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/IR/PatternMatch.h"
87 #include "llvm/Support/CommandLine.h"
88 #include "llvm/Support/Debug.h"
89 #include "llvm/Support/ErrorHandling.h"
90 #include "llvm/Support/MathExtras.h"
91 #include "llvm/Support/raw_ostream.h"
92 #include "llvm/Support/SaveAndRestore.h"
96 #define DEBUG_TYPE "scalar-evolution"
98 STATISTIC(NumArrayLenItCounts,
99 "Number of trip counts computed with array length");
100 STATISTIC(NumTripCountsComputed,
101 "Number of loops with predictable loop counts");
102 STATISTIC(NumTripCountsNotComputed,
103 "Number of loops without predictable loop counts");
104 STATISTIC(NumBruteForceTripCountsComputed,
105 "Number of loops with trip counts computed by force");
107 static cl::opt<unsigned>
108 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
109 cl::desc("Maximum number of iterations SCEV will "
110 "symbolically execute a constant "
114 // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
116 VerifySCEV("verify-scev",
117 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
119 VerifySCEVMap("verify-scev-maps",
120 cl::desc("Verify no dangling value in ScalarEvolution's "
121 "ExprValueMap (slow)"));
123 //===----------------------------------------------------------------------===//
124 // SCEV class definitions
125 //===----------------------------------------------------------------------===//
127 //===----------------------------------------------------------------------===//
128 // Implementation of the SCEV class.
132 void SCEV::dump() const {
137 void SCEV::print(raw_ostream &OS) const {
138 switch (static_cast<SCEVTypes>(getSCEVType())) {
140 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
143 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
144 const SCEV *Op = Trunc->getOperand();
145 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
146 << *Trunc->getType() << ")";
150 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
151 const SCEV *Op = ZExt->getOperand();
152 OS << "(zext " << *Op->getType() << " " << *Op << " to "
153 << *ZExt->getType() << ")";
157 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
158 const SCEV *Op = SExt->getOperand();
159 OS << "(sext " << *Op->getType() << " " << *Op << " to "
160 << *SExt->getType() << ")";
164 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
165 OS << "{" << *AR->getOperand(0);
166 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
167 OS << ",+," << *AR->getOperand(i);
169 if (AR->hasNoUnsignedWrap())
171 if (AR->hasNoSignedWrap())
173 if (AR->hasNoSelfWrap() &&
174 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
176 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
184 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
185 const char *OpStr = nullptr;
186 switch (NAry->getSCEVType()) {
187 case scAddExpr: OpStr = " + "; break;
188 case scMulExpr: OpStr = " * "; break;
189 case scUMaxExpr: OpStr = " umax "; break;
190 case scSMaxExpr: OpStr = " smax "; break;
193 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
196 if (std::next(I) != E)
200 switch (NAry->getSCEVType()) {
203 if (NAry->hasNoUnsignedWrap())
205 if (NAry->hasNoSignedWrap())
211 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
212 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
216 const SCEVUnknown *U = cast<SCEVUnknown>(this);
218 if (U->isSizeOf(AllocTy)) {
219 OS << "sizeof(" << *AllocTy << ")";
222 if (U->isAlignOf(AllocTy)) {
223 OS << "alignof(" << *AllocTy << ")";
229 if (U->isOffsetOf(CTy, FieldNo)) {
230 OS << "offsetof(" << *CTy << ", ";
231 FieldNo->printAsOperand(OS, false);
236 // Otherwise just print it normally.
237 U->getValue()->printAsOperand(OS, false);
240 case scCouldNotCompute:
241 OS << "***COULDNOTCOMPUTE***";
244 llvm_unreachable("Unknown SCEV kind!");
247 Type *SCEV::getType() const {
248 switch (static_cast<SCEVTypes>(getSCEVType())) {
250 return cast<SCEVConstant>(this)->getType();
254 return cast<SCEVCastExpr>(this)->getType();
259 return cast<SCEVNAryExpr>(this)->getType();
261 return cast<SCEVAddExpr>(this)->getType();
263 return cast<SCEVUDivExpr>(this)->getType();
265 return cast<SCEVUnknown>(this)->getType();
266 case scCouldNotCompute:
267 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
269 llvm_unreachable("Unknown SCEV kind!");
272 bool SCEV::isZero() const {
273 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
274 return SC->getValue()->isZero();
278 bool SCEV::isOne() const {
279 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
280 return SC->getValue()->isOne();
284 bool SCEV::isAllOnesValue() const {
285 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
286 return SC->getValue()->isAllOnesValue();
290 bool SCEV::isNonConstantNegative() const {
291 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
292 if (!Mul) return false;
294 // If there is a constant factor, it will be first.
295 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
296 if (!SC) return false;
298 // Return true if the value is negative, this matches things like (-42 * V).
299 return SC->getAPInt().isNegative();
302 SCEVCouldNotCompute::SCEVCouldNotCompute() :
303 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
305 bool SCEVCouldNotCompute::classof(const SCEV *S) {
306 return S->getSCEVType() == scCouldNotCompute;
309 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
311 ID.AddInteger(scConstant);
314 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
315 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
316 UniqueSCEVs.InsertNode(S, IP);
320 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
321 return getConstant(ConstantInt::get(getContext(), Val));
325 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
326 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
327 return getConstant(ConstantInt::get(ITy, V, isSigned));
330 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
331 unsigned SCEVTy, const SCEV *op, Type *ty)
332 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
334 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
335 const SCEV *op, Type *ty)
336 : SCEVCastExpr(ID, scTruncate, op, ty) {
337 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
338 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
339 "Cannot truncate non-integer value!");
342 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
343 const SCEV *op, Type *ty)
344 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
345 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
346 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
347 "Cannot zero extend non-integer value!");
350 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
351 const SCEV *op, Type *ty)
352 : SCEVCastExpr(ID, scSignExtend, op, ty) {
353 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
354 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
355 "Cannot sign extend non-integer value!");
358 void SCEVUnknown::deleted() {
359 // Clear this SCEVUnknown from various maps.
360 SE->forgetMemoizedResults(this);
362 // Remove this SCEVUnknown from the uniquing map.
363 SE->UniqueSCEVs.RemoveNode(this);
365 // Release the value.
369 void SCEVUnknown::allUsesReplacedWith(Value *New) {
370 // Clear this SCEVUnknown from various maps.
371 SE->forgetMemoizedResults(this);
373 // Remove this SCEVUnknown from the uniquing map.
374 SE->UniqueSCEVs.RemoveNode(this);
376 // Update this SCEVUnknown to point to the new value. This is needed
377 // because there may still be outstanding SCEVs which still point to
382 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
383 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
384 if (VCE->getOpcode() == Instruction::PtrToInt)
385 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
386 if (CE->getOpcode() == Instruction::GetElementPtr &&
387 CE->getOperand(0)->isNullValue() &&
388 CE->getNumOperands() == 2)
389 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
391 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
399 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
400 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
401 if (VCE->getOpcode() == Instruction::PtrToInt)
402 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
403 if (CE->getOpcode() == Instruction::GetElementPtr &&
404 CE->getOperand(0)->isNullValue()) {
406 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
407 if (StructType *STy = dyn_cast<StructType>(Ty))
408 if (!STy->isPacked() &&
409 CE->getNumOperands() == 3 &&
410 CE->getOperand(1)->isNullValue()) {
411 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
413 STy->getNumElements() == 2 &&
414 STy->getElementType(0)->isIntegerTy(1)) {
415 AllocTy = STy->getElementType(1);
424 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
425 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
426 if (VCE->getOpcode() == Instruction::PtrToInt)
427 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
428 if (CE->getOpcode() == Instruction::GetElementPtr &&
429 CE->getNumOperands() == 3 &&
430 CE->getOperand(0)->isNullValue() &&
431 CE->getOperand(1)->isNullValue()) {
433 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
434 // Ignore vector types here so that ScalarEvolutionExpander doesn't
435 // emit getelementptrs that index into vectors.
436 if (Ty->isStructTy() || Ty->isArrayTy()) {
438 FieldNo = CE->getOperand(2);
446 //===----------------------------------------------------------------------===//
448 //===----------------------------------------------------------------------===//
451 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
452 /// than the complexity of the RHS. This comparator is used to canonicalize
454 class SCEVComplexityCompare {
455 const LoopInfo *const LI;
457 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
459 // Return true or false if LHS is less than, or at least RHS, respectively.
460 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
461 return compare(LHS, RHS) < 0;
464 // Return negative, zero, or positive, if LHS is less than, equal to, or
465 // greater than RHS, respectively. A three-way result allows recursive
466 // comparisons to be more efficient.
467 int compare(const SCEV *LHS, const SCEV *RHS) const {
468 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
472 // Primarily, sort the SCEVs by their getSCEVType().
473 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
475 return (int)LType - (int)RType;
477 // Aside from the getSCEVType() ordering, the particular ordering
478 // isn't very important except that it's beneficial to be consistent,
479 // so that (a + b) and (b + a) don't end up as different expressions.
480 switch (static_cast<SCEVTypes>(LType)) {
482 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
483 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
485 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
486 // not as complete as it could be.
487 const Value *LV = LU->getValue(), *RV = RU->getValue();
489 // Order pointer values after integer values. This helps SCEVExpander
491 bool LIsPointer = LV->getType()->isPointerTy(),
492 RIsPointer = RV->getType()->isPointerTy();
493 if (LIsPointer != RIsPointer)
494 return (int)LIsPointer - (int)RIsPointer;
496 // Compare getValueID values.
497 unsigned LID = LV->getValueID(),
498 RID = RV->getValueID();
500 return (int)LID - (int)RID;
502 // Sort arguments by their position.
503 if (const Argument *LA = dyn_cast<Argument>(LV)) {
504 const Argument *RA = cast<Argument>(RV);
505 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
506 return (int)LArgNo - (int)RArgNo;
509 // For instructions, compare their loop depth, and their operand
510 // count. This is pretty loose.
511 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
512 const Instruction *RInst = cast<Instruction>(RV);
514 // Compare loop depths.
515 const BasicBlock *LParent = LInst->getParent(),
516 *RParent = RInst->getParent();
517 if (LParent != RParent) {
518 unsigned LDepth = LI->getLoopDepth(LParent),
519 RDepth = LI->getLoopDepth(RParent);
520 if (LDepth != RDepth)
521 return (int)LDepth - (int)RDepth;
524 // Compare the number of operands.
525 unsigned LNumOps = LInst->getNumOperands(),
526 RNumOps = RInst->getNumOperands();
527 return (int)LNumOps - (int)RNumOps;
534 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
535 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
537 // Compare constant values.
538 const APInt &LA = LC->getAPInt();
539 const APInt &RA = RC->getAPInt();
540 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
541 if (LBitWidth != RBitWidth)
542 return (int)LBitWidth - (int)RBitWidth;
543 return LA.ult(RA) ? -1 : 1;
547 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
548 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
550 // Compare addrec loop depths.
551 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
552 if (LLoop != RLoop) {
553 unsigned LDepth = LLoop->getLoopDepth(),
554 RDepth = RLoop->getLoopDepth();
555 if (LDepth != RDepth)
556 return (int)LDepth - (int)RDepth;
559 // Addrec complexity grows with operand count.
560 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
561 if (LNumOps != RNumOps)
562 return (int)LNumOps - (int)RNumOps;
564 // Lexicographically compare.
565 for (unsigned i = 0; i != LNumOps; ++i) {
566 long X = compare(LA->getOperand(i), RA->getOperand(i));
578 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
579 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
581 // Lexicographically compare n-ary expressions.
582 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
583 if (LNumOps != RNumOps)
584 return (int)LNumOps - (int)RNumOps;
586 for (unsigned i = 0; i != LNumOps; ++i) {
589 long X = compare(LC->getOperand(i), RC->getOperand(i));
593 return (int)LNumOps - (int)RNumOps;
597 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
598 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
600 // Lexicographically compare udiv expressions.
601 long X = compare(LC->getLHS(), RC->getLHS());
604 return compare(LC->getRHS(), RC->getRHS());
610 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
611 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
613 // Compare cast expressions by operand.
614 return compare(LC->getOperand(), RC->getOperand());
617 case scCouldNotCompute:
618 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
620 llvm_unreachable("Unknown SCEV kind!");
623 } // end anonymous namespace
625 /// Given a list of SCEV objects, order them by their complexity, and group
626 /// objects of the same complexity together by value. When this routine is
627 /// finished, we know that any duplicates in the vector are consecutive and that
628 /// complexity is monotonically increasing.
630 /// Note that we go take special precautions to ensure that we get deterministic
631 /// results from this routine. In other words, we don't want the results of
632 /// this to depend on where the addresses of various SCEV objects happened to
635 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
637 if (Ops.size() < 2) return; // Noop
638 if (Ops.size() == 2) {
639 // This is the common case, which also happens to be trivially simple.
641 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
642 if (SCEVComplexityCompare(LI)(RHS, LHS))
647 // Do the rough sort by complexity.
648 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
650 // Now that we are sorted by complexity, group elements of the same
651 // complexity. Note that this is, at worst, N^2, but the vector is likely to
652 // be extremely short in practice. Note that we take this approach because we
653 // do not want to depend on the addresses of the objects we are grouping.
654 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
655 const SCEV *S = Ops[i];
656 unsigned Complexity = S->getSCEVType();
658 // If there are any objects of the same complexity and same value as this
660 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
661 if (Ops[j] == S) { // Found a duplicate.
662 // Move it to immediately after i'th element.
663 std::swap(Ops[i+1], Ops[j]);
664 ++i; // no need to rescan it.
665 if (i == e-2) return; // Done!
671 // Returns the size of the SCEV S.
672 static inline int sizeOfSCEV(const SCEV *S) {
673 struct FindSCEVSize {
675 FindSCEVSize() : Size(0) {}
677 bool follow(const SCEV *S) {
679 // Keep looking at all operands of S.
682 bool isDone() const {
688 SCEVTraversal<FindSCEVSize> ST(F);
695 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
697 // Computes the Quotient and Remainder of the division of Numerator by
699 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
700 const SCEV *Denominator, const SCEV **Quotient,
701 const SCEV **Remainder) {
702 assert(Numerator && Denominator && "Uninitialized SCEV");
704 SCEVDivision D(SE, Numerator, Denominator);
706 // Check for the trivial case here to avoid having to check for it in the
708 if (Numerator == Denominator) {
714 if (Numerator->isZero()) {
720 // A simple case when N/1. The quotient is N.
721 if (Denominator->isOne()) {
722 *Quotient = Numerator;
727 // Split the Denominator when it is a product.
728 if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
730 *Quotient = Numerator;
731 for (const SCEV *Op : T->operands()) {
732 divide(SE, *Quotient, Op, &Q, &R);
735 // Bail out when the Numerator is not divisible by one of the terms of
739 *Remainder = Numerator;
748 *Quotient = D.Quotient;
749 *Remainder = D.Remainder;
752 // Except in the trivial case described above, we do not know how to divide
753 // Expr by Denominator for the following functions with empty implementation.
754 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
755 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
756 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
757 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
758 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
759 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
760 void visitUnknown(const SCEVUnknown *Numerator) {}
761 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
763 void visitConstant(const SCEVConstant *Numerator) {
764 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
765 APInt NumeratorVal = Numerator->getAPInt();
766 APInt DenominatorVal = D->getAPInt();
767 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
768 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
770 if (NumeratorBW > DenominatorBW)
771 DenominatorVal = DenominatorVal.sext(NumeratorBW);
772 else if (NumeratorBW < DenominatorBW)
773 NumeratorVal = NumeratorVal.sext(DenominatorBW);
775 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
776 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
777 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
778 Quotient = SE.getConstant(QuotientVal);
779 Remainder = SE.getConstant(RemainderVal);
784 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
785 const SCEV *StartQ, *StartR, *StepQ, *StepR;
786 if (!Numerator->isAffine())
787 return cannotDivide(Numerator);
788 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
789 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
790 // Bail out if the types do not match.
791 Type *Ty = Denominator->getType();
792 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
793 Ty != StepQ->getType() || Ty != StepR->getType())
794 return cannotDivide(Numerator);
795 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
796 Numerator->getNoWrapFlags());
797 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
798 Numerator->getNoWrapFlags());
801 void visitAddExpr(const SCEVAddExpr *Numerator) {
802 SmallVector<const SCEV *, 2> Qs, Rs;
803 Type *Ty = Denominator->getType();
805 for (const SCEV *Op : Numerator->operands()) {
807 divide(SE, Op, Denominator, &Q, &R);
809 // Bail out if types do not match.
810 if (Ty != Q->getType() || Ty != R->getType())
811 return cannotDivide(Numerator);
817 if (Qs.size() == 1) {
823 Quotient = SE.getAddExpr(Qs);
824 Remainder = SE.getAddExpr(Rs);
827 void visitMulExpr(const SCEVMulExpr *Numerator) {
828 SmallVector<const SCEV *, 2> Qs;
829 Type *Ty = Denominator->getType();
831 bool FoundDenominatorTerm = false;
832 for (const SCEV *Op : Numerator->operands()) {
833 // Bail out if types do not match.
834 if (Ty != Op->getType())
835 return cannotDivide(Numerator);
837 if (FoundDenominatorTerm) {
842 // Check whether Denominator divides one of the product operands.
844 divide(SE, Op, Denominator, &Q, &R);
850 // Bail out if types do not match.
851 if (Ty != Q->getType())
852 return cannotDivide(Numerator);
854 FoundDenominatorTerm = true;
858 if (FoundDenominatorTerm) {
863 Quotient = SE.getMulExpr(Qs);
867 if (!isa<SCEVUnknown>(Denominator))
868 return cannotDivide(Numerator);
870 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
871 ValueToValueMap RewriteMap;
872 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
873 cast<SCEVConstant>(Zero)->getValue();
874 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
876 if (Remainder->isZero()) {
877 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
878 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
879 cast<SCEVConstant>(One)->getValue();
881 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
885 // Quotient is (Numerator - Remainder) divided by Denominator.
887 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
888 // This SCEV does not seem to simplify: fail the division here.
889 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
890 return cannotDivide(Numerator);
891 divide(SE, Diff, Denominator, &Q, &R);
893 return cannotDivide(Numerator);
898 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
899 const SCEV *Denominator)
900 : SE(S), Denominator(Denominator) {
901 Zero = SE.getZero(Denominator->getType());
902 One = SE.getOne(Denominator->getType());
904 // We generally do not know how to divide Expr by Denominator. We
905 // initialize the division to a "cannot divide" state to simplify the rest
907 cannotDivide(Numerator);
910 // Convenience function for giving up on the division. We set the quotient to
911 // be equal to zero and the remainder to be equal to the numerator.
912 void cannotDivide(const SCEV *Numerator) {
914 Remainder = Numerator;
918 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
923 //===----------------------------------------------------------------------===//
924 // Simple SCEV method implementations
925 //===----------------------------------------------------------------------===//
927 /// Compute BC(It, K). The result has width W. Assume, K > 0.
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 /// Return the value of this chain of recurrences at the specified iteration
1039 /// number. We can evaluate this recurrence by multiplying each element in the
1040 /// chain by the binomial coefficient corresponding to it. In other words, we
1041 /// 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->getAPInt();
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 (!AR->hasNoUnsignedWrap()) {
1455 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1456 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1459 // If we have special knowledge that this addrec won't overflow,
1460 // we don't need to do any further analysis.
1461 if (AR->hasNoUnsignedWrap())
1462 return getAddRecExpr(
1463 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1464 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1466 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1467 // Note that this serves two purposes: It filters out loops that are
1468 // simply not analyzable, and it covers the case where this code is
1469 // being called from within backedge-taken count analysis, such that
1470 // attempting to ask for the backedge-taken count would likely result
1471 // in infinite recursion. In the later case, the analysis code will
1472 // cope with a conservative value, and it will take care to purge
1473 // that value once it has finished.
1474 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1475 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1476 // Manually compute the final value for AR, checking for
1479 // Check whether the backedge-taken count can be losslessly casted to
1480 // the addrec's type. The count is always unsigned.
1481 const SCEV *CastedMaxBECount =
1482 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1483 const SCEV *RecastedMaxBECount =
1484 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1485 if (MaxBECount == RecastedMaxBECount) {
1486 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1487 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1488 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1489 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1490 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1491 const SCEV *WideMaxBECount =
1492 getZeroExtendExpr(CastedMaxBECount, WideTy);
1493 const SCEV *OperandExtendedAdd =
1494 getAddExpr(WideStart,
1495 getMulExpr(WideMaxBECount,
1496 getZeroExtendExpr(Step, WideTy)));
1497 if (ZAdd == OperandExtendedAdd) {
1498 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1499 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1500 // Return the expression with the addrec on the outside.
1501 return getAddRecExpr(
1502 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1503 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1505 // Similar to above, only this time treat the step value as signed.
1506 // This covers loops that count down.
1507 OperandExtendedAdd =
1508 getAddExpr(WideStart,
1509 getMulExpr(WideMaxBECount,
1510 getSignExtendExpr(Step, WideTy)));
1511 if (ZAdd == OperandExtendedAdd) {
1512 // Cache knowledge of AR NW, which is propagated to this AddRec.
1513 // Negative step causes unsigned wrap, but it still can't self-wrap.
1514 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1515 // Return the expression with the addrec on the outside.
1516 return getAddRecExpr(
1517 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1518 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1523 // Normally, in the cases we can prove no-overflow via a
1524 // backedge guarding condition, we can also compute a backedge
1525 // taken count for the loop. The exceptions are assumptions and
1526 // guards present in the loop -- SCEV is not great at exploiting
1527 // these to compute max backedge taken counts, but can still use
1528 // these to prove lack of overflow. Use this fact to avoid
1529 // doing extra work that may not pay off.
1530 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1531 !AC.assumptions().empty()) {
1532 // If the backedge is guarded by a comparison with the pre-inc
1533 // value the addrec is safe. Also, if the entry is guarded by
1534 // a comparison with the start value and the backedge is
1535 // guarded by a comparison with the post-inc value, the addrec
1537 if (isKnownPositive(Step)) {
1538 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1539 getUnsignedRange(Step).getUnsignedMax());
1540 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1541 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1542 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1543 AR->getPostIncExpr(*this), N))) {
1544 // Cache knowledge of AR NUW, which is propagated to this
1546 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1547 // Return the expression with the addrec on the outside.
1548 return getAddRecExpr(
1549 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1550 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1552 } else if (isKnownNegative(Step)) {
1553 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1554 getSignedRange(Step).getSignedMin());
1555 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1556 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1557 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1558 AR->getPostIncExpr(*this), N))) {
1559 // Cache knowledge of AR NW, which is propagated to this
1560 // AddRec. Negative step causes unsigned wrap, but it
1561 // still can't self-wrap.
1562 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1563 // Return the expression with the addrec on the outside.
1564 return getAddRecExpr(
1565 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1566 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1571 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1572 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1573 return getAddRecExpr(
1574 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1575 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1579 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1580 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1581 if (SA->hasNoUnsignedWrap()) {
1582 // If the addition does not unsign overflow then we can, by definition,
1583 // commute the zero extension with the addition operation.
1584 SmallVector<const SCEV *, 4> Ops;
1585 for (const auto *Op : SA->operands())
1586 Ops.push_back(getZeroExtendExpr(Op, Ty));
1587 return getAddExpr(Ops, SCEV::FlagNUW);
1591 // The cast wasn't folded; create an explicit cast node.
1592 // Recompute the insert position, as it may have been invalidated.
1593 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1594 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1596 UniqueSCEVs.InsertNode(S, IP);
1600 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1602 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1603 "This is not an extending conversion!");
1604 assert(isSCEVable(Ty) &&
1605 "This is not a conversion to a SCEVable type!");
1606 Ty = getEffectiveSCEVType(Ty);
1608 // Fold if the operand is constant.
1609 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1611 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1613 // sext(sext(x)) --> sext(x)
1614 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1615 return getSignExtendExpr(SS->getOperand(), Ty);
1617 // sext(zext(x)) --> zext(x)
1618 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1619 return getZeroExtendExpr(SZ->getOperand(), Ty);
1621 // Before doing any expensive analysis, check to see if we've already
1622 // computed a SCEV for this Op and Ty.
1623 FoldingSetNodeID ID;
1624 ID.AddInteger(scSignExtend);
1628 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1630 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1631 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1632 // It's possible the bits taken off by the truncate were all sign bits. If
1633 // so, we should be able to simplify this further.
1634 const SCEV *X = ST->getOperand();
1635 ConstantRange CR = getSignedRange(X);
1636 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1637 unsigned NewBits = getTypeSizeInBits(Ty);
1638 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1639 CR.sextOrTrunc(NewBits)))
1640 return getTruncateOrSignExtend(X, Ty);
1643 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1644 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1645 if (SA->getNumOperands() == 2) {
1646 auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1647 auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1649 if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1650 const APInt &C1 = SC1->getAPInt();
1651 const APInt &C2 = SC2->getAPInt();
1652 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1653 C2.ugt(C1) && C2.isPowerOf2())
1654 return getAddExpr(getSignExtendExpr(SC1, Ty),
1655 getSignExtendExpr(SMul, Ty));
1660 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1661 if (SA->hasNoSignedWrap()) {
1662 // If the addition does not sign overflow then we can, by definition,
1663 // commute the sign extension with the addition operation.
1664 SmallVector<const SCEV *, 4> Ops;
1665 for (const auto *Op : SA->operands())
1666 Ops.push_back(getSignExtendExpr(Op, Ty));
1667 return getAddExpr(Ops, SCEV::FlagNSW);
1670 // If the input value is a chrec scev, and we can prove that the value
1671 // did not overflow the old, smaller, value, we can sign extend all of the
1672 // operands (often constants). This allows analysis of something like
1673 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1674 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1675 if (AR->isAffine()) {
1676 const SCEV *Start = AR->getStart();
1677 const SCEV *Step = AR->getStepRecurrence(*this);
1678 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1679 const Loop *L = AR->getLoop();
1681 if (!AR->hasNoSignedWrap()) {
1682 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1683 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1686 // If we have special knowledge that this addrec won't overflow,
1687 // we don't need to do any further analysis.
1688 if (AR->hasNoSignedWrap())
1689 return getAddRecExpr(
1690 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1691 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1693 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1694 // Note that this serves two purposes: It filters out loops that are
1695 // simply not analyzable, and it covers the case where this code is
1696 // being called from within backedge-taken count analysis, such that
1697 // attempting to ask for the backedge-taken count would likely result
1698 // in infinite recursion. In the later case, the analysis code will
1699 // cope with a conservative value, and it will take care to purge
1700 // that value once it has finished.
1701 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1702 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1703 // Manually compute the final value for AR, checking for
1706 // Check whether the backedge-taken count can be losslessly casted to
1707 // the addrec's type. The count is always unsigned.
1708 const SCEV *CastedMaxBECount =
1709 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1710 const SCEV *RecastedMaxBECount =
1711 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1712 if (MaxBECount == RecastedMaxBECount) {
1713 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1714 // Check whether Start+Step*MaxBECount has no signed overflow.
1715 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1716 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1717 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1718 const SCEV *WideMaxBECount =
1719 getZeroExtendExpr(CastedMaxBECount, WideTy);
1720 const SCEV *OperandExtendedAdd =
1721 getAddExpr(WideStart,
1722 getMulExpr(WideMaxBECount,
1723 getSignExtendExpr(Step, WideTy)));
1724 if (SAdd == OperandExtendedAdd) {
1725 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1726 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1727 // Return the expression with the addrec on the outside.
1728 return getAddRecExpr(
1729 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1730 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1732 // Similar to above, only this time treat the step value as unsigned.
1733 // This covers loops that count up with an unsigned step.
1734 OperandExtendedAdd =
1735 getAddExpr(WideStart,
1736 getMulExpr(WideMaxBECount,
1737 getZeroExtendExpr(Step, WideTy)));
1738 if (SAdd == OperandExtendedAdd) {
1739 // If AR wraps around then
1741 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1742 // => SAdd != OperandExtendedAdd
1744 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1745 // (SAdd == OperandExtendedAdd => AR is NW)
1747 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1749 // Return the expression with the addrec on the outside.
1750 return getAddRecExpr(
1751 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1752 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1757 // Normally, in the cases we can prove no-overflow via a
1758 // backedge guarding condition, we can also compute a backedge
1759 // taken count for the loop. The exceptions are assumptions and
1760 // guards present in the loop -- SCEV is not great at exploiting
1761 // these to compute max backedge taken counts, but can still use
1762 // these to prove lack of overflow. Use this fact to avoid
1763 // doing extra work that may not pay off.
1765 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1766 !AC.assumptions().empty()) {
1767 // If the backedge is guarded by a comparison with the pre-inc
1768 // value the addrec is safe. Also, if the entry is guarded by
1769 // a comparison with the start value and the backedge is
1770 // guarded by a comparison with the post-inc value, the addrec
1772 ICmpInst::Predicate Pred;
1773 const SCEV *OverflowLimit =
1774 getSignedOverflowLimitForStep(Step, &Pred, this);
1775 if (OverflowLimit &&
1776 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1777 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1778 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1780 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1781 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1782 return getAddRecExpr(
1783 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1784 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1788 // If Start and Step are constants, check if we can apply this
1790 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1791 auto *SC1 = dyn_cast<SCEVConstant>(Start);
1792 auto *SC2 = dyn_cast<SCEVConstant>(Step);
1794 const APInt &C1 = SC1->getAPInt();
1795 const APInt &C2 = SC2->getAPInt();
1796 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1798 Start = getSignExtendExpr(Start, Ty);
1799 const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1800 AR->getNoWrapFlags());
1801 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1805 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1806 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1807 return getAddRecExpr(
1808 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1809 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1813 // If the input value is provably positive and we could not simplify
1814 // away the sext build a zext instead.
1815 if (isKnownNonNegative(Op))
1816 return getZeroExtendExpr(Op, Ty);
1818 // The cast wasn't folded; create an explicit cast node.
1819 // Recompute the insert position, as it may have been invalidated.
1820 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1821 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1823 UniqueSCEVs.InsertNode(S, IP);
1827 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1828 /// unspecified bits out to the given type.
1830 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1832 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1833 "This is not an extending conversion!");
1834 assert(isSCEVable(Ty) &&
1835 "This is not a conversion to a SCEVable type!");
1836 Ty = getEffectiveSCEVType(Ty);
1838 // Sign-extend negative constants.
1839 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1840 if (SC->getAPInt().isNegative())
1841 return getSignExtendExpr(Op, Ty);
1843 // Peel off a truncate cast.
1844 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1845 const SCEV *NewOp = T->getOperand();
1846 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1847 return getAnyExtendExpr(NewOp, Ty);
1848 return getTruncateOrNoop(NewOp, Ty);
1851 // Next try a zext cast. If the cast is folded, use it.
1852 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1853 if (!isa<SCEVZeroExtendExpr>(ZExt))
1856 // Next try a sext cast. If the cast is folded, use it.
1857 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1858 if (!isa<SCEVSignExtendExpr>(SExt))
1861 // Force the cast to be folded into the operands of an addrec.
1862 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1863 SmallVector<const SCEV *, 4> Ops;
1864 for (const SCEV *Op : AR->operands())
1865 Ops.push_back(getAnyExtendExpr(Op, Ty));
1866 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1869 // If the expression is obviously signed, use the sext cast value.
1870 if (isa<SCEVSMaxExpr>(Op))
1873 // Absent any other information, use the zext cast value.
1877 /// Process the given Ops list, which is a list of operands to be added under
1878 /// the given scale, update the given map. This is a helper function for
1879 /// getAddRecExpr. As an example of what it does, given a sequence of operands
1880 /// that would form an add expression like this:
1882 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1884 /// where A and B are constants, update the map with these values:
1886 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1888 /// and add 13 + A*B*29 to AccumulatedConstant.
1889 /// This will allow getAddRecExpr to produce this:
1891 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1893 /// This form often exposes folding opportunities that are hidden in
1894 /// the original operand list.
1896 /// Return true iff it appears that any interesting folding opportunities
1897 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1898 /// the common case where no interesting opportunities are present, and
1899 /// is also used as a check to avoid infinite recursion.
1902 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1903 SmallVectorImpl<const SCEV *> &NewOps,
1904 APInt &AccumulatedConstant,
1905 const SCEV *const *Ops, size_t NumOperands,
1907 ScalarEvolution &SE) {
1908 bool Interesting = false;
1910 // Iterate over the add operands. They are sorted, with constants first.
1912 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1914 // Pull a buried constant out to the outside.
1915 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1917 AccumulatedConstant += Scale * C->getAPInt();
1920 // Next comes everything else. We're especially interested in multiplies
1921 // here, but they're in the middle, so just visit the rest with one loop.
1922 for (; i != NumOperands; ++i) {
1923 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1924 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1926 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
1927 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1928 // A multiplication of a constant with another add; recurse.
1929 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1931 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1932 Add->op_begin(), Add->getNumOperands(),
1935 // A multiplication of a constant with some other value. Update
1937 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1938 const SCEV *Key = SE.getMulExpr(MulOps);
1939 auto Pair = M.insert({Key, NewScale});
1941 NewOps.push_back(Pair.first->first);
1943 Pair.first->second += NewScale;
1944 // The map already had an entry for this value, which may indicate
1945 // a folding opportunity.
1950 // An ordinary operand. Update the map.
1951 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1952 M.insert({Ops[i], Scale});
1954 NewOps.push_back(Pair.first->first);
1956 Pair.first->second += Scale;
1957 // The map already had an entry for this value, which may indicate
1958 // a folding opportunity.
1967 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1968 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1969 // can't-overflow flags for the operation if possible.
1970 static SCEV::NoWrapFlags
1971 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1972 const SmallVectorImpl<const SCEV *> &Ops,
1973 SCEV::NoWrapFlags Flags) {
1974 using namespace std::placeholders;
1975 typedef OverflowingBinaryOperator OBO;
1978 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1980 assert(CanAnalyze && "don't call from other places!");
1982 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1983 SCEV::NoWrapFlags SignOrUnsignWrap =
1984 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1986 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1987 auto IsKnownNonNegative = [&](const SCEV *S) {
1988 return SE->isKnownNonNegative(S);
1991 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
1993 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1995 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1997 if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
1998 Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
2000 // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
2001 // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
2003 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2004 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2005 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2006 Instruction::Add, C, OBO::NoSignedWrap);
2007 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2008 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2010 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2011 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2012 Instruction::Add, C, OBO::NoUnsignedWrap);
2013 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2014 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2021 /// Get a canonical add expression, or something simpler if possible.
2022 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2023 SCEV::NoWrapFlags Flags) {
2024 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2025 "only nuw or nsw allowed");
2026 assert(!Ops.empty() && "Cannot get empty add!");
2027 if (Ops.size() == 1) return Ops[0];
2029 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2030 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2031 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2032 "SCEVAddExpr operand types don't match!");
2035 // Sort by complexity, this groups all similar expression types together.
2036 GroupByComplexity(Ops, &LI);
2038 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2040 // If there are any constants, fold them together.
2042 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2044 assert(Idx < Ops.size());
2045 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2046 // We found two constants, fold them together!
2047 Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2048 if (Ops.size() == 2) return Ops[0];
2049 Ops.erase(Ops.begin()+1); // Erase the folded element
2050 LHSC = cast<SCEVConstant>(Ops[0]);
2053 // If we are left with a constant zero being added, strip it off.
2054 if (LHSC->getValue()->isZero()) {
2055 Ops.erase(Ops.begin());
2059 if (Ops.size() == 1) return Ops[0];
2062 // Okay, check to see if the same value occurs in the operand list more than
2063 // once. If so, merge them together into an multiply expression. Since we
2064 // sorted the list, these values are required to be adjacent.
2065 Type *Ty = Ops[0]->getType();
2066 bool FoundMatch = false;
2067 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2068 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2069 // Scan ahead to count how many equal operands there are.
2071 while (i+Count != e && Ops[i+Count] == Ops[i])
2073 // Merge the values into a multiply.
2074 const SCEV *Scale = getConstant(Ty, Count);
2075 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2076 if (Ops.size() == Count)
2079 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2080 --i; e -= Count - 1;
2084 return getAddExpr(Ops, Flags);
2086 // Check for truncates. If all the operands are truncated from the same
2087 // type, see if factoring out the truncate would permit the result to be
2088 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2089 // if the contents of the resulting outer trunc fold to something simple.
2090 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2091 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2092 Type *DstType = Trunc->getType();
2093 Type *SrcType = Trunc->getOperand()->getType();
2094 SmallVector<const SCEV *, 8> LargeOps;
2096 // Check all the operands to see if they can be represented in the
2097 // source type of the truncate.
2098 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2099 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2100 if (T->getOperand()->getType() != SrcType) {
2104 LargeOps.push_back(T->getOperand());
2105 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2106 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2107 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2108 SmallVector<const SCEV *, 8> LargeMulOps;
2109 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2110 if (const SCEVTruncateExpr *T =
2111 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2112 if (T->getOperand()->getType() != SrcType) {
2116 LargeMulOps.push_back(T->getOperand());
2117 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2118 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2125 LargeOps.push_back(getMulExpr(LargeMulOps));
2132 // Evaluate the expression in the larger type.
2133 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2134 // If it folds to something simple, use it. Otherwise, don't.
2135 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2136 return getTruncateExpr(Fold, DstType);
2140 // Skip past any other cast SCEVs.
2141 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2144 // If there are add operands they would be next.
2145 if (Idx < Ops.size()) {
2146 bool DeletedAdd = false;
2147 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2148 // If we have an add, expand the add operands onto the end of the operands
2150 Ops.erase(Ops.begin()+Idx);
2151 Ops.append(Add->op_begin(), Add->op_end());
2155 // If we deleted at least one add, we added operands to the end of the list,
2156 // and they are not necessarily sorted. Recurse to resort and resimplify
2157 // any operands we just acquired.
2159 return getAddExpr(Ops);
2162 // Skip over the add expression until we get to a multiply.
2163 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2166 // Check to see if there are any folding opportunities present with
2167 // operands multiplied by constant values.
2168 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2169 uint64_t BitWidth = getTypeSizeInBits(Ty);
2170 DenseMap<const SCEV *, APInt> M;
2171 SmallVector<const SCEV *, 8> NewOps;
2172 APInt AccumulatedConstant(BitWidth, 0);
2173 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2174 Ops.data(), Ops.size(),
2175 APInt(BitWidth, 1), *this)) {
2176 struct APIntCompare {
2177 bool operator()(const APInt &LHS, const APInt &RHS) const {
2178 return LHS.ult(RHS);
2182 // Some interesting folding opportunity is present, so its worthwhile to
2183 // re-generate the operands list. Group the operands by constant scale,
2184 // to avoid multiplying by the same constant scale multiple times.
2185 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2186 for (const SCEV *NewOp : NewOps)
2187 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2188 // Re-generate the operands list.
2190 if (AccumulatedConstant != 0)
2191 Ops.push_back(getConstant(AccumulatedConstant));
2192 for (auto &MulOp : MulOpLists)
2193 if (MulOp.first != 0)
2194 Ops.push_back(getMulExpr(getConstant(MulOp.first),
2195 getAddExpr(MulOp.second)));
2198 if (Ops.size() == 1)
2200 return getAddExpr(Ops);
2204 // If we are adding something to a multiply expression, make sure the
2205 // something is not already an operand of the multiply. If so, merge it into
2207 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2208 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2209 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2210 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2211 if (isa<SCEVConstant>(MulOpSCEV))
2213 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2214 if (MulOpSCEV == Ops[AddOp]) {
2215 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2216 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2217 if (Mul->getNumOperands() != 2) {
2218 // If the multiply has more than two operands, we must get the
2220 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2221 Mul->op_begin()+MulOp);
2222 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2223 InnerMul = getMulExpr(MulOps);
2225 const SCEV *One = getOne(Ty);
2226 const SCEV *AddOne = getAddExpr(One, InnerMul);
2227 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2228 if (Ops.size() == 2) return OuterMul;
2230 Ops.erase(Ops.begin()+AddOp);
2231 Ops.erase(Ops.begin()+Idx-1);
2233 Ops.erase(Ops.begin()+Idx);
2234 Ops.erase(Ops.begin()+AddOp-1);
2236 Ops.push_back(OuterMul);
2237 return getAddExpr(Ops);
2240 // Check this multiply against other multiplies being added together.
2241 for (unsigned OtherMulIdx = Idx+1;
2242 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2244 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2245 // If MulOp occurs in OtherMul, we can fold the two multiplies
2247 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2248 OMulOp != e; ++OMulOp)
2249 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2250 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2251 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2252 if (Mul->getNumOperands() != 2) {
2253 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2254 Mul->op_begin()+MulOp);
2255 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2256 InnerMul1 = getMulExpr(MulOps);
2258 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2259 if (OtherMul->getNumOperands() != 2) {
2260 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2261 OtherMul->op_begin()+OMulOp);
2262 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2263 InnerMul2 = getMulExpr(MulOps);
2265 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2266 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2267 if (Ops.size() == 2) return OuterMul;
2268 Ops.erase(Ops.begin()+Idx);
2269 Ops.erase(Ops.begin()+OtherMulIdx-1);
2270 Ops.push_back(OuterMul);
2271 return getAddExpr(Ops);
2277 // If there are any add recurrences in the operands list, see if any other
2278 // added values are loop invariant. If so, we can fold them into the
2280 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2283 // Scan over all recurrences, trying to fold loop invariants into them.
2284 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2285 // Scan all of the other operands to this add and add them to the vector if
2286 // they are loop invariant w.r.t. the recurrence.
2287 SmallVector<const SCEV *, 8> LIOps;
2288 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2289 const Loop *AddRecLoop = AddRec->getLoop();
2290 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2291 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2292 LIOps.push_back(Ops[i]);
2293 Ops.erase(Ops.begin()+i);
2297 // If we found some loop invariants, fold them into the recurrence.
2298 if (!LIOps.empty()) {
2299 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2300 LIOps.push_back(AddRec->getStart());
2302 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2304 // This follows from the fact that the no-wrap flags on the outer add
2305 // expression are applicable on the 0th iteration, when the add recurrence
2306 // will be equal to its start value.
2307 AddRecOps[0] = getAddExpr(LIOps, Flags);
2309 // Build the new addrec. Propagate the NUW and NSW flags if both the
2310 // outer add and the inner addrec are guaranteed to have no overflow.
2311 // Always propagate NW.
2312 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2313 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2315 // If all of the other operands were loop invariant, we are done.
2316 if (Ops.size() == 1) return NewRec;
2318 // Otherwise, add the folded AddRec by the non-invariant parts.
2319 for (unsigned i = 0;; ++i)
2320 if (Ops[i] == AddRec) {
2324 return getAddExpr(Ops);
2327 // Okay, if there weren't any loop invariants to be folded, check to see if
2328 // there are multiple AddRec's with the same loop induction variable being
2329 // added together. If so, we can fold them.
2330 for (unsigned OtherIdx = Idx+1;
2331 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2333 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2334 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2335 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2337 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2339 if (const auto *OtherAddRec = dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2340 if (OtherAddRec->getLoop() == AddRecLoop) {
2341 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2343 if (i >= AddRecOps.size()) {
2344 AddRecOps.append(OtherAddRec->op_begin()+i,
2345 OtherAddRec->op_end());
2348 AddRecOps[i] = getAddExpr(AddRecOps[i],
2349 OtherAddRec->getOperand(i));
2351 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2353 // Step size has changed, so we cannot guarantee no self-wraparound.
2354 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2355 return getAddExpr(Ops);
2358 // Otherwise couldn't fold anything into this recurrence. Move onto the
2362 // Okay, it looks like we really DO need an add expr. Check to see if we
2363 // already have one, otherwise create a new one.
2364 FoldingSetNodeID ID;
2365 ID.AddInteger(scAddExpr);
2366 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2367 ID.AddPointer(Ops[i]);
2370 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2372 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2373 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2374 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2376 UniqueSCEVs.InsertNode(S, IP);
2378 S->setNoWrapFlags(Flags);
2382 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2384 if (j > 1 && k / j != i) Overflow = true;
2388 /// Compute the result of "n choose k", the binomial coefficient. If an
2389 /// intermediate computation overflows, Overflow will be set and the return will
2390 /// be garbage. Overflow is not cleared on absence of overflow.
2391 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2392 // We use the multiplicative formula:
2393 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2394 // At each iteration, we take the n-th term of the numeral and divide by the
2395 // (k-n)th term of the denominator. This division will always produce an
2396 // integral result, and helps reduce the chance of overflow in the
2397 // intermediate computations. However, we can still overflow even when the
2398 // final result would fit.
2400 if (n == 0 || n == k) return 1;
2401 if (k > n) return 0;
2407 for (uint64_t i = 1; i <= k; ++i) {
2408 r = umul_ov(r, n-(i-1), Overflow);
2414 /// Determine if any of the operands in this SCEV are a constant or if
2415 /// any of the add or multiply expressions in this SCEV contain a constant.
2416 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2417 SmallVector<const SCEV *, 4> Ops;
2418 Ops.push_back(StartExpr);
2419 while (!Ops.empty()) {
2420 const SCEV *CurrentExpr = Ops.pop_back_val();
2421 if (isa<SCEVConstant>(*CurrentExpr))
2424 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2425 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2426 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2432 /// Get a canonical multiply expression, or something simpler if possible.
2433 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2434 SCEV::NoWrapFlags Flags) {
2435 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2436 "only nuw or nsw allowed");
2437 assert(!Ops.empty() && "Cannot get empty mul!");
2438 if (Ops.size() == 1) return Ops[0];
2440 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2441 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2442 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2443 "SCEVMulExpr operand types don't match!");
2446 // Sort by complexity, this groups all similar expression types together.
2447 GroupByComplexity(Ops, &LI);
2449 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2451 // If there are any constants, fold them together.
2453 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2455 // C1*(C2+V) -> C1*C2 + C1*V
2456 if (Ops.size() == 2)
2457 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2458 // If any of Add's ops are Adds or Muls with a constant,
2459 // apply this transformation as well.
2460 if (Add->getNumOperands() == 2)
2461 if (containsConstantSomewhere(Add))
2462 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2463 getMulExpr(LHSC, Add->getOperand(1)));
2466 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2467 // We found two constants, fold them together!
2469 ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2470 Ops[0] = getConstant(Fold);
2471 Ops.erase(Ops.begin()+1); // Erase the folded element
2472 if (Ops.size() == 1) return Ops[0];
2473 LHSC = cast<SCEVConstant>(Ops[0]);
2476 // If we are left with a constant one being multiplied, strip it off.
2477 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2478 Ops.erase(Ops.begin());
2480 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2481 // If we have a multiply of zero, it will always be zero.
2483 } else if (Ops[0]->isAllOnesValue()) {
2484 // If we have a mul by -1 of an add, try distributing the -1 among the
2486 if (Ops.size() == 2) {
2487 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2488 SmallVector<const SCEV *, 4> NewOps;
2489 bool AnyFolded = false;
2490 for (const SCEV *AddOp : Add->operands()) {
2491 const SCEV *Mul = getMulExpr(Ops[0], AddOp);
2492 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2493 NewOps.push_back(Mul);
2496 return getAddExpr(NewOps);
2497 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2498 // Negation preserves a recurrence's no self-wrap property.
2499 SmallVector<const SCEV *, 4> Operands;
2500 for (const SCEV *AddRecOp : AddRec->operands())
2501 Operands.push_back(getMulExpr(Ops[0], AddRecOp));
2503 return getAddRecExpr(Operands, AddRec->getLoop(),
2504 AddRec->getNoWrapFlags(SCEV::FlagNW));
2509 if (Ops.size() == 1)
2513 // Skip over the add expression until we get to a multiply.
2514 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2517 // If there are mul operands inline them all into this expression.
2518 if (Idx < Ops.size()) {
2519 bool DeletedMul = false;
2520 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2521 // If we have an mul, expand the mul operands onto the end of the operands
2523 Ops.erase(Ops.begin()+Idx);
2524 Ops.append(Mul->op_begin(), Mul->op_end());
2528 // If we deleted at least one mul, we added operands to the end of the list,
2529 // and they are not necessarily sorted. Recurse to resort and resimplify
2530 // any operands we just acquired.
2532 return getMulExpr(Ops);
2535 // If there are any add recurrences in the operands list, see if any other
2536 // added values are loop invariant. If so, we can fold them into the
2538 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2541 // Scan over all recurrences, trying to fold loop invariants into them.
2542 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2543 // Scan all of the other operands to this mul and add them to the vector if
2544 // they are loop invariant w.r.t. the recurrence.
2545 SmallVector<const SCEV *, 8> LIOps;
2546 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2547 const Loop *AddRecLoop = AddRec->getLoop();
2548 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2549 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2550 LIOps.push_back(Ops[i]);
2551 Ops.erase(Ops.begin()+i);
2555 // If we found some loop invariants, fold them into the recurrence.
2556 if (!LIOps.empty()) {
2557 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2558 SmallVector<const SCEV *, 4> NewOps;
2559 NewOps.reserve(AddRec->getNumOperands());
2560 const SCEV *Scale = getMulExpr(LIOps);
2561 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2562 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2564 // Build the new addrec. Propagate the NUW and NSW flags if both the
2565 // outer mul and the inner addrec are guaranteed to have no overflow.
2567 // No self-wrap cannot be guaranteed after changing the step size, but
2568 // will be inferred if either NUW or NSW is true.
2569 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2570 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2572 // If all of the other operands were loop invariant, we are done.
2573 if (Ops.size() == 1) return NewRec;
2575 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2576 for (unsigned i = 0;; ++i)
2577 if (Ops[i] == AddRec) {
2581 return getMulExpr(Ops);
2584 // Okay, if there weren't any loop invariants to be folded, check to see if
2585 // there are multiple AddRec's with the same loop induction variable being
2586 // multiplied together. If so, we can fold them.
2588 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2589 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2590 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2591 // ]]],+,...up to x=2n}.
2592 // Note that the arguments to choose() are always integers with values
2593 // known at compile time, never SCEV objects.
2595 // The implementation avoids pointless extra computations when the two
2596 // addrec's are of different length (mathematically, it's equivalent to
2597 // an infinite stream of zeros on the right).
2598 bool OpsModified = false;
2599 for (unsigned OtherIdx = Idx+1;
2600 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2602 const SCEVAddRecExpr *OtherAddRec =
2603 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2604 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2607 bool Overflow = false;
2608 Type *Ty = AddRec->getType();
2609 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2610 SmallVector<const SCEV*, 7> AddRecOps;
2611 for (int x = 0, xe = AddRec->getNumOperands() +
2612 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2613 const SCEV *Term = getZero(Ty);
2614 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2615 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2616 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2617 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2618 z < ze && !Overflow; ++z) {
2619 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2621 if (LargerThan64Bits)
2622 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2624 Coeff = Coeff1*Coeff2;
2625 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2626 const SCEV *Term1 = AddRec->getOperand(y-z);
2627 const SCEV *Term2 = OtherAddRec->getOperand(z);
2628 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2631 AddRecOps.push_back(Term);
2634 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2636 if (Ops.size() == 2) return NewAddRec;
2637 Ops[Idx] = NewAddRec;
2638 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2640 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2646 return getMulExpr(Ops);
2648 // Otherwise couldn't fold anything into this recurrence. Move onto the
2652 // Okay, it looks like we really DO need an mul expr. Check to see if we
2653 // already have one, otherwise create a new one.
2654 FoldingSetNodeID ID;
2655 ID.AddInteger(scMulExpr);
2656 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2657 ID.AddPointer(Ops[i]);
2660 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2662 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2663 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2664 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2666 UniqueSCEVs.InsertNode(S, IP);
2668 S->setNoWrapFlags(Flags);
2672 /// Get a canonical unsigned division expression, or something simpler if
2674 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2676 assert(getEffectiveSCEVType(LHS->getType()) ==
2677 getEffectiveSCEVType(RHS->getType()) &&
2678 "SCEVUDivExpr operand types don't match!");
2680 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2681 if (RHSC->getValue()->equalsInt(1))
2682 return LHS; // X udiv 1 --> x
2683 // If the denominator is zero, the result of the udiv is undefined. Don't
2684 // try to analyze it, because the resolution chosen here may differ from
2685 // the resolution chosen in other parts of the compiler.
2686 if (!RHSC->getValue()->isZero()) {
2687 // Determine if the division can be folded into the operands of
2689 // TODO: Generalize this to non-constants by using known-bits information.
2690 Type *Ty = LHS->getType();
2691 unsigned LZ = RHSC->getAPInt().countLeadingZeros();
2692 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2693 // For non-power-of-two values, effectively round the value up to the
2694 // nearest power of two.
2695 if (!RHSC->getAPInt().isPowerOf2())
2697 IntegerType *ExtTy =
2698 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2699 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2700 if (const SCEVConstant *Step =
2701 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2702 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2703 const APInt &StepInt = Step->getAPInt();
2704 const APInt &DivInt = RHSC->getAPInt();
2705 if (!StepInt.urem(DivInt) &&
2706 getZeroExtendExpr(AR, ExtTy) ==
2707 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2708 getZeroExtendExpr(Step, ExtTy),
2709 AR->getLoop(), SCEV::FlagAnyWrap)) {
2710 SmallVector<const SCEV *, 4> Operands;
2711 for (const SCEV *Op : AR->operands())
2712 Operands.push_back(getUDivExpr(Op, RHS));
2713 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
2715 /// Get a canonical UDivExpr for a recurrence.
2716 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2717 // We can currently only fold X%N if X is constant.
2718 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2719 if (StartC && !DivInt.urem(StepInt) &&
2720 getZeroExtendExpr(AR, ExtTy) ==
2721 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2722 getZeroExtendExpr(Step, ExtTy),
2723 AR->getLoop(), SCEV::FlagAnyWrap)) {
2724 const APInt &StartInt = StartC->getAPInt();
2725 const APInt &StartRem = StartInt.urem(StepInt);
2727 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2728 AR->getLoop(), SCEV::FlagNW);
2731 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2732 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2733 SmallVector<const SCEV *, 4> Operands;
2734 for (const SCEV *Op : M->operands())
2735 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2736 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2737 // Find an operand that's safely divisible.
2738 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2739 const SCEV *Op = M->getOperand(i);
2740 const SCEV *Div = getUDivExpr(Op, RHSC);
2741 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2742 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2745 return getMulExpr(Operands);
2749 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2750 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2751 SmallVector<const SCEV *, 4> Operands;
2752 for (const SCEV *Op : A->operands())
2753 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2754 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2756 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2757 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2758 if (isa<SCEVUDivExpr>(Op) ||
2759 getMulExpr(Op, RHS) != A->getOperand(i))
2761 Operands.push_back(Op);
2763 if (Operands.size() == A->getNumOperands())
2764 return getAddExpr(Operands);
2768 // Fold if both operands are constant.
2769 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2770 Constant *LHSCV = LHSC->getValue();
2771 Constant *RHSCV = RHSC->getValue();
2772 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2778 FoldingSetNodeID ID;
2779 ID.AddInteger(scUDivExpr);
2783 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2784 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2786 UniqueSCEVs.InsertNode(S, IP);
2790 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2791 APInt A = C1->getAPInt().abs();
2792 APInt B = C2->getAPInt().abs();
2793 uint32_t ABW = A.getBitWidth();
2794 uint32_t BBW = B.getBitWidth();
2801 return APIntOps::GreatestCommonDivisor(A, B);
2804 /// Get a canonical unsigned division expression, or something simpler if
2805 /// possible. There is no representation for an exact udiv in SCEV IR, but we
2806 /// can attempt to remove factors from the LHS and RHS. We can't do this when
2807 /// it's not exact because the udiv may be clearing bits.
2808 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2810 // TODO: we could try to find factors in all sorts of things, but for now we
2811 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2812 // end of this file for inspiration.
2814 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2816 return getUDivExpr(LHS, RHS);
2818 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2819 // If the mulexpr multiplies by a constant, then that constant must be the
2820 // first element of the mulexpr.
2821 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2822 if (LHSCst == RHSCst) {
2823 SmallVector<const SCEV *, 2> Operands;
2824 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2825 return getMulExpr(Operands);
2828 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2829 // that there's a factor provided by one of the other terms. We need to
2831 APInt Factor = gcd(LHSCst, RHSCst);
2832 if (!Factor.isIntN(1)) {
2834 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
2836 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
2837 SmallVector<const SCEV *, 2> Operands;
2838 Operands.push_back(LHSCst);
2839 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2840 LHS = getMulExpr(Operands);
2842 Mul = dyn_cast<SCEVMulExpr>(LHS);
2844 return getUDivExactExpr(LHS, RHS);
2849 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2850 if (Mul->getOperand(i) == RHS) {
2851 SmallVector<const SCEV *, 2> Operands;
2852 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2853 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2854 return getMulExpr(Operands);
2858 return getUDivExpr(LHS, RHS);
2861 /// Get an add recurrence expression for the specified loop. Simplify the
2862 /// expression as much as possible.
2863 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2865 SCEV::NoWrapFlags Flags) {
2866 SmallVector<const SCEV *, 4> Operands;
2867 Operands.push_back(Start);
2868 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2869 if (StepChrec->getLoop() == L) {
2870 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2871 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2874 Operands.push_back(Step);
2875 return getAddRecExpr(Operands, L, Flags);
2878 /// Get an add recurrence expression for the specified loop. Simplify the
2879 /// expression as much as possible.
2881 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2882 const Loop *L, SCEV::NoWrapFlags Flags) {
2883 if (Operands.size() == 1) return Operands[0];
2885 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2886 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2887 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2888 "SCEVAddRecExpr operand types don't match!");
2889 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2890 assert(isLoopInvariant(Operands[i], L) &&
2891 "SCEVAddRecExpr operand is not loop-invariant!");
2894 if (Operands.back()->isZero()) {
2895 Operands.pop_back();
2896 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2899 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2900 // use that information to infer NUW and NSW flags. However, computing a
2901 // BE count requires calling getAddRecExpr, so we may not yet have a
2902 // meaningful BE count at this point (and if we don't, we'd be stuck
2903 // with a SCEVCouldNotCompute as the cached BE count).
2905 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2907 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2908 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2909 const Loop *NestedLoop = NestedAR->getLoop();
2910 if (L->contains(NestedLoop)
2911 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2912 : (!NestedLoop->contains(L) &&
2913 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2914 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2915 NestedAR->op_end());
2916 Operands[0] = NestedAR->getStart();
2917 // AddRecs require their operands be loop-invariant with respect to their
2918 // loops. Don't perform this transformation if it would break this
2920 bool AllInvariant = all_of(
2921 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
2924 // Create a recurrence for the outer loop with the same step size.
2926 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2927 // inner recurrence has the same property.
2928 SCEV::NoWrapFlags OuterFlags =
2929 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2931 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2932 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
2933 return isLoopInvariant(Op, NestedLoop);
2937 // Ok, both add recurrences are valid after the transformation.
2939 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2940 // the outer recurrence has the same property.
2941 SCEV::NoWrapFlags InnerFlags =
2942 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2943 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2946 // Reset Operands to its original state.
2947 Operands[0] = NestedAR;
2951 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2952 // already have one, otherwise create a new one.
2953 FoldingSetNodeID ID;
2954 ID.AddInteger(scAddRecExpr);
2955 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2956 ID.AddPointer(Operands[i]);
2960 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2962 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2963 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2964 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2965 O, Operands.size(), L);
2966 UniqueSCEVs.InsertNode(S, IP);
2968 S->setNoWrapFlags(Flags);
2973 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2974 const SmallVectorImpl<const SCEV *> &IndexExprs,
2976 // getSCEV(Base)->getType() has the same address space as Base->getType()
2977 // because SCEV::getType() preserves the address space.
2978 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2979 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2980 // instruction to its SCEV, because the Instruction may be guarded by control
2981 // flow and the no-overflow bits may not be valid for the expression in any
2982 // context. This can be fixed similarly to how these flags are handled for
2984 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2986 const SCEV *TotalOffset = getZero(IntPtrTy);
2987 // The address space is unimportant. The first thing we do on CurTy is getting
2988 // its element type.
2989 Type *CurTy = PointerType::getUnqual(PointeeType);
2990 for (const SCEV *IndexExpr : IndexExprs) {
2991 // Compute the (potentially symbolic) offset in bytes for this index.
2992 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2993 // For a struct, add the member offset.
2994 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2995 unsigned FieldNo = Index->getZExtValue();
2996 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2998 // Add the field offset to the running total offset.
2999 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3001 // Update CurTy to the type of the field at Index.
3002 CurTy = STy->getTypeAtIndex(Index);
3004 // Update CurTy to its element type.
3005 CurTy = cast<SequentialType>(CurTy)->getElementType();
3006 // For an array, add the element offset, explicitly scaled.
3007 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
3008 // Getelementptr indices are signed.
3009 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
3011 // Multiply the index by the element size to compute the element offset.
3012 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
3014 // Add the element offset to the running total offset.
3015 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3019 // Add the total offset from all the GEP indices to the base.
3020 return getAddExpr(BaseExpr, TotalOffset, Wrap);
3023 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
3025 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3026 return getSMaxExpr(Ops);
3030 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3031 assert(!Ops.empty() && "Cannot get empty smax!");
3032 if (Ops.size() == 1) return Ops[0];
3034 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3035 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3036 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3037 "SCEVSMaxExpr operand types don't match!");
3040 // Sort by complexity, this groups all similar expression types together.
3041 GroupByComplexity(Ops, &LI);
3043 // If there are any constants, fold them together.
3045 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3047 assert(Idx < Ops.size());
3048 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3049 // We found two constants, fold them together!
3050 ConstantInt *Fold = ConstantInt::get(
3051 getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
3052 Ops[0] = getConstant(Fold);
3053 Ops.erase(Ops.begin()+1); // Erase the folded element
3054 if (Ops.size() == 1) return Ops[0];
3055 LHSC = cast<SCEVConstant>(Ops[0]);
3058 // If we are left with a constant minimum-int, strip it off.
3059 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3060 Ops.erase(Ops.begin());
3062 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3063 // If we have an smax with a constant maximum-int, it will always be
3068 if (Ops.size() == 1) return Ops[0];
3071 // Find the first SMax
3072 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3075 // Check to see if one of the operands is an SMax. If so, expand its operands
3076 // onto our operand list, and recurse to simplify.
3077 if (Idx < Ops.size()) {
3078 bool DeletedSMax = false;
3079 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3080 Ops.erase(Ops.begin()+Idx);
3081 Ops.append(SMax->op_begin(), SMax->op_end());
3086 return getSMaxExpr(Ops);
3089 // Okay, check to see if the same value occurs in the operand list twice. If
3090 // so, delete one. Since we sorted the list, these values are required to
3092 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3093 // X smax Y smax Y --> X smax Y
3094 // X smax Y --> X, if X is always greater than Y
3095 if (Ops[i] == Ops[i+1] ||
3096 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3097 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3099 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3100 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3104 if (Ops.size() == 1) return Ops[0];
3106 assert(!Ops.empty() && "Reduced smax down to nothing!");
3108 // Okay, it looks like we really DO need an smax expr. Check to see if we
3109 // already have one, otherwise create a new one.
3110 FoldingSetNodeID ID;
3111 ID.AddInteger(scSMaxExpr);
3112 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3113 ID.AddPointer(Ops[i]);
3115 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3116 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3117 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3118 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3120 UniqueSCEVs.InsertNode(S, IP);
3124 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3126 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3127 return getUMaxExpr(Ops);
3131 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3132 assert(!Ops.empty() && "Cannot get empty umax!");
3133 if (Ops.size() == 1) return Ops[0];
3135 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3136 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3137 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3138 "SCEVUMaxExpr operand types don't match!");
3141 // Sort by complexity, this groups all similar expression types together.
3142 GroupByComplexity(Ops, &LI);
3144 // If there are any constants, fold them together.
3146 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3148 assert(Idx < Ops.size());
3149 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3150 // We found two constants, fold them together!
3151 ConstantInt *Fold = ConstantInt::get(
3152 getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
3153 Ops[0] = getConstant(Fold);
3154 Ops.erase(Ops.begin()+1); // Erase the folded element
3155 if (Ops.size() == 1) return Ops[0];
3156 LHSC = cast<SCEVConstant>(Ops[0]);
3159 // If we are left with a constant minimum-int, strip it off.
3160 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3161 Ops.erase(Ops.begin());
3163 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3164 // If we have an umax with a constant maximum-int, it will always be
3169 if (Ops.size() == 1) return Ops[0];
3172 // Find the first UMax
3173 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3176 // Check to see if one of the operands is a UMax. If so, expand its operands
3177 // onto our operand list, and recurse to simplify.
3178 if (Idx < Ops.size()) {
3179 bool DeletedUMax = false;
3180 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3181 Ops.erase(Ops.begin()+Idx);
3182 Ops.append(UMax->op_begin(), UMax->op_end());
3187 return getUMaxExpr(Ops);
3190 // Okay, check to see if the same value occurs in the operand list twice. If
3191 // so, delete one. Since we sorted the list, these values are required to
3193 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3194 // X umax Y umax Y --> X umax Y
3195 // X umax Y --> X, if X is always greater than Y
3196 if (Ops[i] == Ops[i+1] ||
3197 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3198 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3200 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3201 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3205 if (Ops.size() == 1) return Ops[0];
3207 assert(!Ops.empty() && "Reduced umax down to nothing!");
3209 // Okay, it looks like we really DO need a umax expr. Check to see if we
3210 // already have one, otherwise create a new one.
3211 FoldingSetNodeID ID;
3212 ID.AddInteger(scUMaxExpr);
3213 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3214 ID.AddPointer(Ops[i]);
3216 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3217 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3218 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3219 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3221 UniqueSCEVs.InsertNode(S, IP);
3225 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3227 // ~smax(~x, ~y) == smin(x, y).
3228 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3231 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3233 // ~umax(~x, ~y) == umin(x, y)
3234 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3237 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3238 // We can bypass creating a target-independent
3239 // constant expression and then folding it back into a ConstantInt.
3240 // This is just a compile-time optimization.
3241 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3244 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3247 // We can bypass creating a target-independent
3248 // constant expression and then folding it back into a ConstantInt.
3249 // This is just a compile-time optimization.
3251 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3254 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3255 // Don't attempt to do anything other than create a SCEVUnknown object
3256 // here. createSCEV only calls getUnknown after checking for all other
3257 // interesting possibilities, and any other code that calls getUnknown
3258 // is doing so in order to hide a value from SCEV canonicalization.
3260 FoldingSetNodeID ID;
3261 ID.AddInteger(scUnknown);
3264 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3265 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3266 "Stale SCEVUnknown in uniquing map!");
3269 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3271 FirstUnknown = cast<SCEVUnknown>(S);
3272 UniqueSCEVs.InsertNode(S, IP);
3276 //===----------------------------------------------------------------------===//
3277 // Basic SCEV Analysis and PHI Idiom Recognition Code
3280 /// Test if values of the given type are analyzable within the SCEV
3281 /// framework. This primarily includes integer types, and it can optionally
3282 /// include pointer types if the ScalarEvolution class has access to
3283 /// target-specific information.
3284 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3285 // Integers and pointers are always SCEVable.
3286 return Ty->isIntegerTy() || Ty->isPointerTy();
3289 /// Return the size in bits of the specified type, for which isSCEVable must
3291 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3292 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3293 return getDataLayout().getTypeSizeInBits(Ty);
3296 /// Return a type with the same bitwidth as the given type and which represents
3297 /// how SCEV will treat the given type, for which isSCEVable must return
3298 /// true. For pointer types, this is the pointer-sized integer type.
3299 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3300 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3302 if (Ty->isIntegerTy())
3305 // The only other support type is pointer.
3306 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3307 return getDataLayout().getIntPtrType(Ty);
3310 const SCEV *ScalarEvolution::getCouldNotCompute() {
3311 return CouldNotCompute.get();
3315 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3316 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3317 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3318 // is set iff if find such SCEVUnknown.
3320 struct FindInvalidSCEVUnknown {
3322 FindInvalidSCEVUnknown() { FindOne = false; }
3323 bool follow(const SCEV *S) {
3324 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3328 if (!cast<SCEVUnknown>(S)->getValue())
3335 bool isDone() const { return FindOne; }
3338 FindInvalidSCEVUnknown F;
3339 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3346 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3347 // a sub SCEV of scAddRecExpr type. FindInvalidSCEVUnknown::FoundOne is set
3348 // iff if such sub scAddRecExpr type SCEV is found.
3349 struct FindAddRecurrence {
3351 FindAddRecurrence() : FoundOne(false) {}
3353 bool follow(const SCEV *S) {
3354 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3359 case scCouldNotCompute:
3365 bool isDone() const { return FoundOne; }
3369 bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
3370 HasRecMapType::iterator I = HasRecMap.find_as(S);
3371 if (I != HasRecMap.end())
3374 FindAddRecurrence F;
3375 SCEVTraversal<FindAddRecurrence> ST(F);
3377 HasRecMap.insert({S, F.FoundOne});
3381 /// Return the Value set from S.
3382 SetVector<Value *> *ScalarEvolution::getSCEVValues(const SCEV *S) {
3383 ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3384 if (SI == ExprValueMap.end())
3387 if (VerifySCEVMap) {
3388 // Check there is no dangling Value in the set returned.
3389 for (const auto &VE : SI->second)
3390 assert(ValueExprMap.count(VE));
3396 /// Erase Value from ValueExprMap and ExprValueMap. If ValueExprMap.erase(V) is
3397 /// not used together with forgetMemoizedResults(S), eraseValueFromMap should be
3398 /// used instead to ensure whenever V->S is removed from ValueExprMap, V is also
3399 /// removed from the set of ExprValueMap[S].
3400 void ScalarEvolution::eraseValueFromMap(Value *V) {
3401 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3402 if (I != ValueExprMap.end()) {
3403 const SCEV *S = I->second;
3404 SetVector<Value *> *SV = getSCEVValues(S);
3405 // Remove V from the set of ExprValueMap[S]
3408 ValueExprMap.erase(V);
3412 /// Return an existing SCEV if it exists, otherwise analyze the expression and
3413 /// create a new one.
3414 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3415 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3417 const SCEV *S = getExistingSCEV(V);
3420 // During PHI resolution, it is possible to create two SCEVs for the same
3421 // V, so it is needed to double check whether V->S is inserted into
3422 // ValueExprMap before insert S->V into ExprValueMap.
3423 std::pair<ValueExprMapType::iterator, bool> Pair =
3424 ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3426 ExprValueMap[S].insert(V);
3431 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3432 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3434 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3435 if (I != ValueExprMap.end()) {
3436 const SCEV *S = I->second;
3437 if (checkValidity(S))
3439 forgetMemoizedResults(S);
3440 ValueExprMap.erase(I);
3445 /// Return a SCEV corresponding to -V = -1*V
3447 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3448 SCEV::NoWrapFlags Flags) {
3449 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3451 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3453 Type *Ty = V->getType();
3454 Ty = getEffectiveSCEVType(Ty);
3456 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3459 /// Return a SCEV corresponding to ~V = -1-V
3460 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3461 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3463 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3465 Type *Ty = V->getType();
3466 Ty = getEffectiveSCEVType(Ty);
3467 const SCEV *AllOnes =
3468 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3469 return getMinusSCEV(AllOnes, V);
3472 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3473 SCEV::NoWrapFlags Flags) {
3474 // Fast path: X - X --> 0.
3476 return getZero(LHS->getType());
3478 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3479 // makes it so that we cannot make much use of NUW.
3480 auto AddFlags = SCEV::FlagAnyWrap;
3481 const bool RHSIsNotMinSigned =
3482 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3483 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3484 // Let M be the minimum representable signed value. Then (-1)*RHS
3485 // signed-wraps if and only if RHS is M. That can happen even for
3486 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3487 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3488 // (-1)*RHS, we need to prove that RHS != M.
3490 // If LHS is non-negative and we know that LHS - RHS does not
3491 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3492 // either by proving that RHS > M or that LHS >= 0.
3493 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3494 AddFlags = SCEV::FlagNSW;
3498 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3499 // RHS is NSW and LHS >= 0.
3501 // The difficulty here is that the NSW flag may have been proven
3502 // relative to a loop that is to be found in a recurrence in LHS and
3503 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3504 // larger scope than intended.
3505 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3507 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3511 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3512 Type *SrcTy = V->getType();
3513 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3514 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3515 "Cannot truncate or zero extend with non-integer arguments!");
3516 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3517 return V; // No conversion
3518 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3519 return getTruncateExpr(V, Ty);
3520 return getZeroExtendExpr(V, Ty);
3524 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3526 Type *SrcTy = V->getType();
3527 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3528 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3529 "Cannot truncate or zero extend with non-integer arguments!");
3530 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3531 return V; // No conversion
3532 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3533 return getTruncateExpr(V, Ty);
3534 return getSignExtendExpr(V, Ty);
3538 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3539 Type *SrcTy = V->getType();
3540 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3541 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3542 "Cannot noop or zero extend with non-integer arguments!");
3543 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3544 "getNoopOrZeroExtend cannot truncate!");
3545 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3546 return V; // No conversion
3547 return getZeroExtendExpr(V, Ty);
3551 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3552 Type *SrcTy = V->getType();
3553 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3554 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3555 "Cannot noop or sign extend with non-integer arguments!");
3556 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3557 "getNoopOrSignExtend cannot truncate!");
3558 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3559 return V; // No conversion
3560 return getSignExtendExpr(V, Ty);
3564 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3565 Type *SrcTy = V->getType();
3566 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3567 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3568 "Cannot noop or any extend with non-integer arguments!");
3569 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3570 "getNoopOrAnyExtend cannot truncate!");
3571 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3572 return V; // No conversion
3573 return getAnyExtendExpr(V, Ty);
3577 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3578 Type *SrcTy = V->getType();
3579 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3580 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3581 "Cannot truncate or noop with non-integer arguments!");
3582 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3583 "getTruncateOrNoop cannot extend!");
3584 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3585 return V; // No conversion
3586 return getTruncateExpr(V, Ty);
3589 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3591 const SCEV *PromotedLHS = LHS;
3592 const SCEV *PromotedRHS = RHS;
3594 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3595 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3597 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3599 return getUMaxExpr(PromotedLHS, PromotedRHS);
3602 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3604 const SCEV *PromotedLHS = LHS;
3605 const SCEV *PromotedRHS = RHS;
3607 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3608 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3610 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3612 return getUMinExpr(PromotedLHS, PromotedRHS);
3615 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3616 // A pointer operand may evaluate to a nonpointer expression, such as null.
3617 if (!V->getType()->isPointerTy())
3620 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3621 return getPointerBase(Cast->getOperand());
3622 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3623 const SCEV *PtrOp = nullptr;
3624 for (const SCEV *NAryOp : NAry->operands()) {
3625 if (NAryOp->getType()->isPointerTy()) {
3626 // Cannot find the base of an expression with multiple pointer operands.
3634 return getPointerBase(PtrOp);
3639 /// Push users of the given Instruction onto the given Worklist.
3641 PushDefUseChildren(Instruction *I,
3642 SmallVectorImpl<Instruction *> &Worklist) {
3643 // Push the def-use children onto the Worklist stack.
3644 for (User *U : I->users())
3645 Worklist.push_back(cast<Instruction>(U));
3648 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3649 SmallVector<Instruction *, 16> Worklist;
3650 PushDefUseChildren(PN, Worklist);
3652 SmallPtrSet<Instruction *, 8> Visited;
3654 while (!Worklist.empty()) {
3655 Instruction *I = Worklist.pop_back_val();
3656 if (!Visited.insert(I).second)
3659 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
3660 if (It != ValueExprMap.end()) {
3661 const SCEV *Old = It->second;
3663 // Short-circuit the def-use traversal if the symbolic name
3664 // ceases to appear in expressions.
3665 if (Old != SymName && !hasOperand(Old, SymName))
3668 // SCEVUnknown for a PHI either means that it has an unrecognized
3669 // structure, it's a PHI that's in the progress of being computed
3670 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3671 // additional loop trip count information isn't going to change anything.
3672 // In the second case, createNodeForPHI will perform the necessary
3673 // updates on its own when it gets to that point. In the third, we do
3674 // want to forget the SCEVUnknown.
3675 if (!isa<PHINode>(I) ||
3676 !isa<SCEVUnknown>(Old) ||
3677 (I != PN && Old == SymName)) {
3678 forgetMemoizedResults(Old);
3679 ValueExprMap.erase(It);
3683 PushDefUseChildren(I, Worklist);
3688 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
3690 static const SCEV *rewrite(const SCEV *S, const Loop *L,
3691 ScalarEvolution &SE) {
3692 SCEVInitRewriter Rewriter(L, SE);
3693 const SCEV *Result = Rewriter.visit(S);
3694 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3697 SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
3698 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3700 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3701 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3706 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3707 // Only allow AddRecExprs for this loop.
3708 if (Expr->getLoop() == L)
3709 return Expr->getStart();
3714 bool isValid() { return Valid; }
3721 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
3723 static const SCEV *rewrite(const SCEV *S, const Loop *L,
3724 ScalarEvolution &SE) {
3725 SCEVShiftRewriter Rewriter(L, SE);
3726 const SCEV *Result = Rewriter.visit(S);
3727 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3730 SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
3731 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3733 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3734 // Only allow AddRecExprs for this loop.
3735 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3740 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3741 if (Expr->getLoop() == L && Expr->isAffine())
3742 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
3746 bool isValid() { return Valid; }
3752 } // end anonymous namespace
3755 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
3756 if (!AR->isAffine())
3757 return SCEV::FlagAnyWrap;
3759 typedef OverflowingBinaryOperator OBO;
3760 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
3762 if (!AR->hasNoSignedWrap()) {
3763 ConstantRange AddRecRange = getSignedRange(AR);
3764 ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
3766 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
3767 Instruction::Add, IncRange, OBO::NoSignedWrap);
3768 if (NSWRegion.contains(AddRecRange))
3769 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
3772 if (!AR->hasNoUnsignedWrap()) {
3773 ConstantRange AddRecRange = getUnsignedRange(AR);
3774 ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
3776 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
3777 Instruction::Add, IncRange, OBO::NoUnsignedWrap);
3778 if (NUWRegion.contains(AddRecRange))
3779 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
3786 /// Represents an abstract binary operation. This may exist as a
3787 /// normal instruction or constant expression, or may have been
3788 /// derived from an expression tree.
3796 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
3797 /// constant expression.
3800 explicit BinaryOp(Operator *Op)
3801 : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
3802 IsNSW(false), IsNUW(false), Op(Op) {
3803 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
3804 IsNSW = OBO->hasNoSignedWrap();
3805 IsNUW = OBO->hasNoUnsignedWrap();
3809 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
3811 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW),
3817 /// Try to map \p V into a BinaryOp, and return \c None on failure.
3818 static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
3819 auto *Op = dyn_cast<Operator>(V);
3823 // Implementation detail: all the cleverness here should happen without
3824 // creating new SCEV expressions -- our caller knowns tricks to avoid creating
3825 // SCEV expressions when possible, and we should not break that.
3827 switch (Op->getOpcode()) {
3828 case Instruction::Add:
3829 case Instruction::Sub:
3830 case Instruction::Mul:
3831 case Instruction::UDiv:
3832 case Instruction::And:
3833 case Instruction::Or:
3834 case Instruction::AShr:
3835 case Instruction::Shl:
3836 return BinaryOp(Op);
3838 case Instruction::Xor:
3839 if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
3840 // If the RHS of the xor is a signbit, then this is just an add.
3841 // Instcombine turns add of signbit into xor as a strength reduction step.
3842 if (RHSC->getValue().isSignBit())
3843 return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
3844 return BinaryOp(Op);
3846 case Instruction::LShr:
3847 // Turn logical shift right of a constant into a unsigned divide.
3848 if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
3849 uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
3851 // If the shift count is not less than the bitwidth, the result of
3852 // the shift is undefined. Don't try to analyze it, because the
3853 // resolution chosen here may differ from the resolution chosen in
3854 // other parts of the compiler.
3855 if (SA->getValue().ult(BitWidth)) {
3857 ConstantInt::get(SA->getContext(),
3858 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3859 return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
3862 return BinaryOp(Op);
3864 case Instruction::ExtractValue: {
3865 auto *EVI = cast<ExtractValueInst>(Op);
3866 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
3869 auto *CI = dyn_cast<CallInst>(EVI->getAggregateOperand());
3873 if (auto *F = CI->getCalledFunction())
3874 switch (F->getIntrinsicID()) {
3875 case Intrinsic::sadd_with_overflow:
3876 case Intrinsic::uadd_with_overflow: {
3877 if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
3878 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3879 CI->getArgOperand(1));
3881 // Now that we know that all uses of the arithmetic-result component of
3882 // CI are guarded by the overflow check, we can go ahead and pretend
3883 // that the arithmetic is non-overflowing.
3884 if (F->getIntrinsicID() == Intrinsic::sadd_with_overflow)
3885 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3886 CI->getArgOperand(1), /* IsNSW = */ true,
3887 /* IsNUW = */ false);
3889 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3890 CI->getArgOperand(1), /* IsNSW = */ false,
3894 case Intrinsic::ssub_with_overflow:
3895 case Intrinsic::usub_with_overflow:
3896 return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
3897 CI->getArgOperand(1));
3899 case Intrinsic::smul_with_overflow:
3900 case Intrinsic::umul_with_overflow:
3901 return BinaryOp(Instruction::Mul, CI->getArgOperand(0),
3902 CI->getArgOperand(1));
3915 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
3916 const Loop *L = LI.getLoopFor(PN->getParent());
3917 if (!L || L->getHeader() != PN->getParent())
3920 // The loop may have multiple entrances or multiple exits; we can analyze
3921 // this phi as an addrec if it has a unique entry value and a unique
3923 Value *BEValueV = nullptr, *StartValueV = nullptr;
3924 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3925 Value *V = PN->getIncomingValue(i);
3926 if (L->contains(PN->getIncomingBlock(i))) {
3929 } else if (BEValueV != V) {
3933 } else if (!StartValueV) {
3935 } else if (StartValueV != V) {
3936 StartValueV = nullptr;
3940 if (BEValueV && StartValueV) {
3941 // While we are analyzing this PHI node, handle its value symbolically.
3942 const SCEV *SymbolicName = getUnknown(PN);
3943 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3944 "PHI node already processed?");
3945 ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
3947 // Using this symbolic name for the PHI, analyze the value coming around
3949 const SCEV *BEValue = getSCEV(BEValueV);
3951 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3952 // has a special value for the first iteration of the loop.
3954 // If the value coming around the backedge is an add with the symbolic
3955 // value we just inserted, then we found a simple induction variable!
3956 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3957 // If there is a single occurrence of the symbolic value, replace it
3958 // with a recurrence.
3959 unsigned FoundIndex = Add->getNumOperands();
3960 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3961 if (Add->getOperand(i) == SymbolicName)
3962 if (FoundIndex == e) {
3967 if (FoundIndex != Add->getNumOperands()) {
3968 // Create an add with everything but the specified operand.
3969 SmallVector<const SCEV *, 8> Ops;
3970 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3971 if (i != FoundIndex)
3972 Ops.push_back(Add->getOperand(i));
3973 const SCEV *Accum = getAddExpr(Ops);
3975 // This is not a valid addrec if the step amount is varying each
3976 // loop iteration, but is not itself an addrec in this loop.
3977 if (isLoopInvariant(Accum, L) ||
3978 (isa<SCEVAddRecExpr>(Accum) &&
3979 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3980 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3982 if (auto BO = MatchBinaryOp(BEValueV, DT)) {
3983 if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
3985 Flags = setFlags(Flags, SCEV::FlagNUW);
3987 Flags = setFlags(Flags, SCEV::FlagNSW);
3989 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3990 // If the increment is an inbounds GEP, then we know the address
3991 // space cannot be wrapped around. We cannot make any guarantee
3992 // about signed or unsigned overflow because pointers are
3993 // unsigned but we may have a negative index from the base
3994 // pointer. We can guarantee that no unsigned wrap occurs if the
3995 // indices form a positive value.
3996 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3997 Flags = setFlags(Flags, SCEV::FlagNW);
3999 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
4000 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
4001 Flags = setFlags(Flags, SCEV::FlagNUW);
4004 // We cannot transfer nuw and nsw flags from subtraction
4005 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
4009 const SCEV *StartVal = getSCEV(StartValueV);
4010 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4012 // Okay, for the entire analysis of this edge we assumed the PHI
4013 // to be symbolic. We now need to go back and purge all of the
4014 // entries for the scalars that use the symbolic expression.
4015 forgetSymbolicName(PN, SymbolicName);
4016 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4018 // We can add Flags to the post-inc expression only if we
4019 // know that it us *undefined behavior* for BEValueV to
4021 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4022 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4023 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4029 // Otherwise, this could be a loop like this:
4030 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
4031 // In this case, j = {1,+,1} and BEValue is j.
4032 // Because the other in-value of i (0) fits the evolution of BEValue
4033 // i really is an addrec evolution.
4035 // We can generalize this saying that i is the shifted value of BEValue
4036 // by one iteration:
4037 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
4038 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
4039 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
4040 if (Shifted != getCouldNotCompute() &&
4041 Start != getCouldNotCompute()) {
4042 const SCEV *StartVal = getSCEV(StartValueV);
4043 if (Start == StartVal) {
4044 // Okay, for the entire analysis of this edge we assumed the PHI
4045 // to be symbolic. We now need to go back and purge all of the
4046 // entries for the scalars that use the symbolic expression.
4047 forgetSymbolicName(PN, SymbolicName);
4048 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
4054 // Remove the temporary PHI node SCEV that has been inserted while intending
4055 // to create an AddRecExpr for this PHI node. We can not keep this temporary
4056 // as it will prevent later (possibly simpler) SCEV expressions to be added
4057 // to the ValueExprMap.
4058 ValueExprMap.erase(PN);
4064 // Checks if the SCEV S is available at BB. S is considered available at BB
4065 // if S can be materialized at BB without introducing a fault.
4066 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
4068 struct CheckAvailable {
4069 bool TraversalDone = false;
4070 bool Available = true;
4072 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
4073 BasicBlock *BB = nullptr;
4076 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
4077 : L(L), BB(BB), DT(DT) {}
4079 bool setUnavailable() {
4080 TraversalDone = true;
4085 bool follow(const SCEV *S) {
4086 switch (S->getSCEVType()) {
4087 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
4088 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
4089 // These expressions are available if their operand(s) is/are.
4092 case scAddRecExpr: {
4093 // We allow add recurrences that are on the loop BB is in, or some
4094 // outer loop. This guarantees availability because the value of the
4095 // add recurrence at BB is simply the "current" value of the induction
4096 // variable. We can relax this in the future; for instance an add
4097 // recurrence on a sibling dominating loop is also available at BB.
4098 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
4099 if (L && (ARLoop == L || ARLoop->contains(L)))
4102 return setUnavailable();
4106 // For SCEVUnknown, we check for simple dominance.
4107 const auto *SU = cast<SCEVUnknown>(S);
4108 Value *V = SU->getValue();
4110 if (isa<Argument>(V))
4113 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
4116 return setUnavailable();
4120 case scCouldNotCompute:
4121 // We do not try to smart about these at all.
4122 return setUnavailable();
4124 llvm_unreachable("switch should be fully covered!");
4127 bool isDone() { return TraversalDone; }
4130 CheckAvailable CA(L, BB, DT);
4131 SCEVTraversal<CheckAvailable> ST(CA);
4134 return CA.Available;
4137 // Try to match a control flow sequence that branches out at BI and merges back
4138 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
4140 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
4141 Value *&C, Value *&LHS, Value *&RHS) {
4142 C = BI->getCondition();
4144 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
4145 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
4147 if (!LeftEdge.isSingleEdge())
4150 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
4152 Use &LeftUse = Merge->getOperandUse(0);
4153 Use &RightUse = Merge->getOperandUse(1);
4155 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
4161 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
4170 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
4171 if (PN->getNumIncomingValues() == 2) {
4172 const Loop *L = LI.getLoopFor(PN->getParent());
4174 // We don't want to break LCSSA, even in a SCEV expression tree.
4175 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
4176 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
4181 // br %cond, label %left, label %right
4187 // V = phi [ %x, %left ], [ %y, %right ]
4189 // as "select %cond, %x, %y"
4191 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
4192 assert(IDom && "At least the entry block should dominate PN");
4194 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
4195 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
4197 if (BI && BI->isConditional() &&
4198 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
4199 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
4200 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
4201 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
4207 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
4208 if (const SCEV *S = createAddRecFromPHI(PN))
4211 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
4214 // If the PHI has a single incoming value, follow that value, unless the
4215 // PHI's incoming blocks are in a different loop, in which case doing so
4216 // risks breaking LCSSA form. Instcombine would normally zap these, but
4217 // it doesn't have DominatorTree information, so it may miss cases.
4218 if (Value *V = SimplifyInstruction(PN, getDataLayout(), &TLI, &DT, &AC))
4219 if (LI.replacementPreservesLCSSAForm(PN, V))
4222 // If it's not a loop phi, we can't handle it yet.
4223 return getUnknown(PN);
4226 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
4230 // Handle "constant" branch or select. This can occur for instance when a
4231 // loop pass transforms an inner loop and moves on to process the outer loop.
4232 if (auto *CI = dyn_cast<ConstantInt>(Cond))
4233 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
4235 // Try to match some simple smax or umax patterns.
4236 auto *ICI = dyn_cast<ICmpInst>(Cond);
4238 return getUnknown(I);
4240 Value *LHS = ICI->getOperand(0);
4241 Value *RHS = ICI->getOperand(1);
4243 switch (ICI->getPredicate()) {
4244 case ICmpInst::ICMP_SLT:
4245 case ICmpInst::ICMP_SLE:
4246 std::swap(LHS, RHS);
4248 case ICmpInst::ICMP_SGT:
4249 case ICmpInst::ICMP_SGE:
4250 // a >s b ? a+x : b+x -> smax(a, b)+x
4251 // a >s b ? b+x : a+x -> smin(a, b)+x
4252 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4253 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
4254 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
4255 const SCEV *LA = getSCEV(TrueVal);
4256 const SCEV *RA = getSCEV(FalseVal);
4257 const SCEV *LDiff = getMinusSCEV(LA, LS);
4258 const SCEV *RDiff = getMinusSCEV(RA, RS);
4260 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4261 LDiff = getMinusSCEV(LA, RS);
4262 RDiff = getMinusSCEV(RA, LS);
4264 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4267 case ICmpInst::ICMP_ULT:
4268 case ICmpInst::ICMP_ULE:
4269 std::swap(LHS, RHS);
4271 case ICmpInst::ICMP_UGT:
4272 case ICmpInst::ICMP_UGE:
4273 // a >u b ? a+x : b+x -> umax(a, b)+x
4274 // a >u b ? b+x : a+x -> umin(a, b)+x
4275 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4276 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4277 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
4278 const SCEV *LA = getSCEV(TrueVal);
4279 const SCEV *RA = getSCEV(FalseVal);
4280 const SCEV *LDiff = getMinusSCEV(LA, LS);
4281 const SCEV *RDiff = getMinusSCEV(RA, RS);
4283 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4284 LDiff = getMinusSCEV(LA, RS);
4285 RDiff = getMinusSCEV(RA, LS);
4287 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4290 case ICmpInst::ICMP_NE:
4291 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4292 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4293 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4294 const SCEV *One = getOne(I->getType());
4295 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4296 const SCEV *LA = getSCEV(TrueVal);
4297 const SCEV *RA = getSCEV(FalseVal);
4298 const SCEV *LDiff = getMinusSCEV(LA, LS);
4299 const SCEV *RDiff = getMinusSCEV(RA, One);
4301 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4304 case ICmpInst::ICMP_EQ:
4305 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4306 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4307 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4308 const SCEV *One = getOne(I->getType());
4309 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4310 const SCEV *LA = getSCEV(TrueVal);
4311 const SCEV *RA = getSCEV(FalseVal);
4312 const SCEV *LDiff = getMinusSCEV(LA, One);
4313 const SCEV *RDiff = getMinusSCEV(RA, LS);
4315 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4322 return getUnknown(I);
4325 /// Expand GEP instructions into add and multiply operations. This allows them
4326 /// to be analyzed by regular SCEV code.
4327 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
4328 // Don't attempt to analyze GEPs over unsized objects.
4329 if (!GEP->getSourceElementType()->isSized())
4330 return getUnknown(GEP);
4332 SmallVector<const SCEV *, 4> IndexExprs;
4333 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4334 IndexExprs.push_back(getSCEV(*Index));
4335 return getGEPExpr(GEP->getSourceElementType(),
4336 getSCEV(GEP->getPointerOperand()),
4337 IndexExprs, GEP->isInBounds());
4341 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4342 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4343 return C->getAPInt().countTrailingZeros();
4345 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4346 return std::min(GetMinTrailingZeros(T->getOperand()),
4347 (uint32_t)getTypeSizeInBits(T->getType()));
4349 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4350 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4351 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4352 getTypeSizeInBits(E->getType()) : OpRes;
4355 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4356 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4357 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4358 getTypeSizeInBits(E->getType()) : OpRes;
4361 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4362 // The result is the min of all operands results.
4363 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4364 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4365 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4369 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4370 // The result is the sum of all operands results.
4371 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4372 uint32_t BitWidth = getTypeSizeInBits(M->getType());
4373 for (unsigned i = 1, e = M->getNumOperands();
4374 SumOpRes != BitWidth && i != e; ++i)
4375 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4380 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4381 // The result is the min of all operands results.
4382 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4383 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4384 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4388 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4389 // The result is the min of all operands results.
4390 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4391 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4392 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4396 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4397 // The result is the min of all operands results.
4398 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4399 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4400 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4404 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4405 // For a SCEVUnknown, ask ValueTracking.
4406 unsigned BitWidth = getTypeSizeInBits(U->getType());
4407 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4408 computeKnownBits(U->getValue(), Zeros, Ones, getDataLayout(), 0, &AC,
4410 return Zeros.countTrailingOnes();
4417 /// Helper method to assign a range to V from metadata present in the IR.
4418 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4419 if (Instruction *I = dyn_cast<Instruction>(V))
4420 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
4421 return getConstantRangeFromMetadata(*MD);
4426 /// Determine the range for a particular SCEV. If SignHint is
4427 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4428 /// with a "cleaner" unsigned (resp. signed) representation.
4430 ScalarEvolution::getRange(const SCEV *S,
4431 ScalarEvolution::RangeSignHint SignHint) {
4432 DenseMap<const SCEV *, ConstantRange> &Cache =
4433 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4436 // See if we've computed this range already.
4437 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4438 if (I != Cache.end())
4441 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4442 return setRange(C, SignHint, ConstantRange(C->getAPInt()));
4444 unsigned BitWidth = getTypeSizeInBits(S->getType());
4445 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4447 // If the value has known zeros, the maximum value will have those known zeros
4449 uint32_t TZ = GetMinTrailingZeros(S);
4451 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4452 ConservativeResult =
4453 ConstantRange(APInt::getMinValue(BitWidth),
4454 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4456 ConservativeResult = ConstantRange(
4457 APInt::getSignedMinValue(BitWidth),
4458 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4461 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4462 ConstantRange X = getRange(Add->getOperand(0), SignHint);
4463 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4464 X = X.add(getRange(Add->getOperand(i), SignHint));
4465 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4468 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4469 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4470 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4471 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4472 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4475 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4476 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4477 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4478 X = X.smax(getRange(SMax->getOperand(i), SignHint));
4479 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4482 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4483 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4484 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4485 X = X.umax(getRange(UMax->getOperand(i), SignHint));
4486 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4489 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4490 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4491 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4492 return setRange(UDiv, SignHint,
4493 ConservativeResult.intersectWith(X.udiv(Y)));
4496 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4497 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4498 return setRange(ZExt, SignHint,
4499 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4502 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4503 ConstantRange X = getRange(SExt->getOperand(), SignHint);
4504 return setRange(SExt, SignHint,
4505 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4508 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4509 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4510 return setRange(Trunc, SignHint,
4511 ConservativeResult.intersectWith(X.truncate(BitWidth)));
4514 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4515 // If there's no unsigned wrap, the value will never be less than its
4517 if (AddRec->hasNoUnsignedWrap())
4518 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4519 if (!C->getValue()->isZero())
4520 ConservativeResult = ConservativeResult.intersectWith(
4521 ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
4523 // If there's no signed wrap, and all the operands have the same sign or
4524 // zero, the value won't ever change sign.
4525 if (AddRec->hasNoSignedWrap()) {
4526 bool AllNonNeg = true;
4527 bool AllNonPos = true;
4528 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4529 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4530 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4533 ConservativeResult = ConservativeResult.intersectWith(
4534 ConstantRange(APInt(BitWidth, 0),
4535 APInt::getSignedMinValue(BitWidth)));
4537 ConservativeResult = ConservativeResult.intersectWith(
4538 ConstantRange(APInt::getSignedMinValue(BitWidth),
4539 APInt(BitWidth, 1)));
4542 // TODO: non-affine addrec
4543 if (AddRec->isAffine()) {
4544 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4545 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4546 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4547 auto RangeFromAffine = getRangeForAffineAR(
4548 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
4550 if (!RangeFromAffine.isFullSet())
4551 ConservativeResult =
4552 ConservativeResult.intersectWith(RangeFromAffine);
4554 auto RangeFromFactoring = getRangeViaFactoring(
4555 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
4557 if (!RangeFromFactoring.isFullSet())
4558 ConservativeResult =
4559 ConservativeResult.intersectWith(RangeFromFactoring);
4563 return setRange(AddRec, SignHint, ConservativeResult);
4566 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4567 // Check if the IR explicitly contains !range metadata.
4568 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4569 if (MDRange.hasValue())
4570 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4572 // Split here to avoid paying the compile-time cost of calling both
4573 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4575 const DataLayout &DL = getDataLayout();
4576 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4577 // For a SCEVUnknown, ask ValueTracking.
4578 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4579 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4580 if (Ones != ~Zeros + 1)
4581 ConservativeResult =
4582 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4584 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4585 "generalize as needed!");
4586 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4588 ConservativeResult = ConservativeResult.intersectWith(
4589 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4590 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4593 return setRange(U, SignHint, ConservativeResult);
4596 return setRange(S, SignHint, ConservativeResult);
4599 ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
4601 const SCEV *MaxBECount,
4602 unsigned BitWidth) {
4603 assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
4604 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
4607 ConstantRange Result(BitWidth, /* isFullSet = */ true);
4609 // Check for overflow. This must be done with ConstantRange arithmetic
4610 // because we could be called from within the ScalarEvolution overflow
4613 MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
4614 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4615 ConstantRange ZExtMaxBECountRange =
4616 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4618 ConstantRange StepSRange = getSignedRange(Step);
4619 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4621 ConstantRange StartURange = getUnsignedRange(Start);
4622 ConstantRange EndURange =
4623 StartURange.add(MaxBECountRange.multiply(StepSRange));
4625 // Check for unsigned overflow.
4626 ConstantRange ZExtStartURange = StartURange.zextOrTrunc(BitWidth * 2 + 1);
4627 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4628 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4630 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4631 EndURange.getUnsignedMin());
4632 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4633 EndURange.getUnsignedMax());
4634 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4637 Result.intersectWith(ConstantRange(Min, Max + 1));
4640 ConstantRange StartSRange = getSignedRange(Start);
4641 ConstantRange EndSRange =
4642 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4644 // Check for signed overflow. This must be done with ConstantRange
4645 // arithmetic because we could be called from within the ScalarEvolution
4646 // overflow checking code.
4647 ConstantRange SExtStartSRange = StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4648 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4649 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4652 APIntOps::smin(StartSRange.getSignedMin(), EndSRange.getSignedMin());
4654 APIntOps::smax(StartSRange.getSignedMax(), EndSRange.getSignedMax());
4655 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4658 Result.intersectWith(ConstantRange(Min, Max + 1));
4664 ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
4666 const SCEV *MaxBECount,
4667 unsigned BitWidth) {
4668 // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
4669 // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
4671 struct SelectPattern {
4672 Value *Condition = nullptr;
4676 explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
4678 Optional<unsigned> CastOp;
4679 APInt Offset(BitWidth, 0);
4681 assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
4684 // Peel off a constant offset:
4685 if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
4686 // In the future we could consider being smarter here and handle
4687 // {Start+Step,+,Step} too.
4688 if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
4691 Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
4692 S = SA->getOperand(1);
4695 // Peel off a cast operation
4696 if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) {
4697 CastOp = SCast->getSCEVType();
4698 S = SCast->getOperand();
4701 using namespace llvm::PatternMatch;
4703 auto *SU = dyn_cast<SCEVUnknown>(S);
4704 const APInt *TrueVal, *FalseVal;
4706 !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
4707 m_APInt(FalseVal)))) {
4708 Condition = nullptr;
4712 TrueValue = *TrueVal;
4713 FalseValue = *FalseVal;
4715 // Re-apply the cast we peeled off earlier
4716 if (CastOp.hasValue())
4719 llvm_unreachable("Unknown SCEV cast type!");
4722 TrueValue = TrueValue.trunc(BitWidth);
4723 FalseValue = FalseValue.trunc(BitWidth);
4726 TrueValue = TrueValue.zext(BitWidth);
4727 FalseValue = FalseValue.zext(BitWidth);
4730 TrueValue = TrueValue.sext(BitWidth);
4731 FalseValue = FalseValue.sext(BitWidth);
4735 // Re-apply the constant offset we peeled off earlier
4736 TrueValue += Offset;
4737 FalseValue += Offset;
4740 bool isRecognized() { return Condition != nullptr; }
4743 SelectPattern StartPattern(*this, BitWidth, Start);
4744 if (!StartPattern.isRecognized())
4745 return ConstantRange(BitWidth, /* isFullSet = */ true);
4747 SelectPattern StepPattern(*this, BitWidth, Step);
4748 if (!StepPattern.isRecognized())
4749 return ConstantRange(BitWidth, /* isFullSet = */ true);
4751 if (StartPattern.Condition != StepPattern.Condition) {
4752 // We don't handle this case today; but we could, by considering four
4753 // possibilities below instead of two. I'm not sure if there are cases where
4754 // that will help over what getRange already does, though.
4755 return ConstantRange(BitWidth, /* isFullSet = */ true);
4758 // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
4759 // construct arbitrary general SCEV expressions here. This function is called
4760 // from deep in the call stack, and calling getSCEV (on a sext instruction,
4761 // say) can end up caching a suboptimal value.
4763 // FIXME: without the explicit `this` receiver below, MSVC errors out with
4764 // C2352 and C2512 (otherwise it isn't needed).
4766 const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
4767 const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
4768 const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
4769 const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
4771 ConstantRange TrueRange =
4772 this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
4773 ConstantRange FalseRange =
4774 this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
4776 return TrueRange.unionWith(FalseRange);
4779 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4780 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4781 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4783 // Return early if there are no flags to propagate to the SCEV.
4784 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4785 if (BinOp->hasNoUnsignedWrap())
4786 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4787 if (BinOp->hasNoSignedWrap())
4788 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4789 if (Flags == SCEV::FlagAnyWrap)
4790 return SCEV::FlagAnyWrap;
4792 return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
4795 bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
4796 // Here we check that I is in the header of the innermost loop containing I,
4797 // since we only deal with instructions in the loop header. The actual loop we
4798 // need to check later will come from an add recurrence, but getting that
4799 // requires computing the SCEV of the operands, which can be expensive. This
4800 // check we can do cheaply to rule out some cases early.
4801 Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
4802 if (InnermostContainingLoop == nullptr ||
4803 InnermostContainingLoop->getHeader() != I->getParent())
4806 // Only proceed if we can prove that I does not yield poison.
4807 if (!isKnownNotFullPoison(I)) return false;
4809 // At this point we know that if I is executed, then it does not wrap
4810 // according to at least one of NSW or NUW. If I is not executed, then we do
4811 // not know if the calculation that I represents would wrap. Multiple
4812 // instructions can map to the same SCEV. If we apply NSW or NUW from I to
4813 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4814 // derived from other instructions that map to the same SCEV. We cannot make
4815 // that guarantee for cases where I is not executed. So we need to find the
4816 // loop that I is considered in relation to and prove that I is executed for
4817 // every iteration of that loop. That implies that the value that I
4818 // calculates does not wrap anywhere in the loop, so then we can apply the
4819 // flags to the SCEV.
4821 // We check isLoopInvariant to disambiguate in case we are adding recurrences
4822 // from different loops, so that we know which loop to prove that I is
4824 for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
4825 // I could be an extractvalue from a call to an overflow intrinsic.
4826 // TODO: We can do better here in some cases.
4827 if (!isSCEVable(I->getOperand(OpIndex)->getType()))
4829 const SCEV *Op = getSCEV(I->getOperand(OpIndex));
4830 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4831 bool AllOtherOpsLoopInvariant = true;
4832 for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
4834 if (OtherOpIndex != OpIndex) {
4835 const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
4836 if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
4837 AllOtherOpsLoopInvariant = false;
4842 if (AllOtherOpsLoopInvariant &&
4843 isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
4850 bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
4851 // If we know that \c I can never be poison period, then that's enough.
4852 if (isSCEVExprNeverPoison(I))
4855 // For an add recurrence specifically, we assume that infinite loops without
4856 // side effects are undefined behavior, and then reason as follows:
4858 // If the add recurrence is poison in any iteration, it is poison on all
4859 // future iterations (since incrementing poison yields poison). If the result
4860 // of the add recurrence is fed into the loop latch condition and the loop
4861 // does not contain any throws or exiting blocks other than the latch, we now
4862 // have the ability to "choose" whether the backedge is taken or not (by
4863 // choosing a sufficiently evil value for the poison feeding into the branch)
4864 // for every iteration including and after the one in which \p I first became
4865 // poison. There are two possibilities (let's call the iteration in which \p
4866 // I first became poison as K):
4868 // 1. In the set of iterations including and after K, the loop body executes
4869 // no side effects. In this case executing the backege an infinte number
4870 // of times will yield undefined behavior.
4872 // 2. In the set of iterations including and after K, the loop body executes
4873 // at least one side effect. In this case, that specific instance of side
4874 // effect is control dependent on poison, which also yields undefined
4877 auto *ExitingBB = L->getExitingBlock();
4878 auto *LatchBB = L->getLoopLatch();
4879 if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
4882 SmallPtrSet<const Instruction *, 16> Pushed;
4883 SmallVector<const Instruction *, 8> PoisonStack;
4885 // We start by assuming \c I, the post-inc add recurrence, is poison. Only
4886 // things that are known to be fully poison under that assumption go on the
4889 PoisonStack.push_back(I);
4891 bool LatchControlDependentOnPoison = false;
4892 while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
4893 const Instruction *Poison = PoisonStack.pop_back_val();
4895 for (auto *PoisonUser : Poison->users()) {
4896 if (propagatesFullPoison(cast<Instruction>(PoisonUser))) {
4897 if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
4898 PoisonStack.push_back(cast<Instruction>(PoisonUser));
4899 } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
4900 assert(BI->isConditional() && "Only possibility!");
4901 if (BI->getParent() == LatchBB) {
4902 LatchControlDependentOnPoison = true;
4909 return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
4912 bool ScalarEvolution::loopHasNoAbnormalExits(const Loop *L) {
4913 auto Itr = LoopHasNoAbnormalExits.find(L);
4914 if (Itr == LoopHasNoAbnormalExits.end()) {
4915 auto NoAbnormalExitInBB = [&](BasicBlock *BB) {
4916 return all_of(*BB, [](Instruction &I) {
4917 return isGuaranteedToTransferExecutionToSuccessor(&I);
4921 auto InsertPair = LoopHasNoAbnormalExits.insert(
4922 {L, all_of(L->getBlocks(), NoAbnormalExitInBB)});
4923 assert(InsertPair.second && "We just checked!");
4924 Itr = InsertPair.first;
4930 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4931 if (!isSCEVable(V->getType()))
4932 return getUnknown(V);
4934 if (Instruction *I = dyn_cast<Instruction>(V)) {
4935 // Don't attempt to analyze instructions in blocks that aren't
4936 // reachable. Such instructions don't matter, and they aren't required
4937 // to obey basic rules for definitions dominating uses which this
4938 // analysis depends on.
4939 if (!DT.isReachableFromEntry(I->getParent()))
4940 return getUnknown(V);
4941 } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4942 return getConstant(CI);
4943 else if (isa<ConstantPointerNull>(V))
4944 return getZero(V->getType());
4945 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4946 return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
4947 else if (!isa<ConstantExpr>(V))
4948 return getUnknown(V);
4950 Operator *U = cast<Operator>(V);
4951 if (auto BO = MatchBinaryOp(U, DT)) {
4952 switch (BO->Opcode) {
4953 case Instruction::Add: {
4954 // The simple thing to do would be to just call getSCEV on both operands
4955 // and call getAddExpr with the result. However if we're looking at a
4956 // bunch of things all added together, this can be quite inefficient,
4957 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4958 // Instead, gather up all the operands and make a single getAddExpr call.
4959 // LLVM IR canonical form means we need only traverse the left operands.
4960 SmallVector<const SCEV *, 4> AddOps;
4963 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
4964 AddOps.push_back(OpSCEV);
4968 // If a NUW or NSW flag can be applied to the SCEV for this
4969 // addition, then compute the SCEV for this addition by itself
4970 // with a separate call to getAddExpr. We need to do that
4971 // instead of pushing the operands of the addition onto AddOps,
4972 // since the flags are only known to apply to this particular
4973 // addition - they may not apply to other additions that can be
4974 // formed with operands from AddOps.
4975 const SCEV *RHS = getSCEV(BO->RHS);
4976 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
4977 if (Flags != SCEV::FlagAnyWrap) {
4978 const SCEV *LHS = getSCEV(BO->LHS);
4979 if (BO->Opcode == Instruction::Sub)
4980 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4982 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4987 if (BO->Opcode == Instruction::Sub)
4988 AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
4990 AddOps.push_back(getSCEV(BO->RHS));
4992 auto NewBO = MatchBinaryOp(BO->LHS, DT);
4993 if (!NewBO || (NewBO->Opcode != Instruction::Add &&
4994 NewBO->Opcode != Instruction::Sub)) {
4995 AddOps.push_back(getSCEV(BO->LHS));
5001 return getAddExpr(AddOps);
5004 case Instruction::Mul: {
5005 SmallVector<const SCEV *, 4> MulOps;
5008 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
5009 MulOps.push_back(OpSCEV);
5013 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
5014 if (Flags != SCEV::FlagAnyWrap) {
5016 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
5021 MulOps.push_back(getSCEV(BO->RHS));
5022 auto NewBO = MatchBinaryOp(BO->LHS, DT);
5023 if (!NewBO || NewBO->Opcode != Instruction::Mul) {
5024 MulOps.push_back(getSCEV(BO->LHS));
5030 return getMulExpr(MulOps);
5032 case Instruction::UDiv:
5033 return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
5034 case Instruction::Sub: {
5035 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5037 Flags = getNoWrapFlagsFromUB(BO->Op);
5038 return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
5040 case Instruction::And:
5041 // For an expression like x&255 that merely masks off the high bits,
5042 // use zext(trunc(x)) as the SCEV expression.
5043 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5044 if (CI->isNullValue())
5045 return getSCEV(BO->RHS);
5046 if (CI->isAllOnesValue())
5047 return getSCEV(BO->LHS);
5048 const APInt &A = CI->getValue();
5050 // Instcombine's ShrinkDemandedConstant may strip bits out of
5051 // constants, obscuring what would otherwise be a low-bits mask.
5052 // Use computeKnownBits to compute what ShrinkDemandedConstant
5053 // knew about to reconstruct a low-bits mask value.
5054 unsigned LZ = A.countLeadingZeros();
5055 unsigned TZ = A.countTrailingZeros();
5056 unsigned BitWidth = A.getBitWidth();
5057 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
5058 computeKnownBits(BO->LHS, KnownZero, KnownOne, getDataLayout(),
5059 0, &AC, nullptr, &DT);
5061 APInt EffectiveMask =
5062 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
5063 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
5064 const SCEV *MulCount = getConstant(ConstantInt::get(
5065 getContext(), APInt::getOneBitSet(BitWidth, TZ)));
5069 getUDivExactExpr(getSCEV(BO->LHS), MulCount),
5070 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
5071 BO->LHS->getType()),
5077 case Instruction::Or:
5078 // If the RHS of the Or is a constant, we may have something like:
5079 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
5080 // optimizations will transparently handle this case.
5082 // In order for this transformation to be safe, the LHS must be of the
5083 // form X*(2^n) and the Or constant must be less than 2^n.
5084 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5085 const SCEV *LHS = getSCEV(BO->LHS);
5086 const APInt &CIVal = CI->getValue();
5087 if (GetMinTrailingZeros(LHS) >=
5088 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
5089 // Build a plain add SCEV.
5090 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
5091 // If the LHS of the add was an addrec and it has no-wrap flags,
5092 // transfer the no-wrap flags, since an or won't introduce a wrap.
5093 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
5094 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
5095 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
5096 OldAR->getNoWrapFlags());
5103 case Instruction::Xor:
5104 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5105 // If the RHS of xor is -1, then this is a not operation.
5106 if (CI->isAllOnesValue())
5107 return getNotSCEV(getSCEV(BO->LHS));
5109 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
5110 // This is a variant of the check for xor with -1, and it handles
5111 // the case where instcombine has trimmed non-demanded bits out
5112 // of an xor with -1.
5113 if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
5114 if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
5115 if (LBO->getOpcode() == Instruction::And &&
5116 LCI->getValue() == CI->getValue())
5117 if (const SCEVZeroExtendExpr *Z =
5118 dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
5119 Type *UTy = BO->LHS->getType();
5120 const SCEV *Z0 = Z->getOperand();
5121 Type *Z0Ty = Z0->getType();
5122 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
5124 // If C is a low-bits mask, the zero extend is serving to
5125 // mask off the high bits. Complement the operand and
5126 // re-apply the zext.
5127 if (APIntOps::isMask(Z0TySize, CI->getValue()))
5128 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
5130 // If C is a single bit, it may be in the sign-bit position
5131 // before the zero-extend. In this case, represent the xor
5132 // using an add, which is equivalent, and re-apply the zext.
5133 APInt Trunc = CI->getValue().trunc(Z0TySize);
5134 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
5136 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
5142 case Instruction::Shl:
5143 // Turn shift left of a constant amount into a multiply.
5144 if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
5145 uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
5147 // If the shift count is not less than the bitwidth, the result of
5148 // the shift is undefined. Don't try to analyze it, because the
5149 // resolution chosen here may differ from the resolution chosen in
5150 // other parts of the compiler.
5151 if (SA->getValue().uge(BitWidth))
5154 // It is currently not resolved how to interpret NSW for left
5155 // shift by BitWidth - 1, so we avoid applying flags in that
5156 // case. Remove this check (or this comment) once the situation
5158 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
5159 // and http://reviews.llvm.org/D8890 .
5160 auto Flags = SCEV::FlagAnyWrap;
5161 if (BO->Op && SA->getValue().ult(BitWidth - 1))
5162 Flags = getNoWrapFlagsFromUB(BO->Op);
5164 Constant *X = ConstantInt::get(getContext(),
5165 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
5166 return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
5170 case Instruction::AShr:
5171 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
5172 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS))
5173 if (Operator *L = dyn_cast<Operator>(BO->LHS))
5174 if (L->getOpcode() == Instruction::Shl &&
5175 L->getOperand(1) == BO->RHS) {
5176 uint64_t BitWidth = getTypeSizeInBits(BO->LHS->getType());
5178 // If the shift count is not less than the bitwidth, the result of
5179 // the shift is undefined. Don't try to analyze it, because the
5180 // resolution chosen here may differ from the resolution chosen in
5181 // other parts of the compiler.
5182 if (CI->getValue().uge(BitWidth))
5185 uint64_t Amt = BitWidth - CI->getZExtValue();
5186 if (Amt == BitWidth)
5187 return getSCEV(L->getOperand(0)); // shift by zero --> noop
5188 return getSignExtendExpr(
5189 getTruncateExpr(getSCEV(L->getOperand(0)),
5190 IntegerType::get(getContext(), Amt)),
5191 BO->LHS->getType());
5197 switch (U->getOpcode()) {
5198 case Instruction::Trunc:
5199 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
5201 case Instruction::ZExt:
5202 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
5204 case Instruction::SExt:
5205 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
5207 case Instruction::BitCast:
5208 // BitCasts are no-op casts so we just eliminate the cast.
5209 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
5210 return getSCEV(U->getOperand(0));
5213 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
5214 // lead to pointer expressions which cannot safely be expanded to GEPs,
5215 // because ScalarEvolution doesn't respect the GEP aliasing rules when
5216 // simplifying integer expressions.
5218 case Instruction::GetElementPtr:
5219 return createNodeForGEP(cast<GEPOperator>(U));
5221 case Instruction::PHI:
5222 return createNodeForPHI(cast<PHINode>(U));
5224 case Instruction::Select:
5225 // U can also be a select constant expr, which let fall through. Since
5226 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
5227 // constant expressions cannot have instructions as operands, we'd have
5228 // returned getUnknown for a select constant expressions anyway.
5229 if (isa<Instruction>(U))
5230 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
5231 U->getOperand(1), U->getOperand(2));
5234 case Instruction::Call:
5235 case Instruction::Invoke:
5236 if (Value *RV = CallSite(U).getReturnedArgOperand())
5241 return getUnknown(V);
5246 //===----------------------------------------------------------------------===//
5247 // Iteration Count Computation Code
5250 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
5251 if (BasicBlock *ExitingBB = L->getExitingBlock())
5252 return getSmallConstantTripCount(L, ExitingBB);
5254 // No trip count information for multiple exits.
5258 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
5259 BasicBlock *ExitingBlock) {
5260 assert(ExitingBlock && "Must pass a non-null exiting block!");
5261 assert(L->isLoopExiting(ExitingBlock) &&
5262 "Exiting block must actually branch out of the loop!");
5263 const SCEVConstant *ExitCount =
5264 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
5268 ConstantInt *ExitConst = ExitCount->getValue();
5270 // Guard against huge trip counts.
5271 if (ExitConst->getValue().getActiveBits() > 32)
5274 // In case of integer overflow, this returns 0, which is correct.
5275 return ((unsigned)ExitConst->getZExtValue()) + 1;
5278 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
5279 if (BasicBlock *ExitingBB = L->getExitingBlock())
5280 return getSmallConstantTripMultiple(L, ExitingBB);
5282 // No trip multiple information for multiple exits.
5286 /// Returns the largest constant divisor of the trip count of this loop as a
5287 /// normal unsigned value, if possible. This means that the actual trip count is
5288 /// always a multiple of the returned value (don't forget the trip count could
5289 /// very well be zero as well!).
5291 /// Returns 1 if the trip count is unknown or not guaranteed to be the
5292 /// multiple of a constant (which is also the case if the trip count is simply
5293 /// constant, use getSmallConstantTripCount for that case), Will also return 1
5294 /// if the trip count is very large (>= 2^32).
5296 /// As explained in the comments for getSmallConstantTripCount, this assumes
5297 /// that control exits the loop via ExitingBlock.
5299 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
5300 BasicBlock *ExitingBlock) {
5301 assert(ExitingBlock && "Must pass a non-null exiting block!");
5302 assert(L->isLoopExiting(ExitingBlock) &&
5303 "Exiting block must actually branch out of the loop!");
5304 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
5305 if (ExitCount == getCouldNotCompute())
5308 // Get the trip count from the BE count by adding 1.
5309 const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
5310 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
5311 // to factor simple cases.
5312 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
5313 TCMul = Mul->getOperand(0);
5315 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
5319 ConstantInt *Result = MulC->getValue();
5321 // Guard against huge trip counts (this requires checking
5322 // for zero to handle the case where the trip count == -1 and the
5324 if (!Result || Result->getValue().getActiveBits() > 32 ||
5325 Result->getValue().getActiveBits() == 0)
5328 return (unsigned)Result->getZExtValue();
5331 /// Get the expression for the number of loop iterations for which this loop is
5332 /// guaranteed not to exit via ExitingBlock. Otherwise return
5333 /// SCEVCouldNotCompute.
5334 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
5335 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
5339 ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
5340 SCEVUnionPredicate &Preds) {
5341 return getPredicatedBackedgeTakenInfo(L).getExact(this, &Preds);
5344 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
5345 return getBackedgeTakenInfo(L).getExact(this);
5348 /// Similar to getBackedgeTakenCount, except return the least SCEV value that is
5349 /// known never to be less than the actual backedge taken count.
5350 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
5351 return getBackedgeTakenInfo(L).getMax(this);
5354 /// Push PHI nodes in the header of the given loop onto the given Worklist.
5356 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
5357 BasicBlock *Header = L->getHeader();
5359 // Push all Loop-header PHIs onto the Worklist stack.
5360 for (BasicBlock::iterator I = Header->begin();
5361 PHINode *PN = dyn_cast<PHINode>(I); ++I)
5362 Worklist.push_back(PN);
5365 const ScalarEvolution::BackedgeTakenInfo &
5366 ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
5367 auto &BTI = getBackedgeTakenInfo(L);
5368 if (BTI.hasFullInfo())
5371 auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
5374 return Pair.first->second;
5376 BackedgeTakenInfo Result =
5377 computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
5379 return PredicatedBackedgeTakenCounts.find(L)->second = Result;
5382 const ScalarEvolution::BackedgeTakenInfo &
5383 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
5384 // Initially insert an invalid entry for this loop. If the insertion
5385 // succeeds, proceed to actually compute a backedge-taken count and
5386 // update the value. The temporary CouldNotCompute value tells SCEV
5387 // code elsewhere that it shouldn't attempt to request a new
5388 // backedge-taken count, which could result in infinite recursion.
5389 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
5390 BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
5392 return Pair.first->second;
5394 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
5395 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
5396 // must be cleared in this scope.
5397 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
5399 if (Result.getExact(this) != getCouldNotCompute()) {
5400 assert(isLoopInvariant(Result.getExact(this), L) &&
5401 isLoopInvariant(Result.getMax(this), L) &&
5402 "Computed backedge-taken count isn't loop invariant for loop!");
5403 ++NumTripCountsComputed;
5405 else if (Result.getMax(this) == getCouldNotCompute() &&
5406 isa<PHINode>(L->getHeader()->begin())) {
5407 // Only count loops that have phi nodes as not being computable.
5408 ++NumTripCountsNotComputed;
5411 // Now that we know more about the trip count for this loop, forget any
5412 // existing SCEV values for PHI nodes in this loop since they are only
5413 // conservative estimates made without the benefit of trip count
5414 // information. This is similar to the code in forgetLoop, except that
5415 // it handles SCEVUnknown PHI nodes specially.
5416 if (Result.hasAnyInfo()) {
5417 SmallVector<Instruction *, 16> Worklist;
5418 PushLoopPHIs(L, Worklist);
5420 SmallPtrSet<Instruction *, 8> Visited;
5421 while (!Worklist.empty()) {
5422 Instruction *I = Worklist.pop_back_val();
5423 if (!Visited.insert(I).second)
5426 ValueExprMapType::iterator It =
5427 ValueExprMap.find_as(static_cast<Value *>(I));
5428 if (It != ValueExprMap.end()) {
5429 const SCEV *Old = It->second;
5431 // SCEVUnknown for a PHI either means that it has an unrecognized
5432 // structure, or it's a PHI that's in the progress of being computed
5433 // by createNodeForPHI. In the former case, additional loop trip
5434 // count information isn't going to change anything. In the later
5435 // case, createNodeForPHI will perform the necessary updates on its
5436 // own when it gets to that point.
5437 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
5438 forgetMemoizedResults(Old);
5439 ValueExprMap.erase(It);
5441 if (PHINode *PN = dyn_cast<PHINode>(I))
5442 ConstantEvolutionLoopExitValue.erase(PN);
5445 PushDefUseChildren(I, Worklist);
5449 // Re-lookup the insert position, since the call to
5450 // computeBackedgeTakenCount above could result in a
5451 // recusive call to getBackedgeTakenInfo (on a different
5452 // loop), which would invalidate the iterator computed
5454 return BackedgeTakenCounts.find(L)->second = Result;
5457 void ScalarEvolution::forgetLoop(const Loop *L) {
5458 // Drop any stored trip count value.
5459 auto RemoveLoopFromBackedgeMap =
5460 [L](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
5461 auto BTCPos = Map.find(L);
5462 if (BTCPos != Map.end()) {
5463 BTCPos->second.clear();
5468 RemoveLoopFromBackedgeMap(BackedgeTakenCounts);
5469 RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts);
5471 // Drop information about expressions based on loop-header PHIs.
5472 SmallVector<Instruction *, 16> Worklist;
5473 PushLoopPHIs(L, Worklist);
5475 SmallPtrSet<Instruction *, 8> Visited;
5476 while (!Worklist.empty()) {
5477 Instruction *I = Worklist.pop_back_val();
5478 if (!Visited.insert(I).second)
5481 ValueExprMapType::iterator It =
5482 ValueExprMap.find_as(static_cast<Value *>(I));
5483 if (It != ValueExprMap.end()) {
5484 forgetMemoizedResults(It->second);
5485 ValueExprMap.erase(It);
5486 if (PHINode *PN = dyn_cast<PHINode>(I))
5487 ConstantEvolutionLoopExitValue.erase(PN);
5490 PushDefUseChildren(I, Worklist);
5493 // Forget all contained loops too, to avoid dangling entries in the
5494 // ValuesAtScopes map.
5498 LoopHasNoAbnormalExits.erase(L);
5501 void ScalarEvolution::forgetValue(Value *V) {
5502 Instruction *I = dyn_cast<Instruction>(V);
5505 // Drop information about expressions based on loop-header PHIs.
5506 SmallVector<Instruction *, 16> Worklist;
5507 Worklist.push_back(I);
5509 SmallPtrSet<Instruction *, 8> Visited;
5510 while (!Worklist.empty()) {
5511 I = Worklist.pop_back_val();
5512 if (!Visited.insert(I).second)
5515 ValueExprMapType::iterator It =
5516 ValueExprMap.find_as(static_cast<Value *>(I));
5517 if (It != ValueExprMap.end()) {
5518 forgetMemoizedResults(It->second);
5519 ValueExprMap.erase(It);
5520 if (PHINode *PN = dyn_cast<PHINode>(I))
5521 ConstantEvolutionLoopExitValue.erase(PN);
5524 PushDefUseChildren(I, Worklist);
5528 /// Get the exact loop backedge taken count considering all loop exits. A
5529 /// computable result can only be returned for loops with a single exit.
5530 /// Returning the minimum taken count among all exits is incorrect because one
5531 /// of the loop's exit limit's may have been skipped. howFarToZero assumes that
5532 /// the limit of each loop test is never skipped. This is a valid assumption as
5533 /// long as the loop exits via that test. For precise results, it is the
5534 /// caller's responsibility to specify the relevant loop exit using
5535 /// getExact(ExitingBlock, SE).
5537 ScalarEvolution::BackedgeTakenInfo::getExact(
5538 ScalarEvolution *SE, SCEVUnionPredicate *Preds) const {
5539 // If any exits were not computable, the loop is not computable.
5540 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
5542 // We need exactly one computable exit.
5543 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
5544 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
5546 const SCEV *BECount = nullptr;
5547 for (auto &ENT : ExitNotTaken) {
5548 assert(ENT.ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5551 BECount = ENT.ExactNotTaken;
5552 else if (BECount != ENT.ExactNotTaken)
5553 return SE->getCouldNotCompute();
5554 if (Preds && ENT.getPred())
5555 Preds->add(ENT.getPred());
5557 assert((Preds || ENT.hasAlwaysTruePred()) &&
5558 "Predicate should be always true!");
5561 assert(BECount && "Invalid not taken count for loop exit");
5565 /// Get the exact not taken count for this loop exit.
5567 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5568 ScalarEvolution *SE) const {
5569 for (auto &ENT : ExitNotTaken)
5570 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePred())
5571 return ENT.ExactNotTaken;
5573 return SE->getCouldNotCompute();
5576 /// getMax - Get the max backedge taken count for the loop.
5578 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5579 for (auto &ENT : ExitNotTaken)
5580 if (!ENT.hasAlwaysTruePred())
5581 return SE->getCouldNotCompute();
5583 return Max ? Max : SE->getCouldNotCompute();
5586 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5587 ScalarEvolution *SE) const {
5588 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
5591 if (!ExitNotTaken.ExitingBlock)
5594 for (auto &ENT : ExitNotTaken)
5595 if (ENT.ExactNotTaken != SE->getCouldNotCompute() &&
5596 SE->hasOperand(ENT.ExactNotTaken, S))
5602 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5603 /// computable exit into a persistent ExitNotTakenInfo array.
5604 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5605 SmallVectorImpl<EdgeInfo> &ExitCounts, bool Complete, const SCEV *MaxCount)
5609 ExitNotTaken.setIncomplete();
5611 unsigned NumExits = ExitCounts.size();
5612 if (NumExits == 0) return;
5614 ExitNotTaken.ExitingBlock = ExitCounts[0].ExitBlock;
5615 ExitNotTaken.ExactNotTaken = ExitCounts[0].Taken;
5617 // Determine the number of ExitNotTakenExtras structures that we need.
5618 unsigned ExtraInfoSize = 0;
5620 ExtraInfoSize = 1 + std::count_if(std::next(ExitCounts.begin()),
5621 ExitCounts.end(), [](EdgeInfo &Entry) {
5622 return !Entry.Pred.isAlwaysTrue();
5624 else if (!ExitCounts[0].Pred.isAlwaysTrue())
5627 ExitNotTakenExtras *ENT = nullptr;
5629 // Allocate the ExitNotTakenExtras structures and initialize the first
5630 // element (ExitNotTaken).
5631 if (ExtraInfoSize > 0) {
5632 ENT = new ExitNotTakenExtras[ExtraInfoSize];
5633 ExitNotTaken.ExtraInfo = &ENT[0];
5634 *ExitNotTaken.getPred() = std::move(ExitCounts[0].Pred);
5640 assert(ENT && "ExitNotTakenExtras is NULL while having more than one exit");
5642 auto &Exits = ExitNotTaken.ExtraInfo->Exits;
5644 // Handle the rare case of multiple computable exits.
5645 for (unsigned i = 1, PredPos = 1; i < NumExits; ++i) {
5646 ExitNotTakenExtras *Ptr = nullptr;
5647 if (!ExitCounts[i].Pred.isAlwaysTrue()) {
5648 Ptr = &ENT[PredPos++];
5649 Ptr->Pred = std::move(ExitCounts[i].Pred);
5652 Exits.emplace_back(ExitCounts[i].ExitBlock, ExitCounts[i].Taken, Ptr);
5656 /// Invalidate this result and free the ExitNotTakenInfo array.
5657 void ScalarEvolution::BackedgeTakenInfo::clear() {
5658 ExitNotTaken.ExitingBlock = nullptr;
5659 ExitNotTaken.ExactNotTaken = nullptr;
5660 delete[] ExitNotTaken.ExtraInfo;
5663 /// Compute the number of times the backedge of the specified loop will execute.
5664 ScalarEvolution::BackedgeTakenInfo
5665 ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
5666 bool AllowPredicates) {
5667 SmallVector<BasicBlock *, 8> ExitingBlocks;
5668 L->getExitingBlocks(ExitingBlocks);
5670 SmallVector<EdgeInfo, 4> ExitCounts;
5671 bool CouldComputeBECount = true;
5672 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5673 const SCEV *MustExitMaxBECount = nullptr;
5674 const SCEV *MayExitMaxBECount = nullptr;
5676 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5677 // and compute maxBECount.
5678 // Do a union of all the predicates here.
5679 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5680 BasicBlock *ExitBB = ExitingBlocks[i];
5681 ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
5683 assert((AllowPredicates || EL.Pred.isAlwaysTrue()) &&
5684 "Predicated exit limit when predicates are not allowed!");
5686 // 1. For each exit that can be computed, add an entry to ExitCounts.
5687 // CouldComputeBECount is true only if all exits can be computed.
5688 if (EL.Exact == getCouldNotCompute())
5689 // We couldn't compute an exact value for this exit, so
5690 // we won't be able to compute an exact value for the loop.
5691 CouldComputeBECount = false;
5693 ExitCounts.emplace_back(EdgeInfo(ExitBB, EL.Exact, EL.Pred));
5695 // 2. Derive the loop's MaxBECount from each exit's max number of
5696 // non-exiting iterations. Partition the loop exits into two kinds:
5697 // LoopMustExits and LoopMayExits.
5699 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5700 // is a LoopMayExit. If any computable LoopMustExit is found, then
5701 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
5702 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
5703 // considered greater than any computable EL.Max.
5704 if (EL.Max != getCouldNotCompute() && Latch &&
5705 DT.dominates(ExitBB, Latch)) {
5706 if (!MustExitMaxBECount)
5707 MustExitMaxBECount = EL.Max;
5709 MustExitMaxBECount =
5710 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5712 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5713 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5714 MayExitMaxBECount = EL.Max;
5717 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5721 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5722 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5723 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5726 ScalarEvolution::ExitLimit
5727 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
5728 bool AllowPredicates) {
5730 // Okay, we've chosen an exiting block. See what condition causes us to exit
5731 // at this block and remember the exit block and whether all other targets
5732 // lead to the loop header.
5733 bool MustExecuteLoopHeader = true;
5734 BasicBlock *Exit = nullptr;
5735 for (auto *SBB : successors(ExitingBlock))
5736 if (!L->contains(SBB)) {
5737 if (Exit) // Multiple exit successors.
5738 return getCouldNotCompute();
5740 } else if (SBB != L->getHeader()) {
5741 MustExecuteLoopHeader = false;
5744 // At this point, we know we have a conditional branch that determines whether
5745 // the loop is exited. However, we don't know if the branch is executed each
5746 // time through the loop. If not, then the execution count of the branch will
5747 // not be equal to the trip count of the loop.
5749 // Currently we check for this by checking to see if the Exit branch goes to
5750 // the loop header. If so, we know it will always execute the same number of
5751 // times as the loop. We also handle the case where the exit block *is* the
5752 // loop header. This is common for un-rotated loops.
5754 // If both of those tests fail, walk up the unique predecessor chain to the
5755 // header, stopping if there is an edge that doesn't exit the loop. If the
5756 // header is reached, the execution count of the branch will be equal to the
5757 // trip count of the loop.
5759 // More extensive analysis could be done to handle more cases here.
5761 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5762 // The simple checks failed, try climbing the unique predecessor chain
5763 // up to the header.
5765 for (BasicBlock *BB = ExitingBlock; BB; ) {
5766 BasicBlock *Pred = BB->getUniquePredecessor();
5768 return getCouldNotCompute();
5769 TerminatorInst *PredTerm = Pred->getTerminator();
5770 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5773 // If the predecessor has a successor that isn't BB and isn't
5774 // outside the loop, assume the worst.
5775 if (L->contains(PredSucc))
5776 return getCouldNotCompute();
5778 if (Pred == L->getHeader()) {
5785 return getCouldNotCompute();
5788 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5789 TerminatorInst *Term = ExitingBlock->getTerminator();
5790 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5791 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5792 // Proceed to the next level to examine the exit condition expression.
5793 return computeExitLimitFromCond(
5794 L, BI->getCondition(), BI->getSuccessor(0), BI->getSuccessor(1),
5795 /*ControlsExit=*/IsOnlyExit, AllowPredicates);
5798 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5799 return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
5800 /*ControlsExit=*/IsOnlyExit);
5802 return getCouldNotCompute();
5805 ScalarEvolution::ExitLimit
5806 ScalarEvolution::computeExitLimitFromCond(const Loop *L,
5811 bool AllowPredicates) {
5812 // Check if the controlling expression for this loop is an And or Or.
5813 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5814 if (BO->getOpcode() == Instruction::And) {
5815 // Recurse on the operands of the and.
5816 bool EitherMayExit = L->contains(TBB);
5817 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5818 ControlsExit && !EitherMayExit,
5820 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5821 ControlsExit && !EitherMayExit,
5823 const SCEV *BECount = getCouldNotCompute();
5824 const SCEV *MaxBECount = getCouldNotCompute();
5825 if (EitherMayExit) {
5826 // Both conditions must be true for the loop to continue executing.
5827 // Choose the less conservative count.
5828 if (EL0.Exact == getCouldNotCompute() ||
5829 EL1.Exact == getCouldNotCompute())
5830 BECount = getCouldNotCompute();
5832 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5833 if (EL0.Max == getCouldNotCompute())
5834 MaxBECount = EL1.Max;
5835 else if (EL1.Max == getCouldNotCompute())
5836 MaxBECount = EL0.Max;
5838 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5840 // Both conditions must be true at the same time for the loop to exit.
5841 // For now, be conservative.
5842 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5843 if (EL0.Max == EL1.Max)
5844 MaxBECount = EL0.Max;
5845 if (EL0.Exact == EL1.Exact)
5846 BECount = EL0.Exact;
5849 SCEVUnionPredicate NP;
5852 // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
5853 // to be more aggressive when computing BECount than when computing
5854 // MaxBECount. In these cases it is possible for EL0.Exact and EL1.Exact
5855 // to match, but for EL0.Max and EL1.Max to not.
5856 if (isa<SCEVCouldNotCompute>(MaxBECount) &&
5857 !isa<SCEVCouldNotCompute>(BECount))
5858 MaxBECount = BECount;
5860 return ExitLimit(BECount, MaxBECount, NP);
5862 if (BO->getOpcode() == Instruction::Or) {
5863 // Recurse on the operands of the or.
5864 bool EitherMayExit = L->contains(FBB);
5865 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5866 ControlsExit && !EitherMayExit,
5868 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5869 ControlsExit && !EitherMayExit,
5871 const SCEV *BECount = getCouldNotCompute();
5872 const SCEV *MaxBECount = getCouldNotCompute();
5873 if (EitherMayExit) {
5874 // Both conditions must be false for the loop to continue executing.
5875 // Choose the less conservative count.
5876 if (EL0.Exact == getCouldNotCompute() ||
5877 EL1.Exact == getCouldNotCompute())
5878 BECount = getCouldNotCompute();
5880 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5881 if (EL0.Max == getCouldNotCompute())
5882 MaxBECount = EL1.Max;
5883 else if (EL1.Max == getCouldNotCompute())
5884 MaxBECount = EL0.Max;
5886 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5888 // Both conditions must be false at the same time for the loop to exit.
5889 // For now, be conservative.
5890 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5891 if (EL0.Max == EL1.Max)
5892 MaxBECount = EL0.Max;
5893 if (EL0.Exact == EL1.Exact)
5894 BECount = EL0.Exact;
5897 SCEVUnionPredicate NP;
5900 return ExitLimit(BECount, MaxBECount, NP);
5904 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5905 // Proceed to the next level to examine the icmp.
5906 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
5908 computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5909 if (EL.hasFullInfo() || !AllowPredicates)
5912 // Try again, but use SCEV predicates this time.
5913 return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit,
5914 /*AllowPredicates=*/true);
5917 // Check for a constant condition. These are normally stripped out by
5918 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5919 // preserve the CFG and is temporarily leaving constant conditions
5921 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5922 if (L->contains(FBB) == !CI->getZExtValue())
5923 // The backedge is always taken.
5924 return getCouldNotCompute();
5926 // The backedge is never taken.
5927 return getZero(CI->getType());
5930 // If it's not an integer or pointer comparison then compute it the hard way.
5931 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5934 ScalarEvolution::ExitLimit
5935 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
5940 bool AllowPredicates) {
5942 // If the condition was exit on true, convert the condition to exit on false
5943 ICmpInst::Predicate Cond;
5944 if (!L->contains(FBB))
5945 Cond = ExitCond->getPredicate();
5947 Cond = ExitCond->getInversePredicate();
5949 // Handle common loops like: for (X = "string"; *X; ++X)
5950 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5951 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5953 computeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5954 if (ItCnt.hasAnyInfo())
5958 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5959 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5961 // Try to evaluate any dependencies out of the loop.
5962 LHS = getSCEVAtScope(LHS, L);
5963 RHS = getSCEVAtScope(RHS, L);
5965 // At this point, we would like to compute how many iterations of the
5966 // loop the predicate will return true for these inputs.
5967 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5968 // If there is a loop-invariant, force it into the RHS.
5969 std::swap(LHS, RHS);
5970 Cond = ICmpInst::getSwappedPredicate(Cond);
5973 // Simplify the operands before analyzing them.
5974 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5976 // If we have a comparison of a chrec against a constant, try to use value
5977 // ranges to answer this query.
5978 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5979 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5980 if (AddRec->getLoop() == L) {
5981 // Form the constant range.
5982 ConstantRange CompRange(
5983 ICmpInst::makeConstantRange(Cond, RHSC->getAPInt()));
5985 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5986 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5990 case ICmpInst::ICMP_NE: { // while (X != Y)
5991 // Convert to: while (X-Y != 0)
5992 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
5994 if (EL.hasAnyInfo()) return EL;
5997 case ICmpInst::ICMP_EQ: { // while (X == Y)
5998 // Convert to: while (X-Y == 0)
5999 ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
6000 if (EL.hasAnyInfo()) return EL;
6003 case ICmpInst::ICMP_SLT:
6004 case ICmpInst::ICMP_ULT: { // while (X < Y)
6005 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
6006 ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
6008 if (EL.hasAnyInfo()) return EL;
6011 case ICmpInst::ICMP_SGT:
6012 case ICmpInst::ICMP_UGT: { // while (X > Y)
6013 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
6015 howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
6017 if (EL.hasAnyInfo()) return EL;
6024 auto *ExhaustiveCount =
6025 computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
6027 if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
6028 return ExhaustiveCount;
6030 return computeShiftCompareExitLimit(ExitCond->getOperand(0),
6031 ExitCond->getOperand(1), L, Cond);
6034 ScalarEvolution::ExitLimit
6035 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
6037 BasicBlock *ExitingBlock,
6038 bool ControlsExit) {
6039 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
6041 // Give up if the exit is the default dest of a switch.
6042 if (Switch->getDefaultDest() == ExitingBlock)
6043 return getCouldNotCompute();
6045 assert(L->contains(Switch->getDefaultDest()) &&
6046 "Default case must not exit the loop!");
6047 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
6048 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
6050 // while (X != Y) --> while (X-Y != 0)
6051 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
6052 if (EL.hasAnyInfo())
6055 return getCouldNotCompute();
6058 static ConstantInt *
6059 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
6060 ScalarEvolution &SE) {
6061 const SCEV *InVal = SE.getConstant(C);
6062 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
6063 assert(isa<SCEVConstant>(Val) &&
6064 "Evaluation of SCEV at constant didn't fold correctly?");
6065 return cast<SCEVConstant>(Val)->getValue();
6068 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
6069 /// compute the backedge execution count.
6070 ScalarEvolution::ExitLimit
6071 ScalarEvolution::computeLoadConstantCompareExitLimit(
6075 ICmpInst::Predicate predicate) {
6077 if (LI->isVolatile()) return getCouldNotCompute();
6079 // Check to see if the loaded pointer is a getelementptr of a global.
6080 // TODO: Use SCEV instead of manually grubbing with GEPs.
6081 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
6082 if (!GEP) return getCouldNotCompute();
6084 // Make sure that it is really a constant global we are gepping, with an
6085 // initializer, and make sure the first IDX is really 0.
6086 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
6087 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
6088 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
6089 !cast<Constant>(GEP->getOperand(1))->isNullValue())
6090 return getCouldNotCompute();
6092 // Okay, we allow one non-constant index into the GEP instruction.
6093 Value *VarIdx = nullptr;
6094 std::vector<Constant*> Indexes;
6095 unsigned VarIdxNum = 0;
6096 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
6097 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
6098 Indexes.push_back(CI);
6099 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
6100 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
6101 VarIdx = GEP->getOperand(i);
6103 Indexes.push_back(nullptr);
6106 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
6108 return getCouldNotCompute();
6110 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
6111 // Check to see if X is a loop variant variable value now.
6112 const SCEV *Idx = getSCEV(VarIdx);
6113 Idx = getSCEVAtScope(Idx, L);
6115 // We can only recognize very limited forms of loop index expressions, in
6116 // particular, only affine AddRec's like {C1,+,C2}.
6117 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
6118 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
6119 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
6120 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
6121 return getCouldNotCompute();
6123 unsigned MaxSteps = MaxBruteForceIterations;
6124 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
6125 ConstantInt *ItCst = ConstantInt::get(
6126 cast<IntegerType>(IdxExpr->getType()), IterationNum);
6127 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
6129 // Form the GEP offset.
6130 Indexes[VarIdxNum] = Val;
6132 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
6134 if (!Result) break; // Cannot compute!
6136 // Evaluate the condition for this iteration.
6137 Result = ConstantExpr::getICmp(predicate, Result, RHS);
6138 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
6139 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
6140 ++NumArrayLenItCounts;
6141 return getConstant(ItCst); // Found terminating iteration!
6144 return getCouldNotCompute();
6147 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
6148 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
6149 ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
6151 return getCouldNotCompute();
6153 const BasicBlock *Latch = L->getLoopLatch();
6155 return getCouldNotCompute();
6157 const BasicBlock *Predecessor = L->getLoopPredecessor();
6159 return getCouldNotCompute();
6161 // Return true if V is of the form "LHS `shift_op` <positive constant>".
6162 // Return LHS in OutLHS and shift_opt in OutOpCode.
6163 auto MatchPositiveShift =
6164 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
6166 using namespace PatternMatch;
6168 ConstantInt *ShiftAmt;
6169 if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6170 OutOpCode = Instruction::LShr;
6171 else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6172 OutOpCode = Instruction::AShr;
6173 else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6174 OutOpCode = Instruction::Shl;
6178 return ShiftAmt->getValue().isStrictlyPositive();
6181 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
6184 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
6185 // %iv.shifted = lshr i32 %iv, <positive constant>
6187 // Return true on a succesful match. Return the corresponding PHI node (%iv
6188 // above) in PNOut and the opcode of the shift operation in OpCodeOut.
6189 auto MatchShiftRecurrence =
6190 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
6191 Optional<Instruction::BinaryOps> PostShiftOpCode;
6194 Instruction::BinaryOps OpC;
6197 // If we encounter a shift instruction, "peel off" the shift operation,
6198 // and remember that we did so. Later when we inspect %iv's backedge
6199 // value, we will make sure that the backedge value uses the same
6202 // Note: the peeled shift operation does not have to be the same
6203 // instruction as the one feeding into the PHI's backedge value. We only
6204 // really care about it being the same *kind* of shift instruction --
6205 // that's all that is required for our later inferences to hold.
6206 if (MatchPositiveShift(LHS, V, OpC)) {
6207 PostShiftOpCode = OpC;
6212 PNOut = dyn_cast<PHINode>(LHS);
6213 if (!PNOut || PNOut->getParent() != L->getHeader())
6216 Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
6220 // The backedge value for the PHI node must be a shift by a positive
6222 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
6224 // of the PHI node itself
6227 // and the kind of shift should be match the kind of shift we peeled
6229 (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
6233 Instruction::BinaryOps OpCode;
6234 if (!MatchShiftRecurrence(LHS, PN, OpCode))
6235 return getCouldNotCompute();
6237 const DataLayout &DL = getDataLayout();
6239 // The key rationale for this optimization is that for some kinds of shift
6240 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
6241 // within a finite number of iterations. If the condition guarding the
6242 // backedge (in the sense that the backedge is taken if the condition is true)
6243 // is false for the value the shift recurrence stabilizes to, then we know
6244 // that the backedge is taken only a finite number of times.
6246 ConstantInt *StableValue = nullptr;
6249 llvm_unreachable("Impossible case!");
6251 case Instruction::AShr: {
6252 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
6253 // bitwidth(K) iterations.
6254 Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
6255 bool KnownZero, KnownOne;
6256 ComputeSignBit(FirstValue, KnownZero, KnownOne, DL, 0, nullptr,
6257 Predecessor->getTerminator(), &DT);
6258 auto *Ty = cast<IntegerType>(RHS->getType());
6260 StableValue = ConstantInt::get(Ty, 0);
6262 StableValue = ConstantInt::get(Ty, -1, true);
6264 return getCouldNotCompute();
6268 case Instruction::LShr:
6269 case Instruction::Shl:
6270 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
6271 // stabilize to 0 in at most bitwidth(K) iterations.
6272 StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
6277 ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
6278 assert(Result->getType()->isIntegerTy(1) &&
6279 "Otherwise cannot be an operand to a branch instruction");
6281 if (Result->isZeroValue()) {
6282 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6283 const SCEV *UpperBound =
6284 getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
6285 SCEVUnionPredicate P;
6286 return ExitLimit(getCouldNotCompute(), UpperBound, P);
6289 return getCouldNotCompute();
6292 /// Return true if we can constant fold an instruction of the specified type,
6293 /// assuming that all operands were constants.
6294 static bool CanConstantFold(const Instruction *I) {
6295 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
6296 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
6300 if (const CallInst *CI = dyn_cast<CallInst>(I))
6301 if (const Function *F = CI->getCalledFunction())
6302 return canConstantFoldCallTo(F);
6306 /// Determine whether this instruction can constant evolve within this loop
6307 /// assuming its operands can all constant evolve.
6308 static bool canConstantEvolve(Instruction *I, const Loop *L) {
6309 // An instruction outside of the loop can't be derived from a loop PHI.
6310 if (!L->contains(I)) return false;
6312 if (isa<PHINode>(I)) {
6313 // We don't currently keep track of the control flow needed to evaluate
6314 // PHIs, so we cannot handle PHIs inside of loops.
6315 return L->getHeader() == I->getParent();
6318 // If we won't be able to constant fold this expression even if the operands
6319 // are constants, bail early.
6320 return CanConstantFold(I);
6323 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
6324 /// recursing through each instruction operand until reaching a loop header phi.
6326 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
6327 DenseMap<Instruction *, PHINode *> &PHIMap) {
6329 // Otherwise, we can evaluate this instruction if all of its operands are
6330 // constant or derived from a PHI node themselves.
6331 PHINode *PHI = nullptr;
6332 for (Value *Op : UseInst->operands()) {
6333 if (isa<Constant>(Op)) continue;
6335 Instruction *OpInst = dyn_cast<Instruction>(Op);
6336 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
6338 PHINode *P = dyn_cast<PHINode>(OpInst);
6340 // If this operand is already visited, reuse the prior result.
6341 // We may have P != PHI if this is the deepest point at which the
6342 // inconsistent paths meet.
6343 P = PHIMap.lookup(OpInst);
6345 // Recurse and memoize the results, whether a phi is found or not.
6346 // This recursive call invalidates pointers into PHIMap.
6347 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
6351 return nullptr; // Not evolving from PHI
6352 if (PHI && PHI != P)
6353 return nullptr; // Evolving from multiple different PHIs.
6356 // This is a expression evolving from a constant PHI!
6360 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
6361 /// in the loop that V is derived from. We allow arbitrary operations along the
6362 /// way, but the operands of an operation must either be constants or a value
6363 /// derived from a constant PHI. If this expression does not fit with these
6364 /// constraints, return null.
6365 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
6366 Instruction *I = dyn_cast<Instruction>(V);
6367 if (!I || !canConstantEvolve(I, L)) return nullptr;
6369 if (PHINode *PN = dyn_cast<PHINode>(I))
6372 // Record non-constant instructions contained by the loop.
6373 DenseMap<Instruction *, PHINode *> PHIMap;
6374 return getConstantEvolvingPHIOperands(I, L, PHIMap);
6377 /// EvaluateExpression - Given an expression that passes the
6378 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
6379 /// in the loop has the value PHIVal. If we can't fold this expression for some
6380 /// reason, return null.
6381 static Constant *EvaluateExpression(Value *V, const Loop *L,
6382 DenseMap<Instruction *, Constant *> &Vals,
6383 const DataLayout &DL,
6384 const TargetLibraryInfo *TLI) {
6385 // Convenient constant check, but redundant for recursive calls.
6386 if (Constant *C = dyn_cast<Constant>(V)) return C;
6387 Instruction *I = dyn_cast<Instruction>(V);
6388 if (!I) return nullptr;
6390 if (Constant *C = Vals.lookup(I)) return C;
6392 // An instruction inside the loop depends on a value outside the loop that we
6393 // weren't given a mapping for, or a value such as a call inside the loop.
6394 if (!canConstantEvolve(I, L)) return nullptr;
6396 // An unmapped PHI can be due to a branch or another loop inside this loop,
6397 // or due to this not being the initial iteration through a loop where we
6398 // couldn't compute the evolution of this particular PHI last time.
6399 if (isa<PHINode>(I)) return nullptr;
6401 std::vector<Constant*> Operands(I->getNumOperands());
6403 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
6404 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
6406 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
6407 if (!Operands[i]) return nullptr;
6410 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
6412 if (!C) return nullptr;
6416 if (CmpInst *CI = dyn_cast<CmpInst>(I))
6417 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6418 Operands[1], DL, TLI);
6419 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
6420 if (!LI->isVolatile())
6421 return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
6423 return ConstantFoldInstOperands(I, Operands, DL, TLI);
6427 // If every incoming value to PN except the one for BB is a specific Constant,
6428 // return that, else return nullptr.
6429 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
6430 Constant *IncomingVal = nullptr;
6432 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
6433 if (PN->getIncomingBlock(i) == BB)
6436 auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
6440 if (IncomingVal != CurrentVal) {
6443 IncomingVal = CurrentVal;
6450 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
6451 /// in the header of its containing loop, we know the loop executes a
6452 /// constant number of times, and the PHI node is just a recurrence
6453 /// involving constants, fold it.
6455 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
6458 auto I = ConstantEvolutionLoopExitValue.find(PN);
6459 if (I != ConstantEvolutionLoopExitValue.end())
6462 if (BEs.ugt(MaxBruteForceIterations))
6463 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
6465 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
6467 DenseMap<Instruction *, Constant *> CurrentIterVals;
6468 BasicBlock *Header = L->getHeader();
6469 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6471 BasicBlock *Latch = L->getLoopLatch();
6475 for (auto &I : *Header) {
6476 PHINode *PHI = dyn_cast<PHINode>(&I);
6478 auto *StartCST = getOtherIncomingValue(PHI, Latch);
6479 if (!StartCST) continue;
6480 CurrentIterVals[PHI] = StartCST;
6482 if (!CurrentIterVals.count(PN))
6483 return RetVal = nullptr;
6485 Value *BEValue = PN->getIncomingValueForBlock(Latch);
6487 // Execute the loop symbolically to determine the exit value.
6488 if (BEs.getActiveBits() >= 32)
6489 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
6491 unsigned NumIterations = BEs.getZExtValue(); // must be in range
6492 unsigned IterationNum = 0;
6493 const DataLayout &DL = getDataLayout();
6494 for (; ; ++IterationNum) {
6495 if (IterationNum == NumIterations)
6496 return RetVal = CurrentIterVals[PN]; // Got exit value!
6498 // Compute the value of the PHIs for the next iteration.
6499 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
6500 DenseMap<Instruction *, Constant *> NextIterVals;
6502 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6504 return nullptr; // Couldn't evaluate!
6505 NextIterVals[PN] = NextPHI;
6507 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
6509 // Also evaluate the other PHI nodes. However, we don't get to stop if we
6510 // cease to be able to evaluate one of them or if they stop evolving,
6511 // because that doesn't necessarily prevent us from computing PN.
6512 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
6513 for (const auto &I : CurrentIterVals) {
6514 PHINode *PHI = dyn_cast<PHINode>(I.first);
6515 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
6516 PHIsToCompute.emplace_back(PHI, I.second);
6518 // We use two distinct loops because EvaluateExpression may invalidate any
6519 // iterators into CurrentIterVals.
6520 for (const auto &I : PHIsToCompute) {
6521 PHINode *PHI = I.first;
6522 Constant *&NextPHI = NextIterVals[PHI];
6523 if (!NextPHI) { // Not already computed.
6524 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6525 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6527 if (NextPHI != I.second)
6528 StoppedEvolving = false;
6531 // If all entries in CurrentIterVals == NextIterVals then we can stop
6532 // iterating, the loop can't continue to change.
6533 if (StoppedEvolving)
6534 return RetVal = CurrentIterVals[PN];
6536 CurrentIterVals.swap(NextIterVals);
6540 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
6543 PHINode *PN = getConstantEvolvingPHI(Cond, L);
6544 if (!PN) return getCouldNotCompute();
6546 // If the loop is canonicalized, the PHI will have exactly two entries.
6547 // That's the only form we support here.
6548 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
6550 DenseMap<Instruction *, Constant *> CurrentIterVals;
6551 BasicBlock *Header = L->getHeader();
6552 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6554 BasicBlock *Latch = L->getLoopLatch();
6555 assert(Latch && "Should follow from NumIncomingValues == 2!");
6557 for (auto &I : *Header) {
6558 PHINode *PHI = dyn_cast<PHINode>(&I);
6561 auto *StartCST = getOtherIncomingValue(PHI, Latch);
6562 if (!StartCST) continue;
6563 CurrentIterVals[PHI] = StartCST;
6565 if (!CurrentIterVals.count(PN))
6566 return getCouldNotCompute();
6568 // Okay, we find a PHI node that defines the trip count of this loop. Execute
6569 // the loop symbolically to determine when the condition gets a value of
6571 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
6572 const DataLayout &DL = getDataLayout();
6573 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
6574 auto *CondVal = dyn_cast_or_null<ConstantInt>(
6575 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
6577 // Couldn't symbolically evaluate.
6578 if (!CondVal) return getCouldNotCompute();
6580 if (CondVal->getValue() == uint64_t(ExitWhen)) {
6581 ++NumBruteForceTripCountsComputed;
6582 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
6585 // Update all the PHI nodes for the next iteration.
6586 DenseMap<Instruction *, Constant *> NextIterVals;
6588 // Create a list of which PHIs we need to compute. We want to do this before
6589 // calling EvaluateExpression on them because that may invalidate iterators
6590 // into CurrentIterVals.
6591 SmallVector<PHINode *, 8> PHIsToCompute;
6592 for (const auto &I : CurrentIterVals) {
6593 PHINode *PHI = dyn_cast<PHINode>(I.first);
6594 if (!PHI || PHI->getParent() != Header) continue;
6595 PHIsToCompute.push_back(PHI);
6597 for (PHINode *PHI : PHIsToCompute) {
6598 Constant *&NextPHI = NextIterVals[PHI];
6599 if (NextPHI) continue; // Already computed!
6601 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6602 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6604 CurrentIterVals.swap(NextIterVals);
6607 // Too many iterations were needed to evaluate.
6608 return getCouldNotCompute();
6611 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
6612 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
6614 // Check to see if we've folded this expression at this loop before.
6615 for (auto &LS : Values)
6617 return LS.second ? LS.second : V;
6619 Values.emplace_back(L, nullptr);
6621 // Otherwise compute it.
6622 const SCEV *C = computeSCEVAtScope(V, L);
6623 for (auto &LS : reverse(ValuesAtScopes[V]))
6624 if (LS.first == L) {
6631 /// This builds up a Constant using the ConstantExpr interface. That way, we
6632 /// will return Constants for objects which aren't represented by a
6633 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
6634 /// Returns NULL if the SCEV isn't representable as a Constant.
6635 static Constant *BuildConstantFromSCEV(const SCEV *V) {
6636 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
6637 case scCouldNotCompute:
6641 return cast<SCEVConstant>(V)->getValue();
6643 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
6644 case scSignExtend: {
6645 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
6646 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
6647 return ConstantExpr::getSExt(CastOp, SS->getType());
6650 case scZeroExtend: {
6651 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
6652 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
6653 return ConstantExpr::getZExt(CastOp, SZ->getType());
6657 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
6658 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
6659 return ConstantExpr::getTrunc(CastOp, ST->getType());
6663 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
6664 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
6665 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6666 unsigned AS = PTy->getAddressSpace();
6667 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6668 C = ConstantExpr::getBitCast(C, DestPtrTy);
6670 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
6671 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
6672 if (!C2) return nullptr;
6675 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
6676 unsigned AS = C2->getType()->getPointerAddressSpace();
6678 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6679 // The offsets have been converted to bytes. We can add bytes to an
6680 // i8* by GEP with the byte count in the first index.
6681 C = ConstantExpr::getBitCast(C, DestPtrTy);
6684 // Don't bother trying to sum two pointers. We probably can't
6685 // statically compute a load that results from it anyway.
6686 if (C2->getType()->isPointerTy())
6689 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6690 if (PTy->getElementType()->isStructTy())
6691 C2 = ConstantExpr::getIntegerCast(
6692 C2, Type::getInt32Ty(C->getContext()), true);
6693 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
6695 C = ConstantExpr::getAdd(C, C2);
6702 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
6703 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
6704 // Don't bother with pointers at all.
6705 if (C->getType()->isPointerTy()) return nullptr;
6706 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
6707 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
6708 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
6709 C = ConstantExpr::getMul(C, C2);
6716 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6717 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6718 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6719 if (LHS->getType() == RHS->getType())
6720 return ConstantExpr::getUDiv(LHS, RHS);
6725 break; // TODO: smax, umax.
6730 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6731 if (isa<SCEVConstant>(V)) return V;
6733 // If this instruction is evolved from a constant-evolving PHI, compute the
6734 // exit value from the loop without using SCEVs.
6735 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6736 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6737 const Loop *LI = this->LI[I->getParent()];
6738 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
6739 if (PHINode *PN = dyn_cast<PHINode>(I))
6740 if (PN->getParent() == LI->getHeader()) {
6741 // Okay, there is no closed form solution for the PHI node. Check
6742 // to see if the loop that contains it has a known backedge-taken
6743 // count. If so, we may be able to force computation of the exit
6745 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6746 if (const SCEVConstant *BTCC =
6747 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6748 // Okay, we know how many times the containing loop executes. If
6749 // this is a constant evolving PHI node, get the final value at
6750 // the specified iteration number.
6752 getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
6753 if (RV) return getSCEV(RV);
6757 // Okay, this is an expression that we cannot symbolically evaluate
6758 // into a SCEV. Check to see if it's possible to symbolically evaluate
6759 // the arguments into constants, and if so, try to constant propagate the
6760 // result. This is particularly useful for computing loop exit values.
6761 if (CanConstantFold(I)) {
6762 SmallVector<Constant *, 4> Operands;
6763 bool MadeImprovement = false;
6764 for (Value *Op : I->operands()) {
6765 if (Constant *C = dyn_cast<Constant>(Op)) {
6766 Operands.push_back(C);
6770 // If any of the operands is non-constant and if they are
6771 // non-integer and non-pointer, don't even try to analyze them
6772 // with scev techniques.
6773 if (!isSCEVable(Op->getType()))
6776 const SCEV *OrigV = getSCEV(Op);
6777 const SCEV *OpV = getSCEVAtScope(OrigV, L);
6778 MadeImprovement |= OrigV != OpV;
6780 Constant *C = BuildConstantFromSCEV(OpV);
6782 if (C->getType() != Op->getType())
6783 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6787 Operands.push_back(C);
6790 // Check to see if getSCEVAtScope actually made an improvement.
6791 if (MadeImprovement) {
6792 Constant *C = nullptr;
6793 const DataLayout &DL = getDataLayout();
6794 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6795 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6796 Operands[1], DL, &TLI);
6797 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6798 if (!LI->isVolatile())
6799 C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
6801 C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
6808 // This is some other type of SCEVUnknown, just return it.
6812 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6813 // Avoid performing the look-up in the common case where the specified
6814 // expression has no loop-variant portions.
6815 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6816 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6817 if (OpAtScope != Comm->getOperand(i)) {
6818 // Okay, at least one of these operands is loop variant but might be
6819 // foldable. Build a new instance of the folded commutative expression.
6820 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6821 Comm->op_begin()+i);
6822 NewOps.push_back(OpAtScope);
6824 for (++i; i != e; ++i) {
6825 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6826 NewOps.push_back(OpAtScope);
6828 if (isa<SCEVAddExpr>(Comm))
6829 return getAddExpr(NewOps);
6830 if (isa<SCEVMulExpr>(Comm))
6831 return getMulExpr(NewOps);
6832 if (isa<SCEVSMaxExpr>(Comm))
6833 return getSMaxExpr(NewOps);
6834 if (isa<SCEVUMaxExpr>(Comm))
6835 return getUMaxExpr(NewOps);
6836 llvm_unreachable("Unknown commutative SCEV type!");
6839 // If we got here, all operands are loop invariant.
6843 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6844 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6845 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6846 if (LHS == Div->getLHS() && RHS == Div->getRHS())
6847 return Div; // must be loop invariant
6848 return getUDivExpr(LHS, RHS);
6851 // If this is a loop recurrence for a loop that does not contain L, then we
6852 // are dealing with the final value computed by the loop.
6853 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6854 // First, attempt to evaluate each operand.
6855 // Avoid performing the look-up in the common case where the specified
6856 // expression has no loop-variant portions.
6857 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6858 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6859 if (OpAtScope == AddRec->getOperand(i))
6862 // Okay, at least one of these operands is loop variant but might be
6863 // foldable. Build a new instance of the folded commutative expression.
6864 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6865 AddRec->op_begin()+i);
6866 NewOps.push_back(OpAtScope);
6867 for (++i; i != e; ++i)
6868 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6870 const SCEV *FoldedRec =
6871 getAddRecExpr(NewOps, AddRec->getLoop(),
6872 AddRec->getNoWrapFlags(SCEV::FlagNW));
6873 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6874 // The addrec may be folded to a nonrecurrence, for example, if the
6875 // induction variable is multiplied by zero after constant folding. Go
6876 // ahead and return the folded value.
6882 // If the scope is outside the addrec's loop, evaluate it by using the
6883 // loop exit value of the addrec.
6884 if (!AddRec->getLoop()->contains(L)) {
6885 // To evaluate this recurrence, we need to know how many times the AddRec
6886 // loop iterates. Compute this now.
6887 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6888 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6890 // Then, evaluate the AddRec.
6891 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6897 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6898 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6899 if (Op == Cast->getOperand())
6900 return Cast; // must be loop invariant
6901 return getZeroExtendExpr(Op, Cast->getType());
6904 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6905 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6906 if (Op == Cast->getOperand())
6907 return Cast; // must be loop invariant
6908 return getSignExtendExpr(Op, Cast->getType());
6911 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6912 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6913 if (Op == Cast->getOperand())
6914 return Cast; // must be loop invariant
6915 return getTruncateExpr(Op, Cast->getType());
6918 llvm_unreachable("Unknown SCEV type!");
6921 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6922 return getSCEVAtScope(getSCEV(V), L);
6925 /// Finds the minimum unsigned root of the following equation:
6927 /// A * X = B (mod N)
6929 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6930 /// A and B isn't important.
6932 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6933 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6934 ScalarEvolution &SE) {
6935 uint32_t BW = A.getBitWidth();
6936 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6937 assert(A != 0 && "A must be non-zero.");
6941 // The gcd of A and N may have only one prime factor: 2. The number of
6942 // trailing zeros in A is its multiplicity
6943 uint32_t Mult2 = A.countTrailingZeros();
6946 // 2. Check if B is divisible by D.
6948 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6949 // is not less than multiplicity of this prime factor for D.
6950 if (B.countTrailingZeros() < Mult2)
6951 return SE.getCouldNotCompute();
6953 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6956 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6957 // bit width during computations.
6958 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6959 APInt Mod(BW + 1, 0);
6960 Mod.setBit(BW - Mult2); // Mod = N / D
6961 APInt I = AD.multiplicativeInverse(Mod);
6963 // 4. Compute the minimum unsigned root of the equation:
6964 // I * (B / D) mod (N / D)
6965 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6967 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6969 return SE.getConstant(Result.trunc(BW));
6972 /// Find the roots of the quadratic equation for the given quadratic chrec
6973 /// {L,+,M,+,N}. This returns either the two roots (which might be the same) or
6974 /// two SCEVCouldNotCompute objects.
6976 static Optional<std::pair<const SCEVConstant *,const SCEVConstant *>>
6977 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6978 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6979 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6980 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6981 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6983 // We currently can only solve this if the coefficients are constants.
6984 if (!LC || !MC || !NC)
6987 uint32_t BitWidth = LC->getAPInt().getBitWidth();
6988 const APInt &L = LC->getAPInt();
6989 const APInt &M = MC->getAPInt();
6990 const APInt &N = NC->getAPInt();
6991 APInt Two(BitWidth, 2);
6992 APInt Four(BitWidth, 4);
6995 using namespace APIntOps;
6997 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6998 // The B coefficient is M-N/2
7002 // The A coefficient is N/2
7003 APInt A(N.sdiv(Two));
7005 // Compute the B^2-4ac term.
7008 SqrtTerm -= Four * (A * C);
7010 if (SqrtTerm.isNegative()) {
7011 // The loop is provably infinite.
7015 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
7016 // integer value or else APInt::sqrt() will assert.
7017 APInt SqrtVal(SqrtTerm.sqrt());
7019 // Compute the two solutions for the quadratic formula.
7020 // The divisions must be performed as signed divisions.
7023 if (TwoA.isMinValue())
7026 LLVMContext &Context = SE.getContext();
7028 ConstantInt *Solution1 =
7029 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
7030 ConstantInt *Solution2 =
7031 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
7033 return std::make_pair(cast<SCEVConstant>(SE.getConstant(Solution1)),
7034 cast<SCEVConstant>(SE.getConstant(Solution2)));
7035 } // end APIntOps namespace
7038 ScalarEvolution::ExitLimit
7039 ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
7040 bool AllowPredicates) {
7042 // This is only used for loops with a "x != y" exit test. The exit condition
7043 // is now expressed as a single expression, V = x-y. So the exit test is
7044 // effectively V != 0. We know and take advantage of the fact that this
7045 // expression only being used in a comparison by zero context.
7047 SCEVUnionPredicate P;
7048 // If the value is a constant
7049 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
7050 // If the value is already zero, the branch will execute zero times.
7051 if (C->getValue()->isZero()) return C;
7052 return getCouldNotCompute(); // Otherwise it will loop infinitely.
7055 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
7056 if (!AddRec && AllowPredicates)
7057 // Try to make this an AddRec using runtime tests, in the first X
7058 // iterations of this loop, where X is the SCEV expression found by the
7060 AddRec = convertSCEVToAddRecWithPredicates(V, L, P);
7062 if (!AddRec || AddRec->getLoop() != L)
7063 return getCouldNotCompute();
7065 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
7066 // the quadratic equation to solve it.
7067 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
7068 if (auto Roots = SolveQuadraticEquation(AddRec, *this)) {
7069 const SCEVConstant *R1 = Roots->first;
7070 const SCEVConstant *R2 = Roots->second;
7071 // Pick the smallest positive root value.
7072 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
7073 CmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
7074 if (!CB->getZExtValue())
7075 std::swap(R1, R2); // R1 is the minimum root now.
7077 // We can only use this value if the chrec ends up with an exact zero
7078 // value at this index. When solving for "X*X != 5", for example, we
7079 // should not accept a root of 2.
7080 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
7082 return ExitLimit(R1, R1, P); // We found a quadratic root!
7085 return getCouldNotCompute();
7088 // Otherwise we can only handle this if it is affine.
7089 if (!AddRec->isAffine())
7090 return getCouldNotCompute();
7092 // If this is an affine expression, the execution count of this branch is
7093 // the minimum unsigned root of the following equation:
7095 // Start + Step*N = 0 (mod 2^BW)
7099 // Step*N = -Start (mod 2^BW)
7101 // where BW is the common bit width of Start and Step.
7103 // Get the initial value for the loop.
7104 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
7105 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
7107 // For now we handle only constant steps.
7109 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
7110 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
7111 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
7112 // We have not yet seen any such cases.
7113 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
7114 if (!StepC || StepC->getValue()->equalsInt(0))
7115 return getCouldNotCompute();
7117 // For positive steps (counting up until unsigned overflow):
7118 // N = -Start/Step (as unsigned)
7119 // For negative steps (counting down to zero):
7121 // First compute the unsigned distance from zero in the direction of Step.
7122 bool CountDown = StepC->getAPInt().isNegative();
7123 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
7125 // Handle unitary steps, which cannot wraparound.
7126 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
7127 // N = Distance (as unsigned)
7128 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
7129 ConstantRange CR = getUnsignedRange(Start);
7130 const SCEV *MaxBECount;
7131 if (!CountDown && CR.getUnsignedMin().isMinValue())
7132 // When counting up, the worst starting value is 1, not 0.
7133 MaxBECount = CR.getUnsignedMax().isMinValue()
7134 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
7135 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
7137 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
7138 : -CR.getUnsignedMin());
7139 return ExitLimit(Distance, MaxBECount, P);
7142 // As a special case, handle the instance where Step is a positive power of
7143 // two. In this case, determining whether Step divides Distance evenly can be
7144 // done by counting and comparing the number of trailing zeros of Step and
7147 const APInt &StepV = StepC->getAPInt();
7148 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
7149 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
7150 // case is not handled as this code is guarded by !CountDown.
7151 if (StepV.isPowerOf2() &&
7152 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
7153 // Here we've constrained the equation to be of the form
7155 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
7157 // where we're operating on a W bit wide integer domain and k is
7158 // non-negative. The smallest unsigned solution for X is the trip count.
7160 // (0) is equivalent to:
7162 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
7163 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
7164 // <=> 2^k * Distance' - X = L * 2^(W - N)
7165 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
7167 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
7170 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
7172 // E.g. say we're solving
7174 // 2 * Val = 2 * X (in i8) ... (3)
7176 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
7178 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
7179 // necessarily the smallest unsigned value of X that satisfies (3).
7180 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
7181 // is i8 1, not i8 -127
7183 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
7185 // Since SCEV does not have a URem node, we construct one using a truncate
7186 // and a zero extend.
7188 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
7189 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
7190 auto *WideTy = Distance->getType();
7193 getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
7194 return ExitLimit(Limit, Limit, P);
7198 // If the condition controls loop exit (the loop exits only if the expression
7199 // is true) and the addition is no-wrap we can use unsigned divide to
7200 // compute the backedge count. In this case, the step may not divide the
7201 // distance, but we don't care because if the condition is "missed" the loop
7202 // will have undefined behavior due to wrapping.
7203 if (ControlsExit && AddRec->hasNoSelfWrap() &&
7204 loopHasNoAbnormalExits(AddRec->getLoop())) {
7206 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
7207 return ExitLimit(Exact, Exact, P);
7210 // Then, try to solve the above equation provided that Start is constant.
7211 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
7212 const SCEV *E = SolveLinEquationWithOverflow(
7213 StepC->getValue()->getValue(), -StartC->getValue()->getValue(), *this);
7214 return ExitLimit(E, E, P);
7216 return getCouldNotCompute();
7219 ScalarEvolution::ExitLimit
7220 ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
7221 // Loops that look like: while (X == 0) are very strange indeed. We don't
7222 // handle them yet except for the trivial case. This could be expanded in the
7223 // future as needed.
7225 // If the value is a constant, check to see if it is known to be non-zero
7226 // already. If so, the backedge will execute zero times.
7227 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
7228 if (!C->getValue()->isNullValue())
7229 return getZero(C->getType());
7230 return getCouldNotCompute(); // Otherwise it will loop infinitely.
7233 // We could implement others, but I really doubt anyone writes loops like
7234 // this, and if they did, they would already be constant folded.
7235 return getCouldNotCompute();
7238 std::pair<BasicBlock *, BasicBlock *>
7239 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
7240 // If the block has a unique predecessor, then there is no path from the
7241 // predecessor to the block that does not go through the direct edge
7242 // from the predecessor to the block.
7243 if (BasicBlock *Pred = BB->getSinglePredecessor())
7246 // A loop's header is defined to be a block that dominates the loop.
7247 // If the header has a unique predecessor outside the loop, it must be
7248 // a block that has exactly one successor that can reach the loop.
7249 if (Loop *L = LI.getLoopFor(BB))
7250 return {L->getLoopPredecessor(), L->getHeader()};
7252 return {nullptr, nullptr};
7255 /// SCEV structural equivalence is usually sufficient for testing whether two
7256 /// expressions are equal, however for the purposes of looking for a condition
7257 /// guarding a loop, it can be useful to be a little more general, since a
7258 /// front-end may have replicated the controlling expression.
7260 static bool HasSameValue(const SCEV *A, const SCEV *B) {
7261 // Quick check to see if they are the same SCEV.
7262 if (A == B) return true;
7264 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
7265 // Not all instructions that are "identical" compute the same value. For
7266 // instance, two distinct alloca instructions allocating the same type are
7267 // identical and do not read memory; but compute distinct values.
7268 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
7271 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
7272 // two different instructions with the same value. Check for this case.
7273 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
7274 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
7275 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
7276 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
7277 if (ComputesEqualValues(AI, BI))
7280 // Otherwise assume they may have a different value.
7284 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
7285 const SCEV *&LHS, const SCEV *&RHS,
7287 bool Changed = false;
7289 // If we hit the max recursion limit bail out.
7293 // Canonicalize a constant to the right side.
7294 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
7295 // Check for both operands constant.
7296 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
7297 if (ConstantExpr::getICmp(Pred,
7299 RHSC->getValue())->isNullValue())
7300 goto trivially_false;
7302 goto trivially_true;
7304 // Otherwise swap the operands to put the constant on the right.
7305 std::swap(LHS, RHS);
7306 Pred = ICmpInst::getSwappedPredicate(Pred);
7310 // If we're comparing an addrec with a value which is loop-invariant in the
7311 // addrec's loop, put the addrec on the left. Also make a dominance check,
7312 // as both operands could be addrecs loop-invariant in each other's loop.
7313 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
7314 const Loop *L = AR->getLoop();
7315 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
7316 std::swap(LHS, RHS);
7317 Pred = ICmpInst::getSwappedPredicate(Pred);
7322 // If there's a constant operand, canonicalize comparisons with boundary
7323 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
7324 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
7325 const APInt &RA = RC->getAPInt();
7327 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7328 case ICmpInst::ICMP_EQ:
7329 case ICmpInst::ICMP_NE:
7330 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
7332 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
7333 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
7334 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
7335 ME->getOperand(0)->isAllOnesValue()) {
7336 RHS = AE->getOperand(1);
7337 LHS = ME->getOperand(1);
7341 case ICmpInst::ICMP_UGE:
7342 if ((RA - 1).isMinValue()) {
7343 Pred = ICmpInst::ICMP_NE;
7344 RHS = getConstant(RA - 1);
7348 if (RA.isMaxValue()) {
7349 Pred = ICmpInst::ICMP_EQ;
7353 if (RA.isMinValue()) goto trivially_true;
7355 Pred = ICmpInst::ICMP_UGT;
7356 RHS = getConstant(RA - 1);
7359 case ICmpInst::ICMP_ULE:
7360 if ((RA + 1).isMaxValue()) {
7361 Pred = ICmpInst::ICMP_NE;
7362 RHS = getConstant(RA + 1);
7366 if (RA.isMinValue()) {
7367 Pred = ICmpInst::ICMP_EQ;
7371 if (RA.isMaxValue()) goto trivially_true;
7373 Pred = ICmpInst::ICMP_ULT;
7374 RHS = getConstant(RA + 1);
7377 case ICmpInst::ICMP_SGE:
7378 if ((RA - 1).isMinSignedValue()) {
7379 Pred = ICmpInst::ICMP_NE;
7380 RHS = getConstant(RA - 1);
7384 if (RA.isMaxSignedValue()) {
7385 Pred = ICmpInst::ICMP_EQ;
7389 if (RA.isMinSignedValue()) goto trivially_true;
7391 Pred = ICmpInst::ICMP_SGT;
7392 RHS = getConstant(RA - 1);
7395 case ICmpInst::ICMP_SLE:
7396 if ((RA + 1).isMaxSignedValue()) {
7397 Pred = ICmpInst::ICMP_NE;
7398 RHS = getConstant(RA + 1);
7402 if (RA.isMinSignedValue()) {
7403 Pred = ICmpInst::ICMP_EQ;
7407 if (RA.isMaxSignedValue()) goto trivially_true;
7409 Pred = ICmpInst::ICMP_SLT;
7410 RHS = getConstant(RA + 1);
7413 case ICmpInst::ICMP_UGT:
7414 if (RA.isMinValue()) {
7415 Pred = ICmpInst::ICMP_NE;
7419 if ((RA + 1).isMaxValue()) {
7420 Pred = ICmpInst::ICMP_EQ;
7421 RHS = getConstant(RA + 1);
7425 if (RA.isMaxValue()) goto trivially_false;
7427 case ICmpInst::ICMP_ULT:
7428 if (RA.isMaxValue()) {
7429 Pred = ICmpInst::ICMP_NE;
7433 if ((RA - 1).isMinValue()) {
7434 Pred = ICmpInst::ICMP_EQ;
7435 RHS = getConstant(RA - 1);
7439 if (RA.isMinValue()) goto trivially_false;
7441 case ICmpInst::ICMP_SGT:
7442 if (RA.isMinSignedValue()) {
7443 Pred = ICmpInst::ICMP_NE;
7447 if ((RA + 1).isMaxSignedValue()) {
7448 Pred = ICmpInst::ICMP_EQ;
7449 RHS = getConstant(RA + 1);
7453 if (RA.isMaxSignedValue()) goto trivially_false;
7455 case ICmpInst::ICMP_SLT:
7456 if (RA.isMaxSignedValue()) {
7457 Pred = ICmpInst::ICMP_NE;
7461 if ((RA - 1).isMinSignedValue()) {
7462 Pred = ICmpInst::ICMP_EQ;
7463 RHS = getConstant(RA - 1);
7467 if (RA.isMinSignedValue()) goto trivially_false;
7472 // Check for obvious equality.
7473 if (HasSameValue(LHS, RHS)) {
7474 if (ICmpInst::isTrueWhenEqual(Pred))
7475 goto trivially_true;
7476 if (ICmpInst::isFalseWhenEqual(Pred))
7477 goto trivially_false;
7480 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
7481 // adding or subtracting 1 from one of the operands.
7483 case ICmpInst::ICMP_SLE:
7484 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
7485 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7487 Pred = ICmpInst::ICMP_SLT;
7489 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
7490 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
7492 Pred = ICmpInst::ICMP_SLT;
7496 case ICmpInst::ICMP_SGE:
7497 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
7498 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
7500 Pred = ICmpInst::ICMP_SGT;
7502 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
7503 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7505 Pred = ICmpInst::ICMP_SGT;
7509 case ICmpInst::ICMP_ULE:
7510 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
7511 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7513 Pred = ICmpInst::ICMP_ULT;
7515 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
7516 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
7517 Pred = ICmpInst::ICMP_ULT;
7521 case ICmpInst::ICMP_UGE:
7522 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
7523 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
7524 Pred = ICmpInst::ICMP_UGT;
7526 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
7527 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7529 Pred = ICmpInst::ICMP_UGT;
7537 // TODO: More simplifications are possible here.
7539 // Recursively simplify until we either hit a recursion limit or nothing
7542 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
7548 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7549 Pred = ICmpInst::ICMP_EQ;
7554 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7555 Pred = ICmpInst::ICMP_NE;
7559 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
7560 return getSignedRange(S).getSignedMax().isNegative();
7563 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
7564 return getSignedRange(S).getSignedMin().isStrictlyPositive();
7567 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
7568 return !getSignedRange(S).getSignedMin().isNegative();
7571 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
7572 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
7575 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
7576 return isKnownNegative(S) || isKnownPositive(S);
7579 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
7580 const SCEV *LHS, const SCEV *RHS) {
7581 // Canonicalize the inputs first.
7582 (void)SimplifyICmpOperands(Pred, LHS, RHS);
7584 // If LHS or RHS is an addrec, check to see if the condition is true in
7585 // every iteration of the loop.
7586 // If LHS and RHS are both addrec, both conditions must be true in
7587 // every iteration of the loop.
7588 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7589 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7590 bool LeftGuarded = false;
7591 bool RightGuarded = false;
7593 const Loop *L = LAR->getLoop();
7594 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
7595 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
7596 if (!RAR) return true;
7601 const Loop *L = RAR->getLoop();
7602 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
7603 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
7604 if (!LAR) return true;
7605 RightGuarded = true;
7608 if (LeftGuarded && RightGuarded)
7611 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
7614 // Otherwise see what can be done with known constant ranges.
7615 return isKnownPredicateViaConstantRanges(Pred, LHS, RHS);
7618 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
7619 ICmpInst::Predicate Pred,
7621 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
7624 // Verify an invariant: inverting the predicate should turn a monotonically
7625 // increasing change to a monotonically decreasing one, and vice versa.
7626 bool IncreasingSwapped;
7627 bool ResultSwapped = isMonotonicPredicateImpl(
7628 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
7630 assert(Result == ResultSwapped && "should be able to analyze both!");
7632 assert(Increasing == !IncreasingSwapped &&
7633 "monotonicity should flip as we flip the predicate");
7639 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
7640 ICmpInst::Predicate Pred,
7643 // A zero step value for LHS means the induction variable is essentially a
7644 // loop invariant value. We don't really depend on the predicate actually
7645 // flipping from false to true (for increasing predicates, and the other way
7646 // around for decreasing predicates), all we care about is that *if* the
7647 // predicate changes then it only changes from false to true.
7649 // A zero step value in itself is not very useful, but there may be places
7650 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
7651 // as general as possible.
7655 return false; // Conservative answer
7657 case ICmpInst::ICMP_UGT:
7658 case ICmpInst::ICMP_UGE:
7659 case ICmpInst::ICMP_ULT:
7660 case ICmpInst::ICMP_ULE:
7661 if (!LHS->hasNoUnsignedWrap())
7664 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
7667 case ICmpInst::ICMP_SGT:
7668 case ICmpInst::ICMP_SGE:
7669 case ICmpInst::ICMP_SLT:
7670 case ICmpInst::ICMP_SLE: {
7671 if (!LHS->hasNoSignedWrap())
7674 const SCEV *Step = LHS->getStepRecurrence(*this);
7676 if (isKnownNonNegative(Step)) {
7677 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
7681 if (isKnownNonPositive(Step)) {
7682 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7691 llvm_unreachable("switch has default clause!");
7694 bool ScalarEvolution::isLoopInvariantPredicate(
7695 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7696 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7697 const SCEV *&InvariantRHS) {
7699 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7700 if (!isLoopInvariant(RHS, L)) {
7701 if (!isLoopInvariant(LHS, L))
7704 std::swap(LHS, RHS);
7705 Pred = ICmpInst::getSwappedPredicate(Pred);
7708 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7709 if (!ArLHS || ArLHS->getLoop() != L)
7713 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7716 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7717 // true as the loop iterates, and the backedge is control dependent on
7718 // "ArLHS `Pred` RHS" == true then we can reason as follows:
7720 // * if the predicate was false in the first iteration then the predicate
7721 // is never evaluated again, since the loop exits without taking the
7723 // * if the predicate was true in the first iteration then it will
7724 // continue to be true for all future iterations since it is
7725 // monotonically increasing.
7727 // For both the above possibilities, we can replace the loop varying
7728 // predicate with its value on the first iteration of the loop (which is
7731 // A similar reasoning applies for a monotonically decreasing predicate, by
7732 // replacing true with false and false with true in the above two bullets.
7734 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7736 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7739 InvariantPred = Pred;
7740 InvariantLHS = ArLHS->getStart();
7745 bool ScalarEvolution::isKnownPredicateViaConstantRanges(
7746 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7747 if (HasSameValue(LHS, RHS))
7748 return ICmpInst::isTrueWhenEqual(Pred);
7750 // This code is split out from isKnownPredicate because it is called from
7751 // within isLoopEntryGuardedByCond.
7754 [&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) {
7755 return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS)
7756 .contains(RangeLHS);
7759 // The check at the top of the function catches the case where the values are
7760 // known to be equal.
7761 if (Pred == CmpInst::ICMP_EQ)
7764 if (Pred == CmpInst::ICMP_NE)
7765 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
7766 CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) ||
7767 isKnownNonZero(getMinusSCEV(LHS, RHS));
7769 if (CmpInst::isSigned(Pred))
7770 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
7772 return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
7775 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
7779 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
7780 // Return Y via OutY.
7781 auto MatchBinaryAddToConst =
7782 [this](const SCEV *Result, const SCEV *X, APInt &OutY,
7783 SCEV::NoWrapFlags ExpectedFlags) {
7784 const SCEV *NonConstOp, *ConstOp;
7785 SCEV::NoWrapFlags FlagsPresent;
7787 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
7788 !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
7791 OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
7792 return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
7801 case ICmpInst::ICMP_SGE:
7802 std::swap(LHS, RHS);
7803 case ICmpInst::ICMP_SLE:
7804 // X s<= (X + C)<nsw> if C >= 0
7805 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
7808 // (X + C)<nsw> s<= X if C <= 0
7809 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
7810 !C.isStrictlyPositive())
7814 case ICmpInst::ICMP_SGT:
7815 std::swap(LHS, RHS);
7816 case ICmpInst::ICMP_SLT:
7817 // X s< (X + C)<nsw> if C > 0
7818 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
7819 C.isStrictlyPositive())
7822 // (X + C)<nsw> s< X if C < 0
7823 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
7831 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7834 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
7837 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7838 // the stack can result in exponential time complexity.
7839 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7841 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7843 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7844 // isKnownPredicate. isKnownPredicate is more powerful, but also more
7845 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7846 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
7847 // use isKnownPredicate later if needed.
7848 return isKnownNonNegative(RHS) &&
7849 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7850 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
7853 bool ScalarEvolution::isImpliedViaGuard(BasicBlock *BB,
7854 ICmpInst::Predicate Pred,
7855 const SCEV *LHS, const SCEV *RHS) {
7856 // No need to even try if we know the module has no guards.
7860 return any_of(*BB, [&](Instruction &I) {
7861 using namespace llvm::PatternMatch;
7864 return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
7865 m_Value(Condition))) &&
7866 isImpliedCond(Pred, LHS, RHS, Condition, false);
7870 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7871 /// protected by a conditional between LHS and RHS. This is used to
7872 /// to eliminate casts.
7874 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7875 ICmpInst::Predicate Pred,
7876 const SCEV *LHS, const SCEV *RHS) {
7877 // Interpret a null as meaning no loop, where there is obviously no guard
7878 // (interprocedural conditions notwithstanding).
7879 if (!L) return true;
7881 if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
7884 BasicBlock *Latch = L->getLoopLatch();
7888 BranchInst *LoopContinuePredicate =
7889 dyn_cast<BranchInst>(Latch->getTerminator());
7890 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7891 isImpliedCond(Pred, LHS, RHS,
7892 LoopContinuePredicate->getCondition(),
7893 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7896 // We don't want more than one activation of the following loops on the stack
7897 // -- that can lead to O(n!) time complexity.
7898 if (WalkingBEDominatingConds)
7901 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7903 // See if we can exploit a trip count to prove the predicate.
7904 const auto &BETakenInfo = getBackedgeTakenInfo(L);
7905 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7906 if (LatchBECount != getCouldNotCompute()) {
7907 // We know that Latch branches back to the loop header exactly
7908 // LatchBECount times. This means the backdege condition at Latch is
7909 // equivalent to "{0,+,1} u< LatchBECount".
7910 Type *Ty = LatchBECount->getType();
7911 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7912 const SCEV *LoopCounter =
7913 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7914 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7919 // Check conditions due to any @llvm.assume intrinsics.
7920 for (auto &AssumeVH : AC.assumptions()) {
7923 auto *CI = cast<CallInst>(AssumeVH);
7924 if (!DT.dominates(CI, Latch->getTerminator()))
7927 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7931 // If the loop is not reachable from the entry block, we risk running into an
7932 // infinite loop as we walk up into the dom tree. These loops do not matter
7933 // anyway, so we just return a conservative answer when we see them.
7934 if (!DT.isReachableFromEntry(L->getHeader()))
7937 if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
7940 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7941 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7943 assert(DTN && "should reach the loop header before reaching the root!");
7945 BasicBlock *BB = DTN->getBlock();
7946 if (isImpliedViaGuard(BB, Pred, LHS, RHS))
7949 BasicBlock *PBB = BB->getSinglePredecessor();
7953 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7954 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7957 Value *Condition = ContinuePredicate->getCondition();
7959 // If we have an edge `E` within the loop body that dominates the only
7960 // latch, the condition guarding `E` also guards the backedge. This
7961 // reasoning works only for loops with a single latch.
7963 BasicBlockEdge DominatingEdge(PBB, BB);
7964 if (DominatingEdge.isSingleEdge()) {
7965 // We're constructively (and conservatively) enumerating edges within the
7966 // loop body that dominate the latch. The dominator tree better agree
7968 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7970 if (isImpliedCond(Pred, LHS, RHS, Condition,
7971 BB != ContinuePredicate->getSuccessor(0)))
7980 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7981 ICmpInst::Predicate Pred,
7982 const SCEV *LHS, const SCEV *RHS) {
7983 // Interpret a null as meaning no loop, where there is obviously no guard
7984 // (interprocedural conditions notwithstanding).
7985 if (!L) return false;
7987 if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
7990 // Starting at the loop predecessor, climb up the predecessor chain, as long
7991 // as there are predecessors that can be found that have unique successors
7992 // leading to the original header.
7993 for (std::pair<BasicBlock *, BasicBlock *>
7994 Pair(L->getLoopPredecessor(), L->getHeader());
7996 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7998 if (isImpliedViaGuard(Pair.first, Pred, LHS, RHS))
8001 BranchInst *LoopEntryPredicate =
8002 dyn_cast<BranchInst>(Pair.first->getTerminator());
8003 if (!LoopEntryPredicate ||
8004 LoopEntryPredicate->isUnconditional())
8007 if (isImpliedCond(Pred, LHS, RHS,
8008 LoopEntryPredicate->getCondition(),
8009 LoopEntryPredicate->getSuccessor(0) != Pair.second))
8013 // Check conditions due to any @llvm.assume intrinsics.
8014 for (auto &AssumeVH : AC.assumptions()) {
8017 auto *CI = cast<CallInst>(AssumeVH);
8018 if (!DT.dominates(CI, L->getHeader()))
8021 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
8029 /// RAII wrapper to prevent recursive application of isImpliedCond.
8030 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
8031 /// currently evaluating isImpliedCond.
8032 struct MarkPendingLoopPredicate {
8034 DenseSet<Value*> &LoopPreds;
8037 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
8038 : Cond(C), LoopPreds(LP) {
8039 Pending = !LoopPreds.insert(Cond).second;
8041 ~MarkPendingLoopPredicate() {
8043 LoopPreds.erase(Cond);
8046 } // end anonymous namespace
8048 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
8049 const SCEV *LHS, const SCEV *RHS,
8050 Value *FoundCondValue,
8052 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
8056 // Recursively handle And and Or conditions.
8057 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
8058 if (BO->getOpcode() == Instruction::And) {
8060 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
8061 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
8062 } else if (BO->getOpcode() == Instruction::Or) {
8064 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
8065 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
8069 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
8070 if (!ICI) return false;
8072 // Now that we found a conditional branch that dominates the loop or controls
8073 // the loop latch. Check to see if it is the comparison we are looking for.
8074 ICmpInst::Predicate FoundPred;
8076 FoundPred = ICI->getInversePredicate();
8078 FoundPred = ICI->getPredicate();
8080 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
8081 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
8083 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
8086 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
8088 ICmpInst::Predicate FoundPred,
8089 const SCEV *FoundLHS,
8090 const SCEV *FoundRHS) {
8091 // Balance the types.
8092 if (getTypeSizeInBits(LHS->getType()) <
8093 getTypeSizeInBits(FoundLHS->getType())) {
8094 if (CmpInst::isSigned(Pred)) {
8095 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
8096 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
8098 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
8099 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
8101 } else if (getTypeSizeInBits(LHS->getType()) >
8102 getTypeSizeInBits(FoundLHS->getType())) {
8103 if (CmpInst::isSigned(FoundPred)) {
8104 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
8105 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
8107 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
8108 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
8112 // Canonicalize the query to match the way instcombine will have
8113 // canonicalized the comparison.
8114 if (SimplifyICmpOperands(Pred, LHS, RHS))
8116 return CmpInst::isTrueWhenEqual(Pred);
8117 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
8118 if (FoundLHS == FoundRHS)
8119 return CmpInst::isFalseWhenEqual(FoundPred);
8121 // Check to see if we can make the LHS or RHS match.
8122 if (LHS == FoundRHS || RHS == FoundLHS) {
8123 if (isa<SCEVConstant>(RHS)) {
8124 std::swap(FoundLHS, FoundRHS);
8125 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
8127 std::swap(LHS, RHS);
8128 Pred = ICmpInst::getSwappedPredicate(Pred);
8132 // Check whether the found predicate is the same as the desired predicate.
8133 if (FoundPred == Pred)
8134 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
8136 // Check whether swapping the found predicate makes it the same as the
8137 // desired predicate.
8138 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
8139 if (isa<SCEVConstant>(RHS))
8140 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
8142 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
8143 RHS, LHS, FoundLHS, FoundRHS);
8146 // Unsigned comparison is the same as signed comparison when both the operands
8147 // are non-negative.
8148 if (CmpInst::isUnsigned(FoundPred) &&
8149 CmpInst::getSignedPredicate(FoundPred) == Pred &&
8150 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
8151 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
8153 // Check if we can make progress by sharpening ranges.
8154 if (FoundPred == ICmpInst::ICMP_NE &&
8155 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
8157 const SCEVConstant *C = nullptr;
8158 const SCEV *V = nullptr;
8160 if (isa<SCEVConstant>(FoundLHS)) {
8161 C = cast<SCEVConstant>(FoundLHS);
8164 C = cast<SCEVConstant>(FoundRHS);
8168 // The guarding predicate tells us that C != V. If the known range
8169 // of V is [C, t), we can sharpen the range to [C + 1, t). The
8170 // range we consider has to correspond to same signedness as the
8171 // predicate we're interested in folding.
8173 APInt Min = ICmpInst::isSigned(Pred) ?
8174 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
8176 if (Min == C->getAPInt()) {
8177 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
8178 // This is true even if (Min + 1) wraps around -- in case of
8179 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
8181 APInt SharperMin = Min + 1;
8184 case ICmpInst::ICMP_SGE:
8185 case ICmpInst::ICMP_UGE:
8186 // We know V `Pred` SharperMin. If this implies LHS `Pred`
8188 if (isImpliedCondOperands(Pred, LHS, RHS, V,
8189 getConstant(SharperMin)))
8192 case ICmpInst::ICMP_SGT:
8193 case ICmpInst::ICMP_UGT:
8194 // We know from the range information that (V `Pred` Min ||
8195 // V == Min). We know from the guarding condition that !(V
8196 // == Min). This gives us
8198 // V `Pred` Min || V == Min && !(V == Min)
8201 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
8203 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
8213 // Check whether the actual condition is beyond sufficient.
8214 if (FoundPred == ICmpInst::ICMP_EQ)
8215 if (ICmpInst::isTrueWhenEqual(Pred))
8216 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
8218 if (Pred == ICmpInst::ICMP_NE)
8219 if (!ICmpInst::isTrueWhenEqual(FoundPred))
8220 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
8223 // Otherwise assume the worst.
8227 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
8228 const SCEV *&L, const SCEV *&R,
8229 SCEV::NoWrapFlags &Flags) {
8230 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
8231 if (!AE || AE->getNumOperands() != 2)
8234 L = AE->getOperand(0);
8235 R = AE->getOperand(1);
8236 Flags = AE->getNoWrapFlags();
8240 bool ScalarEvolution::computeConstantDifference(const SCEV *Less,
8243 // We avoid subtracting expressions here because this function is usually
8244 // fairly deep in the call stack (i.e. is called many times).
8246 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
8247 const auto *LAR = cast<SCEVAddRecExpr>(Less);
8248 const auto *MAR = cast<SCEVAddRecExpr>(More);
8250 if (LAR->getLoop() != MAR->getLoop())
8253 // We look at affine expressions only; not for correctness but to keep
8254 // getStepRecurrence cheap.
8255 if (!LAR->isAffine() || !MAR->isAffine())
8258 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
8261 Less = LAR->getStart();
8262 More = MAR->getStart();
8267 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
8268 const auto &M = cast<SCEVConstant>(More)->getAPInt();
8269 const auto &L = cast<SCEVConstant>(Less)->getAPInt();
8275 SCEV::NoWrapFlags Flags;
8276 if (splitBinaryAdd(Less, L, R, Flags))
8277 if (const auto *LC = dyn_cast<SCEVConstant>(L))
8279 C = -(LC->getAPInt());
8283 if (splitBinaryAdd(More, L, R, Flags))
8284 if (const auto *LC = dyn_cast<SCEVConstant>(L))
8293 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
8294 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
8295 const SCEV *FoundLHS, const SCEV *FoundRHS) {
8296 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
8299 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
8303 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
8304 if (!AddRecFoundLHS)
8307 // We'd like to let SCEV reason about control dependencies, so we constrain
8308 // both the inequalities to be about add recurrences on the same loop. This
8309 // way we can use isLoopEntryGuardedByCond later.
8311 const Loop *L = AddRecFoundLHS->getLoop();
8312 if (L != AddRecLHS->getLoop())
8315 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
8317 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
8320 // Informal proof for (2), assuming (1) [*]:
8322 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
8326 // FoundLHS s< FoundRHS s< INT_MIN - C
8327 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
8328 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
8329 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
8330 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
8331 // <=> FoundLHS + C s< FoundRHS + C
8333 // [*]: (1) can be proved by ruling out overflow.
8335 // [**]: This can be proved by analyzing all the four possibilities:
8336 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
8337 // (A s>= 0, B s>= 0).
8340 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
8341 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
8342 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
8343 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
8344 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
8348 if (!computeConstantDifference(FoundLHS, LHS, LDiff) ||
8349 !computeConstantDifference(FoundRHS, RHS, RDiff) ||
8356 APInt FoundRHSLimit;
8358 if (Pred == CmpInst::ICMP_ULT) {
8359 FoundRHSLimit = -RDiff;
8361 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
8362 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - RDiff;
8365 // Try to prove (1) or (2), as needed.
8366 return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
8367 getConstant(FoundRHSLimit));
8370 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
8371 const SCEV *LHS, const SCEV *RHS,
8372 const SCEV *FoundLHS,
8373 const SCEV *FoundRHS) {
8374 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
8377 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
8380 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
8381 FoundLHS, FoundRHS) ||
8382 // ~x < ~y --> x > y
8383 isImpliedCondOperandsHelper(Pred, LHS, RHS,
8384 getNotSCEV(FoundRHS),
8385 getNotSCEV(FoundLHS));
8389 /// If Expr computes ~A, return A else return nullptr
8390 static const SCEV *MatchNotExpr(const SCEV *Expr) {
8391 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
8392 if (!Add || Add->getNumOperands() != 2 ||
8393 !Add->getOperand(0)->isAllOnesValue())
8396 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
8397 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
8398 !AddRHS->getOperand(0)->isAllOnesValue())
8401 return AddRHS->getOperand(1);
8405 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
8406 template<typename MaxExprType>
8407 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
8408 const SCEV *Candidate) {
8409 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
8410 if (!MaxExpr) return false;
8412 return find(MaxExpr->operands(), Candidate) != MaxExpr->op_end();
8416 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
8417 template<typename MaxExprType>
8418 static bool IsMinConsistingOf(ScalarEvolution &SE,
8419 const SCEV *MaybeMinExpr,
8420 const SCEV *Candidate) {
8421 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
8425 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
8428 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
8429 ICmpInst::Predicate Pred,
8430 const SCEV *LHS, const SCEV *RHS) {
8432 // If both sides are affine addrecs for the same loop, with equal
8433 // steps, and we know the recurrences don't wrap, then we only
8434 // need to check the predicate on the starting values.
8436 if (!ICmpInst::isRelational(Pred))
8439 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
8442 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
8445 if (LAR->getLoop() != RAR->getLoop())
8447 if (!LAR->isAffine() || !RAR->isAffine())
8450 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
8453 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
8454 SCEV::FlagNSW : SCEV::FlagNUW;
8455 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
8458 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
8461 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
8463 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
8464 ICmpInst::Predicate Pred,
8465 const SCEV *LHS, const SCEV *RHS) {
8470 case ICmpInst::ICMP_SGE:
8471 std::swap(LHS, RHS);
8473 case ICmpInst::ICMP_SLE:
8476 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
8478 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
8480 case ICmpInst::ICMP_UGE:
8481 std::swap(LHS, RHS);
8483 case ICmpInst::ICMP_ULE:
8486 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
8488 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
8491 llvm_unreachable("covered switch fell through?!");
8495 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
8496 const SCEV *LHS, const SCEV *RHS,
8497 const SCEV *FoundLHS,
8498 const SCEV *FoundRHS) {
8499 auto IsKnownPredicateFull =
8500 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
8501 return isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
8502 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
8503 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
8504 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
8508 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
8509 case ICmpInst::ICMP_EQ:
8510 case ICmpInst::ICMP_NE:
8511 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
8514 case ICmpInst::ICMP_SLT:
8515 case ICmpInst::ICMP_SLE:
8516 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
8517 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
8520 case ICmpInst::ICMP_SGT:
8521 case ICmpInst::ICMP_SGE:
8522 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
8523 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
8526 case ICmpInst::ICMP_ULT:
8527 case ICmpInst::ICMP_ULE:
8528 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
8529 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
8532 case ICmpInst::ICMP_UGT:
8533 case ICmpInst::ICMP_UGE:
8534 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
8535 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
8543 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
8546 const SCEV *FoundLHS,
8547 const SCEV *FoundRHS) {
8548 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
8549 // The restriction on `FoundRHS` be lifted easily -- it exists only to
8550 // reduce the compile time impact of this optimization.
8553 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
8554 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
8555 !isa<SCEVConstant>(AddLHS->getOperand(0)))
8558 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
8560 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
8561 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
8562 ConstantRange FoundLHSRange =
8563 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
8565 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
8567 APInt Addend = cast<SCEVConstant>(AddLHS->getOperand(0))->getAPInt();
8568 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
8570 // We can also compute the range of values for `LHS` that satisfy the
8571 // consequent, "`LHS` `Pred` `RHS`":
8572 APInt ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
8573 ConstantRange SatisfyingLHSRange =
8574 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
8576 // The antecedent implies the consequent if every value of `LHS` that
8577 // satisfies the antecedent also satisfies the consequent.
8578 return SatisfyingLHSRange.contains(LHSRange);
8581 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
8582 bool IsSigned, bool NoWrap) {
8583 if (NoWrap) return false;
8585 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8586 const SCEV *One = getOne(Stride->getType());
8589 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
8590 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
8591 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8594 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
8595 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
8598 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
8599 APInt MaxValue = APInt::getMaxValue(BitWidth);
8600 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8603 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
8604 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
8607 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
8608 bool IsSigned, bool NoWrap) {
8609 if (NoWrap) return false;
8611 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8612 const SCEV *One = getOne(Stride->getType());
8615 APInt MinRHS = getSignedRange(RHS).getSignedMin();
8616 APInt MinValue = APInt::getSignedMinValue(BitWidth);
8617 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8620 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
8621 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
8624 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
8625 APInt MinValue = APInt::getMinValue(BitWidth);
8626 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8629 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
8630 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
8633 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
8635 const SCEV *One = getOne(Step->getType());
8636 Delta = Equality ? getAddExpr(Delta, Step)
8637 : getAddExpr(Delta, getMinusSCEV(Step, One));
8638 return getUDivExpr(Delta, Step);
8641 ScalarEvolution::ExitLimit
8642 ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
8643 const Loop *L, bool IsSigned,
8644 bool ControlsExit, bool AllowPredicates) {
8645 SCEVUnionPredicate P;
8646 // We handle only IV < Invariant
8647 if (!isLoopInvariant(RHS, L))
8648 return getCouldNotCompute();
8650 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8651 if (!IV && AllowPredicates)
8652 // Try to make this an AddRec using runtime tests, in the first X
8653 // iterations of this loop, where X is the SCEV expression found by the
8655 IV = convertSCEVToAddRecWithPredicates(LHS, L, P);
8657 // Avoid weird loops
8658 if (!IV || IV->getLoop() != L || !IV->isAffine())
8659 return getCouldNotCompute();
8661 bool NoWrap = ControlsExit &&
8662 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8664 const SCEV *Stride = IV->getStepRecurrence(*this);
8666 // Avoid negative or zero stride values
8667 if (!isKnownPositive(Stride))
8668 return getCouldNotCompute();
8670 // Avoid proven overflow cases: this will ensure that the backedge taken count
8671 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8672 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8673 // behaviors like the case of C language.
8674 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
8675 return getCouldNotCompute();
8677 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
8678 : ICmpInst::ICMP_ULT;
8679 const SCEV *Start = IV->getStart();
8680 const SCEV *End = RHS;
8681 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
8682 End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
8684 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
8686 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
8687 : getUnsignedRange(Start).getUnsignedMin();
8689 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8690 : getUnsignedRange(Stride).getUnsignedMin();
8692 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8693 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
8694 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
8696 // Although End can be a MAX expression we estimate MaxEnd considering only
8697 // the case End = RHS. This is safe because in the other case (End - Start)
8698 // is zero, leading to a zero maximum backedge taken count.
8700 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8701 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8703 const SCEV *MaxBECount;
8704 if (isa<SCEVConstant>(BECount))
8705 MaxBECount = BECount;
8707 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8708 getConstant(MinStride), false);
8710 if (isa<SCEVCouldNotCompute>(MaxBECount))
8711 MaxBECount = BECount;
8713 return ExitLimit(BECount, MaxBECount, P);
8716 ScalarEvolution::ExitLimit
8717 ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8718 const Loop *L, bool IsSigned,
8719 bool ControlsExit, bool AllowPredicates) {
8720 SCEVUnionPredicate P;
8721 // We handle only IV > Invariant
8722 if (!isLoopInvariant(RHS, L))
8723 return getCouldNotCompute();
8725 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8726 if (!IV && AllowPredicates)
8727 // Try to make this an AddRec using runtime tests, in the first X
8728 // iterations of this loop, where X is the SCEV expression found by the
8730 IV = convertSCEVToAddRecWithPredicates(LHS, L, P);
8732 // Avoid weird loops
8733 if (!IV || IV->getLoop() != L || !IV->isAffine())
8734 return getCouldNotCompute();
8736 bool NoWrap = ControlsExit &&
8737 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8739 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8741 // Avoid negative or zero stride values
8742 if (!isKnownPositive(Stride))
8743 return getCouldNotCompute();
8745 // Avoid proven overflow cases: this will ensure that the backedge taken count
8746 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8747 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8748 // behaviors like the case of C language.
8749 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8750 return getCouldNotCompute();
8752 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8753 : ICmpInst::ICMP_UGT;
8755 const SCEV *Start = IV->getStart();
8756 const SCEV *End = RHS;
8757 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
8758 End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
8760 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8762 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8763 : getUnsignedRange(Start).getUnsignedMax();
8765 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8766 : getUnsignedRange(Stride).getUnsignedMin();
8768 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8769 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8770 : APInt::getMinValue(BitWidth) + (MinStride - 1);
8772 // Although End can be a MIN expression we estimate MinEnd considering only
8773 // the case End = RHS. This is safe because in the other case (Start - End)
8774 // is zero, leading to a zero maximum backedge taken count.
8776 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8777 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8780 const SCEV *MaxBECount = getCouldNotCompute();
8781 if (isa<SCEVConstant>(BECount))
8782 MaxBECount = BECount;
8784 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8785 getConstant(MinStride), false);
8787 if (isa<SCEVCouldNotCompute>(MaxBECount))
8788 MaxBECount = BECount;
8790 return ExitLimit(BECount, MaxBECount, P);
8793 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
8794 ScalarEvolution &SE) const {
8795 if (Range.isFullSet()) // Infinite loop.
8796 return SE.getCouldNotCompute();
8798 // If the start is a non-zero constant, shift the range to simplify things.
8799 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8800 if (!SC->getValue()->isZero()) {
8801 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8802 Operands[0] = SE.getZero(SC->getType());
8803 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8804 getNoWrapFlags(FlagNW));
8805 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
8806 return ShiftedAddRec->getNumIterationsInRange(
8807 Range.subtract(SC->getAPInt()), SE);
8808 // This is strange and shouldn't happen.
8809 return SE.getCouldNotCompute();
8812 // The only time we can solve this is when we have all constant indices.
8813 // Otherwise, we cannot determine the overflow conditions.
8814 if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
8815 return SE.getCouldNotCompute();
8817 // Okay at this point we know that all elements of the chrec are constants and
8818 // that the start element is zero.
8820 // First check to see if the range contains zero. If not, the first
8822 unsigned BitWidth = SE.getTypeSizeInBits(getType());
8823 if (!Range.contains(APInt(BitWidth, 0)))
8824 return SE.getZero(getType());
8827 // If this is an affine expression then we have this situation:
8828 // Solve {0,+,A} in Range === Ax in Range
8830 // We know that zero is in the range. If A is positive then we know that
8831 // the upper value of the range must be the first possible exit value.
8832 // If A is negative then the lower of the range is the last possible loop
8833 // value. Also note that we already checked for a full range.
8834 APInt One(BitWidth,1);
8835 APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
8836 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8838 // The exit value should be (End+A)/A.
8839 APInt ExitVal = (End + A).udiv(A);
8840 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8842 // Evaluate at the exit value. If we really did fall out of the valid
8843 // range, then we computed our trip count, otherwise wrap around or other
8844 // things must have happened.
8845 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8846 if (Range.contains(Val->getValue()))
8847 return SE.getCouldNotCompute(); // Something strange happened
8849 // Ensure that the previous value is in the range. This is a sanity check.
8850 assert(Range.contains(
8851 EvaluateConstantChrecAtConstant(this,
8852 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8853 "Linear scev computation is off in a bad way!");
8854 return SE.getConstant(ExitValue);
8855 } else if (isQuadratic()) {
8856 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8857 // quadratic equation to solve it. To do this, we must frame our problem in
8858 // terms of figuring out when zero is crossed, instead of when
8859 // Range.getUpper() is crossed.
8860 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8861 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8862 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
8863 // getNoWrapFlags(FlagNW)
8866 // Next, solve the constructed addrec
8868 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE)) {
8869 const SCEVConstant *R1 = Roots->first;
8870 const SCEVConstant *R2 = Roots->second;
8871 // Pick the smallest positive root value.
8872 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
8873 ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
8874 if (!CB->getZExtValue())
8875 std::swap(R1, R2); // R1 is the minimum root now.
8877 // Make sure the root is not off by one. The returned iteration should
8878 // not be in the range, but the previous one should be. When solving
8879 // for "X*X < 5", for example, we should not return a root of 2.
8880 ConstantInt *R1Val =
8881 EvaluateConstantChrecAtConstant(this, R1->getValue(), SE);
8882 if (Range.contains(R1Val->getValue())) {
8883 // The next iteration must be out of the range...
8884 ConstantInt *NextVal =
8885 ConstantInt::get(SE.getContext(), R1->getAPInt() + 1);
8887 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8888 if (!Range.contains(R1Val->getValue()))
8889 return SE.getConstant(NextVal);
8890 return SE.getCouldNotCompute(); // Something strange happened
8893 // If R1 was not in the range, then it is a good return value. Make
8894 // sure that R1-1 WAS in the range though, just in case.
8895 ConstantInt *NextVal =
8896 ConstantInt::get(SE.getContext(), R1->getAPInt() - 1);
8897 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8898 if (Range.contains(R1Val->getValue()))
8900 return SE.getCouldNotCompute(); // Something strange happened
8905 return SE.getCouldNotCompute();
8911 FindUndefs() : Found(false) {}
8913 bool follow(const SCEV *S) {
8914 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
8915 if (isa<UndefValue>(C->getValue()))
8917 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
8918 if (isa<UndefValue>(C->getValue()))
8922 // Keep looking if we haven't found it yet.
8925 bool isDone() const {
8926 // Stop recursion if we have found an undef.
8932 // Return true when S contains at least an undef value.
8934 containsUndefs(const SCEV *S) {
8936 SCEVTraversal<FindUndefs> ST(F);
8943 // Collect all steps of SCEV expressions.
8944 struct SCEVCollectStrides {
8945 ScalarEvolution &SE;
8946 SmallVectorImpl<const SCEV *> &Strides;
8948 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
8949 : SE(SE), Strides(S) {}
8951 bool follow(const SCEV *S) {
8952 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
8953 Strides.push_back(AR->getStepRecurrence(SE));
8956 bool isDone() const { return false; }
8959 // Collect all SCEVUnknown and SCEVMulExpr expressions.
8960 struct SCEVCollectTerms {
8961 SmallVectorImpl<const SCEV *> &Terms;
8963 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
8966 bool follow(const SCEV *S) {
8967 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
8968 if (!containsUndefs(S))
8971 // Stop recursion: once we collected a term, do not walk its operands.
8978 bool isDone() const { return false; }
8981 // Check if a SCEV contains an AddRecExpr.
8982 struct SCEVHasAddRec {
8983 bool &ContainsAddRec;
8985 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
8986 ContainsAddRec = false;
8989 bool follow(const SCEV *S) {
8990 if (isa<SCEVAddRecExpr>(S)) {
8991 ContainsAddRec = true;
8993 // Stop recursion: once we collected a term, do not walk its operands.
9000 bool isDone() const { return false; }
9003 // Find factors that are multiplied with an expression that (possibly as a
9004 // subexpression) contains an AddRecExpr. In the expression:
9006 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
9008 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
9009 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
9010 // parameters as they form a product with an induction variable.
9012 // This collector expects all array size parameters to be in the same MulExpr.
9013 // It might be necessary to later add support for collecting parameters that are
9014 // spread over different nested MulExpr.
9015 struct SCEVCollectAddRecMultiplies {
9016 SmallVectorImpl<const SCEV *> &Terms;
9017 ScalarEvolution &SE;
9019 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
9020 : Terms(T), SE(SE) {}
9022 bool follow(const SCEV *S) {
9023 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
9024 bool HasAddRec = false;
9025 SmallVector<const SCEV *, 0> Operands;
9026 for (auto Op : Mul->operands()) {
9027 if (isa<SCEVUnknown>(Op)) {
9028 Operands.push_back(Op);
9030 bool ContainsAddRec;
9031 SCEVHasAddRec ContiansAddRec(ContainsAddRec);
9032 visitAll(Op, ContiansAddRec);
9033 HasAddRec |= ContainsAddRec;
9036 if (Operands.size() == 0)
9042 Terms.push_back(SE.getMulExpr(Operands));
9043 // Stop recursion: once we collected a term, do not walk its operands.
9050 bool isDone() const { return false; }
9054 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
9056 /// 1) The strides of AddRec expressions.
9057 /// 2) Unknowns that are multiplied with AddRec expressions.
9058 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
9059 SmallVectorImpl<const SCEV *> &Terms) {
9060 SmallVector<const SCEV *, 4> Strides;
9061 SCEVCollectStrides StrideCollector(*this, Strides);
9062 visitAll(Expr, StrideCollector);
9065 dbgs() << "Strides:\n";
9066 for (const SCEV *S : Strides)
9067 dbgs() << *S << "\n";
9070 for (const SCEV *S : Strides) {
9071 SCEVCollectTerms TermCollector(Terms);
9072 visitAll(S, TermCollector);
9076 dbgs() << "Terms:\n";
9077 for (const SCEV *T : Terms)
9078 dbgs() << *T << "\n";
9081 SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
9082 visitAll(Expr, MulCollector);
9085 static bool findArrayDimensionsRec(ScalarEvolution &SE,
9086 SmallVectorImpl<const SCEV *> &Terms,
9087 SmallVectorImpl<const SCEV *> &Sizes) {
9088 int Last = Terms.size() - 1;
9089 const SCEV *Step = Terms[Last];
9091 // End of recursion.
9093 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
9094 SmallVector<const SCEV *, 2> Qs;
9095 for (const SCEV *Op : M->operands())
9096 if (!isa<SCEVConstant>(Op))
9099 Step = SE.getMulExpr(Qs);
9102 Sizes.push_back(Step);
9106 for (const SCEV *&Term : Terms) {
9107 // Normalize the terms before the next call to findArrayDimensionsRec.
9109 SCEVDivision::divide(SE, Term, Step, &Q, &R);
9111 // Bail out when GCD does not evenly divide one of the terms.
9118 // Remove all SCEVConstants.
9119 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
9120 return isa<SCEVConstant>(E);
9124 if (Terms.size() > 0)
9125 if (!findArrayDimensionsRec(SE, Terms, Sizes))
9128 Sizes.push_back(Step);
9132 // Returns true when S contains at least a SCEVUnknown parameter.
9134 containsParameters(const SCEV *S) {
9135 struct FindParameter {
9136 bool FoundParameter;
9137 FindParameter() : FoundParameter(false) {}
9139 bool follow(const SCEV *S) {
9140 if (isa<SCEVUnknown>(S)) {
9141 FoundParameter = true;
9142 // Stop recursion: we found a parameter.
9148 bool isDone() const {
9149 // Stop recursion if we have found a parameter.
9150 return FoundParameter;
9155 SCEVTraversal<FindParameter> ST(F);
9158 return F.FoundParameter;
9161 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
9163 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
9164 for (const SCEV *T : Terms)
9165 if (containsParameters(T))
9170 // Return the number of product terms in S.
9171 static inline int numberOfTerms(const SCEV *S) {
9172 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
9173 return Expr->getNumOperands();
9177 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
9178 if (isa<SCEVConstant>(T))
9181 if (isa<SCEVUnknown>(T))
9184 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
9185 SmallVector<const SCEV *, 2> Factors;
9186 for (const SCEV *Op : M->operands())
9187 if (!isa<SCEVConstant>(Op))
9188 Factors.push_back(Op);
9190 return SE.getMulExpr(Factors);
9196 /// Return the size of an element read or written by Inst.
9197 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
9199 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
9200 Ty = Store->getValueOperand()->getType();
9201 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
9202 Ty = Load->getType();
9206 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
9207 return getSizeOfExpr(ETy, Ty);
9210 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
9211 SmallVectorImpl<const SCEV *> &Sizes,
9212 const SCEV *ElementSize) const {
9213 if (Terms.size() < 1 || !ElementSize)
9216 // Early return when Terms do not contain parameters: we do not delinearize
9217 // non parametric SCEVs.
9218 if (!containsParameters(Terms))
9222 dbgs() << "Terms:\n";
9223 for (const SCEV *T : Terms)
9224 dbgs() << *T << "\n";
9227 // Remove duplicates.
9228 std::sort(Terms.begin(), Terms.end());
9229 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
9231 // Put larger terms first.
9232 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
9233 return numberOfTerms(LHS) > numberOfTerms(RHS);
9236 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9238 // Try to divide all terms by the element size. If term is not divisible by
9239 // element size, proceed with the original term.
9240 for (const SCEV *&Term : Terms) {
9242 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
9247 SmallVector<const SCEV *, 4> NewTerms;
9249 // Remove constant factors.
9250 for (const SCEV *T : Terms)
9251 if (const SCEV *NewT = removeConstantFactors(SE, T))
9252 NewTerms.push_back(NewT);
9255 dbgs() << "Terms after sorting:\n";
9256 for (const SCEV *T : NewTerms)
9257 dbgs() << *T << "\n";
9260 if (NewTerms.empty() ||
9261 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
9266 // The last element to be pushed into Sizes is the size of an element.
9267 Sizes.push_back(ElementSize);
9270 dbgs() << "Sizes:\n";
9271 for (const SCEV *S : Sizes)
9272 dbgs() << *S << "\n";
9276 void ScalarEvolution::computeAccessFunctions(
9277 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
9278 SmallVectorImpl<const SCEV *> &Sizes) {
9280 // Early exit in case this SCEV is not an affine multivariate function.
9284 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
9285 if (!AR->isAffine())
9288 const SCEV *Res = Expr;
9289 int Last = Sizes.size() - 1;
9290 for (int i = Last; i >= 0; i--) {
9292 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
9295 dbgs() << "Res: " << *Res << "\n";
9296 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
9297 dbgs() << "Res divided by Sizes[i]:\n";
9298 dbgs() << "Quotient: " << *Q << "\n";
9299 dbgs() << "Remainder: " << *R << "\n";
9304 // Do not record the last subscript corresponding to the size of elements in
9308 // Bail out if the remainder is too complex.
9309 if (isa<SCEVAddRecExpr>(R)) {
9318 // Record the access function for the current subscript.
9319 Subscripts.push_back(R);
9322 // Also push in last position the remainder of the last division: it will be
9323 // the access function of the innermost dimension.
9324 Subscripts.push_back(Res);
9326 std::reverse(Subscripts.begin(), Subscripts.end());
9329 dbgs() << "Subscripts:\n";
9330 for (const SCEV *S : Subscripts)
9331 dbgs() << *S << "\n";
9335 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
9336 /// sizes of an array access. Returns the remainder of the delinearization that
9337 /// is the offset start of the array. The SCEV->delinearize algorithm computes
9338 /// the multiples of SCEV coefficients: that is a pattern matching of sub
9339 /// expressions in the stride and base of a SCEV corresponding to the
9340 /// computation of a GCD (greatest common divisor) of base and stride. When
9341 /// SCEV->delinearize fails, it returns the SCEV unchanged.
9343 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
9345 /// void foo(long n, long m, long o, double A[n][m][o]) {
9347 /// for (long i = 0; i < n; i++)
9348 /// for (long j = 0; j < m; j++)
9349 /// for (long k = 0; k < o; k++)
9350 /// A[i][j][k] = 1.0;
9353 /// the delinearization input is the following AddRec SCEV:
9355 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
9357 /// From this SCEV, we are able to say that the base offset of the access is %A
9358 /// because it appears as an offset that does not divide any of the strides in
9361 /// CHECK: Base offset: %A
9363 /// and then SCEV->delinearize determines the size of some of the dimensions of
9364 /// the array as these are the multiples by which the strides are happening:
9366 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
9368 /// Note that the outermost dimension remains of UnknownSize because there are
9369 /// no strides that would help identifying the size of the last dimension: when
9370 /// the array has been statically allocated, one could compute the size of that
9371 /// dimension by dividing the overall size of the array by the size of the known
9372 /// dimensions: %m * %o * 8.
9374 /// Finally delinearize provides the access functions for the array reference
9375 /// that does correspond to A[i][j][k] of the above C testcase:
9377 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
9379 /// The testcases are checking the output of a function pass:
9380 /// DelinearizationPass that walks through all loads and stores of a function
9381 /// asking for the SCEV of the memory access with respect to all enclosing
9382 /// loops, calling SCEV->delinearize on that and printing the results.
9384 void ScalarEvolution::delinearize(const SCEV *Expr,
9385 SmallVectorImpl<const SCEV *> &Subscripts,
9386 SmallVectorImpl<const SCEV *> &Sizes,
9387 const SCEV *ElementSize) {
9388 // First step: collect parametric terms.
9389 SmallVector<const SCEV *, 4> Terms;
9390 collectParametricTerms(Expr, Terms);
9395 // Second step: find subscript sizes.
9396 findArrayDimensions(Terms, Sizes, ElementSize);
9401 // Third step: compute the access functions for each subscript.
9402 computeAccessFunctions(Expr, Subscripts, Sizes);
9404 if (Subscripts.empty())
9408 dbgs() << "succeeded to delinearize " << *Expr << "\n";
9409 dbgs() << "ArrayDecl[UnknownSize]";
9410 for (const SCEV *S : Sizes)
9411 dbgs() << "[" << *S << "]";
9413 dbgs() << "\nArrayRef";
9414 for (const SCEV *S : Subscripts)
9415 dbgs() << "[" << *S << "]";
9420 //===----------------------------------------------------------------------===//
9421 // SCEVCallbackVH Class Implementation
9422 //===----------------------------------------------------------------------===//
9424 void ScalarEvolution::SCEVCallbackVH::deleted() {
9425 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9426 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
9427 SE->ConstantEvolutionLoopExitValue.erase(PN);
9428 SE->eraseValueFromMap(getValPtr());
9429 // this now dangles!
9432 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
9433 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9435 // Forget all the expressions associated with users of the old value,
9436 // so that future queries will recompute the expressions using the new
9438 Value *Old = getValPtr();
9439 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
9440 SmallPtrSet<User *, 8> Visited;
9441 while (!Worklist.empty()) {
9442 User *U = Worklist.pop_back_val();
9443 // Deleting the Old value will cause this to dangle. Postpone
9444 // that until everything else is done.
9447 if (!Visited.insert(U).second)
9449 if (PHINode *PN = dyn_cast<PHINode>(U))
9450 SE->ConstantEvolutionLoopExitValue.erase(PN);
9451 SE->eraseValueFromMap(U);
9452 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
9454 // Delete the Old value.
9455 if (PHINode *PN = dyn_cast<PHINode>(Old))
9456 SE->ConstantEvolutionLoopExitValue.erase(PN);
9457 SE->eraseValueFromMap(Old);
9458 // this now dangles!
9461 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
9462 : CallbackVH(V), SE(se) {}
9464 //===----------------------------------------------------------------------===//
9465 // ScalarEvolution Class Implementation
9466 //===----------------------------------------------------------------------===//
9468 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
9469 AssumptionCache &AC, DominatorTree &DT,
9471 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
9472 CouldNotCompute(new SCEVCouldNotCompute()),
9473 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9474 ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
9475 FirstUnknown(nullptr) {
9477 // To use guards for proving predicates, we need to scan every instruction in
9478 // relevant basic blocks, and not just terminators. Doing this is a waste of
9479 // time if the IR does not actually contain any calls to
9480 // @llvm.experimental.guard, so do a quick check and remember this beforehand.
9482 // This pessimizes the case where a pass that preserves ScalarEvolution wants
9483 // to _add_ guards to the module when there weren't any before, and wants
9484 // ScalarEvolution to optimize based on those guards. For now we prefer to be
9485 // efficient in lieu of being smart in that rather obscure case.
9487 auto *GuardDecl = F.getParent()->getFunction(
9488 Intrinsic::getName(Intrinsic::experimental_guard));
9489 HasGuards = GuardDecl && !GuardDecl->use_empty();
9492 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
9493 : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT),
9494 LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
9495 ValueExprMap(std::move(Arg.ValueExprMap)),
9496 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9497 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
9498 PredicatedBackedgeTakenCounts(
9499 std::move(Arg.PredicatedBackedgeTakenCounts)),
9500 ConstantEvolutionLoopExitValue(
9501 std::move(Arg.ConstantEvolutionLoopExitValue)),
9502 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
9503 LoopDispositions(std::move(Arg.LoopDispositions)),
9504 BlockDispositions(std::move(Arg.BlockDispositions)),
9505 UnsignedRanges(std::move(Arg.UnsignedRanges)),
9506 SignedRanges(std::move(Arg.SignedRanges)),
9507 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
9508 UniquePreds(std::move(Arg.UniquePreds)),
9509 SCEVAllocator(std::move(Arg.SCEVAllocator)),
9510 FirstUnknown(Arg.FirstUnknown) {
9511 Arg.FirstUnknown = nullptr;
9514 ScalarEvolution::~ScalarEvolution() {
9515 // Iterate through all the SCEVUnknown instances and call their
9516 // destructors, so that they release their references to their values.
9517 for (SCEVUnknown *U = FirstUnknown; U;) {
9518 SCEVUnknown *Tmp = U;
9520 Tmp->~SCEVUnknown();
9522 FirstUnknown = nullptr;
9524 ExprValueMap.clear();
9525 ValueExprMap.clear();
9528 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
9529 // that a loop had multiple computable exits.
9530 for (auto &BTCI : BackedgeTakenCounts)
9531 BTCI.second.clear();
9532 for (auto &BTCI : PredicatedBackedgeTakenCounts)
9533 BTCI.second.clear();
9535 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
9536 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
9537 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
9540 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
9541 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
9544 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
9546 // Print all inner loops first
9548 PrintLoopInfo(OS, SE, I);
9551 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9554 SmallVector<BasicBlock *, 8> ExitBlocks;
9555 L->getExitBlocks(ExitBlocks);
9556 if (ExitBlocks.size() != 1)
9557 OS << "<multiple exits> ";
9559 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
9560 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
9562 OS << "Unpredictable backedge-taken count. ";
9567 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9570 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
9571 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
9573 OS << "Unpredictable max backedge-taken count. ";
9578 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9581 SCEVUnionPredicate Pred;
9582 auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
9583 if (!isa<SCEVCouldNotCompute>(PBT)) {
9584 OS << "Predicated backedge-taken count is " << *PBT << "\n";
9585 OS << " Predicates:\n";
9588 OS << "Unpredictable predicated backedge-taken count. ";
9593 static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
9595 case ScalarEvolution::LoopVariant:
9597 case ScalarEvolution::LoopInvariant:
9599 case ScalarEvolution::LoopComputable:
9600 return "Computable";
9602 llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!");
9605 void ScalarEvolution::print(raw_ostream &OS) const {
9606 // ScalarEvolution's implementation of the print method is to print
9607 // out SCEV values of all instructions that are interesting. Doing
9608 // this potentially causes it to create new SCEV objects though,
9609 // which technically conflicts with the const qualifier. This isn't
9610 // observable from outside the class though, so casting away the
9611 // const isn't dangerous.
9612 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9614 OS << "Classifying expressions for: ";
9615 F.printAsOperand(OS, /*PrintType=*/false);
9617 for (Instruction &I : instructions(F))
9618 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
9621 const SCEV *SV = SE.getSCEV(&I);
9623 if (!isa<SCEVCouldNotCompute>(SV)) {
9625 SE.getUnsignedRange(SV).print(OS);
9627 SE.getSignedRange(SV).print(OS);
9630 const Loop *L = LI.getLoopFor(I.getParent());
9632 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
9636 if (!isa<SCEVCouldNotCompute>(AtUse)) {
9638 SE.getUnsignedRange(AtUse).print(OS);
9640 SE.getSignedRange(AtUse).print(OS);
9645 OS << "\t\t" "Exits: ";
9646 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
9647 if (!SE.isLoopInvariant(ExitValue, L)) {
9648 OS << "<<Unknown>>";
9654 for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
9656 OS << "\t\t" "LoopDispositions: { ";
9662 Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9663 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
9666 for (auto *InnerL : depth_first(L)) {
9670 OS << "\t\t" "LoopDispositions: { ";
9676 InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9677 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
9686 OS << "Determining loop execution counts for: ";
9687 F.printAsOperand(OS, /*PrintType=*/false);
9690 PrintLoopInfo(OS, &SE, I);
9693 ScalarEvolution::LoopDisposition
9694 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
9695 auto &Values = LoopDispositions[S];
9696 for (auto &V : Values) {
9697 if (V.getPointer() == L)
9700 Values.emplace_back(L, LoopVariant);
9701 LoopDisposition D = computeLoopDisposition(S, L);
9702 auto &Values2 = LoopDispositions[S];
9703 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9704 if (V.getPointer() == L) {
9712 ScalarEvolution::LoopDisposition
9713 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
9714 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9716 return LoopInvariant;
9720 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
9721 case scAddRecExpr: {
9722 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9724 // If L is the addrec's loop, it's computable.
9725 if (AR->getLoop() == L)
9726 return LoopComputable;
9728 // Add recurrences are never invariant in the function-body (null loop).
9732 // This recurrence is variant w.r.t. L if L contains AR's loop.
9733 if (L->contains(AR->getLoop()))
9736 // This recurrence is invariant w.r.t. L if AR's loop contains L.
9737 if (AR->getLoop()->contains(L))
9738 return LoopInvariant;
9740 // This recurrence is variant w.r.t. L if any of its operands
9742 for (auto *Op : AR->operands())
9743 if (!isLoopInvariant(Op, L))
9746 // Otherwise it's loop-invariant.
9747 return LoopInvariant;
9753 bool HasVarying = false;
9754 for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
9755 LoopDisposition D = getLoopDisposition(Op, L);
9756 if (D == LoopVariant)
9758 if (D == LoopComputable)
9761 return HasVarying ? LoopComputable : LoopInvariant;
9764 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9765 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
9766 if (LD == LoopVariant)
9768 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
9769 if (RD == LoopVariant)
9771 return (LD == LoopInvariant && RD == LoopInvariant) ?
9772 LoopInvariant : LoopComputable;
9775 // All non-instruction values are loop invariant. All instructions are loop
9776 // invariant if they are not contained in the specified loop.
9777 // Instructions are never considered invariant in the function body
9778 // (null loop) because they are defined within the "loop".
9779 if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
9780 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
9781 return LoopInvariant;
9782 case scCouldNotCompute:
9783 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9785 llvm_unreachable("Unknown SCEV kind!");
9788 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
9789 return getLoopDisposition(S, L) == LoopInvariant;
9792 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
9793 return getLoopDisposition(S, L) == LoopComputable;
9796 ScalarEvolution::BlockDisposition
9797 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9798 auto &Values = BlockDispositions[S];
9799 for (auto &V : Values) {
9800 if (V.getPointer() == BB)
9803 Values.emplace_back(BB, DoesNotDominateBlock);
9804 BlockDisposition D = computeBlockDisposition(S, BB);
9805 auto &Values2 = BlockDispositions[S];
9806 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9807 if (V.getPointer() == BB) {
9815 ScalarEvolution::BlockDisposition
9816 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9817 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9819 return ProperlyDominatesBlock;
9823 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
9824 case scAddRecExpr: {
9825 // This uses a "dominates" query instead of "properly dominates" query
9826 // to test for proper dominance too, because the instruction which
9827 // produces the addrec's value is a PHI, and a PHI effectively properly
9828 // dominates its entire containing block.
9829 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9830 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9831 return DoesNotDominateBlock;
9833 // FALL THROUGH into SCEVNAryExpr handling.
9838 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9840 for (const SCEV *NAryOp : NAry->operands()) {
9841 BlockDisposition D = getBlockDisposition(NAryOp, BB);
9842 if (D == DoesNotDominateBlock)
9843 return DoesNotDominateBlock;
9844 if (D == DominatesBlock)
9847 return Proper ? ProperlyDominatesBlock : DominatesBlock;
9850 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9851 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9852 BlockDisposition LD = getBlockDisposition(LHS, BB);
9853 if (LD == DoesNotDominateBlock)
9854 return DoesNotDominateBlock;
9855 BlockDisposition RD = getBlockDisposition(RHS, BB);
9856 if (RD == DoesNotDominateBlock)
9857 return DoesNotDominateBlock;
9858 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9859 ProperlyDominatesBlock : DominatesBlock;
9862 if (Instruction *I =
9863 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9864 if (I->getParent() == BB)
9865 return DominatesBlock;
9866 if (DT.properlyDominates(I->getParent(), BB))
9867 return ProperlyDominatesBlock;
9868 return DoesNotDominateBlock;
9870 return ProperlyDominatesBlock;
9871 case scCouldNotCompute:
9872 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9874 llvm_unreachable("Unknown SCEV kind!");
9877 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9878 return getBlockDisposition(S, BB) >= DominatesBlock;
9881 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9882 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9885 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9886 // Search for a SCEV expression node within an expression tree.
9887 // Implements SCEVTraversal::Visitor.
9892 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
9894 bool follow(const SCEV *S) {
9895 IsFound |= (S == Node);
9898 bool isDone() const { return IsFound; }
9901 SCEVSearch Search(Op);
9902 visitAll(S, Search);
9903 return Search.IsFound;
9906 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9907 ValuesAtScopes.erase(S);
9908 LoopDispositions.erase(S);
9909 BlockDispositions.erase(S);
9910 UnsignedRanges.erase(S);
9911 SignedRanges.erase(S);
9912 ExprValueMap.erase(S);
9915 auto RemoveSCEVFromBackedgeMap =
9916 [S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
9917 for (auto I = Map.begin(), E = Map.end(); I != E;) {
9918 BackedgeTakenInfo &BEInfo = I->second;
9919 if (BEInfo.hasOperand(S, this)) {
9927 RemoveSCEVFromBackedgeMap(BackedgeTakenCounts);
9928 RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts);
9931 typedef DenseMap<const Loop *, std::string> VerifyMap;
9933 /// replaceSubString - Replaces all occurrences of From in Str with To.
9934 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9936 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9937 Str.replace(Pos, From.size(), To.data(), To.size());
9942 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9944 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9945 std::string &S = Map[L];
9947 raw_string_ostream OS(S);
9948 SE.getBackedgeTakenCount(L)->print(OS);
9950 // false and 0 are semantically equivalent. This can happen in dead loops.
9951 replaceSubString(OS.str(), "false", "0");
9952 // Remove wrap flags, their use in SCEV is highly fragile.
9953 // FIXME: Remove this when SCEV gets smarter about them.
9954 replaceSubString(OS.str(), "<nw>", "");
9955 replaceSubString(OS.str(), "<nsw>", "");
9956 replaceSubString(OS.str(), "<nuw>", "");
9959 for (auto *R : reverse(*L))
9960 getLoopBackedgeTakenCounts(R, Map, SE); // recurse.
9963 void ScalarEvolution::verify() const {
9964 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9966 // Gather stringified backedge taken counts for all loops using SCEV's caches.
9967 // FIXME: It would be much better to store actual values instead of strings,
9968 // but SCEV pointers will change if we drop the caches.
9969 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9970 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9971 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9973 // Gather stringified backedge taken counts for all loops using a fresh
9974 // ScalarEvolution object.
9975 ScalarEvolution SE2(F, TLI, AC, DT, LI);
9976 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9977 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9979 // Now compare whether they're the same with and without caches. This allows
9980 // verifying that no pass changed the cache.
9981 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
9982 "New loops suddenly appeared!");
9984 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
9985 OldE = BackedgeDumpsOld.end(),
9986 NewI = BackedgeDumpsNew.begin();
9987 OldI != OldE; ++OldI, ++NewI) {
9988 assert(OldI->first == NewI->first && "Loop order changed!");
9990 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
9992 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
9993 // means that a pass is buggy or SCEV has to learn a new pattern but is
9994 // usually not harmful.
9995 if (OldI->second != NewI->second &&
9996 OldI->second.find("undef") == std::string::npos &&
9997 NewI->second.find("undef") == std::string::npos &&
9998 OldI->second != "***COULDNOTCOMPUTE***" &&
9999 NewI->second != "***COULDNOTCOMPUTE***") {
10000 dbgs() << "SCEVValidator: SCEV for loop '"
10001 << OldI->first->getHeader()->getName()
10002 << "' changed from '" << OldI->second
10003 << "' to '" << NewI->second << "'!\n";
10008 // TODO: Verify more things.
10011 char ScalarEvolutionAnalysis::PassID;
10013 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
10014 AnalysisManager<Function> &AM) {
10015 return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
10016 AM.getResult<AssumptionAnalysis>(F),
10017 AM.getResult<DominatorTreeAnalysis>(F),
10018 AM.getResult<LoopAnalysis>(F));
10022 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> &AM) {
10023 AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
10024 return PreservedAnalyses::all();
10027 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
10028 "Scalar Evolution Analysis", false, true)
10029 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
10030 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
10031 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
10032 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
10033 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
10034 "Scalar Evolution Analysis", false, true)
10035 char ScalarEvolutionWrapperPass::ID = 0;
10037 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
10038 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
10041 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
10042 SE.reset(new ScalarEvolution(
10043 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
10044 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
10045 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
10046 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
10050 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
10052 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
10056 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
10063 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
10064 AU.setPreservesAll();
10065 AU.addRequiredTransitive<AssumptionCacheTracker>();
10066 AU.addRequiredTransitive<LoopInfoWrapperPass>();
10067 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
10068 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
10071 const SCEVPredicate *
10072 ScalarEvolution::getEqualPredicate(const SCEVUnknown *LHS,
10073 const SCEVConstant *RHS) {
10074 FoldingSetNodeID ID;
10075 // Unique this node based on the arguments
10076 ID.AddInteger(SCEVPredicate::P_Equal);
10077 ID.AddPointer(LHS);
10078 ID.AddPointer(RHS);
10079 void *IP = nullptr;
10080 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
10082 SCEVEqualPredicate *Eq = new (SCEVAllocator)
10083 SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
10084 UniquePreds.InsertNode(Eq, IP);
10088 const SCEVPredicate *ScalarEvolution::getWrapPredicate(
10089 const SCEVAddRecExpr *AR,
10090 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
10091 FoldingSetNodeID ID;
10092 // Unique this node based on the arguments
10093 ID.AddInteger(SCEVPredicate::P_Wrap);
10095 ID.AddInteger(AddedFlags);
10096 void *IP = nullptr;
10097 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
10099 auto *OF = new (SCEVAllocator)
10100 SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
10101 UniquePreds.InsertNode(OF, IP);
10107 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
10109 // Rewrites \p S in the context of a loop L and the predicate A.
10110 // If Assume is true, rewrite is free to add further predicates to A
10111 // such that the result will be an AddRecExpr.
10112 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
10113 SCEVUnionPredicate &A, bool Assume) {
10114 SCEVPredicateRewriter Rewriter(L, SE, A, Assume);
10115 return Rewriter.visit(S);
10118 SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
10119 SCEVUnionPredicate &P, bool Assume)
10120 : SCEVRewriteVisitor(SE), P(P), L(L), Assume(Assume) {}
10122 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
10123 auto ExprPreds = P.getPredicatesForExpr(Expr);
10124 for (auto *Pred : ExprPreds)
10125 if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred))
10126 if (IPred->getLHS() == Expr)
10127 return IPred->getRHS();
10132 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
10133 const SCEV *Operand = visit(Expr->getOperand());
10134 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
10135 if (AR && AR->getLoop() == L && AR->isAffine()) {
10136 // This couldn't be folded because the operand didn't have the nuw
10137 // flag. Add the nusw flag as an assumption that we could make.
10138 const SCEV *Step = AR->getStepRecurrence(SE);
10139 Type *Ty = Expr->getType();
10140 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
10141 return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
10142 SE.getSignExtendExpr(Step, Ty), L,
10143 AR->getNoWrapFlags());
10145 return SE.getZeroExtendExpr(Operand, Expr->getType());
10148 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
10149 const SCEV *Operand = visit(Expr->getOperand());
10150 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
10151 if (AR && AR->getLoop() == L && AR->isAffine()) {
10152 // This couldn't be folded because the operand didn't have the nsw
10153 // flag. Add the nssw flag as an assumption that we could make.
10154 const SCEV *Step = AR->getStepRecurrence(SE);
10155 Type *Ty = Expr->getType();
10156 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
10157 return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
10158 SE.getSignExtendExpr(Step, Ty), L,
10159 AR->getNoWrapFlags());
10161 return SE.getSignExtendExpr(Operand, Expr->getType());
10165 bool addOverflowAssumption(const SCEVAddRecExpr *AR,
10166 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
10167 auto *A = SE.getWrapPredicate(AR, AddedFlags);
10169 // Check if we've already made this assumption.
10178 SCEVUnionPredicate &P;
10182 } // end anonymous namespace
10184 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
10185 SCEVUnionPredicate &Preds) {
10186 return SCEVPredicateRewriter::rewrite(S, L, *this, Preds, false);
10189 const SCEVAddRecExpr *
10190 ScalarEvolution::convertSCEVToAddRecWithPredicates(const SCEV *S, const Loop *L,
10191 SCEVUnionPredicate &Preds) {
10192 SCEVUnionPredicate TransformPreds;
10193 S = SCEVPredicateRewriter::rewrite(S, L, *this, TransformPreds, true);
10194 auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
10199 // Since the transformation was successful, we can now transfer the SCEV
10201 Preds.add(&TransformPreds);
10205 /// SCEV predicates
10206 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
10207 SCEVPredicateKind Kind)
10208 : FastID(ID), Kind(Kind) {}
10210 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
10211 const SCEVUnknown *LHS,
10212 const SCEVConstant *RHS)
10213 : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {}
10215 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
10216 const auto *Op = dyn_cast<SCEVEqualPredicate>(N);
10221 return Op->LHS == LHS && Op->RHS == RHS;
10224 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
10226 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
10228 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
10229 OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
10232 SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
10233 const SCEVAddRecExpr *AR,
10234 IncrementWrapFlags Flags)
10235 : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
10237 const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }
10239 bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
10240 const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
10242 return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
10245 bool SCEVWrapPredicate::isAlwaysTrue() const {
10246 SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
10247 IncrementWrapFlags IFlags = Flags;
10249 if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
10250 IFlags = clearFlags(IFlags, IncrementNSSW);
10252 return IFlags == IncrementAnyWrap;
10255 void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
10256 OS.indent(Depth) << *getExpr() << " Added Flags: ";
10257 if (SCEVWrapPredicate::IncrementNUSW & getFlags())
10259 if (SCEVWrapPredicate::IncrementNSSW & getFlags())
10264 SCEVWrapPredicate::IncrementWrapFlags
10265 SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
10266 ScalarEvolution &SE) {
10267 IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
10268 SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
10270 // We can safely transfer the NSW flag as NSSW.
10271 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
10272 ImpliedFlags = IncrementNSSW;
10274 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
10275 // If the increment is positive, the SCEV NUW flag will also imply the
10276 // WrapPredicate NUSW flag.
10277 if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
10278 if (Step->getValue()->getValue().isNonNegative())
10279 ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
10282 return ImpliedFlags;
10285 /// Union predicates don't get cached so create a dummy set ID for it.
10286 SCEVUnionPredicate::SCEVUnionPredicate()
10287 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
10289 bool SCEVUnionPredicate::isAlwaysTrue() const {
10290 return all_of(Preds,
10291 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
10294 ArrayRef<const SCEVPredicate *>
10295 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
10296 auto I = SCEVToPreds.find(Expr);
10297 if (I == SCEVToPreds.end())
10298 return ArrayRef<const SCEVPredicate *>();
10302 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
10303 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
10304 return all_of(Set->Preds,
10305 [this](const SCEVPredicate *I) { return this->implies(I); });
10307 auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
10308 if (ScevPredsIt == SCEVToPreds.end())
10310 auto &SCEVPreds = ScevPredsIt->second;
10312 return any_of(SCEVPreds,
10313 [N](const SCEVPredicate *I) { return I->implies(N); });
10316 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
10318 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
10319 for (auto Pred : Preds)
10320 Pred->print(OS, Depth);
10323 void SCEVUnionPredicate::add(const SCEVPredicate *N) {
10324 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
10325 for (auto Pred : Set->Preds)
10333 const SCEV *Key = N->getExpr();
10334 assert(Key && "Only SCEVUnionPredicate doesn't have an "
10335 " associated expression!");
10337 SCEVToPreds[Key].push_back(N);
10338 Preds.push_back(N);
10341 PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
10343 : SE(SE), L(L), Generation(0), BackedgeCount(nullptr) {}
10345 const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
10346 const SCEV *Expr = SE.getSCEV(V);
10347 RewriteEntry &Entry = RewriteMap[Expr];
10349 // If we already have an entry and the version matches, return it.
10350 if (Entry.second && Generation == Entry.first)
10351 return Entry.second;
10353 // We found an entry but it's stale. Rewrite the stale entry
10354 // acording to the current predicate.
10356 Expr = Entry.second;
10358 const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
10359 Entry = {Generation, NewSCEV};
10364 const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
10365 if (!BackedgeCount) {
10366 SCEVUnionPredicate BackedgePred;
10367 BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
10368 addPredicate(BackedgePred);
10370 return BackedgeCount;
10373 void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
10374 if (Preds.implies(&Pred))
10377 updateGeneration();
10380 const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
10384 void PredicatedScalarEvolution::updateGeneration() {
10385 // If the generation number wrapped recompute everything.
10386 if (++Generation == 0) {
10387 for (auto &II : RewriteMap) {
10388 const SCEV *Rewritten = II.second.second;
10389 II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
10394 void PredicatedScalarEvolution::setNoOverflow(
10395 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
10396 const SCEV *Expr = getSCEV(V);
10397 const auto *AR = cast<SCEVAddRecExpr>(Expr);
10399 auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
10401 // Clear the statically implied flags.
10402 Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
10403 addPredicate(*SE.getWrapPredicate(AR, Flags));
10405 auto II = FlagsMap.insert({V, Flags});
10407 II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
10410 bool PredicatedScalarEvolution::hasNoOverflow(
10411 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
10412 const SCEV *Expr = getSCEV(V);
10413 const auto *AR = cast<SCEVAddRecExpr>(Expr);
10415 Flags = SCEVWrapPredicate::clearFlags(
10416 Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
10418 auto II = FlagsMap.find(V);
10420 if (II != FlagsMap.end())
10421 Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);
10423 return Flags == SCEVWrapPredicate::IncrementAnyWrap;
10426 const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
10427 const SCEV *Expr = this->getSCEV(V);
10428 auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, Preds);
10433 updateGeneration();
10434 RewriteMap[SE.getSCEV(V)] = {Generation, New};
10438 PredicatedScalarEvolution::PredicatedScalarEvolution(
10439 const PredicatedScalarEvolution &Init)
10440 : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
10441 Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
10442 for (const auto &I : Init.FlagsMap)
10443 FlagsMap.insert(I);
10446 void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
10448 for (auto *BB : L.getBlocks())
10449 for (auto &I : *BB) {
10450 if (!SE.isSCEVable(I.getType()))
10453 auto *Expr = SE.getSCEV(&I);
10454 auto II = RewriteMap.find(Expr);
10456 if (II == RewriteMap.end())
10459 // Don't print things that are not interesting.
10460 if (II->second.second == Expr)
10463 OS.indent(Depth) << "[PSE]" << I << ":\n";
10464 OS.indent(Depth + 2) << *Expr << "\n";
10465 OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";