized objects.
4037 if (!Base->getType()->getPointerElementType()->isSized())
4038 return getUnknown(GEP);
4040 SmallVector<const SCEV *, 4> IndexExprs;
4041 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4042 IndexExprs.push_back(getSCEV(*Index));
4043 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
4047 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
4048 /// guaranteed to end in (at every loop iteration). It is, at the same time,
4049 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
4050 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
4052 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4053 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4054 return C->getValue()->getValue().countTrailingZeros();
4056 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4057 return std::min(GetMinTrailingZeros(T->getOperand()),
4058 (uint32_t)getTypeSizeInBits(T->getType()));
4060 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4061 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4062 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4063 getTypeSizeInBits(E->getType()) : OpRes;
4066 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4067 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4068 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4069 getTypeSizeInBits(E->getType()) : OpRes;
4072 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4073 // The result is the min of all operands results.
4074 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4075 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4076 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4080 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4081 // The result is the sum of all operands results.
4082 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4083 uint32_t BitWidth = getTypeSizeInBits(M->getType());
4084 for (unsigned i = 1, e = M->getNumOperands();
4085 SumOpRes != BitWidth && i != e; ++i)
4086 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4091 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4092 // The result is the min of all operands results.
4093 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4094 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4095 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4099 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4100 // The result is the min of all operands results.
4101 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4102 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4103 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4107 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4108 // The result is the min of all operands results.
4109 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4110 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4111 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4115 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4116 // For a SCEVUnknown, ask ValueTracking.
4117 unsigned BitWidth = getTypeSizeInBits(U->getType());
4118 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4119 computeKnownBits(U->getValue(), Zeros, Ones, getDataLayout(), 0, &AC,
4121 return Zeros.countTrailingOnes();
4128 /// GetRangeFromMetadata - Helper method to assign a range to V from
4129 /// metadata present in the IR.
4130 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4131 if (Instruction *I = dyn_cast<Instruction>(V))
4132 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
4133 return getConstantRangeFromMetadata(*MD);
4138 /// getRange - Determine the range for a particular SCEV. If SignHint is
4139 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4140 /// with a "cleaner" unsigned (resp. signed) representation.
4143 ScalarEvolution::getRange(const SCEV *S,
4144 ScalarEvolution::RangeSignHint SignHint) {
4145 DenseMap<const SCEV *, ConstantRange> &Cache =
4146 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4149 // See if we've computed this range already.
4150 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4151 if (I != Cache.end())
4154 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4155 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
4157 unsigned BitWidth = getTypeSizeInBits(S->getType());
4158 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4160 // If the value has known zeros, the maximum value will have those known zeros
4162 uint32_t TZ = GetMinTrailingZeros(S);
4164 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4165 ConservativeResult =
4166 ConstantRange(APInt::getMinValue(BitWidth),
4167 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4169 ConservativeResult = ConstantRange(
4170 APInt::getSignedMinValue(BitWidth),
4171 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4174 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4175 ConstantRange X = getRange(Add->getOperand(0), SignHint);
4176 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4177 X = X.add(getRange(Add->getOperand(i), SignHint));
4178 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4181 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4182 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4183 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4184 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4185 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4188 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4189 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4190 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4191 X = X.smax(getRange(SMax->getOperand(i), SignHint));
4192 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4195 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4196 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4197 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4198 X = X.umax(getRange(UMax->getOperand(i), SignHint));
4199 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4202 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4203 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4204 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4205 return setRange(UDiv, SignHint,
4206 ConservativeResult.intersectWith(X.udiv(Y)));
4209 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4210 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4211 return setRange(ZExt, SignHint,
4212 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4215 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4216 ConstantRange X = getRange(SExt->getOperand(), SignHint);
4217 return setRange(SExt, SignHint,
4218 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4221 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4222 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4223 return setRange(Trunc, SignHint,
4224 ConservativeResult.intersectWith(X.truncate(BitWidth)));
4227 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4228 // If there's no unsigned wrap, the value will never be less than its
4230 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
4231 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4232 if (!C->getValue()->isZero())
4233 ConservativeResult =
4234 ConservativeResult.intersectWith(
4235 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
4237 // If there's no signed wrap, and all the operands have the same sign or
4238 // zero, the value won't ever change sign.
4239 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
4240 bool AllNonNeg = true;
4241 bool AllNonPos = true;
4242 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4243 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4244 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4247 ConservativeResult = ConservativeResult.intersectWith(
4248 ConstantRange(APInt(BitWidth, 0),
4249 APInt::getSignedMinValue(BitWidth)));
4251 ConservativeResult = ConservativeResult.intersectWith(
4252 ConstantRange(APInt::getSignedMinValue(BitWidth),
4253 APInt(BitWidth, 1)));
4256 // TODO: non-affine addrec
4257 if (AddRec->isAffine()) {
4258 Type *Ty = AddRec->getType();
4259 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4260 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4261 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4263 // Check for overflow. This must be done with ConstantRange arithmetic
4264 // because we could be called from within the ScalarEvolution overflow
4267 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4268 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4269 ConstantRange ZExtMaxBECountRange =
4270 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4272 const SCEV *Start = AddRec->getStart();
4273 const SCEV *Step = AddRec->getStepRecurrence(*this);
4274 ConstantRange StepSRange = getSignedRange(Step);
4275 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4277 ConstantRange StartURange = getUnsignedRange(Start);
4278 ConstantRange EndURange =
4279 StartURange.add(MaxBECountRange.multiply(StepSRange));
4281 // Check for unsigned overflow.
4282 ConstantRange ZExtStartURange =
4283 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4284 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4285 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4287 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4288 EndURange.getUnsignedMin());
4289 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4290 EndURange.getUnsignedMax());
4291 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4293 ConservativeResult =
4294 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4297 ConstantRange StartSRange = getSignedRange(Start);
4298 ConstantRange EndSRange =
4299 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4301 // Check for signed overflow. This must be done with ConstantRange
4302 // arithmetic because we could be called from within the ScalarEvolution
4303 // overflow checking code.
4304 ConstantRange SExtStartSRange =
4305 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4306 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4307 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4309 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4310 EndSRange.getSignedMin());
4311 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4312 EndSRange.getSignedMax());
4313 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4315 ConservativeResult =
4316 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4321 return setRange(AddRec, SignHint, ConservativeResult);
4324 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4325 // Check if the IR explicitly contains !range metadata.
4326 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4327 if (MDRange.hasValue())
4328 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4330 // Split here to avoid paying the compile-time cost of calling both
4331 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4333 const DataLayout &DL = getDataLayout();
4334 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4335 // For a SCEVUnknown, ask ValueTracking.
4336 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4337 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4338 if (Ones != ~Zeros + 1)
4339 ConservativeResult =
4340 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4342 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4343 "generalize as needed!");
4344 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4346 ConservativeResult = ConservativeResult.intersectWith(
4347 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4348 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4351 return setRange(U, SignHint, ConservativeResult);
4354 return setRange(S, SignHint, ConservativeResult);
4357 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4358 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4359 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4361 // Return early if there are no flags to propagate to the SCEV.
4362 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4363 if (BinOp->hasNoUnsignedWrap())
4364 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4365 if (BinOp->hasNoSignedWrap())
4366 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4367 if (Flags == SCEV::FlagAnyWrap) {
4368 return SCEV::FlagAnyWrap;
4371 // Here we check that BinOp is in the header of the innermost loop
4372 // containing BinOp, since we only deal with instructions in the loop
4373 // header. The actual loop we need to check later will come from an add
4374 // recurrence, but getting that requires computing the SCEV of the operands,
4375 // which can be expensive. This check we can do cheaply to rule out some
4377 Loop *innermostContainingLoop = LI.getLoopFor(BinOp->getParent());
4378 if (innermostContainingLoop == nullptr ||
4379 innermostContainingLoop->getHeader() != BinOp->getParent())
4380 return SCEV::FlagAnyWrap;
4382 // Only proceed if we can prove that BinOp does not yield poison.
4383 if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
4385 // At this point we know that if V is executed, then it does not wrap
4386 // according to at least one of NSW or NUW. If V is not executed, then we do
4387 // not know if the calculation that V represents would wrap. Multiple
4388 // instructions can map to the same SCEV. If we apply NSW or NUW from V to
4389 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4390 // derived from other instructions that map to the same SCEV. We cannot make
4391 // that guarantee for cases where V is not executed. So we need to find the
4392 // loop that V is considered in relation to and prove that V is executed for
4393 // every iteration of that loop. That implies that the value that V
4394 // calculates does not wrap anywhere in the loop, so then we can apply the
4395 // flags to the SCEV.
4397 // We check isLoopInvariant to disambiguate in case we are adding two
4398 // recurrences from different loops, so that we know which loop to prove
4399 // that V is executed in.
4400 for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
4401 const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
4402 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4403 const int OtherOpIndex = 1 - OpIndex;
4404 const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
4405 if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
4406 isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
4410 return SCEV::FlagAnyWrap;
4413 /// createSCEV - We know that there is no SCEV for the specified value. Analyze
4416 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4417 if (!isSCEVable(V->getType()))
4418 return getUnknown(V);
4420 unsigned Opcode = Instruction::UserOp1;
4421 if (Instruction *I = dyn_cast<Instruction>(V)) {
4422 Opcode = I->getOpcode();
4424 // Don't attempt to analyze instructions in blocks that aren't
4425 // reachable. Such instructions don't matter, and they aren't required
4426 // to obey basic rules for definitions dominating uses which this
4427 // analysis depends on.
4428 if (!DT.isReachableFromEntry(I->getParent()))
4429 return getUnknown(V);
4430 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4431 Opcode = CE->getOpcode();
4432 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4433 return getConstant(CI);
4434 else if (isa<ConstantPointerNull>(V))
4435 return getZero(V->getType());
4436 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4437 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4439 return getUnknown(V);
4441 Operator *U = cast<Operator>(V);
4443 case Instruction::Add: {
4444 // The simple thing to do would be to just call getSCEV on both operands
4445 // and call getAddExpr with the result. However if we're looking at a
4446 // bunch of things all added together, this can be quite inefficient,
4447 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4448 // Instead, gather up all the operands and make a single getAddExpr call.
4449 // LLVM IR canonical form means we need only traverse the left operands.
4450 SmallVector<const SCEV *, 4> AddOps;
4451 for (Value *Op = U;; Op = U->getOperand(0)) {
4452 U = dyn_cast<Operator>(Op);
4453 unsigned Opcode = U ? U->getOpcode() : 0;
4454 if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
4455 assert(Op != V && "V should be an add");
4456 AddOps.push_back(getSCEV(Op));
4460 if (auto *OpSCEV = getExistingSCEV(U)) {
4461 AddOps.push_back(OpSCEV);
4465 // If a NUW or NSW flag can be applied to the SCEV for this
4466 // addition, then compute the SCEV for this addition by itself
4467 // with a separate call to getAddExpr. We need to do that
4468 // instead of pushing the operands of the addition onto AddOps,
4469 // since the flags are only known to apply to this particular
4470 // addition - they may not apply to other additions that can be
4471 // formed with operands from AddOps.
4472 const SCEV *RHS = getSCEV(U->getOperand(1));
4473 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4474 if (Flags != SCEV::FlagAnyWrap) {
4475 const SCEV *LHS = getSCEV(U->getOperand(0));
4476 if (Opcode == Instruction::Sub)
4477 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4479 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4483 if (Opcode == Instruction::Sub)
4484 AddOps.push_back(getNegativeSCEV(RHS));
4486 AddOps.push_back(RHS);
4488 return getAddExpr(AddOps);
4491 case Instruction::Mul: {
4492 SmallVector<const SCEV *, 4> MulOps;
4493 for (Value *Op = U;; Op = U->getOperand(0)) {
4494 U = dyn_cast<Operator>(Op);
4495 if (!U || U->getOpcode() != Instruction::Mul) {
4496 assert(Op != V && "V should be a mul");
4497 MulOps.push_back(getSCEV(Op));
4501 if (auto *OpSCEV = getExistingSCEV(U)) {
4502 MulOps.push_back(OpSCEV);
4506 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4507 if (Flags != SCEV::FlagAnyWrap) {
4508 MulOps.push_back(getMulExpr(getSCEV(U->getOperand(0)),
4509 getSCEV(U->getOperand(1)), Flags));
4513 MulOps.push_back(getSCEV(U->getOperand(1)));
4515 return getMulExpr(MulOps);
4517 case Instruction::UDiv:
4518 return getUDivExpr(getSCEV(U->getOperand(0)),
4519 getSCEV(U->getOperand(1)));
4520 case Instruction::Sub:
4521 return getMinusSCEV(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)),
4522 getNoWrapFlagsFromUB(U));
4523 case Instruction::And:
4524 // For an expression like x&255 that merely masks off the high bits,
4525 // use zext(trunc(x)) as the SCEV expression.
4526 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4527 if (CI->isNullValue())
4528 return getSCEV(U->getOperand(1));
4529 if (CI->isAllOnesValue())
4530 return getSCEV(U->getOperand(0));
4531 const APInt &A = CI->getValue();
4533 // Instcombine's ShrinkDemandedConstant may strip bits out of
4534 // constants, obscuring what would otherwise be a low-bits mask.
4535 // Use computeKnownBits to compute what ShrinkDemandedConstant
4536 // knew about to reconstruct a low-bits mask value.
4537 unsigned LZ = A.countLeadingZeros();
4538 unsigned TZ = A.countTrailingZeros();
4539 unsigned BitWidth = A.getBitWidth();
4540 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4541 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, getDataLayout(),
4542 0, &AC, nullptr, &DT);
4544 APInt EffectiveMask =
4545 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4546 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4547 const SCEV *MulCount = getConstant(
4548 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4552 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4553 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4560 case Instruction::Or:
4561 // If the RHS of the Or is a constant, we may have something like:
4562 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4563 // optimizations will transparently handle this case.
4565 // In order for this transformation to be safe, the LHS must be of the
4566 // form X*(2^n) and the Or constant must be less than 2^n.
4567 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4568 const SCEV *LHS = getSCEV(U->getOperand(0));
4569 const APInt &CIVal = CI->getValue();
4570 if (GetMinTrailingZeros(LHS) >=
4571 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4572 // Build a plain add SCEV.
4573 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4574 // If the LHS of the add was an addrec and it has no-wrap flags,
4575 // transfer the no-wrap flags, since an or won't introduce a wrap.
4576 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4577 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4578 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4579 OldAR->getNoWrapFlags());
4585 case Instruction::Xor:
4586 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4587 // If the RHS of the xor is a signbit, then this is just an add.
4588 // Instcombine turns add of signbit into xor as a strength reduction step.
4589 if (CI->getValue().isSignBit())
4590 return getAddExpr(getSCEV(U->getOperand(0)),
4591 getSCEV(U->getOperand(1)));
4593 // If the RHS of xor is -1, then this is a not operation.
4594 if (CI->isAllOnesValue())
4595 return getNotSCEV(getSCEV(U->getOperand(0)));
4597 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4598 // This is a variant of the check for xor with -1, and it handles
4599 // the case where instcombine has trimmed non-demanded bits out
4600 // of an xor with -1.
4601 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4602 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4603 if (BO->getOpcode() == Instruction::And &&
4604 LCI->getValue() == CI->getValue())
4605 if (const SCEVZeroExtendExpr *Z =
4606 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4607 Type *UTy = U->getType();
4608 const SCEV *Z0 = Z->getOperand();
4609 Type *Z0Ty = Z0->getType();
4610 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4612 // If C is a low-bits mask, the zero extend is serving to
4613 // mask off the high bits. Complement the operand and
4614 // re-apply the zext.
4615 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4616 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4618 // If C is a single bit, it may be in the sign-bit position
4619 // before the zero-extend. In this case, represent the xor
4620 // using an add, which is equivalent, and re-apply the zext.
4621 APInt Trunc = CI->getValue().trunc(Z0TySize);
4622 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4624 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4630 case Instruction::Shl:
4631 // Turn shift left of a constant amount into a multiply.
4632 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4633 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4635 // If the shift count is not less than the bitwidth, the result of
4636 // the shift is undefined. Don't try to analyze it, because the
4637 // resolution chosen here may differ from the resolution chosen in
4638 // other parts of the compiler.
4639 if (SA->getValue().uge(BitWidth))
4642 // It is currently not resolved how to interpret NSW for left
4643 // shift by BitWidth - 1, so we avoid applying flags in that
4644 // case. Remove this check (or this comment) once the situation
4646 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
4647 // and http://reviews.llvm.org/D8890 .
4648 auto Flags = SCEV::FlagAnyWrap;
4649 if (SA->getValue().ult(BitWidth - 1)) Flags = getNoWrapFlagsFromUB(U);
4651 Constant *X = ConstantInt::get(getContext(),
4652 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4653 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X), Flags);
4657 case Instruction::LShr:
4658 // Turn logical shift right of a constant into a unsigned divide.
4659 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4660 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4662 // If the shift count is not less than the bitwidth, the result of
4663 // the shift is undefined. Don't try to analyze it, because the
4664 // resolution chosen here may differ from the resolution chosen in
4665 // other parts of the compiler.
4666 if (SA->getValue().uge(BitWidth))
4669 Constant *X = ConstantInt::get(getContext(),
4670 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4671 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4675 case Instruction::AShr:
4676 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4677 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4678 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4679 if (L->getOpcode() == Instruction::Shl &&
4680 L->getOperand(1) == U->getOperand(1)) {
4681 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4683 // If the shift count is not less than the bitwidth, the result of
4684 // the shift is undefined. Don't try to analyze it, because the
4685 // resolution chosen here may differ from the resolution chosen in
4686 // other parts of the compiler.
4687 if (CI->getValue().uge(BitWidth))
4690 uint64_t Amt = BitWidth - CI->getZExtValue();
4691 if (Amt == BitWidth)
4692 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4694 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4695 IntegerType::get(getContext(),
4701 case Instruction::Trunc:
4702 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4704 case Instruction::ZExt:
4705 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4707 case Instruction::SExt:
4708 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4710 case Instruction::BitCast:
4711 // BitCasts are no-op casts so we just eliminate the cast.
4712 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4713 return getSCEV(U->getOperand(0));
4716 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4717 // lead to pointer expressions which cannot safely be expanded to GEPs,
4718 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4719 // simplifying integer expressions.
4721 case Instruction::GetElementPtr:
4722 return createNodeForGEP(cast<GEPOperator>(U));
4724 case Instruction::PHI:
4725 return createNodeForPHI(cast<PHINode>(U));
4727 case Instruction::Select:
4728 // U can also be a select constant expr, which let fall through. Since
4729 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
4730 // constant expressions cannot have instructions as operands, we'd have
4731 // returned getUnknown for a select constant expressions anyway.
4732 if (isa<Instruction>(U))
4733 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
4734 U->getOperand(1), U->getOperand(2));
4736 default: // We cannot analyze this expression.
4740 return getUnknown(V);
4745 //===----------------------------------------------------------------------===//
4746 // Iteration Count Computation Code
4749 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4750 if (BasicBlock *ExitingBB = L->getExitingBlock())
4751 return getSmallConstantTripCount(L, ExitingBB);
4753 // No trip count information for multiple exits.
4757 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4758 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4759 /// constant. Will also return 0 if the maximum trip count is very large (>=
4762 /// This "trip count" assumes that control exits via ExitingBlock. More
4763 /// precisely, it is the number of times that control may reach ExitingBlock
4764 /// before taking the branch. For loops with multiple exits, it may not be the
4765 /// number times that the loop header executes because the loop may exit
4766 /// prematurely via another branch.
4767 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4768 BasicBlock *ExitingBlock) {
4769 assert(ExitingBlock && "Must pass a non-null exiting block!");
4770 assert(L->isLoopExiting(ExitingBlock) &&
4771 "Exiting block must actually branch out of the loop!");
4772 const SCEVConstant *ExitCount =
4773 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4777 ConstantInt *ExitConst = ExitCount->getValue();
4779 // Guard against huge trip counts.
4780 if (ExitConst->getValue().getActiveBits() > 32)
4783 // In case of integer overflow, this returns 0, which is correct.
4784 return ((unsigned)ExitConst->getZExtValue()) + 1;
4787 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4788 if (BasicBlock *ExitingBB = L->getExitingBlock())
4789 return getSmallConstantTripMultiple(L, ExitingBB);
4791 // No trip multiple information for multiple exits.
4795 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4796 /// trip count of this loop as a normal unsigned value, if possible. This
4797 /// means that the actual trip count is always a multiple of the returned
4798 /// value (don't forget the trip count could very well be zero as well!).
4800 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4801 /// multiple of a constant (which is also the case if the trip count is simply
4802 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4803 /// if the trip count is very large (>= 2^32).
4805 /// As explained in the comments for getSmallConstantTripCount, this assumes
4806 /// that control exits the loop via ExitingBlock.
4808 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4809 BasicBlock *ExitingBlock) {
4810 assert(ExitingBlock && "Must pass a non-null exiting block!");
4811 assert(L->isLoopExiting(ExitingBlock) &&
4812 "Exiting block must actually branch out of the loop!");
4813 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4814 if (ExitCount == getCouldNotCompute())
4817 // Get the trip count from the BE count by adding 1.
4818 const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
4819 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4820 // to factor simple cases.
4821 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4822 TCMul = Mul->getOperand(0);
4824 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4828 ConstantInt *Result = MulC->getValue();
4830 // Guard against huge trip counts (this requires checking
4831 // for zero to handle the case where the trip count == -1 and the
4833 if (!Result || Result->getValue().getActiveBits() > 32 ||
4834 Result->getValue().getActiveBits() == 0)
4837 return (unsigned)Result->getZExtValue();
4840 // getExitCount - Get the expression for the number of loop iterations for which
4841 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4842 // SCEVCouldNotCompute.
4843 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4844 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4847 /// getBackedgeTakenCount - If the specified loop has a predictable
4848 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4849 /// object. The backedge-taken count is the number of times the loop header
4850 /// will be branched to from within the loop. This is one less than the
4851 /// trip count of the loop, since it doesn't count the first iteration,
4852 /// when the header is branched to from outside the loop.
4854 /// Note that it is not valid to call this method on a loop without a
4855 /// loop-invariant backedge-taken count (see
4856 /// hasLoopInvariantBackedgeTakenCount).
4858 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4859 return getBackedgeTakenInfo(L).getExact(this);
4862 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4863 /// return the least SCEV value that is known never to be less than the
4864 /// actual backedge taken count.
4865 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4866 return getBackedgeTakenInfo(L).getMax(this);
4869 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4870 /// onto the given Worklist.
4872 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4873 BasicBlock *Header = L->getHeader();
4875 // Push all Loop-header PHIs onto the Worklist stack.
4876 for (BasicBlock::iterator I = Header->begin();
4877 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4878 Worklist.push_back(PN);
4881 const ScalarEvolution::BackedgeTakenInfo &
4882 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4883 // Initially insert an invalid entry for this loop. If the insertion
4884 // succeeds, proceed to actually compute a backedge-taken count and
4885 // update the value. The temporary CouldNotCompute value tells SCEV
4886 // code elsewhere that it shouldn't attempt to request a new
4887 // backedge-taken count, which could result in infinite recursion.
4888 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4889 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4891 return Pair.first->second;
4893 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
4894 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4895 // must be cleared in this scope.
4896 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
4898 if (Result.getExact(this) != getCouldNotCompute()) {
4899 assert(isLoopInvariant(Result.getExact(this), L) &&
4900 isLoopInvariant(Result.getMax(this), L) &&
4901 "Computed backedge-taken count isn't loop invariant for loop!");
4902 ++NumTripCountsComputed;
4904 else if (Result.getMax(this) == getCouldNotCompute() &&
4905 isa<PHINode>(L->getHeader()->begin())) {
4906 // Only count loops that have phi nodes as not being computable.
4907 ++NumTripCountsNotComputed;
4910 // Now that we know more about the trip count for this loop, forget any
4911 // existing SCEV values for PHI nodes in this loop since they are only
4912 // conservative estimates made without the benefit of trip count
4913 // information. This is similar to the code in forgetLoop, except that
4914 // it handles SCEVUnknown PHI nodes specially.
4915 if (Result.hasAnyInfo()) {
4916 SmallVector<Instruction *, 16> Worklist;
4917 PushLoopPHIs(L, Worklist);
4919 SmallPtrSet<Instruction *, 8> Visited;
4920 while (!Worklist.empty()) {
4921 Instruction *I = Worklist.pop_back_val();
4922 if (!Visited.insert(I).second)
4925 ValueExprMapType::iterator It =
4926 ValueExprMap.find_as(static_cast<Value *>(I));
4927 if (It != ValueExprMap.end()) {
4928 const SCEV *Old = It->second;
4930 // SCEVUnknown for a PHI either means that it has an unrecognized
4931 // structure, or it's a PHI that's in the progress of being computed
4932 // by createNodeForPHI. In the former case, additional loop trip
4933 // count information isn't going to change anything. In the later
4934 // case, createNodeForPHI will perform the necessary updates on its
4935 // own when it gets to that point.
4936 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4937 forgetMemoizedResults(Old);
4938 ValueExprMap.erase(It);
4940 if (PHINode *PN = dyn_cast<PHINode>(I))
4941 ConstantEvolutionLoopExitValue.erase(PN);
4944 PushDefUseChildren(I, Worklist);
4948 // Re-lookup the insert position, since the call to
4949 // computeBackedgeTakenCount above could result in a
4950 // recusive call to getBackedgeTakenInfo (on a different
4951 // loop), which would invalidate the iterator computed
4953 return BackedgeTakenCounts.find(L)->second = Result;
4956 /// forgetLoop - This method should be called by the client when it has
4957 /// changed a loop in a way that may effect ScalarEvolution's ability to
4958 /// compute a trip count, or if the loop is deleted.
4959 void ScalarEvolution::forgetLoop(const Loop *L) {
4960 // Drop any stored trip count value.
4961 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4962 BackedgeTakenCounts.find(L);
4963 if (BTCPos != BackedgeTakenCounts.end()) {
4964 BTCPos->second.clear();
4965 BackedgeTakenCounts.erase(BTCPos);
4968 // Drop information about expressions based on loop-header PHIs.
4969 SmallVector<Instruction *, 16> Worklist;
4970 PushLoopPHIs(L, Worklist);
4972 SmallPtrSet<Instruction *, 8> Visited;
4973 while (!Worklist.empty()) {
4974 Instruction *I = Worklist.pop_back_val();
4975 if (!Visited.insert(I).second)
4978 ValueExprMapType::iterator It =
4979 ValueExprMap.find_as(static_cast<Value *>(I));
4980 if (It != ValueExprMap.end()) {
4981 forgetMemoizedResults(It->second);
4982 ValueExprMap.erase(It);
4983 if (PHINode *PN = dyn_cast<PHINode>(I))
4984 ConstantEvolutionLoopExitValue.erase(PN);
4987 PushDefUseChildren(I, Worklist);
4990 // Forget all contained loops too, to avoid dangling entries in the
4991 // ValuesAtScopes map.
4992 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4996 /// forgetValue - This method should be called by the client when it has
4997 /// changed a value in a way that may effect its value, or which may
4998 /// disconnect it from a def-use chain linking it to a loop.
4999 void ScalarEvolution::forgetValue(Value *V) {
5000 Instruction *I = dyn_cast<Instruction>(V);
5003 // Drop information about expressions based on loop-header PHIs.
5004 SmallVector<Instruction *, 16> Worklist;
5005 Worklist.push_back(I);
5007 SmallPtrSet<Instruction *, 8> Visited;
5008 while (!Worklist.empty()) {
5009 I = Worklist.pop_back_val();
5010 if (!Visited.insert(I).second)
5013 ValueExprMapType::iterator It =
5014 ValueExprMap.find_as(static_cast<Value *>(I));
5015 if (It != ValueExprMap.end()) {
5016 forgetMemoizedResults(It->second);
5017 ValueExprMap.erase(It);
5018 if (PHINode *PN = dyn_cast<PHINode>(I))
5019 ConstantEvolutionLoopExitValue.erase(PN);
5022 PushDefUseChildren(I, Worklist);
5026 /// getExact - Get the exact loop backedge taken count considering all loop
5027 /// exits. A computable result can only be returned for loops with a single
5028 /// exit. Returning the minimum taken count among all exits is incorrect
5029 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
5030 /// assumes that the limit of each loop test is never skipped. This is a valid
5031 /// assumption as long as the loop exits via that test. For precise results, it
5032 /// is the caller's responsibility to specify the relevant loop exit using
5033 /// getExact(ExitingBlock, SE).
5035 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
5036 // If any exits were not computable, the loop is not computable.
5037 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
5039 // We need exactly one computable exit.
5040 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
5041 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
5043 const SCEV *BECount = nullptr;
5044 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5045 ENT != nullptr; ENT = ENT->getNextExit()) {
5047 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5050 BECount = ENT->ExactNotTaken;
5051 else if (BECount != ENT->ExactNotTaken)
5052 return SE->getCouldNotCompute();
5054 assert(BECount && "Invalid not taken count for loop exit");
5058 /// getExact - Get the exact not taken count for this loop exit.
5060 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5061 ScalarEvolution *SE) const {
5062 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5063 ENT != nullptr; ENT = ENT->getNextExit()) {
5065 if (ENT->ExitingBlock == ExitingBlock)
5066 return ENT->ExactNotTaken;
5068 return SE->getCouldNotCompute();
5071 /// getMax - Get the max backedge taken count for the loop.
5073 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5074 return Max ? Max : SE->getCouldNotCompute();
5077 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5078 ScalarEvolution *SE) const {
5079 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
5082 if (!ExitNotTaken.ExitingBlock)
5085 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5086 ENT != nullptr; ENT = ENT->getNextExit()) {
5088 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
5089 && SE->hasOperand(ENT->ExactNotTaken, S)) {
5096 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5097 /// computable exit into a persistent ExitNotTakenInfo array.
5098 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5099 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
5100 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
5103 ExitNotTaken.setIncomplete();
5105 unsigned NumExits = ExitCounts.size();
5106 if (NumExits == 0) return;
5108 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
5109 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
5110 if (NumExits == 1) return;
5112 // Handle the rare case of multiple computable exits.
5113 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
5115 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
5116 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
5117 PrevENT->setNextExit(ENT);
5118 ENT->ExitingBlock = ExitCounts[i].first;
5119 ENT->ExactNotTaken = ExitCounts[i].second;
5123 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
5124 void ScalarEvolution::BackedgeTakenInfo::clear() {
5125 ExitNotTaken.ExitingBlock = nullptr;
5126 ExitNotTaken.ExactNotTaken = nullptr;
5127 delete[] ExitNotTaken.getNextExit();
5130 /// computeBackedgeTakenCount - Compute the number of times the backedge
5131 /// of the specified loop will execute.
5132 ScalarEvolution::BackedgeTakenInfo
5133 ScalarEvolution::computeBackedgeTakenCount(const Loop *L) {
5134 SmallVector<BasicBlock *, 8> ExitingBlocks;
5135 L->getExitingBlocks(ExitingBlocks);
5137 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
5138 bool CouldComputeBECount = true;
5139 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5140 const SCEV *MustExitMaxBECount = nullptr;
5141 const SCEV *MayExitMaxBECount = nullptr;
5143 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5144 // and compute maxBECount.
5145 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5146 BasicBlock *ExitBB = ExitingBlocks[i];
5147 ExitLimit EL = computeExitLimit(L, ExitBB);
5149 // 1. For each exit that can be computed, add an entry to ExitCounts.
5150 // CouldComputeBECount is true only if all exits can be computed.
5151 if (EL.Exact == getCouldNotCompute())
5152 // We couldn't compute an exact value for this exit, so
5153 // we won't be able to compute an exact value for the loop.
5154 CouldComputeBECount = false;
5156 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
5158 // 2. Derive the loop's MaxBECount from each exit's max number of
5159 // non-exiting iterations. Partition the loop exits into two kinds:
5160 // LoopMustExits and LoopMayExits.
5162 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5163 // is a LoopMayExit. If any computable LoopMustExit is found, then
5164 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
5165 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
5166 // considered greater than any computable EL.Max.
5167 if (EL.Max != getCouldNotCompute() && Latch &&
5168 DT.dominates(ExitBB, Latch)) {
5169 if (!MustExitMaxBECount)
5170 MustExitMaxBECount = EL.Max;
5172 MustExitMaxBECount =
5173 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5175 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5176 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5177 MayExitMaxBECount = EL.Max;
5180 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5184 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5185 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5186 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5189 ScalarEvolution::ExitLimit
5190 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
5192 // Okay, we've chosen an exiting block. See what condition causes us to exit
5193 // at this block and remember the exit block and whether all other targets
5194 // lead to the loop header.
5195 bool MustExecuteLoopHeader = true;
5196 BasicBlock *Exit = nullptr;
5197 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5199 if (!L->contains(*SI)) {
5200 if (Exit) // Multiple exit successors.
5201 return getCouldNotCompute();
5203 } else if (*SI != L->getHeader()) {
5204 MustExecuteLoopHeader = false;
5207 // At this point, we know we have a conditional branch that determines whether
5208 // the loop is exited. However, we don't know if the branch is executed each
5209 // time through the loop. If not, then the execution count of the branch will
5210 // not be equal to the trip count of the loop.
5212 // Currently we check for this by checking to see if the Exit branch goes to
5213 // the loop header. If so, we know it will always execute the same number of
5214 // times as the loop. We also handle the case where the exit block *is* the
5215 // loop header. This is common for un-rotated loops.
5217 // If both of those tests fail, walk up the unique predecessor chain to the
5218 // header, stopping if there is an edge that doesn't exit the loop. If the
5219 // header is reached, the execution count of the branch will be equal to the
5220 // trip count of the loop.
5222 // More extensive analysis could be done to handle more cases here.
5224 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5225 // The simple checks failed, try climbing the unique predecessor chain
5226 // up to the header.
5228 for (BasicBlock *BB = ExitingBlock; BB; ) {
5229 BasicBlock *Pred = BB->getUniquePredecessor();
5231 return getCouldNotCompute();
5232 TerminatorInst *PredTerm = Pred->getTerminator();
5233 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5236 // If the predecessor has a successor that isn't BB and isn't
5237 // outside the loop, assume the worst.
5238 if (L->contains(PredSucc))
5239 return getCouldNotCompute();
5241 if (Pred == L->getHeader()) {
5248 return getCouldNotCompute();
5251 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5252 TerminatorInst *Term = ExitingBlock->getTerminator();
5253 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5254 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5255 // Proceed to the next level to examine the exit condition expression.
5256 return computeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5257 BI->getSuccessor(1),
5258 /*ControlsExit=*/IsOnlyExit);
5261 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5262 return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
5263 /*ControlsExit=*/IsOnlyExit);
5265 return getCouldNotCompute();
5268 /// computeExitLimitFromCond - Compute the number of times the
5269 /// backedge of the specified loop will execute if its exit condition
5270 /// were a conditional branch of ExitCond, TBB, and FBB.
5272 /// @param ControlsExit is true if ExitCond directly controls the exit
5273 /// branch. In this case, we can assume that the loop exits only if the
5274 /// condition is true and can infer that failing to meet the condition prior to
5275 /// integer wraparound results in undefined behavior.
5276 ScalarEvolution::ExitLimit
5277 ScalarEvolution::computeExitLimitFromCond(const Loop *L,
5281 bool ControlsExit) {
5282 // Check if the controlling expression for this loop is an And or Or.
5283 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5284 if (BO->getOpcode() == Instruction::And) {
5285 // Recurse on the operands of the and.
5286 bool EitherMayExit = L->contains(TBB);
5287 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5288 ControlsExit && !EitherMayExit);
5289 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5290 ControlsExit && !EitherMayExit);
5291 const SCEV *BECount = getCouldNotCompute();
5292 const SCEV *MaxBECount = getCouldNotCompute();
5293 if (EitherMayExit) {
5294 // Both conditions must be true for the loop to continue executing.
5295 // Choose the less conservative count.
5296 if (EL0.Exact == getCouldNotCompute() ||
5297 EL1.Exact == getCouldNotCompute())
5298 BECount = getCouldNotCompute();
5300 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5301 if (EL0.Max == getCouldNotCompute())
5302 MaxBECount = EL1.Max;
5303 else if (EL1.Max == getCouldNotCompute())
5304 MaxBECount = EL0.Max;
5306 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5308 // Both conditions must be true at the same time for the loop to exit.
5309 // For now, be conservative.
5310 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5311 if (EL0.Max == EL1.Max)
5312 MaxBECount = EL0.Max;
5313 if (EL0.Exact == EL1.Exact)
5314 BECount = EL0.Exact;
5317 return ExitLimit(BECount, MaxBECount);
5319 if (BO->getOpcode() == Instruction::Or) {
5320 // Recurse on the operands of the or.
5321 bool EitherMayExit = L->contains(FBB);
5322 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5323 ControlsExit && !EitherMayExit);
5324 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5325 ControlsExit && !EitherMayExit);
5326 const SCEV *BECount = getCouldNotCompute();
5327 const SCEV *MaxBECount = getCouldNotCompute();
5328 if (EitherMayExit) {
5329 // Both conditions must be false for the loop to continue executing.
5330 // Choose the less conservative count.
5331 if (EL0.Exact == getCouldNotCompute() ||
5332 EL1.Exact == getCouldNotCompute())
5333 BECount = getCouldNotCompute();
5335 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5336 if (EL0.Max == getCouldNotCompute())
5337 MaxBECount = EL1.Max;
5338 else if (EL1.Max == getCouldNotCompute())
5339 MaxBECount = EL0.Max;
5341 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5343 // Both conditions must be false at the same time for the loop to exit.
5344 // For now, be conservative.
5345 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5346 if (EL0.Max == EL1.Max)
5347 MaxBECount = EL0.Max;
5348 if (EL0.Exact == EL1.Exact)
5349 BECount = EL0.Exact;
5352 return ExitLimit(BECount, MaxBECount);
5356 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5357 // Proceed to the next level to examine the icmp.
5358 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5359 return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5361 // Check for a constant condition. These are normally stripped out by
5362 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5363 // preserve the CFG and is temporarily leaving constant conditions
5365 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5366 if (L->contains(FBB) == !CI->getZExtValue())
5367 // The backedge is always taken.
5368 return getCouldNotCompute();
5370 // The backedge is never taken.
5371 return getZero(CI->getType());
5374 // If it's not an integer or pointer comparison then compute it the hard way.
5375 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5378 ScalarEvolution::ExitLimit
5379 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
5383 bool ControlsExit) {
5385 // If the condition was exit on true, convert the condition to exit on false
5386 ICmpInst::Predicate Cond;
5387 if (!L->contains(FBB))
5388 Cond = ExitCond->getPredicate();
5390 Cond = ExitCond->getInversePredicate();
5392 // Handle common loops like: for (X = "string"; *X; ++X)
5393 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5394 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5396 computeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5397 if (ItCnt.hasAnyInfo())
5401 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5402 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5404 // Try to evaluate any dependencies out of the loop.
5405 LHS = getSCEVAtScope(LHS, L);
5406 RHS = getSCEVAtScope(RHS, L);
5408 // At this point, we would like to compute how many iterations of the
5409 // loop the predicate will return true for these inputs.
5410 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5411 // If there is a loop-invariant, force it into the RHS.
5412 std::swap(LHS, RHS);
5413 Cond = ICmpInst::getSwappedPredicate(Cond);
5416 // Simplify the operands before analyzing them.
5417 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5419 // If we have a comparison of a chrec against a constant, try to use value
5420 // ranges to answer this query.
5421 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5422 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5423 if (AddRec->getLoop() == L) {
5424 // Form the constant range.
5425 ConstantRange CompRange(
5426 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5428 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5429 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5433 case ICmpInst::ICMP_NE: { // while (X != Y)
5434 // Convert to: while (X-Y != 0)
5435 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5436 if (EL.hasAnyInfo()) return EL;
5439 case ICmpInst::ICMP_EQ: { // while (X == Y)
5440 // Convert to: while (X-Y == 0)
5441 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5442 if (EL.hasAnyInfo()) return EL;
5445 case ICmpInst::ICMP_SLT:
5446 case ICmpInst::ICMP_ULT: { // while (X < Y)
5447 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5448 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5449 if (EL.hasAnyInfo()) return EL;
5452 case ICmpInst::ICMP_SGT:
5453 case ICmpInst::ICMP_UGT: { // while (X > Y)
5454 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5455 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5456 if (EL.hasAnyInfo()) return EL;
5462 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5465 ScalarEvolution::ExitLimit
5466 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
5468 BasicBlock *ExitingBlock,
5469 bool ControlsExit) {
5470 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5472 // Give up if the exit is the default dest of a switch.
5473 if (Switch->getDefaultDest() == ExitingBlock)
5474 return getCouldNotCompute();
5476 assert(L->contains(Switch->getDefaultDest()) &&
5477 "Default case must not exit the loop!");
5478 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5479 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5481 // while (X != Y) --> while (X-Y != 0)
5482 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5483 if (EL.hasAnyInfo())
5486 return getCouldNotCompute();
5489 static ConstantInt *
5490 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5491 ScalarEvolution &SE) {
5492 const SCEV *InVal = SE.getConstant(C);
5493 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5494 assert(isa<SCEVConstant>(Val) &&
5495 "Evaluation of SCEV at constant didn't fold correctly?");
5496 return cast<SCEVConstant>(Val)->getValue();
5499 /// computeLoadConstantCompareExitLimit - Given an exit condition of
5500 /// 'icmp op load X, cst', try to see if we can compute the backedge
5501 /// execution count.
5502 ScalarEvolution::ExitLimit
5503 ScalarEvolution::computeLoadConstantCompareExitLimit(
5507 ICmpInst::Predicate predicate) {
5509 if (LI->isVolatile()) return getCouldNotCompute();
5511 // Check to see if the loaded pointer is a getelementptr of a global.
5512 // TODO: Use SCEV instead of manually grubbing with GEPs.
5513 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5514 if (!GEP) return getCouldNotCompute();
5516 // Make sure that it is really a constant global we are gepping, with an
5517 // initializer, and make sure the first IDX is really 0.
5518 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5519 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5520 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5521 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5522 return getCouldNotCompute();
5524 // Okay, we allow one non-constant index into the GEP instruction.
5525 Value *VarIdx = nullptr;
5526 std::vector<Constant*> Indexes;
5527 unsigned VarIdxNum = 0;
5528 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5529 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5530 Indexes.push_back(CI);
5531 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5532 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5533 VarIdx = GEP->getOperand(i);
5535 Indexes.push_back(nullptr);
5538 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5540 return getCouldNotCompute();
5542 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5543 // Check to see if X is a loop variant variable value now.
5544 const SCEV *Idx = getSCEV(VarIdx);
5545 Idx = getSCEVAtScope(Idx, L);
5547 // We can only recognize very limited forms of loop index expressions, in
5548 // particular, only affine AddRec's like {C1,+,C2}.
5549 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5550 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5551 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5552 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5553 return getCouldNotCompute();
5555 unsigned MaxSteps = MaxBruteForceIterations;
5556 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5557 ConstantInt *ItCst = ConstantInt::get(
5558 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5559 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5561 // Form the GEP offset.
5562 Indexes[VarIdxNum] = Val;
5564 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5566 if (!Result) break; // Cannot compute!
5568 // Evaluate the condition for this iteration.
5569 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5570 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5571 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5572 ++NumArrayLenItCounts;
5573 return getConstant(ItCst); // Found terminating iteration!
5576 return getCouldNotCompute();
5580 /// CanConstantFold - Return true if we can constant fold an instruction of the
5581 /// specified type, assuming that all operands were constants.
5582 static bool CanConstantFold(const Instruction *I) {
5583 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5584 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5588 if (const CallInst *CI = dyn_cast<CallInst>(I))
5589 if (const Function *F = CI->getCalledFunction())
5590 return canConstantFoldCallTo(F);
5594 /// Determine whether this instruction can constant evolve within this loop
5595 /// assuming its operands can all constant evolve.
5596 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5597 // An instruction outside of the loop can't be derived from a loop PHI.
5598 if (!L->contains(I)) return false;
5600 if (isa<PHINode>(I)) {
5601 // We don't currently keep track of the control flow needed to evaluate
5602 // PHIs, so we cannot handle PHIs inside of loops.
5603 return L->getHeader() == I->getParent();
5606 // If we won't be able to constant fold this expression even if the operands
5607 // are constants, bail early.
5608 return CanConstantFold(I);
5611 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5612 /// recursing through each instruction operand until reaching a loop header phi.
5614 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5615 DenseMap<Instruction *, PHINode *> &PHIMap) {
5617 // Otherwise, we can evaluate this instruction if all of its operands are
5618 // constant or derived from a PHI node themselves.
5619 PHINode *PHI = nullptr;
5620 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5621 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5623 if (isa<Constant>(*OpI)) continue;
5625 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5626 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5628 PHINode *P = dyn_cast<PHINode>(OpInst);
5630 // If this operand is already visited, reuse the prior result.
5631 // We may have P != PHI if this is the deepest point at which the
5632 // inconsistent paths meet.
5633 P = PHIMap.lookup(OpInst);
5635 // Recurse and memoize the results, whether a phi is found or not.
5636 // This recursive call invalidates pointers into PHIMap.
5637 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5641 return nullptr; // Not evolving from PHI
5642 if (PHI && PHI != P)
5643 return nullptr; // Evolving from multiple different PHIs.
5646 // This is a expression evolving from a constant PHI!
5650 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5651 /// in the loop that V is derived from. We allow arbitrary operations along the
5652 /// way, but the operands of an operation must either be constants or a value
5653 /// derived from a constant PHI. If this expression does not fit with these
5654 /// constraints, return null.
5655 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5656 Instruction *I = dyn_cast<Instruction>(V);
5657 if (!I || !canConstantEvolve(I, L)) return nullptr;
5659 if (PHINode *PN = dyn_cast<PHINode>(I))
5662 // Record non-constant instructions contained by the loop.
5663 DenseMap<Instruction *, PHINode *> PHIMap;
5664 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5667 /// EvaluateExpression - Given an expression that passes the
5668 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5669 /// in the loop has the value PHIVal. If we can't fold this expression for some
5670 /// reason, return null.
5671 static Constant *EvaluateExpression(Value *V, const Loop *L,
5672 DenseMap<Instruction *, Constant *> &Vals,
5673 const DataLayout &DL,
5674 const TargetLibraryInfo *TLI) {
5675 // Convenient constant check, but redundant for recursive calls.
5676 if (Constant *C = dyn_cast<Constant>(V)) return C;
5677 Instruction *I = dyn_cast<Instruction>(V);
5678 if (!I) return nullptr;
5680 if (Constant *C = Vals.lookup(I)) return C;
5682 // An instruction inside the loop depends on a value outside the loop that we
5683 // weren't given a mapping for, or a value such as a call inside the loop.
5684 if (!canConstantEvolve(I, L)) return nullptr;
5686 // An unmapped PHI can be due to a branch or another loop inside this loop,
5687 // or due to this not being the initial iteration through a loop where we
5688 // couldn't compute the evolution of this particular PHI last time.
5689 if (isa<PHINode>(I)) return nullptr;
5691 std::vector<Constant*> Operands(I->getNumOperands());
5693 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5694 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5696 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5697 if (!Operands[i]) return nullptr;
5700 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5702 if (!C) return nullptr;
5706 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5707 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5708 Operands[1], DL, TLI);
5709 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5710 if (!LI->isVolatile())
5711 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5713 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5717 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5718 /// in the header of its containing loop, we know the loop executes a
5719 /// constant number of times, and the PHI node is just a recurrence
5720 /// involving constants, fold it.
5722 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5725 auto I = ConstantEvolutionLoopExitValue.find(PN);
5726 if (I != ConstantEvolutionLoopExitValue.end())
5729 if (BEs.ugt(MaxBruteForceIterations))
5730 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5732 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5734 DenseMap<Instruction *, Constant *> CurrentIterVals;
5735 BasicBlock *Header = L->getHeader();
5736 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5738 BasicBlock *Latch = L->getLoopLatch();
5742 // Since the loop has one latch, the PHI node must have two entries. One
5743 // entry must be a constant (coming in from outside of the loop), and the
5744 // second must be derived from the same PHI.
5746 BasicBlock *NonLatch = Latch == PN->getIncomingBlock(0)
5747 ? PN->getIncomingBlock(1)
5748 : PN->getIncomingBlock(0);
5750 assert(PN->getNumIncomingValues() == 2 && "Follows from having one latch!");
5752 // Note: not all PHI nodes in the same block have to have their incoming
5753 // values in the same order, so we use the basic block to look up the incoming
5754 // value, not an index.
5756 for (auto &I : *Header) {
5757 PHINode *PHI = dyn_cast<PHINode>(&I);
5760 dyn_cast<Constant>(PHI->getIncomingValueForBlock(NonLatch));
5761 if (!StartCST) continue;
5762 CurrentIterVals[PHI] = StartCST;
5764 if (!CurrentIterVals.count(PN))
5765 return RetVal = nullptr;
5767 Value *BEValue = PN->getIncomingValueForBlock(Latch);
5769 // Execute the loop symbolically to determine the exit value.
5770 if (BEs.getActiveBits() >= 32)
5771 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5773 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5774 unsigned IterationNum = 0;
5775 const DataLayout &DL = getDataLayout();
5776 for (; ; ++IterationNum) {
5777 if (IterationNum == NumIterations)
5778 return RetVal = CurrentIterVals[PN]; // Got exit value!
5780 // Compute the value of the PHIs for the next iteration.
5781 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5782 DenseMap<Instruction *, Constant *> NextIterVals;
5784 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5786 return nullptr; // Couldn't evaluate!
5787 NextIterVals[PN] = NextPHI;
5789 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5791 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5792 // cease to be able to evaluate one of them or if they stop evolving,
5793 // because that doesn't necessarily prevent us from computing PN.
5794 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5795 for (const auto &I : CurrentIterVals) {
5796 PHINode *PHI = dyn_cast<PHINode>(I.first);
5797 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5798 PHIsToCompute.emplace_back(PHI, I.second);
5800 // We use two distinct loops because EvaluateExpression may invalidate any
5801 // iterators into CurrentIterVals.
5802 for (const auto &I : PHIsToCompute) {
5803 PHINode *PHI = I.first;
5804 Constant *&NextPHI = NextIterVals[PHI];
5805 if (!NextPHI) { // Not already computed.
5806 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
5807 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5809 if (NextPHI != I.second)
5810 StoppedEvolving = false;
5813 // If all entries in CurrentIterVals == NextIterVals then we can stop
5814 // iterating, the loop can't continue to change.
5815 if (StoppedEvolving)
5816 return RetVal = CurrentIterVals[PN];
5818 CurrentIterVals.swap(NextIterVals);
5822 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
5825 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5826 if (!PN) return getCouldNotCompute();
5828 // If the loop is canonicalized, the PHI will have exactly two entries.
5829 // That's the only form we support here.
5830 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5832 DenseMap<Instruction *, Constant *> CurrentIterVals;
5833 BasicBlock *Header = L->getHeader();
5834 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5836 BasicBlock *Latch = L->getLoopLatch();
5837 assert(Latch && "Should follow from NumIncomingValues == 2!");
5839 // NonLatch is the preheader, or something equivalent.
5840 BasicBlock *NonLatch = Latch == PN->getIncomingBlock(0)
5841 ? PN->getIncomingBlock(1)
5842 : PN->getIncomingBlock(0);
5844 // Note: not all PHI nodes in the same block have to have their incoming
5845 // values in the same order, so we use the basic block to look up the incoming
5846 // value, not an index.
5848 for (auto &I : *Header) {
5849 PHINode *PHI = dyn_cast<PHINode>(&I);
5853 dyn_cast<Constant>(PHI->getIncomingValueForBlock(NonLatch));
5854 if (!StartCST) continue;
5855 CurrentIterVals[PHI] = StartCST;
5857 if (!CurrentIterVals.count(PN))
5858 return getCouldNotCompute();
5860 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5861 // the loop symbolically to determine when the condition gets a value of
5863 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5864 const DataLayout &DL = getDataLayout();
5865 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5866 auto *CondVal = dyn_cast_or_null<ConstantInt>(
5867 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
5869 // Couldn't symbolically evaluate.
5870 if (!CondVal) return getCouldNotCompute();
5872 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5873 ++NumBruteForceTripCountsComputed;
5874 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5877 // Update all the PHI nodes for the next iteration.
5878 DenseMap<Instruction *, Constant *> NextIterVals;
5880 // Create a list of which PHIs we need to compute. We want to do this before
5881 // calling EvaluateExpression on them because that may invalidate iterators
5882 // into CurrentIterVals.
5883 SmallVector<PHINode *, 8> PHIsToCompute;
5884 for (const auto &I : CurrentIterVals) {
5885 PHINode *PHI = dyn_cast<PHINode>(I.first);
5886 if (!PHI || PHI->getParent() != Header) continue;
5887 PHIsToCompute.push_back(PHI);
5889 for (PHINode *PHI : PHIsToCompute) {
5890 Constant *&NextPHI = NextIterVals[PHI];
5891 if (NextPHI) continue; // Already computed!
5893 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
5894 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5896 CurrentIterVals.swap(NextIterVals);
5899 // Too many iterations were needed to evaluate.
5900 return getCouldNotCompute();
5903 /// getSCEVAtScope - Return a SCEV expression for the specified value
5904 /// at the specified scope in the program. The L value specifies a loop
5905 /// nest to evaluate the expression at, where null is the top-level or a
5906 /// specified loop is immediately inside of the loop.
5908 /// This method can be used to compute the exit value for a variable defined
5909 /// in a loop by querying what the value will hold in the parent loop.
5911 /// In the case that a relevant loop exit value cannot be computed, the
5912 /// original value V is returned.
5913 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5914 // Check to see if we've folded this expression at this loop before.
5915 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5916 for (unsigned u = 0; u < Values.size(); u++) {
5917 if (Values[u].first == L)
5918 return Values[u].second ? Values[u].second : V;
5920 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5921 // Otherwise compute it.
5922 const SCEV *C = computeSCEVAtScope(V, L);
5923 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5924 for (unsigned u = Values2.size(); u > 0; u--) {
5925 if (Values2[u - 1].first == L) {
5926 Values2[u - 1].second = C;
5933 /// This builds up a Constant using the ConstantExpr interface. That way, we
5934 /// will return Constants for objects which aren't represented by a
5935 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5936 /// Returns NULL if the SCEV isn't representable as a Constant.
5937 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5938 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5939 case scCouldNotCompute:
5943 return cast<SCEVConstant>(V)->getValue();
5945 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5946 case scSignExtend: {
5947 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5948 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5949 return ConstantExpr::getSExt(CastOp, SS->getType());
5952 case scZeroExtend: {
5953 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5954 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5955 return ConstantExpr::getZExt(CastOp, SZ->getType());
5959 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5960 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5961 return ConstantExpr::getTrunc(CastOp, ST->getType());
5965 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5966 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5967 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5968 unsigned AS = PTy->getAddressSpace();
5969 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5970 C = ConstantExpr::getBitCast(C, DestPtrTy);
5972 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5973 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5974 if (!C2) return nullptr;
5977 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5978 unsigned AS = C2->getType()->getPointerAddressSpace();
5980 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5981 // The offsets have been converted to bytes. We can add bytes to an
5982 // i8* by GEP with the byte count in the first index.
5983 C = ConstantExpr::getBitCast(C, DestPtrTy);
5986 // Don't bother trying to sum two pointers. We probably can't
5987 // statically compute a load that results from it anyway.
5988 if (C2->getType()->isPointerTy())
5991 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5992 if (PTy->getElementType()->isStructTy())
5993 C2 = ConstantExpr::getIntegerCast(
5994 C2, Type::getInt32Ty(C->getContext()), true);
5995 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
5997 C = ConstantExpr::getAdd(C, C2);
6004 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
6005 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
6006 // Don't bother with pointers at all.
6007 if (C->getType()->isPointerTy()) return nullptr;
6008 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
6009 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
6010 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
6011 C = ConstantExpr::getMul(C, C2);
6018 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6019 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6020 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6021 if (LHS->getType() == RHS->getType())
6022 return ConstantExpr::getUDiv(LHS, RHS);
6027 break; // TODO: smax, umax.
6032 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6033 if (isa<SCEVConstant>(V)) return V;
6035 // If this instruction is evolved from a constant-evolving PHI, compute the
6036 // exit value from the loop without using SCEVs.
6037 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6038 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6039 const Loop *LI = this->LI[I->getParent()];
6040 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
6041 if (PHINode *PN = dyn_cast<PHINode>(I))
6042 if (PN->getParent() == LI->getHeader()) {
6043 // Okay, there is no closed form solution for the PHI node. Check
6044 // to see if the loop that contains it has a known backedge-taken
6045 // count. If so, we may be able to force computation of the exit
6047 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6048 if (const SCEVConstant *BTCC =
6049 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6050 // Okay, we know how many times the containing loop executes. If
6051 // this is a constant evolving PHI node, get the final value at
6052 // the specified iteration number.
6053 Constant *RV = getConstantEvolutionLoopExitValue(PN,
6054 BTCC->getValue()->getValue(),
6056 if (RV) return getSCEV(RV);
6060 // Okay, this is an expression that we cannot symbolically evaluate
6061 // into a SCEV. Check to see if it's possible to symbolically evaluate
6062 // the arguments into constants, and if so, try to constant propagate the
6063 // result. This is particularly useful for computing loop exit values.
6064 if (CanConstantFold(I)) {
6065 SmallVector<Constant *, 4> Operands;
6066 bool MadeImprovement = false;
6067 for (Value *Op : I->operands()) {
6068 if (Constant *C = dyn_cast<Constant>(Op)) {
6069 Operands.push_back(C);
6073 // If any of the operands is non-constant and if they are
6074 // non-integer and non-pointer, don't even try to analyze them
6075 // with scev techniques.
6076 if (!isSCEVable(Op->getType()))
6079 const SCEV *OrigV = getSCEV(Op);
6080 const SCEV *OpV = getSCEVAtScope(OrigV, L);
6081 MadeImprovement |= OrigV != OpV;
6083 Constant *C = BuildConstantFromSCEV(OpV);
6085 if (C->getType() != Op->getType())
6086 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6090 Operands.push_back(C);
6093 // Check to see if getSCEVAtScope actually made an improvement.
6094 if (MadeImprovement) {
6095 Constant *C = nullptr;
6096 const DataLayout &DL = getDataLayout();
6097 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6098 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6099 Operands[1], DL, &TLI);
6100 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6101 if (!LI->isVolatile())
6102 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
6104 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
6112 // This is some other type of SCEVUnknown, just return it.
6116 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6117 // Avoid performing the look-up in the common case where the specified
6118 // expression has no loop-variant portions.
6119 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6120 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6121 if (OpAtScope != Comm->getOperand(i)) {
6122 // Okay, at least one of these operands is loop variant but might be
6123 // foldable. Build a new instance of the folded commutative expression.
6124 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6125 Comm->op_begin()+i);
6126 NewOps.push_back(OpAtScope);
6128 for (++i; i != e; ++i) {
6129 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6130 NewOps.push_back(OpAtScope);
6132 if (isa<SCEVAddExpr>(Comm))
6133 return getAddExpr(NewOps);
6134 if (isa<SCEVMulExpr>(Comm))
6135 return getMulExpr(NewOps);
6136 if (isa<SCEVSMaxExpr>(Comm))
6137 return getSMaxExpr(NewOps);
6138 if (isa<SCEVUMaxExpr>(Comm))
6139 return getUMaxExpr(NewOps);
6140 llvm_unreachable("Unknown commutative SCEV type!");
6143 // If we got here, all operands are loop invariant.
6147 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6148 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6149 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6150 if (LHS == Div->getLHS() && RHS == Div->getRHS())
6151 return Div; // must be loop invariant
6152 return getUDivExpr(LHS, RHS);
6155 // If this is a loop recurrence for a loop that does not contain L, then we
6156 // are dealing with the final value computed by the loop.
6157 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6158 // First, attempt to evaluate each operand.
6159 // Avoid performing the look-up in the common case where the specified
6160 // expression has no loop-variant portions.
6161 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6162 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6163 if (OpAtScope == AddRec->getOperand(i))
6166 // Okay, at least one of these operands is loop variant but might be
6167 // foldable. Build a new instance of the folded commutative expression.
6168 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6169 AddRec->op_begin()+i);
6170 NewOps.push_back(OpAtScope);
6171 for (++i; i != e; ++i)
6172 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6174 const SCEV *FoldedRec =
6175 getAddRecExpr(NewOps, AddRec->getLoop(),
6176 AddRec->getNoWrapFlags(SCEV::FlagNW));
6177 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6178 // The addrec may be folded to a nonrecurrence, for example, if the
6179 // induction variable is multiplied by zero after constant folding. Go
6180 // ahead and return the folded value.
6186 // If the scope is outside the addrec's loop, evaluate it by using the
6187 // loop exit value of the addrec.
6188 if (!AddRec->getLoop()->contains(L)) {
6189 // To evaluate this recurrence, we need to know how many times the AddRec
6190 // loop iterates. Compute this now.
6191 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6192 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6194 // Then, evaluate the AddRec.
6195 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6201 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6202 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6203 if (Op == Cast->getOperand())
6204 return Cast; // must be loop invariant
6205 return getZeroExtendExpr(Op, Cast->getType());
6208 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6209 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6210 if (Op == Cast->getOperand())
6211 return Cast; // must be loop invariant
6212 return getSignExtendExpr(Op, Cast->getType());
6215 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6216 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6217 if (Op == Cast->getOperand())
6218 return Cast; // must be loop invariant
6219 return getTruncateExpr(Op, Cast->getType());
6222 llvm_unreachable("Unknown SCEV type!");
6225 /// getSCEVAtScope - This is a convenience function which does
6226 /// getSCEVAtScope(getSCEV(V), L).
6227 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6228 return getSCEVAtScope(getSCEV(V), L);
6231 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6232 /// following equation:
6234 /// A * X = B (mod N)
6236 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6237 /// A and B isn't important.
6239 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6240 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6241 ScalarEvolution &SE) {
6242 uint32_t BW = A.getBitWidth();
6243 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6244 assert(A != 0 && "A must be non-zero.");
6248 // The gcd of A and N may have only one prime factor: 2. The number of
6249 // trailing zeros in A is its multiplicity
6250 uint32_t Mult2 = A.countTrailingZeros();
6253 // 2. Check if B is divisible by D.
6255 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6256 // is not less than multiplicity of this prime factor for D.
6257 if (B.countTrailingZeros() < Mult2)
6258 return SE.getCouldNotCompute();
6260 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6263 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6264 // bit width during computations.
6265 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6266 APInt Mod(BW + 1, 0);
6267 Mod.setBit(BW - Mult2); // Mod = N / D
6268 APInt I = AD.multiplicativeInverse(Mod);
6270 // 4. Compute the minimum unsigned root of the equation:
6271 // I * (B / D) mod (N / D)
6272 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6274 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6276 return SE.getConstant(Result.trunc(BW));
6279 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6280 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6281 /// might be the same) or two SCEVCouldNotCompute objects.
6283 static std::pair<const SCEV *,const SCEV *>
6284 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6285 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6286 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6287 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6288 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6290 // We currently can only solve this if the coefficients are constants.
6291 if (!LC || !MC || !NC) {
6292 const SCEV *CNC = SE.getCouldNotCompute();
6293 return std::make_pair(CNC, CNC);
6296 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6297 const APInt &L = LC->getValue()->getValue();
6298 const APInt &M = MC->getValue()->getValue();
6299 const APInt &N = NC->getValue()->getValue();
6300 APInt Two(BitWidth, 2);
6301 APInt Four(BitWidth, 4);
6304 using namespace APIntOps;
6306 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6307 // The B coefficient is M-N/2
6311 // The A coefficient is N/2
6312 APInt A(N.sdiv(Two));
6314 // Compute the B^2-4ac term.
6317 SqrtTerm -= Four * (A * C);
6319 if (SqrtTerm.isNegative()) {
6320 // The loop is provably infinite.
6321 const SCEV *CNC = SE.getCouldNotCompute();
6322 return std::make_pair(CNC, CNC);
6325 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6326 // integer value or else APInt::sqrt() will assert.
6327 APInt SqrtVal(SqrtTerm.sqrt());
6329 // Compute the two solutions for the quadratic formula.
6330 // The divisions must be performed as signed divisions.
6333 if (TwoA.isMinValue()) {
6334 const SCEV *CNC = SE.getCouldNotCompute();
6335 return std::make_pair(CNC, CNC);
6338 LLVMContext &Context = SE.getContext();
6340 ConstantInt *Solution1 =
6341 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6342 ConstantInt *Solution2 =
6343 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6345 return std::make_pair(SE.getConstant(Solution1),
6346 SE.getConstant(Solution2));
6347 } // end APIntOps namespace
6350 /// HowFarToZero - Return the number of times a backedge comparing the specified
6351 /// value to zero will execute. If not computable, return CouldNotCompute.
6353 /// This is only used for loops with a "x != y" exit test. The exit condition is
6354 /// now expressed as a single expression, V = x-y. So the exit test is
6355 /// effectively V != 0. We know and take advantage of the fact that this
6356 /// expression only being used in a comparison by zero context.
6357 ScalarEvolution::ExitLimit
6358 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6359 // If the value is a constant
6360 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6361 // If the value is already zero, the branch will execute zero times.
6362 if (C->getValue()->isZero()) return C;
6363 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6366 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6367 if (!AddRec || AddRec->getLoop() != L)
6368 return getCouldNotCompute();
6370 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6371 // the quadratic equation to solve it.
6372 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6373 std::pair<const SCEV *,const SCEV *> Roots =
6374 SolveQuadraticEquation(AddRec, *this);
6375 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6376 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6378 // Pick the smallest positive root value.
6379 if (ConstantInt *CB =
6380 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6383 if (!CB->getZExtValue())
6384 std::swap(R1, R2); // R1 is the minimum root now.
6386 // We can only use this value if the chrec ends up with an exact zero
6387 // value at this index. When solving for "X*X != 5", for example, we
6388 // should not accept a root of 2.
6389 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6391 return R1; // We found a quadratic root!
6394 return getCouldNotCompute();
6397 // Otherwise we can only handle this if it is affine.
6398 if (!AddRec->isAffine())
6399 return getCouldNotCompute();
6401 // If this is an affine expression, the execution count of this branch is
6402 // the minimum unsigned root of the following equation:
6404 // Start + Step*N = 0 (mod 2^BW)
6408 // Step*N = -Start (mod 2^BW)
6410 // where BW is the common bit width of Start and Step.
6412 // Get the initial value for the loop.
6413 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6414 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6416 // For now we handle only constant steps.
6418 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6419 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6420 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6421 // We have not yet seen any such cases.
6422 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6423 if (!StepC || StepC->getValue()->equalsInt(0))
6424 return getCouldNotCompute();
6426 // For positive steps (counting up until unsigned overflow):
6427 // N = -Start/Step (as unsigned)
6428 // For negative steps (counting down to zero):
6430 // First compute the unsigned distance from zero in the direction of Step.
6431 bool CountDown = StepC->getValue()->getValue().isNegative();
6432 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6434 // Handle unitary steps, which cannot wraparound.
6435 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6436 // N = Distance (as unsigned)
6437 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6438 ConstantRange CR = getUnsignedRange(Start);
6439 const SCEV *MaxBECount;
6440 if (!CountDown && CR.getUnsignedMin().isMinValue())
6441 // When counting up, the worst starting value is 1, not 0.
6442 MaxBECount = CR.getUnsignedMax().isMinValue()
6443 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6444 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6446 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6447 : -CR.getUnsignedMin());
6448 return ExitLimit(Distance, MaxBECount);
6451 // As a special case, handle the instance where Step is a positive power of
6452 // two. In this case, determining whether Step divides Distance evenly can be
6453 // done by counting and comparing the number of trailing zeros of Step and
6456 const APInt &StepV = StepC->getValue()->getValue();
6457 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6458 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6459 // case is not handled as this code is guarded by !CountDown.
6460 if (StepV.isPowerOf2() &&
6461 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
6462 // Here we've constrained the equation to be of the form
6464 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
6466 // where we're operating on a W bit wide integer domain and k is
6467 // non-negative. The smallest unsigned solution for X is the trip count.
6469 // (0) is equivalent to:
6471 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
6472 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
6473 // <=> 2^k * Distance' - X = L * 2^(W - N)
6474 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
6476 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
6479 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
6481 // E.g. say we're solving
6483 // 2 * Val = 2 * X (in i8) ... (3)
6485 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
6487 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
6488 // necessarily the smallest unsigned value of X that satisfies (3).
6489 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
6490 // is i8 1, not i8 -127
6492 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
6494 // Since SCEV does not have a URem node, we construct one using a truncate
6495 // and a zero extend.
6497 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
6498 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
6499 auto *WideTy = Distance->getType();
6501 return getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
6505 // If the condition controls loop exit (the loop exits only if the expression
6506 // is true) and the addition is no-wrap we can use unsigned divide to
6507 // compute the backedge count. In this case, the step may not divide the
6508 // distance, but we don't care because if the condition is "missed" the loop
6509 // will have undefined behavior due to wrapping.
6510 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6512 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6513 return ExitLimit(Exact, Exact);
6516 // Then, try to solve the above equation provided that Start is constant.
6517 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6518 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6519 -StartC->getValue()->getValue(),
6521 return getCouldNotCompute();
6524 /// HowFarToNonZero - Return the number of times a backedge checking the
6525 /// specified value for nonzero will execute. If not computable, return
6527 ScalarEvolution::ExitLimit
6528 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6529 // Loops that look like: while (X == 0) are very strange indeed. We don't
6530 // handle them yet except for the trivial case. This could be expanded in the
6531 // future as needed.
6533 // If the value is a constant, check to see if it is known to be non-zero
6534 // already. If so, the backedge will execute zero times.
6535 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6536 if (!C->getValue()->isNullValue())
6537 return getZero(C->getType());
6538 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6541 // We could implement others, but I really doubt anyone writes loops like
6542 // this, and if they did, they would already be constant folded.
6543 return getCouldNotCompute();
6546 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6547 /// (which may not be an immediate predecessor) which has exactly one
6548 /// successor from which BB is reachable, or null if no such block is
6551 std::pair<BasicBlock *, BasicBlock *>
6552 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6553 // If the block has a unique predecessor, then there is no path from the
6554 // predecessor to the block that does not go through the direct edge
6555 // from the predecessor to the block.
6556 if (BasicBlock *Pred = BB->getSinglePredecessor())
6557 return std::make_pair(Pred, BB);
6559 // A loop's header is defined to be a block that dominates the loop.
6560 // If the header has a unique predecessor outside the loop, it must be
6561 // a block that has exactly one successor that can reach the loop.
6562 if (Loop *L = LI.getLoopFor(BB))
6563 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6565 return std::pair<BasicBlock *, BasicBlock *>();
6568 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6569 /// testing whether two expressions are equal, however for the purposes of
6570 /// looking for a condition guarding a loop, it can be useful to be a little
6571 /// more general, since a front-end may have replicated the controlling
6574 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6575 // Quick check to see if they are the same SCEV.
6576 if (A == B) return true;
6578 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
6579 // Not all instructions that are "identical" compute the same value. For
6580 // instance, two distinct alloca instructions allocating the same type are
6581 // identical and do not read memory; but compute distinct values.
6582 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
6585 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6586 // two different instructions with the same value. Check for this case.
6587 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6588 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6589 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6590 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6591 if (ComputesEqualValues(AI, BI))
6594 // Otherwise assume they may have a different value.
6598 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6599 /// predicate Pred. Return true iff any changes were made.
6601 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6602 const SCEV *&LHS, const SCEV *&RHS,
6604 bool Changed = false;
6606 // If we hit the max recursion limit bail out.
6610 // Canonicalize a constant to the right side.
6611 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6612 // Check for both operands constant.
6613 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6614 if (ConstantExpr::getICmp(Pred,
6616 RHSC->getValue())->isNullValue())
6617 goto trivially_false;
6619 goto trivially_true;
6621 // Otherwise swap the operands to put the constant on the right.
6622 std::swap(LHS, RHS);
6623 Pred = ICmpInst::getSwappedPredicate(Pred);
6627 // If we're comparing an addrec with a value which is loop-invariant in the
6628 // addrec's loop, put the addrec on the left. Also make a dominance check,
6629 // as both operands could be addrecs loop-invariant in each other's loop.
6630 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6631 const Loop *L = AR->getLoop();
6632 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6633 std::swap(LHS, RHS);
6634 Pred = ICmpInst::getSwappedPredicate(Pred);
6639 // If there's a constant operand, canonicalize comparisons with boundary
6640 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6641 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6642 const APInt &RA = RC->getValue()->getValue();
6644 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6645 case ICmpInst::ICMP_EQ:
6646 case ICmpInst::ICMP_NE:
6647 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6649 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6650 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6651 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6652 ME->getOperand(0)->isAllOnesValue()) {
6653 RHS = AE->getOperand(1);
6654 LHS = ME->getOperand(1);
6658 case ICmpInst::ICMP_UGE:
6659 if ((RA - 1).isMinValue()) {
6660 Pred = ICmpInst::ICMP_NE;
6661 RHS = getConstant(RA - 1);
6665 if (RA.isMaxValue()) {
6666 Pred = ICmpInst::ICMP_EQ;
6670 if (RA.isMinValue()) goto trivially_true;
6672 Pred = ICmpInst::ICMP_UGT;
6673 RHS = getConstant(RA - 1);
6676 case ICmpInst::ICMP_ULE:
6677 if ((RA + 1).isMaxValue()) {
6678 Pred = ICmpInst::ICMP_NE;
6679 RHS = getConstant(RA + 1);
6683 if (RA.isMinValue()) {
6684 Pred = ICmpInst::ICMP_EQ;
6688 if (RA.isMaxValue()) goto trivially_true;
6690 Pred = ICmpInst::ICMP_ULT;
6691 RHS = getConstant(RA + 1);
6694 case ICmpInst::ICMP_SGE:
6695 if ((RA - 1).isMinSignedValue()) {
6696 Pred = ICmpInst::ICMP_NE;
6697 RHS = getConstant(RA - 1);
6701 if (RA.isMaxSignedValue()) {
6702 Pred = ICmpInst::ICMP_EQ;
6706 if (RA.isMinSignedValue()) goto trivially_true;
6708 Pred = ICmpInst::ICMP_SGT;
6709 RHS = getConstant(RA - 1);
6712 case ICmpInst::ICMP_SLE:
6713 if ((RA + 1).isMaxSignedValue()) {
6714 Pred = ICmpInst::ICMP_NE;
6715 RHS = getConstant(RA + 1);
6719 if (RA.isMinSignedValue()) {
6720 Pred = ICmpInst::ICMP_EQ;
6724 if (RA.isMaxSignedValue()) goto trivially_true;
6726 Pred = ICmpInst::ICMP_SLT;
6727 RHS = getConstant(RA + 1);
6730 case ICmpInst::ICMP_UGT:
6731 if (RA.isMinValue()) {
6732 Pred = ICmpInst::ICMP_NE;
6736 if ((RA + 1).isMaxValue()) {
6737 Pred = ICmpInst::ICMP_EQ;
6738 RHS = getConstant(RA + 1);
6742 if (RA.isMaxValue()) goto trivially_false;
6744 case ICmpInst::ICMP_ULT:
6745 if (RA.isMaxValue()) {
6746 Pred = ICmpInst::ICMP_NE;
6750 if ((RA - 1).isMinValue()) {
6751 Pred = ICmpInst::ICMP_EQ;
6752 RHS = getConstant(RA - 1);
6756 if (RA.isMinValue()) goto trivially_false;
6758 case ICmpInst::ICMP_SGT:
6759 if (RA.isMinSignedValue()) {
6760 Pred = ICmpInst::ICMP_NE;
6764 if ((RA + 1).isMaxSignedValue()) {
6765 Pred = ICmpInst::ICMP_EQ;
6766 RHS = getConstant(RA + 1);
6770 if (RA.isMaxSignedValue()) goto trivially_false;
6772 case ICmpInst::ICMP_SLT:
6773 if (RA.isMaxSignedValue()) {
6774 Pred = ICmpInst::ICMP_NE;
6778 if ((RA - 1).isMinSignedValue()) {
6779 Pred = ICmpInst::ICMP_EQ;
6780 RHS = getConstant(RA - 1);
6784 if (RA.isMinSignedValue()) goto trivially_false;
6789 // Check for obvious equality.
6790 if (HasSameValue(LHS, RHS)) {
6791 if (ICmpInst::isTrueWhenEqual(Pred))
6792 goto trivially_true;
6793 if (ICmpInst::isFalseWhenEqual(Pred))
6794 goto trivially_false;
6797 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6798 // adding or subtracting 1 from one of the operands.
6800 case ICmpInst::ICMP_SLE:
6801 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6802 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6804 Pred = ICmpInst::ICMP_SLT;
6806 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6807 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6809 Pred = ICmpInst::ICMP_SLT;
6813 case ICmpInst::ICMP_SGE:
6814 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6815 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6817 Pred = ICmpInst::ICMP_SGT;
6819 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6820 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6822 Pred = ICmpInst::ICMP_SGT;
6826 case ICmpInst::ICMP_ULE:
6827 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6828 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6830 Pred = ICmpInst::ICMP_ULT;
6832 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6833 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6835 Pred = ICmpInst::ICMP_ULT;
6839 case ICmpInst::ICMP_UGE:
6840 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6841 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6843 Pred = ICmpInst::ICMP_UGT;
6845 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6846 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6848 Pred = ICmpInst::ICMP_UGT;
6856 // TODO: More simplifications are possible here.
6858 // Recursively simplify until we either hit a recursion limit or nothing
6861 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6867 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6868 Pred = ICmpInst::ICMP_EQ;
6873 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6874 Pred = ICmpInst::ICMP_NE;
6878 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6879 return getSignedRange(S).getSignedMax().isNegative();
6882 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6883 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6886 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6887 return !getSignedRange(S).getSignedMin().isNegative();
6890 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6891 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6894 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6895 return isKnownNegative(S) || isKnownPositive(S);
6898 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6899 const SCEV *LHS, const SCEV *RHS) {
6900 // Canonicalize the inputs first.
6901 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6903 // If LHS or RHS is an addrec, check to see if the condition is true in
6904 // every iteration of the loop.
6905 // If LHS and RHS are both addrec, both conditions must be true in
6906 // every iteration of the loop.
6907 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6908 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6909 bool LeftGuarded = false;
6910 bool RightGuarded = false;
6912 const Loop *L = LAR->getLoop();
6913 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6914 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6915 if (!RAR) return true;
6920 const Loop *L = RAR->getLoop();
6921 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6922 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6923 if (!LAR) return true;
6924 RightGuarded = true;
6927 if (LeftGuarded && RightGuarded)
6930 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
6933 // Otherwise see what can be done with known constant ranges.
6934 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6937 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
6938 ICmpInst::Predicate Pred,
6940 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
6943 // Verify an invariant: inverting the predicate should turn a monotonically
6944 // increasing change to a monotonically decreasing one, and vice versa.
6945 bool IncreasingSwapped;
6946 bool ResultSwapped = isMonotonicPredicateImpl(
6947 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
6949 assert(Result == ResultSwapped && "should be able to analyze both!");
6951 assert(Increasing == !IncreasingSwapped &&
6952 "monotonicity should flip as we flip the predicate");
6958 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
6959 ICmpInst::Predicate Pred,
6962 // A zero step value for LHS means the induction variable is essentially a
6963 // loop invariant value. We don't really depend on the predicate actually
6964 // flipping from false to true (for increasing predicates, and the other way
6965 // around for decreasing predicates), all we care about is that *if* the
6966 // predicate changes then it only changes from false to true.
6968 // A zero step value in itself is not very useful, but there may be places
6969 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
6970 // as general as possible.
6974 return false; // Conservative answer
6976 case ICmpInst::ICMP_UGT:
6977 case ICmpInst::ICMP_UGE:
6978 case ICmpInst::ICMP_ULT:
6979 case ICmpInst::ICMP_ULE:
6980 if (!LHS->getNoWrapFlags(SCEV::FlagNUW))
6983 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
6986 case ICmpInst::ICMP_SGT:
6987 case ICmpInst::ICMP_SGE:
6988 case ICmpInst::ICMP_SLT:
6989 case ICmpInst::ICMP_SLE: {
6990 if (!LHS->getNoWrapFlags(SCEV::FlagNSW))
6993 const SCEV *Step = LHS->getStepRecurrence(*this);
6995 if (isKnownNonNegative(Step)) {
6996 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
7000 if (isKnownNonPositive(Step)) {
7001 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7010 llvm_unreachable("switch has default clause!");
7013 bool ScalarEvolution::isLoopInvariantPredicate(
7014 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7015 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7016 const SCEV *&InvariantRHS) {
7018 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7019 if (!isLoopInvariant(RHS, L)) {
7020 if (!isLoopInvariant(LHS, L))
7023 std::swap(LHS, RHS);
7024 Pred = ICmpInst::getSwappedPredicate(Pred);
7027 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7028 if (!ArLHS || ArLHS->getLoop() != L)
7032 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7035 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7036 // true as the loop iterates, and the backedge is control dependent on
7037 // "ArLHS `Pred` RHS" == true then we can reason as follows:
7039 // * if the predicate was false in the first iteration then the predicate
7040 // is never evaluated again, since the loop exits without taking the
7042 // * if the predicate was true in the first iteration then it will
7043 // continue to be true for all future iterations since it is
7044 // monotonically increasing.
7046 // For both the above possibilities, we can replace the loop varying
7047 // predicate with its value on the first iteration of the loop (which is
7050 // A similar reasoning applies for a monotonically decreasing predicate, by
7051 // replacing true with false and false with true in the above two bullets.
7053 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7055 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7058 InvariantPred = Pred;
7059 InvariantLHS = ArLHS->getStart();
7065 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
7066 const SCEV *LHS, const SCEV *RHS) {
7067 if (HasSameValue(LHS, RHS))
7068 return ICmpInst::isTrueWhenEqual(Pred);
7070 // This code is split out from isKnownPredicate because it is called from
7071 // within isLoopEntryGuardedByCond.
7074 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7075 case ICmpInst::ICMP_SGT:
7076 std::swap(LHS, RHS);
7077 case ICmpInst::ICMP_SLT: {
7078 ConstantRange LHSRange = getSignedRange(LHS);
7079 ConstantRange RHSRange = getSignedRange(RHS);
7080 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
7082 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
7086 case ICmpInst::ICMP_SGE:
7087 std::swap(LHS, RHS);
7088 case ICmpInst::ICMP_SLE: {
7089 ConstantRange LHSRange = getSignedRange(LHS);
7090 ConstantRange RHSRange = getSignedRange(RHS);
7091 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
7093 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
7097 case ICmpInst::ICMP_UGT:
7098 std::swap(LHS, RHS);
7099 case ICmpInst::ICMP_ULT: {
7100 ConstantRange LHSRange = getUnsignedRange(LHS);
7101 ConstantRange RHSRange = getUnsignedRange(RHS);
7102 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
7104 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
7108 case ICmpInst::ICMP_UGE:
7109 std::swap(LHS, RHS);
7110 case ICmpInst::ICMP_ULE: {
7111 ConstantRange LHSRange = getUnsignedRange(LHS);
7112 ConstantRange RHSRange = getUnsignedRange(RHS);
7113 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
7115 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
7119 case ICmpInst::ICMP_NE: {
7120 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
7122 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
7125 const SCEV *Diff = getMinusSCEV(LHS, RHS);
7126 if (isKnownNonZero(Diff))
7130 case ICmpInst::ICMP_EQ:
7131 // The check at the top of the function catches the case where
7132 // the values are known to be equal.
7138 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
7142 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
7143 // Return Y via OutY.
7144 auto MatchBinaryAddToConst =
7145 [this](const SCEV *Result, const SCEV *X, APInt &OutY,
7146 SCEV::NoWrapFlags ExpectedFlags) {
7147 const SCEV *NonConstOp, *ConstOp;
7148 SCEV::NoWrapFlags FlagsPresent;
7150 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
7151 !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
7154 OutY = cast<SCEVConstant>(ConstOp)->getValue()->getValue();
7155 return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
7164 case ICmpInst::ICMP_SGE:
7165 std::swap(LHS, RHS);
7166 case ICmpInst::ICMP_SLE:
7167 // X s<= (X + C)<nsw> if C >= 0
7168 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
7171 // (X + C)<nsw> s<= X if C <= 0
7172 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
7173 !C.isStrictlyPositive())
7176 case ICmpInst::ICMP_SGT:
7177 std::swap(LHS, RHS);
7178 case ICmpInst::ICMP_SLT:
7179 // X s< (X + C)<nsw> if C > 0
7180 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
7181 C.isStrictlyPositive())
7184 // (X + C)<nsw> s< X if C < 0
7185 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
7192 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7195 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
7198 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7199 // the stack can result in exponential time complexity.
7200 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7202 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7204 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7205 // isKnownPredicate. isKnownPredicate is more powerful, but also more
7206 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7207 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
7208 // use isKnownPredicate later if needed.
7209 if (isKnownNonNegative(RHS) &&
7210 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7211 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS))
7217 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7218 /// protected by a conditional between LHS and RHS. This is used to
7219 /// to eliminate casts.
7221 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7222 ICmpInst::Predicate Pred,
7223 const SCEV *LHS, const SCEV *RHS) {
7224 // Interpret a null as meaning no loop, where there is obviously no guard
7225 // (interprocedural conditions notwithstanding).
7226 if (!L) return true;
7228 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7230 BasicBlock *Latch = L->getLoopLatch();
7234 BranchInst *LoopContinuePredicate =
7235 dyn_cast<BranchInst>(Latch->getTerminator());
7236 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7237 isImpliedCond(Pred, LHS, RHS,
7238 LoopContinuePredicate->getCondition(),
7239 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7242 // We don't want more than one activation of the following loops on the stack
7243 // -- that can lead to O(n!) time complexity.
7244 if (WalkingBEDominatingConds)
7247 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7249 // See if we can exploit a trip count to prove the predicate.
7250 const auto &BETakenInfo = getBackedgeTakenInfo(L);
7251 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7252 if (LatchBECount != getCouldNotCompute()) {
7253 // We know that Latch branches back to the loop header exactly
7254 // LatchBECount times. This means the backdege condition at Latch is
7255 // equivalent to "{0,+,1} u< LatchBECount".
7256 Type *Ty = LatchBECount->getType();
7257 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7258 const SCEV *LoopCounter =
7259 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7260 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7265 // Check conditions due to any @llvm.assume intrinsics.
7266 for (auto &AssumeVH : AC.assumptions()) {
7269 auto *CI = cast<CallInst>(AssumeVH);
7270 if (!DT.dominates(CI, Latch->getTerminator()))
7273 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7277 // If the loop is not reachable from the entry block, we risk running into an
7278 // infinite loop as we walk up into the dom tree. These loops do not matter
7279 // anyway, so we just return a conservative answer when we see them.
7280 if (!DT.isReachableFromEntry(L->getHeader()))
7283 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7284 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7286 assert(DTN && "should reach the loop header before reaching the root!");
7288 BasicBlock *BB = DTN->getBlock();
7289 BasicBlock *PBB = BB->getSinglePredecessor();
7293 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7294 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7297 Value *Condition = ContinuePredicate->getCondition();
7299 // If we have an edge `E` within the loop body that dominates the only
7300 // latch, the condition guarding `E` also guards the backedge. This
7301 // reasoning works only for loops with a single latch.
7303 BasicBlockEdge DominatingEdge(PBB, BB);
7304 if (DominatingEdge.isSingleEdge()) {
7305 // We're constructively (and conservatively) enumerating edges within the
7306 // loop body that dominate the latch. The dominator tree better agree
7308 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7310 if (isImpliedCond(Pred, LHS, RHS, Condition,
7311 BB != ContinuePredicate->getSuccessor(0)))
7319 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7320 /// by a conditional between LHS and RHS. This is used to help avoid max
7321 /// expressions in loop trip counts, and to eliminate casts.
7323 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7324 ICmpInst::Predicate Pred,
7325 const SCEV *LHS, const SCEV *RHS) {
7326 // Interpret a null as meaning no loop, where there is obviously no guard
7327 // (interprocedural conditions notwithstanding).
7328 if (!L) return false;
7330 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7332 // Starting at the loop predecessor, climb up the predecessor chain, as long
7333 // as there are predecessors that can be found that have unique successors
7334 // leading to the original header.
7335 for (std::pair<BasicBlock *, BasicBlock *>
7336 Pair(L->getLoopPredecessor(), L->getHeader());
7338 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7340 BranchInst *LoopEntryPredicate =
7341 dyn_cast<BranchInst>(Pair.first->getTerminator());
7342 if (!LoopEntryPredicate ||
7343 LoopEntryPredicate->isUnconditional())
7346 if (isImpliedCond(Pred, LHS, RHS,
7347 LoopEntryPredicate->getCondition(),
7348 LoopEntryPredicate->getSuccessor(0) != Pair.second))
7352 // Check conditions due to any @llvm.assume intrinsics.
7353 for (auto &AssumeVH : AC.assumptions()) {
7356 auto *CI = cast<CallInst>(AssumeVH);
7357 if (!DT.dominates(CI, L->getHeader()))
7360 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7368 /// RAII wrapper to prevent recursive application of isImpliedCond.
7369 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7370 /// currently evaluating isImpliedCond.
7371 struct MarkPendingLoopPredicate {
7373 DenseSet<Value*> &LoopPreds;
7376 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7377 : Cond(C), LoopPreds(LP) {
7378 Pending = !LoopPreds.insert(Cond).second;
7380 ~MarkPendingLoopPredicate() {
7382 LoopPreds.erase(Cond);
7385 } // end anonymous namespace
7387 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7388 /// and RHS is true whenever the given Cond value evaluates to true.
7389 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7390 const SCEV *LHS, const SCEV *RHS,
7391 Value *FoundCondValue,
7393 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7397 // Recursively handle And and Or conditions.
7398 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7399 if (BO->getOpcode() == Instruction::And) {
7401 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7402 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7403 } else if (BO->getOpcode() == Instruction::Or) {
7405 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7406 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7410 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
7411 if (!ICI) return false;
7413 // Now that we found a conditional branch that dominates the loop or controls
7414 // the loop latch. Check to see if it is the comparison we are looking for.
7415 ICmpInst::Predicate FoundPred;
7417 FoundPred = ICI->getInversePredicate();
7419 FoundPred = ICI->getPredicate();
7421 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
7422 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
7424 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
7427 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
7429 ICmpInst::Predicate FoundPred,
7430 const SCEV *FoundLHS,
7431 const SCEV *FoundRHS) {
7432 // Balance the types.
7433 if (getTypeSizeInBits(LHS->getType()) <
7434 getTypeSizeInBits(FoundLHS->getType())) {
7435 if (CmpInst::isSigned(Pred)) {
7436 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
7437 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
7439 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
7440 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
7442 } else if (getTypeSizeInBits(LHS->getType()) >
7443 getTypeSizeInBits(FoundLHS->getType())) {
7444 if (CmpInst::isSigned(FoundPred)) {
7445 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
7446 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
7448 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
7449 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
7453 // Canonicalize the query to match the way instcombine will have
7454 // canonicalized the comparison.
7455 if (SimplifyICmpOperands(Pred, LHS, RHS))
7457 return CmpInst::isTrueWhenEqual(Pred);
7458 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
7459 if (FoundLHS == FoundRHS)
7460 return CmpInst::isFalseWhenEqual(FoundPred);
7462 // Check to see if we can make the LHS or RHS match.
7463 if (LHS == FoundRHS || RHS == FoundLHS) {
7464 if (isa<SCEVConstant>(RHS)) {
7465 std::swap(FoundLHS, FoundRHS);
7466 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
7468 std::swap(LHS, RHS);
7469 Pred = ICmpInst::getSwappedPredicate(Pred);
7473 // Check whether the found predicate is the same as the desired predicate.
7474 if (FoundPred == Pred)
7475 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7477 // Check whether swapping the found predicate makes it the same as the
7478 // desired predicate.
7479 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
7480 if (isa<SCEVConstant>(RHS))
7481 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
7483 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
7484 RHS, LHS, FoundLHS, FoundRHS);
7487 // Unsigned comparison is the same as signed comparison when both the operands
7488 // are non-negative.
7489 if (CmpInst::isUnsigned(FoundPred) &&
7490 CmpInst::getSignedPredicate(FoundPred) == Pred &&
7491 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
7492 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7494 // Check if we can make progress by sharpening ranges.
7495 if (FoundPred == ICmpInst::ICMP_NE &&
7496 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
7498 const SCEVConstant *C = nullptr;
7499 const SCEV *V = nullptr;
7501 if (isa<SCEVConstant>(FoundLHS)) {
7502 C = cast<SCEVConstant>(FoundLHS);
7505 C = cast<SCEVConstant>(FoundRHS);
7509 // The guarding predicate tells us that C != V. If the known range
7510 // of V is [C, t), we can sharpen the range to [C + 1, t). The
7511 // range we consider has to correspond to same signedness as the
7512 // predicate we're interested in folding.
7514 APInt Min = ICmpInst::isSigned(Pred) ?
7515 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7517 if (Min == C->getValue()->getValue()) {
7518 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7519 // This is true even if (Min + 1) wraps around -- in case of
7520 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7522 APInt SharperMin = Min + 1;
7525 case ICmpInst::ICMP_SGE:
7526 case ICmpInst::ICMP_UGE:
7527 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7529 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7530 getConstant(SharperMin)))
7533 case ICmpInst::ICMP_SGT:
7534 case ICmpInst::ICMP_UGT:
7535 // We know from the range information that (V `Pred` Min ||
7536 // V == Min). We know from the guarding condition that !(V
7537 // == Min). This gives us
7539 // V `Pred` Min || V == Min && !(V == Min)
7542 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7544 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7554 // Check whether the actual condition is beyond sufficient.
7555 if (FoundPred == ICmpInst::ICMP_EQ)
7556 if (ICmpInst::isTrueWhenEqual(Pred))
7557 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7559 if (Pred == ICmpInst::ICMP_NE)
7560 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7561 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7564 // Otherwise assume the worst.
7568 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
7569 const SCEV *&L, const SCEV *&R,
7570 SCEV::NoWrapFlags &Flags) {
7571 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
7572 if (!AE || AE->getNumOperands() != 2)
7575 L = AE->getOperand(0);
7576 R = AE->getOperand(1);
7577 Flags = AE->getNoWrapFlags();
7581 bool ScalarEvolution::computeConstantDifference(const SCEV *Less,
7584 // We avoid subtracting expressions here because this function is usually
7585 // fairly deep in the call stack (i.e. is called many times).
7587 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
7588 const auto *LAR = cast<SCEVAddRecExpr>(Less);
7589 const auto *MAR = cast<SCEVAddRecExpr>(More);
7591 if (LAR->getLoop() != MAR->getLoop())
7594 // We look at affine expressions only; not for correctness but to keep
7595 // getStepRecurrence cheap.
7596 if (!LAR->isAffine() || !MAR->isAffine())
7599 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
7602 Less = LAR->getStart();
7603 More = MAR->getStart();
7608 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
7609 const auto &M = cast<SCEVConstant>(More)->getValue()->getValue();
7610 const auto &L = cast<SCEVConstant>(Less)->getValue()->getValue();
7616 SCEV::NoWrapFlags Flags;
7617 if (splitBinaryAdd(Less, L, R, Flags))
7618 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7620 C = -(LC->getValue()->getValue());
7624 if (splitBinaryAdd(More, L, R, Flags))
7625 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7627 C = LC->getValue()->getValue();
7634 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
7635 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
7636 const SCEV *FoundLHS, const SCEV *FoundRHS) {
7637 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
7640 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7644 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
7645 if (!AddRecFoundLHS)
7648 // We'd like to let SCEV reason about control dependencies, so we constrain
7649 // both the inequalities to be about add recurrences on the same loop. This
7650 // way we can use isLoopEntryGuardedByCond later.
7652 const Loop *L = AddRecFoundLHS->getLoop();
7653 if (L != AddRecLHS->getLoop())
7656 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
7658 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
7661 // Informal proof for (2), assuming (1) [*]:
7663 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
7667 // FoundLHS s< FoundRHS s< INT_MIN - C
7668 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
7669 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
7670 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
7671 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
7672 // <=> FoundLHS + C s< FoundRHS + C
7674 // [*]: (1) can be proved by ruling out overflow.
7676 // [**]: This can be proved by analyzing all the four possibilities:
7677 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
7678 // (A s>= 0, B s>= 0).
7681 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
7682 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
7683 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
7684 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
7685 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
7689 if (!computeConstantDifference(FoundLHS, LHS, LDiff) ||
7690 !computeConstantDifference(FoundRHS, RHS, RDiff) ||
7697 APInt FoundRHSLimit;
7699 if (Pred == CmpInst::ICMP_ULT) {
7700 FoundRHSLimit = -RDiff;
7702 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
7703 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - RDiff;
7706 // Try to prove (1) or (2), as needed.
7707 return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
7708 getConstant(FoundRHSLimit));
7711 /// isImpliedCondOperands - Test whether the condition described by Pred,
7712 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7713 /// and FoundRHS is true.
7714 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7715 const SCEV *LHS, const SCEV *RHS,
7716 const SCEV *FoundLHS,
7717 const SCEV *FoundRHS) {
7718 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7721 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
7724 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7725 FoundLHS, FoundRHS) ||
7726 // ~x < ~y --> x > y
7727 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7728 getNotSCEV(FoundRHS),
7729 getNotSCEV(FoundLHS));
7733 /// If Expr computes ~A, return A else return nullptr
7734 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7735 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7736 if (!Add || Add->getNumOperands() != 2 ||
7737 !Add->getOperand(0)->isAllOnesValue())
7740 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7741 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
7742 !AddRHS->getOperand(0)->isAllOnesValue())
7745 return AddRHS->getOperand(1);
7749 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7750 template<typename MaxExprType>
7751 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7752 const SCEV *Candidate) {
7753 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7754 if (!MaxExpr) return false;
7756 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7757 return It != MaxExpr->op_end();
7761 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7762 template<typename MaxExprType>
7763 static bool IsMinConsistingOf(ScalarEvolution &SE,
7764 const SCEV *MaybeMinExpr,
7765 const SCEV *Candidate) {
7766 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7770 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7773 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
7774 ICmpInst::Predicate Pred,
7775 const SCEV *LHS, const SCEV *RHS) {
7777 // If both sides are affine addrecs for the same loop, with equal
7778 // steps, and we know the recurrences don't wrap, then we only
7779 // need to check the predicate on the starting values.
7781 if (!ICmpInst::isRelational(Pred))
7784 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7787 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7790 if (LAR->getLoop() != RAR->getLoop())
7792 if (!LAR->isAffine() || !RAR->isAffine())
7795 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
7798 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
7799 SCEV::FlagNSW : SCEV::FlagNUW;
7800 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
7803 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
7806 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7808 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7809 ICmpInst::Predicate Pred,
7810 const SCEV *LHS, const SCEV *RHS) {
7815 case ICmpInst::ICMP_SGE:
7816 std::swap(LHS, RHS);
7818 case ICmpInst::ICMP_SLE:
7821 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7823 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7825 case ICmpInst::ICMP_UGE:
7826 std::swap(LHS, RHS);
7828 case ICmpInst::ICMP_ULE:
7831 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7833 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7836 llvm_unreachable("covered switch fell through?!");
7839 /// isImpliedCondOperandsHelper - Test whether the condition described by
7840 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7841 /// FoundLHS, and FoundRHS is true.
7843 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7844 const SCEV *LHS, const SCEV *RHS,
7845 const SCEV *FoundLHS,
7846 const SCEV *FoundRHS) {
7847 auto IsKnownPredicateFull =
7848 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7849 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7850 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
7851 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
7852 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
7856 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7857 case ICmpInst::ICMP_EQ:
7858 case ICmpInst::ICMP_NE:
7859 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7862 case ICmpInst::ICMP_SLT:
7863 case ICmpInst::ICMP_SLE:
7864 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7865 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7868 case ICmpInst::ICMP_SGT:
7869 case ICmpInst::ICMP_SGE:
7870 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7871 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7874 case ICmpInst::ICMP_ULT:
7875 case ICmpInst::ICMP_ULE:
7876 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7877 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7880 case ICmpInst::ICMP_UGT:
7881 case ICmpInst::ICMP_UGE:
7882 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7883 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7891 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
7892 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
7893 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
7896 const SCEV *FoundLHS,
7897 const SCEV *FoundRHS) {
7898 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
7899 // The restriction on `FoundRHS` be lifted easily -- it exists only to
7900 // reduce the compile time impact of this optimization.
7903 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
7904 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
7905 !isa<SCEVConstant>(AddLHS->getOperand(0)))
7908 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
7910 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
7911 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
7912 ConstantRange FoundLHSRange =
7913 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
7915 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
7918 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
7919 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
7921 // We can also compute the range of values for `LHS` that satisfy the
7922 // consequent, "`LHS` `Pred` `RHS`":
7923 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
7924 ConstantRange SatisfyingLHSRange =
7925 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
7927 // The antecedent implies the consequent if every value of `LHS` that
7928 // satisfies the antecedent also satisfies the consequent.
7929 return SatisfyingLHSRange.contains(LHSRange);
7932 // Verify if an linear IV with positive stride can overflow when in a
7933 // less-than comparison, knowing the invariant term of the comparison, the
7934 // stride and the knowledge of NSW/NUW flags on the recurrence.
7935 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7936 bool IsSigned, bool NoWrap) {
7937 if (NoWrap) return false;
7939 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7940 const SCEV *One = getOne(Stride->getType());
7943 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7944 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7945 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7948 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7949 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7952 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7953 APInt MaxValue = APInt::getMaxValue(BitWidth);
7954 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7957 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7958 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7961 // Verify if an linear IV with negative stride can overflow when in a
7962 // greater-than comparison, knowing the invariant term of the comparison,
7963 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7964 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7965 bool IsSigned, bool NoWrap) {
7966 if (NoWrap) return false;
7968 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7969 const SCEV *One = getOne(Stride->getType());
7972 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7973 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7974 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7977 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7978 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7981 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7982 APInt MinValue = APInt::getMinValue(BitWidth);
7983 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7986 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7987 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7990 // Compute the backedge taken count knowing the interval difference, the
7991 // stride and presence of the equality in the comparison.
7992 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7994 const SCEV *One = getOne(Step->getType());
7995 Delta = Equality ? getAddExpr(Delta, Step)
7996 : getAddExpr(Delta, getMinusSCEV(Step, One));
7997 return getUDivExpr(Delta, Step);
8000 /// HowManyLessThans - Return the number of times a backedge containing the
8001 /// specified less-than comparison will execute. If not computable, return
8002 /// CouldNotCompute.
8004 /// @param ControlsExit is true when the LHS < RHS condition directly controls
8005 /// the branch (loops exits only if condition is true). In this case, we can use
8006 /// NoWrapFlags to skip overflow checks.
8007 ScalarEvolution::ExitLimit
8008 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
8009 const Loop *L, bool IsSigned,
8010 bool ControlsExit) {
8011 // We handle only IV < Invariant
8012 if (!isLoopInvariant(RHS, L))
8013 return getCouldNotCompute();
8015 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8017 // Avoid weird loops
8018 if (!IV || IV->getLoop() != L || !IV->isAffine())
8019 return getCouldNotCompute();
8021 bool NoWrap = ControlsExit &&
8022 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8024 const SCEV *Stride = IV->getStepRecurrence(*this);
8026 // Avoid negative or zero stride values
8027 if (!isKnownPositive(Stride))
8028 return getCouldNotCompute();
8030 // Avoid proven overflow cases: this will ensure that the backedge taken count
8031 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8032 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8033 // behaviors like the case of C language.
8034 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
8035 return getCouldNotCompute();
8037 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
8038 : ICmpInst::ICMP_ULT;
8039 const SCEV *Start = IV->getStart();
8040 const SCEV *End = RHS;
8041 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
8042 const SCEV *Diff = getMinusSCEV(RHS, Start);
8043 // If we have NoWrap set, then we can assume that the increment won't
8044 // overflow, in which case if RHS - Start is a constant, we don't need to
8045 // do a max operation since we can just figure it out statically
8046 if (NoWrap && isa<SCEVConstant>(Diff)) {
8047 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
8051 End = IsSigned ? getSMaxExpr(RHS, Start)
8052 : getUMaxExpr(RHS, Start);
8055 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
8057 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
8058 : getUnsignedRange(Start).getUnsignedMin();
8060 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8061 : getUnsignedRange(Stride).getUnsignedMin();
8063 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8064 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
8065 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
8067 // Although End can be a MAX expression we estimate MaxEnd considering only
8068 // the case End = RHS. This is safe because in the other case (End - Start)
8069 // is zero, leading to a zero maximum backedge taken count.
8071 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8072 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8074 const SCEV *MaxBECount;
8075 if (isa<SCEVConstant>(BECount))
8076 MaxBECount = BECount;
8078 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8079 getConstant(MinStride), false);
8081 if (isa<SCEVCouldNotCompute>(MaxBECount))
8082 MaxBECount = BECount;
8084 return ExitLimit(BECount, MaxBECount);
8087 ScalarEvolution::ExitLimit
8088 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8089 const Loop *L, bool IsSigned,
8090 bool ControlsExit) {
8091 // We handle only IV > Invariant
8092 if (!isLoopInvariant(RHS, L))
8093 return getCouldNotCompute();
8095 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8097 // Avoid weird loops
8098 if (!IV || IV->getLoop() != L || !IV->isAffine())
8099 return getCouldNotCompute();
8101 bool NoWrap = ControlsExit &&
8102 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8104 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8106 // Avoid negative or zero stride values
8107 if (!isKnownPositive(Stride))
8108 return getCouldNotCompute();
8110 // Avoid proven overflow cases: this will ensure that the backedge taken count
8111 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8112 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8113 // behaviors like the case of C language.
8114 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8115 return getCouldNotCompute();
8117 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8118 : ICmpInst::ICMP_UGT;
8120 const SCEV *Start = IV->getStart();
8121 const SCEV *End = RHS;
8122 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
8123 const SCEV *Diff = getMinusSCEV(RHS, Start);
8124 // If we have NoWrap set, then we can assume that the increment won't
8125 // overflow, in which case if RHS - Start is a constant, we don't need to
8126 // do a max operation since we can just figure it out statically
8127 if (NoWrap && isa<SCEVConstant>(Diff)) {
8128 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
8129 if (!D.isNegative())
8132 End = IsSigned ? getSMinExpr(RHS, Start)
8133 : getUMinExpr(RHS, Start);
8136 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8138 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8139 : getUnsignedRange(Start).getUnsignedMax();
8141 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8142 : getUnsignedRange(Stride).getUnsignedMin();
8144 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8145 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8146 : APInt::getMinValue(BitWidth) + (MinStride - 1);
8148 // Although End can be a MIN expression we estimate MinEnd considering only
8149 // the case End = RHS. This is safe because in the other case (Start - End)
8150 // is zero, leading to a zero maximum backedge taken count.
8152 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8153 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8156 const SCEV *MaxBECount = getCouldNotCompute();
8157 if (isa<SCEVConstant>(BECount))
8158 MaxBECount = BECount;
8160 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8161 getConstant(MinStride), false);
8163 if (isa<SCEVCouldNotCompute>(MaxBECount))
8164 MaxBECount = BECount;
8166 return ExitLimit(BECount, MaxBECount);
8169 /// getNumIterationsInRange - Return the number of iterations of this loop that
8170 /// produce values in the specified constant range. Another way of looking at
8171 /// this is that it returns the first iteration number where the value is not in
8172 /// the condition, thus computing the exit count. If the iteration count can't
8173 /// be computed, an instance of SCEVCouldNotCompute is returned.
8174 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
8175 ScalarEvolution &SE) const {
8176 if (Range.isFullSet()) // Infinite loop.
8177 return SE.getCouldNotCompute();
8179 // If the start is a non-zero constant, shift the range to simplify things.
8180 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8181 if (!SC->getValue()->isZero()) {
8182 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8183 Operands[0] = SE.getZero(SC->getType());
8184 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8185 getNoWrapFlags(FlagNW));
8186 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
8187 return ShiftedAddRec->getNumIterationsInRange(
8188 Range.subtract(SC->getValue()->getValue()), SE);
8189 // This is strange and shouldn't happen.
8190 return SE.getCouldNotCompute();
8193 // The only time we can solve this is when we have all constant indices.
8194 // Otherwise, we cannot determine the overflow conditions.
8195 if (std::any_of(op_begin(), op_end(),
8196 [](const SCEV *Op) { return !isa<SCEVConstant>(Op);}))
8197 return SE.getCouldNotCompute();
8199 // Okay at this point we know that all elements of the chrec are constants and
8200 // that the start element is zero.
8202 // First check to see if the range contains zero. If not, the first
8204 unsigned BitWidth = SE.getTypeSizeInBits(getType());
8205 if (!Range.contains(APInt(BitWidth, 0)))
8206 return SE.getZero(getType());
8209 // If this is an affine expression then we have this situation:
8210 // Solve {0,+,A} in Range === Ax in Range
8212 // We know that zero is in the range. If A is positive then we know that
8213 // the upper value of the range must be the first possible exit value.
8214 // If A is negative then the lower of the range is the last possible loop
8215 // value. Also note that we already checked for a full range.
8216 APInt One(BitWidth,1);
8217 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
8218 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8220 // The exit value should be (End+A)/A.
8221 APInt ExitVal = (End + A).udiv(A);
8222 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8224 // Evaluate at the exit value. If we really did fall out of the valid
8225 // range, then we computed our trip count, otherwise wrap around or other
8226 // things must have happened.
8227 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8228 if (Range.contains(Val->getValue()))
8229 return SE.getCouldNotCompute(); // Something strange happened
8231 // Ensure that the previous value is in the range. This is a sanity check.
8232 assert(Range.contains(
8233 EvaluateConstantChrecAtConstant(this,
8234 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8235 "Linear scev computation is off in a bad way!");
8236 return SE.getConstant(ExitValue);
8237 } else if (isQuadratic()) {
8238 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8239 // quadratic equation to solve it. To do this, we must frame our problem in
8240 // terms of figuring out when zero is crossed, instead of when
8241 // Range.getUpper() is crossed.
8242 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8243 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8244 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
8245 // getNoWrapFlags(FlagNW)
8248 // Next, solve the constructed addrec
8249 std::pair<const SCEV *,const SCEV *> Roots =
8250 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
8251 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
8252 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
8254 // Pick the smallest positive root value.
8255 if (ConstantInt *CB =
8256 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
8257 R1->getValue(), R2->getValue()))) {
8258 if (!CB->getZExtValue())
8259 std::swap(R1, R2); // R1 is the minimum root now.
8261 // Make sure the root is not off by one. The returned iteration should
8262 // not be in the range, but the previous one should be. When solving
8263 // for "X*X < 5", for example, we should not return a root of 2.
8264 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
8267 if (Range.contains(R1Val->getValue())) {
8268 // The next iteration must be out of the range...
8269 ConstantInt *NextVal =
8270 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
8272 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8273 if (!Range.contains(R1Val->getValue()))
8274 return SE.getConstant(NextVal);
8275 return SE.getCouldNotCompute(); // Something strange happened
8278 // If R1 was not in the range, then it is a good return value. Make
8279 // sure that R1-1 WAS in the range though, just in case.
8280 ConstantInt *NextVal =
8281 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
8282 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8283 if (Range.contains(R1Val->getValue()))
8285 return SE.getCouldNotCompute(); // Something strange happened
8290 return SE.getCouldNotCompute();
8296 FindUndefs() : Found(false) {}
8298 bool follow(const SCEV *S) {
8299 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
8300 if (isa<UndefValue>(C->getValue()))
8302 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
8303 if (isa<UndefValue>(C->getValue()))
8307 // Keep looking if we haven't found it yet.
8310 bool isDone() const {
8311 // Stop recursion if we have found an undef.
8317 // Return true when S contains at least an undef value.
8319 containsUndefs(const SCEV *S) {
8321 SCEVTraversal<FindUndefs> ST(F);
8328 // Collect all steps of SCEV expressions.
8329 struct SCEVCollectStrides {
8330 ScalarEvolution &SE;
8331 SmallVectorImpl<const SCEV *> &Strides;
8333 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
8334 : SE(SE), Strides(S) {}
8336 bool follow(const SCEV *S) {
8337 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
8338 Strides.push_back(AR->getStepRecurrence(SE));
8341 bool isDone() const { return false; }
8344 // Collect all SCEVUnknown and SCEVMulExpr expressions.
8345 struct SCEVCollectTerms {
8346 SmallVectorImpl<const SCEV *> &Terms;
8348 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
8351 bool follow(const SCEV *S) {
8352 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
8353 if (!containsUndefs(S))
8356 // Stop recursion: once we collected a term, do not walk its operands.
8363 bool isDone() const { return false; }
8366 // Check if a SCEV contains an AddRecExpr.
8367 struct SCEVHasAddRec {
8368 bool &ContainsAddRec;
8370 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
8371 ContainsAddRec = false;
8374 bool follow(const SCEV *S) {
8375 if (isa<SCEVAddRecExpr>(S)) {
8376 ContainsAddRec = true;
8378 // Stop recursion: once we collected a term, do not walk its operands.
8385 bool isDone() const { return false; }
8388 // Find factors that are multiplied with an expression that (possibly as a
8389 // subexpression) contains an AddRecExpr. In the expression:
8391 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
8393 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
8394 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
8395 // parameters as they form a product with an induction variable.
8397 // This collector expects all array size parameters to be in the same MulExpr.
8398 // It might be necessary to later add support for collecting parameters that are
8399 // spread over different nested MulExpr.
8400 struct SCEVCollectAddRecMultiplies {
8401 SmallVectorImpl<const SCEV *> &Terms;
8402 ScalarEvolution &SE;
8404 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
8405 : Terms(T), SE(SE) {}
8407 bool follow(const SCEV *S) {
8408 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
8409 bool HasAddRec = false;
8410 SmallVector<const SCEV *, 0> Operands;
8411 for (auto Op : Mul->operands()) {
8412 if (isa<SCEVUnknown>(Op)) {
8413 Operands.push_back(Op);
8415 bool ContainsAddRec;
8416 SCEVHasAddRec ContiansAddRec(ContainsAddRec);
8417 visitAll(Op, ContiansAddRec);
8418 HasAddRec |= ContainsAddRec;
8421 if (Operands.size() == 0)
8427 Terms.push_back(SE.getMulExpr(Operands));
8428 // Stop recursion: once we collected a term, do not walk its operands.
8435 bool isDone() const { return false; }
8439 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
8441 /// 1) The strides of AddRec expressions.
8442 /// 2) Unknowns that are multiplied with AddRec expressions.
8443 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
8444 SmallVectorImpl<const SCEV *> &Terms) {
8445 SmallVector<const SCEV *, 4> Strides;
8446 SCEVCollectStrides StrideCollector(*this, Strides);
8447 visitAll(Expr, StrideCollector);
8450 dbgs() << "Strides:\n";
8451 for (const SCEV *S : Strides)
8452 dbgs() << *S << "\n";
8455 for (const SCEV *S : Strides) {
8456 SCEVCollectTerms TermCollector(Terms);
8457 visitAll(S, TermCollector);
8461 dbgs() << "Terms:\n";
8462 for (const SCEV *T : Terms)
8463 dbgs() << *T << "\n";
8466 SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
8467 visitAll(Expr, MulCollector);
8470 static bool findArrayDimensionsRec(ScalarEvolution &SE,
8471 SmallVectorImpl<const SCEV *> &Terms,
8472 SmallVectorImpl<const SCEV *> &Sizes) {
8473 int Last = Terms.size() - 1;
8474 const SCEV *Step = Terms[Last];
8476 // End of recursion.
8478 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
8479 SmallVector<const SCEV *, 2> Qs;
8480 for (const SCEV *Op : M->operands())
8481 if (!isa<SCEVConstant>(Op))
8484 Step = SE.getMulExpr(Qs);
8487 Sizes.push_back(Step);
8491 for (const SCEV *&Term : Terms) {
8492 // Normalize the terms before the next call to findArrayDimensionsRec.
8494 SCEVDivision::divide(SE, Term, Step, &Q, &R);
8496 // Bail out when GCD does not evenly divide one of the terms.
8503 // Remove all SCEVConstants.
8504 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
8505 return isa<SCEVConstant>(E);
8509 if (Terms.size() > 0)
8510 if (!findArrayDimensionsRec(SE, Terms, Sizes))
8513 Sizes.push_back(Step);
8518 struct FindParameter {
8519 bool FoundParameter;
8520 FindParameter() : FoundParameter(false) {}
8522 bool follow(const SCEV *S) {
8523 if (isa<SCEVUnknown>(S)) {
8524 FoundParameter = true;
8525 // Stop recursion: we found a parameter.
8531 bool isDone() const {
8532 // Stop recursion if we have found a parameter.
8533 return FoundParameter;
8538 // Returns true when S contains at least a SCEVUnknown parameter.
8540 containsParameters(const SCEV *S) {
8542 SCEVTraversal<FindParameter> ST(F);
8545 return F.FoundParameter;
8548 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
8550 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
8551 for (const SCEV *T : Terms)
8552 if (containsParameters(T))
8557 // Return the number of product terms in S.
8558 static inline int numberOfTerms(const SCEV *S) {
8559 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
8560 return Expr->getNumOperands();
8564 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
8565 if (isa<SCEVConstant>(T))
8568 if (isa<SCEVUnknown>(T))
8571 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
8572 SmallVector<const SCEV *, 2> Factors;
8573 for (const SCEV *Op : M->operands())
8574 if (!isa<SCEVConstant>(Op))
8575 Factors.push_back(Op);
8577 return SE.getMulExpr(Factors);
8583 /// Return the size of an element read or written by Inst.
8584 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
8586 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
8587 Ty = Store->getValueOperand()->getType();
8588 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
8589 Ty = Load->getType();
8593 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
8594 return getSizeOfExpr(ETy, Ty);
8597 /// Second step of delinearization: compute the array dimensions Sizes from the
8598 /// set of Terms extracted from the memory access function of this SCEVAddRec.
8599 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
8600 SmallVectorImpl<const SCEV *> &Sizes,
8601 const SCEV *ElementSize) const {
8603 if (Terms.size() < 1 || !ElementSize)
8606 // Early return when Terms do not contain parameters: we do not delinearize
8607 // non parametric SCEVs.
8608 if (!containsParameters(Terms))
8612 dbgs() << "Terms:\n";
8613 for (const SCEV *T : Terms)
8614 dbgs() << *T << "\n";
8617 // Remove duplicates.
8618 std::sort(Terms.begin(), Terms.end());
8619 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
8621 // Put larger terms first.
8622 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
8623 return numberOfTerms(LHS) > numberOfTerms(RHS);
8626 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8628 // Try to divide all terms by the element size. If term is not divisible by
8629 // element size, proceed with the original term.
8630 for (const SCEV *&Term : Terms) {
8632 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
8637 SmallVector<const SCEV *, 4> NewTerms;
8639 // Remove constant factors.
8640 for (const SCEV *T : Terms)
8641 if (const SCEV *NewT = removeConstantFactors(SE, T))
8642 NewTerms.push_back(NewT);
8645 dbgs() << "Terms after sorting:\n";
8646 for (const SCEV *T : NewTerms)
8647 dbgs() << *T << "\n";
8650 if (NewTerms.empty() ||
8651 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
8656 // The last element to be pushed into Sizes is the size of an element.
8657 Sizes.push_back(ElementSize);
8660 dbgs() << "Sizes:\n";
8661 for (const SCEV *S : Sizes)
8662 dbgs() << *S << "\n";
8666 /// Third step of delinearization: compute the access functions for the
8667 /// Subscripts based on the dimensions in Sizes.
8668 void ScalarEvolution::computeAccessFunctions(
8669 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
8670 SmallVectorImpl<const SCEV *> &Sizes) {
8672 // Early exit in case this SCEV is not an affine multivariate function.
8676 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
8677 if (!AR->isAffine())
8680 const SCEV *Res = Expr;
8681 int Last = Sizes.size() - 1;
8682 for (int i = Last; i >= 0; i--) {
8684 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
8687 dbgs() << "Res: " << *Res << "\n";
8688 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
8689 dbgs() << "Res divided by Sizes[i]:\n";
8690 dbgs() << "Quotient: " << *Q << "\n";
8691 dbgs() << "Remainder: " << *R << "\n";
8696 // Do not record the last subscript corresponding to the size of elements in
8700 // Bail out if the remainder is too complex.
8701 if (isa<SCEVAddRecExpr>(R)) {
8710 // Record the access function for the current subscript.
8711 Subscripts.push_back(R);
8714 // Also push in last position the remainder of the last division: it will be
8715 // the access function of the innermost dimension.
8716 Subscripts.push_back(Res);
8718 std::reverse(Subscripts.begin(), Subscripts.end());
8721 dbgs() << "Subscripts:\n";
8722 for (const SCEV *S : Subscripts)
8723 dbgs() << *S << "\n";
8727 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
8728 /// sizes of an array access. Returns the remainder of the delinearization that
8729 /// is the offset start of the array. The SCEV->delinearize algorithm computes
8730 /// the multiples of SCEV coefficients: that is a pattern matching of sub
8731 /// expressions in the stride and base of a SCEV corresponding to the
8732 /// computation of a GCD (greatest common divisor) of base and stride. When
8733 /// SCEV->delinearize fails, it returns the SCEV unchanged.
8735 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
8737 /// void foo(long n, long m, long o, double A[n][m][o]) {
8739 /// for (long i = 0; i < n; i++)
8740 /// for (long j = 0; j < m; j++)
8741 /// for (long k = 0; k < o; k++)
8742 /// A[i][j][k] = 1.0;
8745 /// the delinearization input is the following AddRec SCEV:
8747 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
8749 /// From this SCEV, we are able to say that the base offset of the access is %A
8750 /// because it appears as an offset that does not divide any of the strides in
8753 /// CHECK: Base offset: %A
8755 /// and then SCEV->delinearize determines the size of some of the dimensions of
8756 /// the array as these are the multiples by which the strides are happening:
8758 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
8760 /// Note that the outermost dimension remains of UnknownSize because there are
8761 /// no strides that would help identifying the size of the last dimension: when
8762 /// the array has been statically allocated, one could compute the size of that
8763 /// dimension by dividing the overall size of the array by the size of the known
8764 /// dimensions: %m * %o * 8.
8766 /// Finally delinearize provides the access functions for the array reference
8767 /// that does correspond to A[i][j][k] of the above C testcase:
8769 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
8771 /// The testcases are checking the output of a function pass:
8772 /// DelinearizationPass that walks through all loads and stores of a function
8773 /// asking for the SCEV of the memory access with respect to all enclosing
8774 /// loops, calling SCEV->delinearize on that and printing the results.
8776 void ScalarEvolution::delinearize(const SCEV *Expr,
8777 SmallVectorImpl<const SCEV *> &Subscripts,
8778 SmallVectorImpl<const SCEV *> &Sizes,
8779 const SCEV *ElementSize) {
8780 // First step: collect parametric terms.
8781 SmallVector<const SCEV *, 4> Terms;
8782 collectParametricTerms(Expr, Terms);
8787 // Second step: find subscript sizes.
8788 findArrayDimensions(Terms, Sizes, ElementSize);
8793 // Third step: compute the access functions for each subscript.
8794 computeAccessFunctions(Expr, Subscripts, Sizes);
8796 if (Subscripts.empty())
8800 dbgs() << "succeeded to delinearize " << *Expr << "\n";
8801 dbgs() << "ArrayDecl[UnknownSize]";
8802 for (const SCEV *S : Sizes)
8803 dbgs() << "[" << *S << "]";
8805 dbgs() << "\nArrayRef";
8806 for (const SCEV *S : Subscripts)
8807 dbgs() << "[" << *S << "]";
8812 //===----------------------------------------------------------------------===//
8813 // SCEVCallbackVH Class Implementation
8814 //===----------------------------------------------------------------------===//
8816 void ScalarEvolution::SCEVCallbackVH::deleted() {
8817 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8818 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
8819 SE->ConstantEvolutionLoopExitValue.erase(PN);
8820 SE->ValueExprMap.erase(getValPtr());
8821 // this now dangles!
8824 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
8825 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8827 // Forget all the expressions associated with users of the old value,
8828 // so that future queries will recompute the expressions using the new
8830 Value *Old = getValPtr();
8831 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
8832 SmallPtrSet<User *, 8> Visited;
8833 while (!Worklist.empty()) {
8834 User *U = Worklist.pop_back_val();
8835 // Deleting the Old value will cause this to dangle. Postpone
8836 // that until everything else is done.
8839 if (!Visited.insert(U).second)
8841 if (PHINode *PN = dyn_cast<PHINode>(U))
8842 SE->ConstantEvolutionLoopExitValue.erase(PN);
8843 SE->ValueExprMap.erase(U);
8844 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
8846 // Delete the Old value.
8847 if (PHINode *PN = dyn_cast<PHINode>(Old))
8848 SE->ConstantEvolutionLoopExitValue.erase(PN);
8849 SE->ValueExprMap.erase(Old);
8850 // this now dangles!
8853 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
8854 : CallbackVH(V), SE(se) {}
8856 //===----------------------------------------------------------------------===//
8857 // ScalarEvolution Class Implementation
8858 //===----------------------------------------------------------------------===//
8860 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
8861 AssumptionCache &AC, DominatorTree &DT,
8863 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
8864 CouldNotCompute(new SCEVCouldNotCompute()),
8865 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
8866 ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
8867 FirstUnknown(nullptr) {}
8869 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
8870 : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
8871 CouldNotCompute(std::move(Arg.CouldNotCompute)),
8872 ValueExprMap(std::move(Arg.ValueExprMap)),
8873 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
8874 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
8875 ConstantEvolutionLoopExitValue(
8876 std::move(Arg.ConstantEvolutionLoopExitValue)),
8877 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
8878 LoopDispositions(std::move(Arg.LoopDispositions)),
8879 BlockDispositions(std::move(Arg.BlockDispositions)),
8880 UnsignedRanges(std::move(Arg.UnsignedRanges)),
8881 SignedRanges(std::move(Arg.SignedRanges)),
8882 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
8883 SCEVAllocator(std::move(Arg.SCEVAllocator)),
8884 FirstUnknown(Arg.FirstUnknown) {
8885 Arg.FirstUnknown = nullptr;
8888 ScalarEvolution::~ScalarEvolution() {
8889 // Iterate through all the SCEVUnknown instances and call their
8890 // destructors, so that they release their references to their values.
8891 for (SCEVUnknown *U = FirstUnknown; U;) {
8892 SCEVUnknown *Tmp = U;
8894 Tmp->~SCEVUnknown();
8896 FirstUnknown = nullptr;
8898 ValueExprMap.clear();
8900 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
8901 // that a loop had multiple computable exits.
8902 for (auto &BTCI : BackedgeTakenCounts)
8903 BTCI.second.clear();
8905 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
8906 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
8907 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
8910 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8911 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8914 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8916 // Print all inner loops first
8917 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8918 PrintLoopInfo(OS, SE, *I);
8921 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8924 SmallVector<BasicBlock *, 8> ExitBlocks;
8925 L->getExitBlocks(ExitBlocks);
8926 if (ExitBlocks.size() != 1)
8927 OS << "<multiple exits> ";
8929 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8930 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8932 OS << "Unpredictable backedge-taken count. ";
8937 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8940 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8941 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8943 OS << "Unpredictable max backedge-taken count. ";
8949 void ScalarEvolution::print(raw_ostream &OS) const {
8950 // ScalarEvolution's implementation of the print method is to print
8951 // out SCEV values of all instructions that are interesting. Doing
8952 // this potentially causes it to create new SCEV objects though,
8953 // which technically conflicts with the const qualifier. This isn't
8954 // observable from outside the class though, so casting away the
8955 // const isn't dangerous.
8956 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8958 OS << "Classifying expressions for: ";
8959 F.printAsOperand(OS, /*PrintType=*/false);
8961 for (Instruction &I : instructions(F))
8962 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
8965 const SCEV *SV = SE.getSCEV(&I);
8967 if (!isa<SCEVCouldNotCompute>(SV)) {
8969 SE.getUnsignedRange(SV).print(OS);
8971 SE.getSignedRange(SV).print(OS);
8974 const Loop *L = LI.getLoopFor(I.getParent());
8976 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8980 if (!isa<SCEVCouldNotCompute>(AtUse)) {
8982 SE.getUnsignedRange(AtUse).print(OS);
8984 SE.getSignedRange(AtUse).print(OS);
8989 OS << "\t\t" "Exits: ";
8990 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8991 if (!SE.isLoopInvariant(ExitValue, L)) {
8992 OS << "<<Unknown>>";
9001 OS << "Determining loop execution counts for: ";
9002 F.printAsOperand(OS, /*PrintType=*/false);
9004 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
9005 PrintLoopInfo(OS, &SE, *I);
9008 ScalarEvolution::LoopDisposition
9009 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
9010 auto &Values = LoopDispositions[S];
9011 for (auto &V : Values) {
9012 if (V.getPointer() == L)
9015 Values.emplace_back(L, LoopVariant);
9016 LoopDisposition D = computeLoopDisposition(S, L);
9017 auto &Values2 = LoopDispositions[S];
9018 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9019 if (V.getPointer() == L) {
9027 ScalarEvolution::LoopDisposition
9028 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
9029 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9031 return LoopInvariant;
9035 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
9036 case scAddRecExpr: {
9037 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9039 // If L is the addrec's loop, it's computable.
9040 if (AR->getLoop() == L)
9041 return LoopComputable;
9043 // Add recurrences are never invariant in the function-body (null loop).
9047 // This recurrence is variant w.r.t. L if L contains AR's loop.
9048 if (L->contains(AR->getLoop()))
9051 // This recurrence is invariant w.r.t. L if AR's loop contains L.
9052 if (AR->getLoop()->contains(L))
9053 return LoopInvariant;
9055 // This recurrence is variant w.r.t. L if any of its operands
9057 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
9059 if (!isLoopInvariant(*I, L))
9062 // Otherwise it's loop-invariant.
9063 return LoopInvariant;
9069 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9070 bool HasVarying = false;
9071 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
9073 LoopDisposition D = getLoopDisposition(*I, L);
9074 if (D == LoopVariant)
9076 if (D == LoopComputable)
9079 return HasVarying ? LoopComputable : LoopInvariant;
9082 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9083 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
9084 if (LD == LoopVariant)
9086 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
9087 if (RD == LoopVariant)
9089 return (LD == LoopInvariant && RD == LoopInvariant) ?
9090 LoopInvariant : LoopComputable;
9093 // All non-instruction values are loop invariant. All instructions are loop
9094 // invariant if they are not contained in the specified loop.
9095 // Instructions are never considered invariant in the function body
9096 // (null loop) because they are defined within the "loop".
9097 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
9098 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
9099 return LoopInvariant;
9100 case scCouldNotCompute:
9101 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9103 llvm_unreachable("Unknown SCEV kind!");
9106 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
9107 return getLoopDisposition(S, L) == LoopInvariant;
9110 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
9111 return getLoopDisposition(S, L) == LoopComputable;
9114 ScalarEvolution::BlockDisposition
9115 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9116 auto &Values = BlockDispositions[S];
9117 for (auto &V : Values) {
9118 if (V.getPointer() == BB)
9121 Values.emplace_back(BB, DoesNotDominateBlock);
9122 BlockDisposition D = computeBlockDisposition(S, BB);
9123 auto &Values2 = BlockDispositions[S];
9124 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9125 if (V.getPointer() == BB) {
9133 ScalarEvolution::BlockDisposition
9134 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9135 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9137 return ProperlyDominatesBlock;
9141 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
9142 case scAddRecExpr: {
9143 // This uses a "dominates" query instead of "properly dominates" query
9144 // to test for proper dominance too, because the instruction which
9145 // produces the addrec's value is a PHI, and a PHI effectively properly
9146 // dominates its entire containing block.
9147 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9148 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9149 return DoesNotDominateBlock;
9151 // FALL THROUGH into SCEVNAryExpr handling.
9156 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9158 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
9160 BlockDisposition D = getBlockDisposition(*I, BB);
9161 if (D == DoesNotDominateBlock)
9162 return DoesNotDominateBlock;
9163 if (D == DominatesBlock)
9166 return Proper ? ProperlyDominatesBlock : DominatesBlock;
9169 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9170 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9171 BlockDisposition LD = getBlockDisposition(LHS, BB);
9172 if (LD == DoesNotDominateBlock)
9173 return DoesNotDominateBlock;
9174 BlockDisposition RD = getBlockDisposition(RHS, BB);
9175 if (RD == DoesNotDominateBlock)
9176 return DoesNotDominateBlock;
9177 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9178 ProperlyDominatesBlock : DominatesBlock;
9181 if (Instruction *I =
9182 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9183 if (I->getParent() == BB)
9184 return DominatesBlock;
9185 if (DT.properlyDominates(I->getParent(), BB))
9186 return ProperlyDominatesBlock;
9187 return DoesNotDominateBlock;
9189 return ProperlyDominatesBlock;
9190 case scCouldNotCompute:
9191 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9193 llvm_unreachable("Unknown SCEV kind!");
9196 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9197 return getBlockDisposition(S, BB) >= DominatesBlock;
9200 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9201 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9205 // Search for a SCEV expression node within an expression tree.
9206 // Implements SCEVTraversal::Visitor.
9211 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
9213 bool follow(const SCEV *S) {
9214 IsFound |= (S == Node);
9217 bool isDone() const { return IsFound; }
9221 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9222 SCEVSearch Search(Op);
9223 visitAll(S, Search);
9224 return Search.IsFound;
9227 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9228 ValuesAtScopes.erase(S);
9229 LoopDispositions.erase(S);
9230 BlockDispositions.erase(S);
9231 UnsignedRanges.erase(S);
9232 SignedRanges.erase(S);
9234 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
9235 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
9236 BackedgeTakenInfo &BEInfo = I->second;
9237 if (BEInfo.hasOperand(S, this)) {
9239 BackedgeTakenCounts.erase(I++);
9246 typedef DenseMap<const Loop *, std::string> VerifyMap;
9248 /// replaceSubString - Replaces all occurrences of From in Str with To.
9249 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9251 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9252 Str.replace(Pos, From.size(), To.data(), To.size());
9257 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9259 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9260 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
9261 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
9263 std::string &S = Map[L];
9265 raw_string_ostream OS(S);
9266 SE.getBackedgeTakenCount(L)->print(OS);
9268 // false and 0 are semantically equivalent. This can happen in dead loops.
9269 replaceSubString(OS.str(), "false", "0");
9270 // Remove wrap flags, their use in SCEV is highly fragile.
9271 // FIXME: Remove this when SCEV gets smarter about them.
9272 replaceSubString(OS.str(), "<nw>", "");
9273 replaceSubString(OS.str(), "<nsw>", "");
9274 replaceSubString(OS.str(), "<nuw>", "");
9279 void ScalarEvolution::verify() const {
9280 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9282 // Gather stringified backedge taken counts for all loops using SCEV's caches.
9283 // FIXME: It would be much better to store actual values instead of strings,
9284 // but SCEV pointers will change if we drop the caches.
9285 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9286 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9287 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9289 // Gather stringified backedge taken counts for all loops using a fresh
9290 // ScalarEvolution object.
9291 ScalarEvolution SE2(F, TLI, AC, DT, LI);
9292 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9293 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9295 // Now compare whether they're the same with and without caches. This allows
9296 // verifying that no pass changed the cache.
9297 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
9298 "New loops suddenly appeared!");
9300 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
9301 OldE = BackedgeDumpsOld.end(),
9302 NewI = BackedgeDumpsNew.begin();
9303 OldI != OldE; ++OldI, ++NewI) {
9304 assert(OldI->first == NewI->first && "Loop order changed!");
9306 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
9308 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
9309 // means that a pass is buggy or SCEV has to learn a new pattern but is
9310 // usually not harmful.
9311 if (OldI->second != NewI->second &&
9312 OldI->second.find("undef") == std::string::npos &&
9313 NewI->second.find("undef") == std::string::npos &&
9314 OldI->second != "***COULDNOTCOMPUTE***" &&
9315 NewI->second != "***COULDNOTCOMPUTE***") {
9316 dbgs() << "SCEVValidator: SCEV for loop '"
9317 << OldI->first->getHeader()->getName()
9318 << "' changed from '" << OldI->second
9319 << "' to '" << NewI->second << "'!\n";
9324 // TODO: Verify more things.
9327 char ScalarEvolutionAnalysis::PassID;
9329 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
9330 AnalysisManager<Function> *AM) {
9331 return ScalarEvolution(F, AM->getResult<TargetLibraryAnalysis>(F),
9332 AM->getResult<AssumptionAnalysis>(F),
9333 AM->getResult<DominatorTreeAnalysis>(F),
9334 AM->getResult<LoopAnalysis>(F));
9338 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> *AM) {
9339 AM->getResult<ScalarEvolutionAnalysis>(F).print(OS);
9340 return PreservedAnalyses::all();
9343 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
9344 "Scalar Evolution Analysis", false, true)
9345 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
9346 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
9347 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
9348 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
9349 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
9350 "Scalar Evolution Analysis", false, true)
9351 char ScalarEvolutionWrapperPass::ID = 0;
9353 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
9354 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
9357 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
9358 SE.reset(new ScalarEvolution(
9359 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
9360 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
9361 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
9362 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
9366 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
9368 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
9372 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
9379 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
9380 AU.setPreservesAll();
9381 AU.addRequiredTransitive<AssumptionCacheTracker>();
9382 AU.addRequiredTransitive<LoopInfoWrapperPass>();
9383 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
9384 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();