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 XDEBUG when the test suite is clean.
116 VerifySCEV("verify-scev",
117 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
119 //===----------------------------------------------------------------------===//
120 // SCEV class definitions
121 //===----------------------------------------------------------------------===//
123 //===----------------------------------------------------------------------===//
124 // Implementation of the SCEV class.
128 void SCEV::dump() const {
133 void SCEV::print(raw_ostream &OS) const {
134 switch (static_cast<SCEVTypes>(getSCEVType())) {
136 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
139 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
140 const SCEV *Op = Trunc->getOperand();
141 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
142 << *Trunc->getType() << ")";
146 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
147 const SCEV *Op = ZExt->getOperand();
148 OS << "(zext " << *Op->getType() << " " << *Op << " to "
149 << *ZExt->getType() << ")";
153 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
154 const SCEV *Op = SExt->getOperand();
155 OS << "(sext " << *Op->getType() << " " << *Op << " to "
156 << *SExt->getType() << ")";
160 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
161 OS << "{" << *AR->getOperand(0);
162 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
163 OS << ",+," << *AR->getOperand(i);
165 if (AR->getNoWrapFlags(FlagNUW))
167 if (AR->getNoWrapFlags(FlagNSW))
169 if (AR->getNoWrapFlags(FlagNW) &&
170 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
172 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
180 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
181 const char *OpStr = nullptr;
182 switch (NAry->getSCEVType()) {
183 case scAddExpr: OpStr = " + "; break;
184 case scMulExpr: OpStr = " * "; break;
185 case scUMaxExpr: OpStr = " umax "; break;
186 case scSMaxExpr: OpStr = " smax "; break;
189 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
192 if (std::next(I) != E)
196 switch (NAry->getSCEVType()) {
199 if (NAry->getNoWrapFlags(FlagNUW))
201 if (NAry->getNoWrapFlags(FlagNSW))
207 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
208 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
212 const SCEVUnknown *U = cast<SCEVUnknown>(this);
214 if (U->isSizeOf(AllocTy)) {
215 OS << "sizeof(" << *AllocTy << ")";
218 if (U->isAlignOf(AllocTy)) {
219 OS << "alignof(" << *AllocTy << ")";
225 if (U->isOffsetOf(CTy, FieldNo)) {
226 OS << "offsetof(" << *CTy << ", ";
227 FieldNo->printAsOperand(OS, false);
232 // Otherwise just print it normally.
233 U->getValue()->printAsOperand(OS, false);
236 case scCouldNotCompute:
237 OS << "***COULDNOTCOMPUTE***";
240 llvm_unreachable("Unknown SCEV kind!");
243 Type *SCEV::getType() const {
244 switch (static_cast<SCEVTypes>(getSCEVType())) {
246 return cast<SCEVConstant>(this)->getType();
250 return cast<SCEVCastExpr>(this)->getType();
255 return cast<SCEVNAryExpr>(this)->getType();
257 return cast<SCEVAddExpr>(this)->getType();
259 return cast<SCEVUDivExpr>(this)->getType();
261 return cast<SCEVUnknown>(this)->getType();
262 case scCouldNotCompute:
263 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
265 llvm_unreachable("Unknown SCEV kind!");
268 bool SCEV::isZero() const {
269 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
270 return SC->getValue()->isZero();
274 bool SCEV::isOne() const {
275 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
276 return SC->getValue()->isOne();
280 bool SCEV::isAllOnesValue() const {
281 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
282 return SC->getValue()->isAllOnesValue();
286 /// isNonConstantNegative - Return true if the specified scev is negated, but
288 bool SCEV::isNonConstantNegative() const {
289 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
290 if (!Mul) return false;
292 // If there is a constant factor, it will be first.
293 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
294 if (!SC) return false;
296 // Return true if the value is negative, this matches things like (-42 * V).
297 return SC->getValue()->getValue().isNegative();
300 SCEVCouldNotCompute::SCEVCouldNotCompute() :
301 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
303 bool SCEVCouldNotCompute::classof(const SCEV *S) {
304 return S->getSCEVType() == scCouldNotCompute;
307 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
309 ID.AddInteger(scConstant);
312 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
313 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
314 UniqueSCEVs.InsertNode(S, IP);
318 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
319 return getConstant(ConstantInt::get(getContext(), Val));
323 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
324 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
325 return getConstant(ConstantInt::get(ITy, V, isSigned));
328 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
329 unsigned SCEVTy, const SCEV *op, Type *ty)
330 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
332 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
333 const SCEV *op, Type *ty)
334 : SCEVCastExpr(ID, scTruncate, op, ty) {
335 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
336 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
337 "Cannot truncate non-integer value!");
340 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
341 const SCEV *op, Type *ty)
342 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
343 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
344 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
345 "Cannot zero extend non-integer value!");
348 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
349 const SCEV *op, Type *ty)
350 : SCEVCastExpr(ID, scSignExtend, op, ty) {
351 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
352 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
353 "Cannot sign extend non-integer value!");
356 void SCEVUnknown::deleted() {
357 // Clear this SCEVUnknown from various maps.
358 SE->forgetMemoizedResults(this);
360 // Remove this SCEVUnknown from the uniquing map.
361 SE->UniqueSCEVs.RemoveNode(this);
363 // Release the value.
367 void SCEVUnknown::allUsesReplacedWith(Value *New) {
368 // Clear this SCEVUnknown from various maps.
369 SE->forgetMemoizedResults(this);
371 // Remove this SCEVUnknown from the uniquing map.
372 SE->UniqueSCEVs.RemoveNode(this);
374 // Update this SCEVUnknown to point to the new value. This is needed
375 // because there may still be outstanding SCEVs which still point to
380 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
381 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
382 if (VCE->getOpcode() == Instruction::PtrToInt)
383 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
384 if (CE->getOpcode() == Instruction::GetElementPtr &&
385 CE->getOperand(0)->isNullValue() &&
386 CE->getNumOperands() == 2)
387 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
389 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
397 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
398 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
399 if (VCE->getOpcode() == Instruction::PtrToInt)
400 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
401 if (CE->getOpcode() == Instruction::GetElementPtr &&
402 CE->getOperand(0)->isNullValue()) {
404 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
405 if (StructType *STy = dyn_cast<StructType>(Ty))
406 if (!STy->isPacked() &&
407 CE->getNumOperands() == 3 &&
408 CE->getOperand(1)->isNullValue()) {
409 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
411 STy->getNumElements() == 2 &&
412 STy->getElementType(0)->isIntegerTy(1)) {
413 AllocTy = STy->getElementType(1);
422 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
423 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
424 if (VCE->getOpcode() == Instruction::PtrToInt)
425 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
426 if (CE->getOpcode() == Instruction::GetElementPtr &&
427 CE->getNumOperands() == 3 &&
428 CE->getOperand(0)->isNullValue() &&
429 CE->getOperand(1)->isNullValue()) {
431 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
432 // Ignore vector types here so that ScalarEvolutionExpander doesn't
433 // emit getelementptrs that index into vectors.
434 if (Ty->isStructTy() || Ty->isArrayTy()) {
436 FieldNo = CE->getOperand(2);
444 //===----------------------------------------------------------------------===//
446 //===----------------------------------------------------------------------===//
449 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
450 /// than the complexity of the RHS. This comparator is used to canonicalize
452 class SCEVComplexityCompare {
453 const LoopInfo *const LI;
455 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
457 // Return true or false if LHS is less than, or at least RHS, respectively.
458 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
459 return compare(LHS, RHS) < 0;
462 // Return negative, zero, or positive, if LHS is less than, equal to, or
463 // greater than RHS, respectively. A three-way result allows recursive
464 // comparisons to be more efficient.
465 int compare(const SCEV *LHS, const SCEV *RHS) const {
466 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
470 // Primarily, sort the SCEVs by their getSCEVType().
471 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
473 return (int)LType - (int)RType;
475 // Aside from the getSCEVType() ordering, the particular ordering
476 // isn't very important except that it's beneficial to be consistent,
477 // so that (a + b) and (b + a) don't end up as different expressions.
478 switch (static_cast<SCEVTypes>(LType)) {
480 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
481 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
483 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
484 // not as complete as it could be.
485 const Value *LV = LU->getValue(), *RV = RU->getValue();
487 // Order pointer values after integer values. This helps SCEVExpander
489 bool LIsPointer = LV->getType()->isPointerTy(),
490 RIsPointer = RV->getType()->isPointerTy();
491 if (LIsPointer != RIsPointer)
492 return (int)LIsPointer - (int)RIsPointer;
494 // Compare getValueID values.
495 unsigned LID = LV->getValueID(),
496 RID = RV->getValueID();
498 return (int)LID - (int)RID;
500 // Sort arguments by their position.
501 if (const Argument *LA = dyn_cast<Argument>(LV)) {
502 const Argument *RA = cast<Argument>(RV);
503 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
504 return (int)LArgNo - (int)RArgNo;
507 // For instructions, compare their loop depth, and their operand
508 // count. This is pretty loose.
509 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
510 const Instruction *RInst = cast<Instruction>(RV);
512 // Compare loop depths.
513 const BasicBlock *LParent = LInst->getParent(),
514 *RParent = RInst->getParent();
515 if (LParent != RParent) {
516 unsigned LDepth = LI->getLoopDepth(LParent),
517 RDepth = LI->getLoopDepth(RParent);
518 if (LDepth != RDepth)
519 return (int)LDepth - (int)RDepth;
522 // Compare the number of operands.
523 unsigned LNumOps = LInst->getNumOperands(),
524 RNumOps = RInst->getNumOperands();
525 return (int)LNumOps - (int)RNumOps;
532 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
533 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
535 // Compare constant values.
536 const APInt &LA = LC->getValue()->getValue();
537 const APInt &RA = RC->getValue()->getValue();
538 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
539 if (LBitWidth != RBitWidth)
540 return (int)LBitWidth - (int)RBitWidth;
541 return LA.ult(RA) ? -1 : 1;
545 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
546 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
548 // Compare addrec loop depths.
549 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
550 if (LLoop != RLoop) {
551 unsigned LDepth = LLoop->getLoopDepth(),
552 RDepth = RLoop->getLoopDepth();
553 if (LDepth != RDepth)
554 return (int)LDepth - (int)RDepth;
557 // Addrec complexity grows with operand count.
558 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
559 if (LNumOps != RNumOps)
560 return (int)LNumOps - (int)RNumOps;
562 // Lexicographically compare.
563 for (unsigned i = 0; i != LNumOps; ++i) {
564 long X = compare(LA->getOperand(i), RA->getOperand(i));
576 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
577 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
579 // Lexicographically compare n-ary expressions.
580 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
581 if (LNumOps != RNumOps)
582 return (int)LNumOps - (int)RNumOps;
584 for (unsigned i = 0; i != LNumOps; ++i) {
587 long X = compare(LC->getOperand(i), RC->getOperand(i));
591 return (int)LNumOps - (int)RNumOps;
595 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
596 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
598 // Lexicographically compare udiv expressions.
599 long X = compare(LC->getLHS(), RC->getLHS());
602 return compare(LC->getRHS(), RC->getRHS());
608 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
609 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
611 // Compare cast expressions by operand.
612 return compare(LC->getOperand(), RC->getOperand());
615 case scCouldNotCompute:
616 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
618 llvm_unreachable("Unknown SCEV kind!");
623 /// GroupByComplexity - Given a list of SCEV objects, order them by their
624 /// complexity, and group objects of the same complexity together by value.
625 /// When this routine is finished, we know that any duplicates in the vector are
626 /// consecutive and that complexity is monotonically increasing.
628 /// Note that we go take special precautions to ensure that we get deterministic
629 /// results from this routine. In other words, we don't want the results of
630 /// this to depend on where the addresses of various SCEV objects happened to
633 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
635 if (Ops.size() < 2) return; // Noop
636 if (Ops.size() == 2) {
637 // This is the common case, which also happens to be trivially simple.
639 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
640 if (SCEVComplexityCompare(LI)(RHS, LHS))
645 // Do the rough sort by complexity.
646 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
648 // Now that we are sorted by complexity, group elements of the same
649 // complexity. Note that this is, at worst, N^2, but the vector is likely to
650 // be extremely short in practice. Note that we take this approach because we
651 // do not want to depend on the addresses of the objects we are grouping.
652 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
653 const SCEV *S = Ops[i];
654 unsigned Complexity = S->getSCEVType();
656 // If there are any objects of the same complexity and same value as this
658 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
659 if (Ops[j] == S) { // Found a duplicate.
660 // Move it to immediately after i'th element.
661 std::swap(Ops[i+1], Ops[j]);
662 ++i; // no need to rescan it.
663 if (i == e-2) return; // Done!
670 struct FindSCEVSize {
672 FindSCEVSize() : Size(0) {}
674 bool follow(const SCEV *S) {
676 // Keep looking at all operands of S.
679 bool isDone() const {
685 // Returns the size of the SCEV S.
686 static inline int sizeOfSCEV(const SCEV *S) {
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<const 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->getValue()->getValue();
766 APInt DenominatorVal = D->getValue()->getValue();
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 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
929 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
932 // Handle the simplest case efficiently.
934 return SE.getTruncateOrZeroExtend(It, ResultTy);
936 // We are using the following formula for BC(It, K):
938 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
940 // Suppose, W is the bitwidth of the return value. We must be prepared for
941 // overflow. Hence, we must assure that the result of our computation is
942 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
943 // safe in modular arithmetic.
945 // However, this code doesn't use exactly that formula; the formula it uses
946 // is something like the following, where T is the number of factors of 2 in
947 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
950 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
952 // This formula is trivially equivalent to the previous formula. However,
953 // this formula can be implemented much more efficiently. The trick is that
954 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
955 // arithmetic. To do exact division in modular arithmetic, all we have
956 // to do is multiply by the inverse. Therefore, this step can be done at
959 // The next issue is how to safely do the division by 2^T. The way this
960 // is done is by doing the multiplication step at a width of at least W + T
961 // bits. This way, the bottom W+T bits of the product are accurate. Then,
962 // when we perform the division by 2^T (which is equivalent to a right shift
963 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
964 // truncated out after the division by 2^T.
966 // In comparison to just directly using the first formula, this technique
967 // is much more efficient; using the first formula requires W * K bits,
968 // but this formula less than W + K bits. Also, the first formula requires
969 // a division step, whereas this formula only requires multiplies and shifts.
971 // It doesn't matter whether the subtraction step is done in the calculation
972 // width or the input iteration count's width; if the subtraction overflows,
973 // the result must be zero anyway. We prefer here to do it in the width of
974 // the induction variable because it helps a lot for certain cases; CodeGen
975 // isn't smart enough to ignore the overflow, which leads to much less
976 // efficient code if the width of the subtraction is wider than the native
979 // (It's possible to not widen at all by pulling out factors of 2 before
980 // the multiplication; for example, K=2 can be calculated as
981 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
982 // extra arithmetic, so it's not an obvious win, and it gets
983 // much more complicated for K > 3.)
985 // Protection from insane SCEVs; this bound is conservative,
986 // but it probably doesn't matter.
988 return SE.getCouldNotCompute();
990 unsigned W = SE.getTypeSizeInBits(ResultTy);
992 // Calculate K! / 2^T and T; we divide out the factors of two before
993 // multiplying for calculating K! / 2^T to avoid overflow.
994 // Other overflow doesn't matter because we only care about the bottom
995 // W bits of the result.
996 APInt OddFactorial(W, 1);
998 for (unsigned i = 3; i <= K; ++i) {
1000 unsigned TwoFactors = Mult.countTrailingZeros();
1002 Mult = Mult.lshr(TwoFactors);
1003 OddFactorial *= Mult;
1006 // We need at least W + T bits for the multiplication step
1007 unsigned CalculationBits = W + T;
1009 // Calculate 2^T, at width T+W.
1010 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1012 // Calculate the multiplicative inverse of K! / 2^T;
1013 // this multiplication factor will perform the exact division by
1015 APInt Mod = APInt::getSignedMinValue(W+1);
1016 APInt MultiplyFactor = OddFactorial.zext(W+1);
1017 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1018 MultiplyFactor = MultiplyFactor.trunc(W);
1020 // Calculate the product, at width T+W
1021 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1023 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1024 for (unsigned i = 1; i != K; ++i) {
1025 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1026 Dividend = SE.getMulExpr(Dividend,
1027 SE.getTruncateOrZeroExtend(S, CalculationTy));
1031 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1033 // Truncate the result, and divide by K! / 2^T.
1035 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1036 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1039 /// evaluateAtIteration - Return the value of this chain of recurrences at
1040 /// the specified iteration number. We can evaluate this recurrence by
1041 /// multiplying each element in the chain by the binomial coefficient
1042 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1044 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1046 /// where BC(It, k) stands for binomial coefficient.
1048 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1049 ScalarEvolution &SE) const {
1050 const SCEV *Result = getStart();
1051 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1052 // The computation is correct in the face of overflow provided that the
1053 // multiplication is performed _after_ the evaluation of the binomial
1055 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1056 if (isa<SCEVCouldNotCompute>(Coeff))
1059 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1064 //===----------------------------------------------------------------------===//
1065 // SCEV Expression folder implementations
1066 //===----------------------------------------------------------------------===//
1068 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1070 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1071 "This is not a truncating conversion!");
1072 assert(isSCEVable(Ty) &&
1073 "This is not a conversion to a SCEVable type!");
1074 Ty = getEffectiveSCEVType(Ty);
1076 FoldingSetNodeID ID;
1077 ID.AddInteger(scTruncate);
1081 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1083 // Fold if the operand is constant.
1084 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1086 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1088 // trunc(trunc(x)) --> trunc(x)
1089 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1090 return getTruncateExpr(ST->getOperand(), Ty);
1092 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1093 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1094 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1096 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1097 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1098 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1100 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1101 // eliminate all the truncates, or we replace other casts with truncates.
1102 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1103 SmallVector<const SCEV *, 4> Operands;
1104 bool hasTrunc = false;
1105 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1106 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1107 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1108 hasTrunc = isa<SCEVTruncateExpr>(S);
1109 Operands.push_back(S);
1112 return getAddExpr(Operands);
1113 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1116 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1117 // eliminate all the truncates, or we replace other casts with truncates.
1118 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1119 SmallVector<const SCEV *, 4> Operands;
1120 bool hasTrunc = false;
1121 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1122 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1123 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1124 hasTrunc = isa<SCEVTruncateExpr>(S);
1125 Operands.push_back(S);
1128 return getMulExpr(Operands);
1129 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1132 // If the input value is a chrec scev, truncate the chrec's operands.
1133 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1134 SmallVector<const SCEV *, 4> Operands;
1135 for (const SCEV *Op : AddRec->operands())
1136 Operands.push_back(getTruncateExpr(Op, Ty));
1137 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1140 // The cast wasn't folded; create an explicit cast node. We can reuse
1141 // the existing insert position since if we get here, we won't have
1142 // made any changes which would invalidate it.
1143 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1145 UniqueSCEVs.InsertNode(S, IP);
1149 // Get the limit of a recurrence such that incrementing by Step cannot cause
1150 // signed overflow as long as the value of the recurrence within the
1151 // loop does not exceed this limit before incrementing.
1152 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1153 ICmpInst::Predicate *Pred,
1154 ScalarEvolution *SE) {
1155 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1156 if (SE->isKnownPositive(Step)) {
1157 *Pred = ICmpInst::ICMP_SLT;
1158 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1159 SE->getSignedRange(Step).getSignedMax());
1161 if (SE->isKnownNegative(Step)) {
1162 *Pred = ICmpInst::ICMP_SGT;
1163 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1164 SE->getSignedRange(Step).getSignedMin());
1169 // Get the limit of a recurrence such that incrementing by Step cannot cause
1170 // unsigned overflow as long as the value of the recurrence within the loop does
1171 // not exceed this limit before incrementing.
1172 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1173 ICmpInst::Predicate *Pred,
1174 ScalarEvolution *SE) {
1175 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1176 *Pred = ICmpInst::ICMP_ULT;
1178 return SE->getConstant(APInt::getMinValue(BitWidth) -
1179 SE->getUnsignedRange(Step).getUnsignedMax());
1184 struct ExtendOpTraitsBase {
1185 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1188 // Used to make code generic over signed and unsigned overflow.
1189 template <typename ExtendOp> struct ExtendOpTraits {
1192 // static const SCEV::NoWrapFlags WrapType;
1194 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1196 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1197 // ICmpInst::Predicate *Pred,
1198 // ScalarEvolution *SE);
1202 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1203 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1205 static const GetExtendExprTy GetExtendExpr;
1207 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1208 ICmpInst::Predicate *Pred,
1209 ScalarEvolution *SE) {
1210 return getSignedOverflowLimitForStep(Step, Pred, SE);
1214 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1215 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1218 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1219 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1221 static const GetExtendExprTy GetExtendExpr;
1223 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1224 ICmpInst::Predicate *Pred,
1225 ScalarEvolution *SE) {
1226 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1230 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1231 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1234 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1235 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1236 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1237 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1238 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1239 // expression "Step + sext/zext(PreIncAR)" is congruent with
1240 // "sext/zext(PostIncAR)"
1241 template <typename ExtendOpTy>
1242 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1243 ScalarEvolution *SE) {
1244 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1245 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1247 const Loop *L = AR->getLoop();
1248 const SCEV *Start = AR->getStart();
1249 const SCEV *Step = AR->getStepRecurrence(*SE);
1251 // Check for a simple looking step prior to loop entry.
1252 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1256 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1257 // subtraction is expensive. For this purpose, perform a quick and dirty
1258 // difference, by checking for Step in the operand list.
1259 SmallVector<const SCEV *, 4> DiffOps;
1260 for (const SCEV *Op : SA->operands())
1262 DiffOps.push_back(Op);
1264 if (DiffOps.size() == SA->getNumOperands())
1267 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1270 // 1. NSW/NUW flags on the step increment.
1271 auto PreStartFlags =
1272 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1273 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1274 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1275 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1277 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1278 // "S+X does not sign/unsign-overflow".
1281 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1282 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1283 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1286 // 2. Direct overflow check on the step operation's expression.
1287 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1288 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1289 const SCEV *OperandExtendedStart =
1290 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1291 (SE->*GetExtendExpr)(Step, WideTy));
1292 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1293 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1294 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1295 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1296 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1297 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1302 // 3. Loop precondition.
1303 ICmpInst::Predicate Pred;
1304 const SCEV *OverflowLimit =
1305 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1307 if (OverflowLimit &&
1308 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1314 // Get the normalized zero or sign extended expression for this AddRec's Start.
1315 template <typename ExtendOpTy>
1316 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1317 ScalarEvolution *SE) {
1318 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1320 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1322 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1324 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1325 (SE->*GetExtendExpr)(PreStart, Ty));
1328 // Try to prove away overflow by looking at "nearby" add recurrences. A
1329 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1330 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1334 // {S,+,X} == {S-T,+,X} + T
1335 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1337 // If ({S-T,+,X} + T) does not overflow ... (1)
1339 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1341 // If {S-T,+,X} does not overflow ... (2)
1343 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1344 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1346 // If (S-T)+T does not overflow ... (3)
1348 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1349 // == {Ext(S),+,Ext(X)} == LHS
1351 // Thus, if (1), (2) and (3) are true for some T, then
1352 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1354 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1355 // does not overflow" restricted to the 0th iteration. Therefore we only need
1356 // to check for (1) and (2).
1358 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1359 // is `Delta` (defined below).
1361 template <typename ExtendOpTy>
1362 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1365 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1367 // We restrict `Start` to a constant to prevent SCEV from spending too much
1368 // time here. It is correct (but more expensive) to continue with a
1369 // non-constant `Start` and do a general SCEV subtraction to compute
1370 // `PreStart` below.
1372 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1376 APInt StartAI = StartC->getValue()->getValue();
1378 for (unsigned Delta : {-2, -1, 1, 2}) {
1379 const SCEV *PreStart = getConstant(StartAI - Delta);
1381 FoldingSetNodeID ID;
1382 ID.AddInteger(scAddRecExpr);
1383 ID.AddPointer(PreStart);
1384 ID.AddPointer(Step);
1388 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1390 // Give up if we don't already have the add recurrence we need because
1391 // actually constructing an add recurrence is relatively expensive.
1392 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1393 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1394 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1395 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1396 DeltaS, &Pred, this);
1397 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1405 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1407 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1408 "This is not an extending conversion!");
1409 assert(isSCEVable(Ty) &&
1410 "This is not a conversion to a SCEVable type!");
1411 Ty = getEffectiveSCEVType(Ty);
1413 // Fold if the operand is constant.
1414 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1416 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1418 // zext(zext(x)) --> zext(x)
1419 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1420 return getZeroExtendExpr(SZ->getOperand(), Ty);
1422 // Before doing any expensive analysis, check to see if we've already
1423 // computed a SCEV for this Op and Ty.
1424 FoldingSetNodeID ID;
1425 ID.AddInteger(scZeroExtend);
1429 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1431 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1432 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1433 // It's possible the bits taken off by the truncate were all zero bits. If
1434 // so, we should be able to simplify this further.
1435 const SCEV *X = ST->getOperand();
1436 ConstantRange CR = getUnsignedRange(X);
1437 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1438 unsigned NewBits = getTypeSizeInBits(Ty);
1439 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1440 CR.zextOrTrunc(NewBits)))
1441 return getTruncateOrZeroExtend(X, Ty);
1444 // If the input value is a chrec scev, and we can prove that the value
1445 // did not overflow the old, smaller, value, we can zero extend all of the
1446 // operands (often constants). This allows analysis of something like
1447 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1448 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1449 if (AR->isAffine()) {
1450 const SCEV *Start = AR->getStart();
1451 const SCEV *Step = AR->getStepRecurrence(*this);
1452 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1453 const Loop *L = AR->getLoop();
1455 // If we have special knowledge that this addrec won't overflow,
1456 // we don't need to do any further analysis.
1457 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1458 return getAddRecExpr(
1459 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1460 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1462 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1463 // Note that this serves two purposes: It filters out loops that are
1464 // simply not analyzable, and it covers the case where this code is
1465 // being called from within backedge-taken count analysis, such that
1466 // attempting to ask for the backedge-taken count would likely result
1467 // in infinite recursion. In the later case, the analysis code will
1468 // cope with a conservative value, and it will take care to purge
1469 // that value once it has finished.
1470 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1471 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1472 // Manually compute the final value for AR, checking for
1475 // Check whether the backedge-taken count can be losslessly casted to
1476 // the addrec's type. The count is always unsigned.
1477 const SCEV *CastedMaxBECount =
1478 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1479 const SCEV *RecastedMaxBECount =
1480 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1481 if (MaxBECount == RecastedMaxBECount) {
1482 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1483 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1484 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1485 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1486 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1487 const SCEV *WideMaxBECount =
1488 getZeroExtendExpr(CastedMaxBECount, WideTy);
1489 const SCEV *OperandExtendedAdd =
1490 getAddExpr(WideStart,
1491 getMulExpr(WideMaxBECount,
1492 getZeroExtendExpr(Step, WideTy)));
1493 if (ZAdd == OperandExtendedAdd) {
1494 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1495 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1496 // Return the expression with the addrec on the outside.
1497 return getAddRecExpr(
1498 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1499 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1501 // Similar to above, only this time treat the step value as signed.
1502 // This covers loops that count down.
1503 OperandExtendedAdd =
1504 getAddExpr(WideStart,
1505 getMulExpr(WideMaxBECount,
1506 getSignExtendExpr(Step, WideTy)));
1507 if (ZAdd == OperandExtendedAdd) {
1508 // Cache knowledge of AR NW, which is propagated to this AddRec.
1509 // Negative step causes unsigned wrap, but it still can't self-wrap.
1510 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1511 // Return the expression with the addrec on the outside.
1512 return getAddRecExpr(
1513 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1514 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1518 // If the backedge is guarded by a comparison with the pre-inc value
1519 // the addrec is safe. Also, if the entry is guarded by a comparison
1520 // with the start value and the backedge is guarded by a comparison
1521 // with the post-inc value, the addrec is safe.
1522 if (isKnownPositive(Step)) {
1523 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1524 getUnsignedRange(Step).getUnsignedMax());
1525 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1526 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1527 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1528 AR->getPostIncExpr(*this), N))) {
1529 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1530 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1531 // Return the expression with the addrec on the outside.
1532 return getAddRecExpr(
1533 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1534 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1536 } else if (isKnownNegative(Step)) {
1537 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1538 getSignedRange(Step).getSignedMin());
1539 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1540 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1541 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1542 AR->getPostIncExpr(*this), N))) {
1543 // Cache knowledge of AR NW, which is propagated to this AddRec.
1544 // Negative step causes unsigned wrap, but it still can't self-wrap.
1545 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1546 // Return the expression with the addrec on the outside.
1547 return getAddRecExpr(
1548 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1549 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1554 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1555 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1556 return getAddRecExpr(
1557 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1558 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1562 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1563 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1564 if (SA->getNoWrapFlags(SCEV::FlagNUW)) {
1565 // If the addition does not unsign overflow then we can, by definition,
1566 // commute the zero extension with the addition operation.
1567 SmallVector<const SCEV *, 4> Ops;
1568 for (const auto *Op : SA->operands())
1569 Ops.push_back(getZeroExtendExpr(Op, Ty));
1570 return getAddExpr(Ops, SCEV::FlagNUW);
1574 // The cast wasn't folded; create an explicit cast node.
1575 // Recompute the insert position, as it may have been invalidated.
1576 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1577 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1579 UniqueSCEVs.InsertNode(S, IP);
1583 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1585 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1586 "This is not an extending conversion!");
1587 assert(isSCEVable(Ty) &&
1588 "This is not a conversion to a SCEVable type!");
1589 Ty = getEffectiveSCEVType(Ty);
1591 // Fold if the operand is constant.
1592 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1594 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1596 // sext(sext(x)) --> sext(x)
1597 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1598 return getSignExtendExpr(SS->getOperand(), Ty);
1600 // sext(zext(x)) --> zext(x)
1601 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1602 return getZeroExtendExpr(SZ->getOperand(), Ty);
1604 // Before doing any expensive analysis, check to see if we've already
1605 // computed a SCEV for this Op and Ty.
1606 FoldingSetNodeID ID;
1607 ID.AddInteger(scSignExtend);
1611 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1613 // If the input value is provably positive, build a zext instead.
1614 if (isKnownNonNegative(Op))
1615 return getZeroExtendExpr(Op, Ty);
1617 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1618 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1619 // It's possible the bits taken off by the truncate were all sign bits. If
1620 // so, we should be able to simplify this further.
1621 const SCEV *X = ST->getOperand();
1622 ConstantRange CR = getSignedRange(X);
1623 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1624 unsigned NewBits = getTypeSizeInBits(Ty);
1625 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1626 CR.sextOrTrunc(NewBits)))
1627 return getTruncateOrSignExtend(X, Ty);
1630 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1631 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1632 if (SA->getNumOperands() == 2) {
1633 auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1634 auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1636 if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1637 const APInt &C1 = SC1->getValue()->getValue();
1638 const APInt &C2 = SC2->getValue()->getValue();
1639 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1640 C2.ugt(C1) && C2.isPowerOf2())
1641 return getAddExpr(getSignExtendExpr(SC1, Ty),
1642 getSignExtendExpr(SMul, Ty));
1647 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1648 if (SA->getNoWrapFlags(SCEV::FlagNSW)) {
1649 // If the addition does not sign overflow then we can, by definition,
1650 // commute the sign extension with the addition operation.
1651 SmallVector<const SCEV *, 4> Ops;
1652 for (const auto *Op : SA->operands())
1653 Ops.push_back(getSignExtendExpr(Op, Ty));
1654 return getAddExpr(Ops, SCEV::FlagNSW);
1657 // If the input value is a chrec scev, and we can prove that the value
1658 // did not overflow the old, smaller, value, we can sign extend all of the
1659 // operands (often constants). This allows analysis of something like
1660 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1661 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1662 if (AR->isAffine()) {
1663 const SCEV *Start = AR->getStart();
1664 const SCEV *Step = AR->getStepRecurrence(*this);
1665 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1666 const Loop *L = AR->getLoop();
1668 // If we have special knowledge that this addrec won't overflow,
1669 // we don't need to do any further analysis.
1670 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1671 return getAddRecExpr(
1672 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1673 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1675 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1676 // Note that this serves two purposes: It filters out loops that are
1677 // simply not analyzable, and it covers the case where this code is
1678 // being called from within backedge-taken count analysis, such that
1679 // attempting to ask for the backedge-taken count would likely result
1680 // in infinite recursion. In the later case, the analysis code will
1681 // cope with a conservative value, and it will take care to purge
1682 // that value once it has finished.
1683 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1684 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1685 // Manually compute the final value for AR, checking for
1688 // Check whether the backedge-taken count can be losslessly casted to
1689 // the addrec's type. The count is always unsigned.
1690 const SCEV *CastedMaxBECount =
1691 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1692 const SCEV *RecastedMaxBECount =
1693 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1694 if (MaxBECount == RecastedMaxBECount) {
1695 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1696 // Check whether Start+Step*MaxBECount has no signed overflow.
1697 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1698 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1699 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1700 const SCEV *WideMaxBECount =
1701 getZeroExtendExpr(CastedMaxBECount, WideTy);
1702 const SCEV *OperandExtendedAdd =
1703 getAddExpr(WideStart,
1704 getMulExpr(WideMaxBECount,
1705 getSignExtendExpr(Step, WideTy)));
1706 if (SAdd == OperandExtendedAdd) {
1707 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1708 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1709 // Return the expression with the addrec on the outside.
1710 return getAddRecExpr(
1711 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1712 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1714 // Similar to above, only this time treat the step value as unsigned.
1715 // This covers loops that count up with an unsigned step.
1716 OperandExtendedAdd =
1717 getAddExpr(WideStart,
1718 getMulExpr(WideMaxBECount,
1719 getZeroExtendExpr(Step, WideTy)));
1720 if (SAdd == OperandExtendedAdd) {
1721 // If AR wraps around then
1723 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1724 // => SAdd != OperandExtendedAdd
1726 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1727 // (SAdd == OperandExtendedAdd => AR is NW)
1729 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1731 // Return the expression with the addrec on the outside.
1732 return getAddRecExpr(
1733 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1734 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1738 // If the backedge is guarded by a comparison with the pre-inc value
1739 // the addrec is safe. Also, if the entry is guarded by a comparison
1740 // with the start value and the backedge is guarded by a comparison
1741 // with the post-inc value, the addrec is safe.
1742 ICmpInst::Predicate Pred;
1743 const SCEV *OverflowLimit =
1744 getSignedOverflowLimitForStep(Step, &Pred, this);
1745 if (OverflowLimit &&
1746 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1747 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1748 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1750 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1751 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1752 return getAddRecExpr(
1753 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1754 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1757 // If Start and Step are constants, check if we can apply this
1759 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1760 auto *SC1 = dyn_cast<SCEVConstant>(Start);
1761 auto *SC2 = dyn_cast<SCEVConstant>(Step);
1763 const APInt &C1 = SC1->getValue()->getValue();
1764 const APInt &C2 = SC2->getValue()->getValue();
1765 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1767 Start = getSignExtendExpr(Start, Ty);
1768 const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1769 AR->getNoWrapFlags());
1770 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1774 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1775 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1776 return getAddRecExpr(
1777 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1778 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1782 // The cast wasn't folded; create an explicit cast node.
1783 // Recompute the insert position, as it may have been invalidated.
1784 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1785 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1787 UniqueSCEVs.InsertNode(S, IP);
1791 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1792 /// unspecified bits out to the given type.
1794 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1796 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1797 "This is not an extending conversion!");
1798 assert(isSCEVable(Ty) &&
1799 "This is not a conversion to a SCEVable type!");
1800 Ty = getEffectiveSCEVType(Ty);
1802 // Sign-extend negative constants.
1803 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1804 if (SC->getValue()->getValue().isNegative())
1805 return getSignExtendExpr(Op, Ty);
1807 // Peel off a truncate cast.
1808 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1809 const SCEV *NewOp = T->getOperand();
1810 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1811 return getAnyExtendExpr(NewOp, Ty);
1812 return getTruncateOrNoop(NewOp, Ty);
1815 // Next try a zext cast. If the cast is folded, use it.
1816 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1817 if (!isa<SCEVZeroExtendExpr>(ZExt))
1820 // Next try a sext cast. If the cast is folded, use it.
1821 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1822 if (!isa<SCEVSignExtendExpr>(SExt))
1825 // Force the cast to be folded into the operands of an addrec.
1826 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1827 SmallVector<const SCEV *, 4> Ops;
1828 for (const SCEV *Op : AR->operands())
1829 Ops.push_back(getAnyExtendExpr(Op, Ty));
1830 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1833 // If the expression is obviously signed, use the sext cast value.
1834 if (isa<SCEVSMaxExpr>(Op))
1837 // Absent any other information, use the zext cast value.
1841 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1842 /// a list of operands to be added under the given scale, update the given
1843 /// map. This is a helper function for getAddRecExpr. As an example of
1844 /// what it does, given a sequence of operands that would form an add
1845 /// expression like this:
1847 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1849 /// where A and B are constants, update the map with these values:
1851 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1853 /// and add 13 + A*B*29 to AccumulatedConstant.
1854 /// This will allow getAddRecExpr to produce this:
1856 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1858 /// This form often exposes folding opportunities that are hidden in
1859 /// the original operand list.
1861 /// Return true iff it appears that any interesting folding opportunities
1862 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1863 /// the common case where no interesting opportunities are present, and
1864 /// is also used as a check to avoid infinite recursion.
1867 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1868 SmallVectorImpl<const SCEV *> &NewOps,
1869 APInt &AccumulatedConstant,
1870 const SCEV *const *Ops, size_t NumOperands,
1872 ScalarEvolution &SE) {
1873 bool Interesting = false;
1875 // Iterate over the add operands. They are sorted, with constants first.
1877 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1879 // Pull a buried constant out to the outside.
1880 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1882 AccumulatedConstant += Scale * C->getValue()->getValue();
1885 // Next comes everything else. We're especially interested in multiplies
1886 // here, but they're in the middle, so just visit the rest with one loop.
1887 for (; i != NumOperands; ++i) {
1888 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1889 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1891 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1892 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1893 // A multiplication of a constant with another add; recurse.
1894 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1896 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1897 Add->op_begin(), Add->getNumOperands(),
1900 // A multiplication of a constant with some other value. Update
1902 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1903 const SCEV *Key = SE.getMulExpr(MulOps);
1904 auto Pair = M.insert(std::make_pair(Key, NewScale));
1906 NewOps.push_back(Pair.first->first);
1908 Pair.first->second += NewScale;
1909 // The map already had an entry for this value, which may indicate
1910 // a folding opportunity.
1915 // An ordinary operand. Update the map.
1916 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1917 M.insert(std::make_pair(Ops[i], Scale));
1919 NewOps.push_back(Pair.first->first);
1921 Pair.first->second += Scale;
1922 // The map already had an entry for this value, which may indicate
1923 // a folding opportunity.
1933 struct APIntCompare {
1934 bool operator()(const APInt &LHS, const APInt &RHS) const {
1935 return LHS.ult(RHS);
1940 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1941 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1942 // can't-overflow flags for the operation if possible.
1943 static SCEV::NoWrapFlags
1944 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1945 const SmallVectorImpl<const SCEV *> &Ops,
1946 SCEV::NoWrapFlags Flags) {
1947 using namespace std::placeholders;
1948 typedef OverflowingBinaryOperator OBO;
1951 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1953 assert(CanAnalyze && "don't call from other places!");
1955 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1956 SCEV::NoWrapFlags SignOrUnsignWrap =
1957 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1959 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1960 auto IsKnownNonNegative =
1961 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1963 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
1965 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1967 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1969 if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
1970 Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
1972 // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
1973 // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
1975 const APInt &C = cast<SCEVConstant>(Ops[0])->getValue()->getValue();
1976 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
1978 ConstantRange::makeNoWrapRegion(Instruction::Add, C, OBO::NoSignedWrap);
1979 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
1980 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
1982 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
1984 ConstantRange::makeNoWrapRegion(Instruction::Add, C,
1985 OBO::NoUnsignedWrap);
1986 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
1987 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
1994 /// getAddExpr - Get a canonical add expression, or something simpler if
1996 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1997 SCEV::NoWrapFlags Flags) {
1998 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1999 "only nuw or nsw allowed");
2000 assert(!Ops.empty() && "Cannot get empty add!");
2001 if (Ops.size() == 1) return Ops[0];
2003 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2004 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2005 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2006 "SCEVAddExpr operand types don't match!");
2009 // Sort by complexity, this groups all similar expression types together.
2010 GroupByComplexity(Ops, &LI);
2012 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2014 // If there are any constants, fold them together.
2016 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2018 assert(Idx < Ops.size());
2019 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2020 // We found two constants, fold them together!
2021 Ops[0] = getConstant(LHSC->getValue()->getValue() +
2022 RHSC->getValue()->getValue());
2023 if (Ops.size() == 2) return Ops[0];
2024 Ops.erase(Ops.begin()+1); // Erase the folded element
2025 LHSC = cast<SCEVConstant>(Ops[0]);
2028 // If we are left with a constant zero being added, strip it off.
2029 if (LHSC->getValue()->isZero()) {
2030 Ops.erase(Ops.begin());
2034 if (Ops.size() == 1) return Ops[0];
2037 // Okay, check to see if the same value occurs in the operand list more than
2038 // once. If so, merge them together into an multiply expression. Since we
2039 // sorted the list, these values are required to be adjacent.
2040 Type *Ty = Ops[0]->getType();
2041 bool FoundMatch = false;
2042 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2043 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2044 // Scan ahead to count how many equal operands there are.
2046 while (i+Count != e && Ops[i+Count] == Ops[i])
2048 // Merge the values into a multiply.
2049 const SCEV *Scale = getConstant(Ty, Count);
2050 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2051 if (Ops.size() == Count)
2054 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2055 --i; e -= Count - 1;
2059 return getAddExpr(Ops, Flags);
2061 // Check for truncates. If all the operands are truncated from the same
2062 // type, see if factoring out the truncate would permit the result to be
2063 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2064 // if the contents of the resulting outer trunc fold to something simple.
2065 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2066 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2067 Type *DstType = Trunc->getType();
2068 Type *SrcType = Trunc->getOperand()->getType();
2069 SmallVector<const SCEV *, 8> LargeOps;
2071 // Check all the operands to see if they can be represented in the
2072 // source type of the truncate.
2073 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2074 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2075 if (T->getOperand()->getType() != SrcType) {
2079 LargeOps.push_back(T->getOperand());
2080 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2081 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2082 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2083 SmallVector<const SCEV *, 8> LargeMulOps;
2084 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2085 if (const SCEVTruncateExpr *T =
2086 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2087 if (T->getOperand()->getType() != SrcType) {
2091 LargeMulOps.push_back(T->getOperand());
2092 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2093 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2100 LargeOps.push_back(getMulExpr(LargeMulOps));
2107 // Evaluate the expression in the larger type.
2108 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2109 // If it folds to something simple, use it. Otherwise, don't.
2110 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2111 return getTruncateExpr(Fold, DstType);
2115 // Skip past any other cast SCEVs.
2116 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2119 // If there are add operands they would be next.
2120 if (Idx < Ops.size()) {
2121 bool DeletedAdd = false;
2122 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2123 // If we have an add, expand the add operands onto the end of the operands
2125 Ops.erase(Ops.begin()+Idx);
2126 Ops.append(Add->op_begin(), Add->op_end());
2130 // If we deleted at least one add, we added operands to the end of the list,
2131 // and they are not necessarily sorted. Recurse to resort and resimplify
2132 // any operands we just acquired.
2134 return getAddExpr(Ops);
2137 // Skip over the add expression until we get to a multiply.
2138 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2141 // Check to see if there are any folding opportunities present with
2142 // operands multiplied by constant values.
2143 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2144 uint64_t BitWidth = getTypeSizeInBits(Ty);
2145 DenseMap<const SCEV *, APInt> M;
2146 SmallVector<const SCEV *, 8> NewOps;
2147 APInt AccumulatedConstant(BitWidth, 0);
2148 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2149 Ops.data(), Ops.size(),
2150 APInt(BitWidth, 1), *this)) {
2151 // Some interesting folding opportunity is present, so its worthwhile to
2152 // re-generate the operands list. Group the operands by constant scale,
2153 // to avoid multiplying by the same constant scale multiple times.
2154 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2155 for (const SCEV *NewOp : NewOps)
2156 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2157 // Re-generate the operands list.
2159 if (AccumulatedConstant != 0)
2160 Ops.push_back(getConstant(AccumulatedConstant));
2161 for (auto &MulOp : MulOpLists)
2162 if (MulOp.first != 0)
2163 Ops.push_back(getMulExpr(getConstant(MulOp.first),
2164 getAddExpr(MulOp.second)));
2167 if (Ops.size() == 1)
2169 return getAddExpr(Ops);
2173 // If we are adding something to a multiply expression, make sure the
2174 // something is not already an operand of the multiply. If so, merge it into
2176 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2177 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2178 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2179 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2180 if (isa<SCEVConstant>(MulOpSCEV))
2182 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2183 if (MulOpSCEV == Ops[AddOp]) {
2184 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2185 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2186 if (Mul->getNumOperands() != 2) {
2187 // If the multiply has more than two operands, we must get the
2189 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2190 Mul->op_begin()+MulOp);
2191 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2192 InnerMul = getMulExpr(MulOps);
2194 const SCEV *One = getOne(Ty);
2195 const SCEV *AddOne = getAddExpr(One, InnerMul);
2196 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2197 if (Ops.size() == 2) return OuterMul;
2199 Ops.erase(Ops.begin()+AddOp);
2200 Ops.erase(Ops.begin()+Idx-1);
2202 Ops.erase(Ops.begin()+Idx);
2203 Ops.erase(Ops.begin()+AddOp-1);
2205 Ops.push_back(OuterMul);
2206 return getAddExpr(Ops);
2209 // Check this multiply against other multiplies being added together.
2210 for (unsigned OtherMulIdx = Idx+1;
2211 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2213 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2214 // If MulOp occurs in OtherMul, we can fold the two multiplies
2216 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2217 OMulOp != e; ++OMulOp)
2218 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2219 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2220 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2221 if (Mul->getNumOperands() != 2) {
2222 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2223 Mul->op_begin()+MulOp);
2224 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2225 InnerMul1 = getMulExpr(MulOps);
2227 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2228 if (OtherMul->getNumOperands() != 2) {
2229 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2230 OtherMul->op_begin()+OMulOp);
2231 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2232 InnerMul2 = getMulExpr(MulOps);
2234 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2235 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2236 if (Ops.size() == 2) return OuterMul;
2237 Ops.erase(Ops.begin()+Idx);
2238 Ops.erase(Ops.begin()+OtherMulIdx-1);
2239 Ops.push_back(OuterMul);
2240 return getAddExpr(Ops);
2246 // If there are any add recurrences in the operands list, see if any other
2247 // added values are loop invariant. If so, we can fold them into the
2249 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2252 // Scan over all recurrences, trying to fold loop invariants into them.
2253 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2254 // Scan all of the other operands to this add and add them to the vector if
2255 // they are loop invariant w.r.t. the recurrence.
2256 SmallVector<const SCEV *, 8> LIOps;
2257 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2258 const Loop *AddRecLoop = AddRec->getLoop();
2259 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2260 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2261 LIOps.push_back(Ops[i]);
2262 Ops.erase(Ops.begin()+i);
2266 // If we found some loop invariants, fold them into the recurrence.
2267 if (!LIOps.empty()) {
2268 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2269 LIOps.push_back(AddRec->getStart());
2271 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2273 AddRecOps[0] = getAddExpr(LIOps);
2275 // Build the new addrec. Propagate the NUW and NSW flags if both the
2276 // outer add and the inner addrec are guaranteed to have no overflow.
2277 // Always propagate NW.
2278 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2279 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2281 // If all of the other operands were loop invariant, we are done.
2282 if (Ops.size() == 1) return NewRec;
2284 // Otherwise, add the folded AddRec by the non-invariant parts.
2285 for (unsigned i = 0;; ++i)
2286 if (Ops[i] == AddRec) {
2290 return getAddExpr(Ops);
2293 // Okay, if there weren't any loop invariants to be folded, check to see if
2294 // there are multiple AddRec's with the same loop induction variable being
2295 // added together. If so, we can fold them.
2296 for (unsigned OtherIdx = Idx+1;
2297 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2299 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2300 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2301 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2303 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2305 if (const auto *OtherAddRec = dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2306 if (OtherAddRec->getLoop() == AddRecLoop) {
2307 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2309 if (i >= AddRecOps.size()) {
2310 AddRecOps.append(OtherAddRec->op_begin()+i,
2311 OtherAddRec->op_end());
2314 AddRecOps[i] = getAddExpr(AddRecOps[i],
2315 OtherAddRec->getOperand(i));
2317 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2319 // Step size has changed, so we cannot guarantee no self-wraparound.
2320 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2321 return getAddExpr(Ops);
2324 // Otherwise couldn't fold anything into this recurrence. Move onto the
2328 // Okay, it looks like we really DO need an add expr. Check to see if we
2329 // already have one, otherwise create a new one.
2330 FoldingSetNodeID ID;
2331 ID.AddInteger(scAddExpr);
2332 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2333 ID.AddPointer(Ops[i]);
2336 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2338 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2339 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2340 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2342 UniqueSCEVs.InsertNode(S, IP);
2344 S->setNoWrapFlags(Flags);
2348 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2350 if (j > 1 && k / j != i) Overflow = true;
2354 /// Compute the result of "n choose k", the binomial coefficient. If an
2355 /// intermediate computation overflows, Overflow will be set and the return will
2356 /// be garbage. Overflow is not cleared on absence of overflow.
2357 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2358 // We use the multiplicative formula:
2359 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2360 // At each iteration, we take the n-th term of the numeral and divide by the
2361 // (k-n)th term of the denominator. This division will always produce an
2362 // integral result, and helps reduce the chance of overflow in the
2363 // intermediate computations. However, we can still overflow even when the
2364 // final result would fit.
2366 if (n == 0 || n == k) return 1;
2367 if (k > n) return 0;
2373 for (uint64_t i = 1; i <= k; ++i) {
2374 r = umul_ov(r, n-(i-1), Overflow);
2380 /// Determine if any of the operands in this SCEV are a constant or if
2381 /// any of the add or multiply expressions in this SCEV contain a constant.
2382 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2383 SmallVector<const SCEV *, 4> Ops;
2384 Ops.push_back(StartExpr);
2385 while (!Ops.empty()) {
2386 const SCEV *CurrentExpr = Ops.pop_back_val();
2387 if (isa<SCEVConstant>(*CurrentExpr))
2390 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2391 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2392 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2398 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2400 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2401 SCEV::NoWrapFlags Flags) {
2402 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2403 "only nuw or nsw allowed");
2404 assert(!Ops.empty() && "Cannot get empty mul!");
2405 if (Ops.size() == 1) return Ops[0];
2407 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2408 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2409 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2410 "SCEVMulExpr operand types don't match!");
2413 // Sort by complexity, this groups all similar expression types together.
2414 GroupByComplexity(Ops, &LI);
2416 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2418 // If there are any constants, fold them together.
2420 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2422 // C1*(C2+V) -> C1*C2 + C1*V
2423 if (Ops.size() == 2)
2424 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2425 // If any of Add's ops are Adds or Muls with a constant,
2426 // apply this transformation as well.
2427 if (Add->getNumOperands() == 2)
2428 if (containsConstantSomewhere(Add))
2429 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2430 getMulExpr(LHSC, Add->getOperand(1)));
2433 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2434 // We found two constants, fold them together!
2435 ConstantInt *Fold = ConstantInt::get(getContext(),
2436 LHSC->getValue()->getValue() *
2437 RHSC->getValue()->getValue());
2438 Ops[0] = getConstant(Fold);
2439 Ops.erase(Ops.begin()+1); // Erase the folded element
2440 if (Ops.size() == 1) return Ops[0];
2441 LHSC = cast<SCEVConstant>(Ops[0]);
2444 // If we are left with a constant one being multiplied, strip it off.
2445 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2446 Ops.erase(Ops.begin());
2448 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2449 // If we have a multiply of zero, it will always be zero.
2451 } else if (Ops[0]->isAllOnesValue()) {
2452 // If we have a mul by -1 of an add, try distributing the -1 among the
2454 if (Ops.size() == 2) {
2455 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2456 SmallVector<const SCEV *, 4> NewOps;
2457 bool AnyFolded = false;
2458 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2459 E = Add->op_end(); I != E; ++I) {
2460 const SCEV *Mul = getMulExpr(Ops[0], *I);
2461 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2462 NewOps.push_back(Mul);
2465 return getAddExpr(NewOps);
2466 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2467 // Negation preserves a recurrence's no self-wrap property.
2468 SmallVector<const SCEV *, 4> Operands;
2469 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2470 E = AddRec->op_end(); I != E; ++I) {
2471 Operands.push_back(getMulExpr(Ops[0], *I));
2473 return getAddRecExpr(Operands, AddRec->getLoop(),
2474 AddRec->getNoWrapFlags(SCEV::FlagNW));
2479 if (Ops.size() == 1)
2483 // Skip over the add expression until we get to a multiply.
2484 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2487 // If there are mul operands inline them all into this expression.
2488 if (Idx < Ops.size()) {
2489 bool DeletedMul = false;
2490 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2491 // If we have an mul, expand the mul operands onto the end of the operands
2493 Ops.erase(Ops.begin()+Idx);
2494 Ops.append(Mul->op_begin(), Mul->op_end());
2498 // If we deleted at least one mul, we added operands to the end of the list,
2499 // and they are not necessarily sorted. Recurse to resort and resimplify
2500 // any operands we just acquired.
2502 return getMulExpr(Ops);
2505 // If there are any add recurrences in the operands list, see if any other
2506 // added values are loop invariant. If so, we can fold them into the
2508 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2511 // Scan over all recurrences, trying to fold loop invariants into them.
2512 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2513 // Scan all of the other operands to this mul and add them to the vector if
2514 // they are loop invariant w.r.t. the recurrence.
2515 SmallVector<const SCEV *, 8> LIOps;
2516 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2517 const Loop *AddRecLoop = AddRec->getLoop();
2518 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2519 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2520 LIOps.push_back(Ops[i]);
2521 Ops.erase(Ops.begin()+i);
2525 // If we found some loop invariants, fold them into the recurrence.
2526 if (!LIOps.empty()) {
2527 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2528 SmallVector<const SCEV *, 4> NewOps;
2529 NewOps.reserve(AddRec->getNumOperands());
2530 const SCEV *Scale = getMulExpr(LIOps);
2531 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2532 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2534 // Build the new addrec. Propagate the NUW and NSW flags if both the
2535 // outer mul and the inner addrec are guaranteed to have no overflow.
2537 // No self-wrap cannot be guaranteed after changing the step size, but
2538 // will be inferred if either NUW or NSW is true.
2539 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2540 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2542 // If all of the other operands were loop invariant, we are done.
2543 if (Ops.size() == 1) return NewRec;
2545 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2546 for (unsigned i = 0;; ++i)
2547 if (Ops[i] == AddRec) {
2551 return getMulExpr(Ops);
2554 // Okay, if there weren't any loop invariants to be folded, check to see if
2555 // there are multiple AddRec's with the same loop induction variable being
2556 // multiplied together. If so, we can fold them.
2558 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2559 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2560 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2561 // ]]],+,...up to x=2n}.
2562 // Note that the arguments to choose() are always integers with values
2563 // known at compile time, never SCEV objects.
2565 // The implementation avoids pointless extra computations when the two
2566 // addrec's are of different length (mathematically, it's equivalent to
2567 // an infinite stream of zeros on the right).
2568 bool OpsModified = false;
2569 for (unsigned OtherIdx = Idx+1;
2570 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2572 const SCEVAddRecExpr *OtherAddRec =
2573 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2574 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2577 bool Overflow = false;
2578 Type *Ty = AddRec->getType();
2579 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2580 SmallVector<const SCEV*, 7> AddRecOps;
2581 for (int x = 0, xe = AddRec->getNumOperands() +
2582 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2583 const SCEV *Term = getZero(Ty);
2584 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2585 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2586 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2587 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2588 z < ze && !Overflow; ++z) {
2589 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2591 if (LargerThan64Bits)
2592 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2594 Coeff = Coeff1*Coeff2;
2595 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2596 const SCEV *Term1 = AddRec->getOperand(y-z);
2597 const SCEV *Term2 = OtherAddRec->getOperand(z);
2598 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2601 AddRecOps.push_back(Term);
2604 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2606 if (Ops.size() == 2) return NewAddRec;
2607 Ops[Idx] = NewAddRec;
2608 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2610 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2616 return getMulExpr(Ops);
2618 // Otherwise couldn't fold anything into this recurrence. Move onto the
2622 // Okay, it looks like we really DO need an mul expr. Check to see if we
2623 // already have one, otherwise create a new one.
2624 FoldingSetNodeID ID;
2625 ID.AddInteger(scMulExpr);
2626 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2627 ID.AddPointer(Ops[i]);
2630 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2632 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2633 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2634 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2636 UniqueSCEVs.InsertNode(S, IP);
2638 S->setNoWrapFlags(Flags);
2642 /// getUDivExpr - Get a canonical unsigned division expression, or something
2643 /// simpler if possible.
2644 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2646 assert(getEffectiveSCEVType(LHS->getType()) ==
2647 getEffectiveSCEVType(RHS->getType()) &&
2648 "SCEVUDivExpr operand types don't match!");
2650 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2651 if (RHSC->getValue()->equalsInt(1))
2652 return LHS; // X udiv 1 --> x
2653 // If the denominator is zero, the result of the udiv is undefined. Don't
2654 // try to analyze it, because the resolution chosen here may differ from
2655 // the resolution chosen in other parts of the compiler.
2656 if (!RHSC->getValue()->isZero()) {
2657 // Determine if the division can be folded into the operands of
2659 // TODO: Generalize this to non-constants by using known-bits information.
2660 Type *Ty = LHS->getType();
2661 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2662 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2663 // For non-power-of-two values, effectively round the value up to the
2664 // nearest power of two.
2665 if (!RHSC->getValue()->getValue().isPowerOf2())
2667 IntegerType *ExtTy =
2668 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2669 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2670 if (const SCEVConstant *Step =
2671 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2672 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2673 const APInt &StepInt = Step->getValue()->getValue();
2674 const APInt &DivInt = RHSC->getValue()->getValue();
2675 if (!StepInt.urem(DivInt) &&
2676 getZeroExtendExpr(AR, ExtTy) ==
2677 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2678 getZeroExtendExpr(Step, ExtTy),
2679 AR->getLoop(), SCEV::FlagAnyWrap)) {
2680 SmallVector<const SCEV *, 4> Operands;
2681 for (const SCEV *Op : AR->operands())
2682 Operands.push_back(getUDivExpr(Op, RHS));
2683 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
2685 /// Get a canonical UDivExpr for a recurrence.
2686 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2687 // We can currently only fold X%N if X is constant.
2688 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2689 if (StartC && !DivInt.urem(StepInt) &&
2690 getZeroExtendExpr(AR, ExtTy) ==
2691 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2692 getZeroExtendExpr(Step, ExtTy),
2693 AR->getLoop(), SCEV::FlagAnyWrap)) {
2694 const APInt &StartInt = StartC->getValue()->getValue();
2695 const APInt &StartRem = StartInt.urem(StepInt);
2697 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2698 AR->getLoop(), SCEV::FlagNW);
2701 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2702 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2703 SmallVector<const SCEV *, 4> Operands;
2704 for (const SCEV *Op : M->operands())
2705 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2706 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2707 // Find an operand that's safely divisible.
2708 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2709 const SCEV *Op = M->getOperand(i);
2710 const SCEV *Div = getUDivExpr(Op, RHSC);
2711 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2712 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2715 return getMulExpr(Operands);
2719 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2720 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2721 SmallVector<const SCEV *, 4> Operands;
2722 for (const SCEV *Op : A->operands())
2723 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2724 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2726 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2727 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2728 if (isa<SCEVUDivExpr>(Op) ||
2729 getMulExpr(Op, RHS) != A->getOperand(i))
2731 Operands.push_back(Op);
2733 if (Operands.size() == A->getNumOperands())
2734 return getAddExpr(Operands);
2738 // Fold if both operands are constant.
2739 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2740 Constant *LHSCV = LHSC->getValue();
2741 Constant *RHSCV = RHSC->getValue();
2742 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2748 FoldingSetNodeID ID;
2749 ID.AddInteger(scUDivExpr);
2753 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2754 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2756 UniqueSCEVs.InsertNode(S, IP);
2760 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2761 APInt A = C1->getValue()->getValue().abs();
2762 APInt B = C2->getValue()->getValue().abs();
2763 uint32_t ABW = A.getBitWidth();
2764 uint32_t BBW = B.getBitWidth();
2771 return APIntOps::GreatestCommonDivisor(A, B);
2774 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2775 /// something simpler if possible. There is no representation for an exact udiv
2776 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2777 /// We can't do this when it's not exact because the udiv may be clearing bits.
2778 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2780 // TODO: we could try to find factors in all sorts of things, but for now we
2781 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2782 // end of this file for inspiration.
2784 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2786 return getUDivExpr(LHS, RHS);
2788 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2789 // If the mulexpr multiplies by a constant, then that constant must be the
2790 // first element of the mulexpr.
2791 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2792 if (LHSCst == RHSCst) {
2793 SmallVector<const SCEV *, 2> Operands;
2794 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2795 return getMulExpr(Operands);
2798 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2799 // that there's a factor provided by one of the other terms. We need to
2801 APInt Factor = gcd(LHSCst, RHSCst);
2802 if (!Factor.isIntN(1)) {
2803 LHSCst = cast<SCEVConstant>(
2804 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2805 RHSCst = cast<SCEVConstant>(
2806 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2807 SmallVector<const SCEV *, 2> Operands;
2808 Operands.push_back(LHSCst);
2809 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2810 LHS = getMulExpr(Operands);
2812 Mul = dyn_cast<SCEVMulExpr>(LHS);
2814 return getUDivExactExpr(LHS, RHS);
2819 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2820 if (Mul->getOperand(i) == RHS) {
2821 SmallVector<const SCEV *, 2> Operands;
2822 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2823 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2824 return getMulExpr(Operands);
2828 return getUDivExpr(LHS, RHS);
2831 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2832 /// Simplify the expression as much as possible.
2833 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2835 SCEV::NoWrapFlags Flags) {
2836 SmallVector<const SCEV *, 4> Operands;
2837 Operands.push_back(Start);
2838 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2839 if (StepChrec->getLoop() == L) {
2840 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2841 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2844 Operands.push_back(Step);
2845 return getAddRecExpr(Operands, L, Flags);
2848 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2849 /// Simplify the expression as much as possible.
2851 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2852 const Loop *L, SCEV::NoWrapFlags Flags) {
2853 if (Operands.size() == 1) return Operands[0];
2855 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2856 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2857 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2858 "SCEVAddRecExpr operand types don't match!");
2859 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2860 assert(isLoopInvariant(Operands[i], L) &&
2861 "SCEVAddRecExpr operand is not loop-invariant!");
2864 if (Operands.back()->isZero()) {
2865 Operands.pop_back();
2866 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2869 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2870 // use that information to infer NUW and NSW flags. However, computing a
2871 // BE count requires calling getAddRecExpr, so we may not yet have a
2872 // meaningful BE count at this point (and if we don't, we'd be stuck
2873 // with a SCEVCouldNotCompute as the cached BE count).
2875 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2877 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2878 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2879 const Loop *NestedLoop = NestedAR->getLoop();
2880 if (L->contains(NestedLoop)
2881 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2882 : (!NestedLoop->contains(L) &&
2883 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2884 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2885 NestedAR->op_end());
2886 Operands[0] = NestedAR->getStart();
2887 // AddRecs require their operands be loop-invariant with respect to their
2888 // loops. Don't perform this transformation if it would break this
2890 bool AllInvariant = all_of(
2891 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
2894 // Create a recurrence for the outer loop with the same step size.
2896 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2897 // inner recurrence has the same property.
2898 SCEV::NoWrapFlags OuterFlags =
2899 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2901 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2902 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
2903 return isLoopInvariant(Op, NestedLoop);
2907 // Ok, both add recurrences are valid after the transformation.
2909 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2910 // the outer recurrence has the same property.
2911 SCEV::NoWrapFlags InnerFlags =
2912 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2913 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2916 // Reset Operands to its original state.
2917 Operands[0] = NestedAR;
2921 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2922 // already have one, otherwise create a new one.
2923 FoldingSetNodeID ID;
2924 ID.AddInteger(scAddRecExpr);
2925 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2926 ID.AddPointer(Operands[i]);
2930 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2932 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2933 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2934 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2935 O, Operands.size(), L);
2936 UniqueSCEVs.InsertNode(S, IP);
2938 S->setNoWrapFlags(Flags);
2943 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2944 const SmallVectorImpl<const SCEV *> &IndexExprs,
2946 // getSCEV(Base)->getType() has the same address space as Base->getType()
2947 // because SCEV::getType() preserves the address space.
2948 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2949 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2950 // instruction to its SCEV, because the Instruction may be guarded by control
2951 // flow and the no-overflow bits may not be valid for the expression in any
2952 // context. This can be fixed similarly to how these flags are handled for
2954 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2956 const SCEV *TotalOffset = getZero(IntPtrTy);
2957 // The address space is unimportant. The first thing we do on CurTy is getting
2958 // its element type.
2959 Type *CurTy = PointerType::getUnqual(PointeeType);
2960 for (const SCEV *IndexExpr : IndexExprs) {
2961 // Compute the (potentially symbolic) offset in bytes for this index.
2962 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2963 // For a struct, add the member offset.
2964 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2965 unsigned FieldNo = Index->getZExtValue();
2966 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2968 // Add the field offset to the running total offset.
2969 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2971 // Update CurTy to the type of the field at Index.
2972 CurTy = STy->getTypeAtIndex(Index);
2974 // Update CurTy to its element type.
2975 CurTy = cast<SequentialType>(CurTy)->getElementType();
2976 // For an array, add the element offset, explicitly scaled.
2977 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2978 // Getelementptr indices are signed.
2979 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2981 // Multiply the index by the element size to compute the element offset.
2982 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2984 // Add the element offset to the running total offset.
2985 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2989 // Add the total offset from all the GEP indices to the base.
2990 return getAddExpr(BaseExpr, TotalOffset, Wrap);
2993 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2995 SmallVector<const SCEV *, 2> Ops;
2998 return getSMaxExpr(Ops);
3002 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3003 assert(!Ops.empty() && "Cannot get empty smax!");
3004 if (Ops.size() == 1) return Ops[0];
3006 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3007 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3008 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3009 "SCEVSMaxExpr operand types don't match!");
3012 // Sort by complexity, this groups all similar expression types together.
3013 GroupByComplexity(Ops, &LI);
3015 // If there are any constants, fold them together.
3017 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3019 assert(Idx < Ops.size());
3020 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3021 // We found two constants, fold them together!
3022 ConstantInt *Fold = ConstantInt::get(getContext(),
3023 APIntOps::smax(LHSC->getValue()->getValue(),
3024 RHSC->getValue()->getValue()));
3025 Ops[0] = getConstant(Fold);
3026 Ops.erase(Ops.begin()+1); // Erase the folded element
3027 if (Ops.size() == 1) return Ops[0];
3028 LHSC = cast<SCEVConstant>(Ops[0]);
3031 // If we are left with a constant minimum-int, strip it off.
3032 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3033 Ops.erase(Ops.begin());
3035 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3036 // If we have an smax with a constant maximum-int, it will always be
3041 if (Ops.size() == 1) return Ops[0];
3044 // Find the first SMax
3045 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3048 // Check to see if one of the operands is an SMax. If so, expand its operands
3049 // onto our operand list, and recurse to simplify.
3050 if (Idx < Ops.size()) {
3051 bool DeletedSMax = false;
3052 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3053 Ops.erase(Ops.begin()+Idx);
3054 Ops.append(SMax->op_begin(), SMax->op_end());
3059 return getSMaxExpr(Ops);
3062 // Okay, check to see if the same value occurs in the operand list twice. If
3063 // so, delete one. Since we sorted the list, these values are required to
3065 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3066 // X smax Y smax Y --> X smax Y
3067 // X smax Y --> X, if X is always greater than Y
3068 if (Ops[i] == Ops[i+1] ||
3069 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3070 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3072 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3073 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3077 if (Ops.size() == 1) return Ops[0];
3079 assert(!Ops.empty() && "Reduced smax down to nothing!");
3081 // Okay, it looks like we really DO need an smax expr. Check to see if we
3082 // already have one, otherwise create a new one.
3083 FoldingSetNodeID ID;
3084 ID.AddInteger(scSMaxExpr);
3085 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3086 ID.AddPointer(Ops[i]);
3088 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3089 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3090 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3091 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3093 UniqueSCEVs.InsertNode(S, IP);
3097 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3099 SmallVector<const SCEV *, 2> Ops;
3102 return getUMaxExpr(Ops);
3106 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3107 assert(!Ops.empty() && "Cannot get empty umax!");
3108 if (Ops.size() == 1) return Ops[0];
3110 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3111 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3112 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3113 "SCEVUMaxExpr operand types don't match!");
3116 // Sort by complexity, this groups all similar expression types together.
3117 GroupByComplexity(Ops, &LI);
3119 // If there are any constants, fold them together.
3121 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3123 assert(Idx < Ops.size());
3124 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3125 // We found two constants, fold them together!
3126 ConstantInt *Fold = ConstantInt::get(getContext(),
3127 APIntOps::umax(LHSC->getValue()->getValue(),
3128 RHSC->getValue()->getValue()));
3129 Ops[0] = getConstant(Fold);
3130 Ops.erase(Ops.begin()+1); // Erase the folded element
3131 if (Ops.size() == 1) return Ops[0];
3132 LHSC = cast<SCEVConstant>(Ops[0]);
3135 // If we are left with a constant minimum-int, strip it off.
3136 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3137 Ops.erase(Ops.begin());
3139 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3140 // If we have an umax with a constant maximum-int, it will always be
3145 if (Ops.size() == 1) return Ops[0];
3148 // Find the first UMax
3149 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3152 // Check to see if one of the operands is a UMax. If so, expand its operands
3153 // onto our operand list, and recurse to simplify.
3154 if (Idx < Ops.size()) {
3155 bool DeletedUMax = false;
3156 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3157 Ops.erase(Ops.begin()+Idx);
3158 Ops.append(UMax->op_begin(), UMax->op_end());
3163 return getUMaxExpr(Ops);
3166 // Okay, check to see if the same value occurs in the operand list twice. If
3167 // so, delete one. Since we sorted the list, these values are required to
3169 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3170 // X umax Y umax Y --> X umax Y
3171 // X umax Y --> X, if X is always greater than Y
3172 if (Ops[i] == Ops[i+1] ||
3173 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3174 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3176 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3177 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3181 if (Ops.size() == 1) return Ops[0];
3183 assert(!Ops.empty() && "Reduced umax down to nothing!");
3185 // Okay, it looks like we really DO need a umax expr. Check to see if we
3186 // already have one, otherwise create a new one.
3187 FoldingSetNodeID ID;
3188 ID.AddInteger(scUMaxExpr);
3189 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3190 ID.AddPointer(Ops[i]);
3192 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3193 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3194 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3195 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3197 UniqueSCEVs.InsertNode(S, IP);
3201 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3203 // ~smax(~x, ~y) == smin(x, y).
3204 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3207 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3209 // ~umax(~x, ~y) == umin(x, y)
3210 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3213 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3214 // We can bypass creating a target-independent
3215 // constant expression and then folding it back into a ConstantInt.
3216 // This is just a compile-time optimization.
3217 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3220 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3223 // We can bypass creating a target-independent
3224 // constant expression and then folding it back into a ConstantInt.
3225 // This is just a compile-time optimization.
3227 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3230 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3231 // Don't attempt to do anything other than create a SCEVUnknown object
3232 // here. createSCEV only calls getUnknown after checking for all other
3233 // interesting possibilities, and any other code that calls getUnknown
3234 // is doing so in order to hide a value from SCEV canonicalization.
3236 FoldingSetNodeID ID;
3237 ID.AddInteger(scUnknown);
3240 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3241 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3242 "Stale SCEVUnknown in uniquing map!");
3245 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3247 FirstUnknown = cast<SCEVUnknown>(S);
3248 UniqueSCEVs.InsertNode(S, IP);
3252 //===----------------------------------------------------------------------===//
3253 // Basic SCEV Analysis and PHI Idiom Recognition Code
3256 /// isSCEVable - Test if values of the given type are analyzable within
3257 /// the SCEV framework. This primarily includes integer types, and it
3258 /// can optionally include pointer types if the ScalarEvolution class
3259 /// has access to target-specific information.
3260 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3261 // Integers and pointers are always SCEVable.
3262 return Ty->isIntegerTy() || Ty->isPointerTy();
3265 /// getTypeSizeInBits - Return the size in bits of the specified type,
3266 /// for which isSCEVable must return true.
3267 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3268 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3269 return getDataLayout().getTypeSizeInBits(Ty);
3272 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3273 /// the given type and which represents how SCEV will treat the given
3274 /// type, for which isSCEVable must return true. For pointer types,
3275 /// this is the pointer-sized integer type.
3276 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3277 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3279 if (Ty->isIntegerTy())
3282 // The only other support type is pointer.
3283 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3284 return getDataLayout().getIntPtrType(Ty);
3287 const SCEV *ScalarEvolution::getCouldNotCompute() {
3288 return CouldNotCompute.get();
3292 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3293 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3294 // is set iff if find such SCEVUnknown.
3296 struct FindInvalidSCEVUnknown {
3298 FindInvalidSCEVUnknown() { FindOne = false; }
3299 bool follow(const SCEV *S) {
3300 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3304 if (!cast<SCEVUnknown>(S)->getValue())
3311 bool isDone() const { return FindOne; }
3315 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3316 FindInvalidSCEVUnknown F;
3317 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3323 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3324 /// expression and create a new one.
3325 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3326 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3328 const SCEV *S = getExistingSCEV(V);
3331 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3336 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3337 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3339 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3340 if (I != ValueExprMap.end()) {
3341 const SCEV *S = I->second;
3342 if (checkValidity(S))
3344 ValueExprMap.erase(I);
3349 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3351 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3352 SCEV::NoWrapFlags Flags) {
3353 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3355 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3357 Type *Ty = V->getType();
3358 Ty = getEffectiveSCEVType(Ty);
3360 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3363 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3364 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3365 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3367 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3369 Type *Ty = V->getType();
3370 Ty = getEffectiveSCEVType(Ty);
3371 const SCEV *AllOnes =
3372 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3373 return getMinusSCEV(AllOnes, V);
3376 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3377 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3378 SCEV::NoWrapFlags Flags) {
3379 // Fast path: X - X --> 0.
3381 return getZero(LHS->getType());
3383 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3384 // makes it so that we cannot make much use of NUW.
3385 auto AddFlags = SCEV::FlagAnyWrap;
3386 const bool RHSIsNotMinSigned =
3387 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3388 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3389 // Let M be the minimum representable signed value. Then (-1)*RHS
3390 // signed-wraps if and only if RHS is M. That can happen even for
3391 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3392 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3393 // (-1)*RHS, we need to prove that RHS != M.
3395 // If LHS is non-negative and we know that LHS - RHS does not
3396 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3397 // either by proving that RHS > M or that LHS >= 0.
3398 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3399 AddFlags = SCEV::FlagNSW;
3403 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3404 // RHS is NSW and LHS >= 0.
3406 // The difficulty here is that the NSW flag may have been proven
3407 // relative to a loop that is to be found in a recurrence in LHS and
3408 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3409 // larger scope than intended.
3410 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3412 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3415 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3416 /// input value to the specified type. If the type must be extended, it is zero
3419 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3420 Type *SrcTy = V->getType();
3421 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3422 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3423 "Cannot truncate or zero extend with non-integer arguments!");
3424 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3425 return V; // No conversion
3426 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3427 return getTruncateExpr(V, Ty);
3428 return getZeroExtendExpr(V, Ty);
3431 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3432 /// input value to the specified type. If the type must be extended, it is sign
3435 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3437 Type *SrcTy = V->getType();
3438 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3439 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3440 "Cannot truncate or zero extend with non-integer arguments!");
3441 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3442 return V; // No conversion
3443 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3444 return getTruncateExpr(V, Ty);
3445 return getSignExtendExpr(V, Ty);
3448 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3449 /// input value to the specified type. If the type must be extended, it is zero
3450 /// extended. The conversion must not be narrowing.
3452 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3453 Type *SrcTy = V->getType();
3454 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3455 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3456 "Cannot noop or zero extend with non-integer arguments!");
3457 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3458 "getNoopOrZeroExtend cannot truncate!");
3459 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3460 return V; // No conversion
3461 return getZeroExtendExpr(V, Ty);
3464 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3465 /// input value to the specified type. If the type must be extended, it is sign
3466 /// extended. The conversion must not be narrowing.
3468 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3469 Type *SrcTy = V->getType();
3470 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3471 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3472 "Cannot noop or sign extend with non-integer arguments!");
3473 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3474 "getNoopOrSignExtend cannot truncate!");
3475 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3476 return V; // No conversion
3477 return getSignExtendExpr(V, Ty);
3480 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3481 /// the input value to the specified type. If the type must be extended,
3482 /// it is extended with unspecified bits. The conversion must not be
3485 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3486 Type *SrcTy = V->getType();
3487 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3488 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3489 "Cannot noop or any extend with non-integer arguments!");
3490 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3491 "getNoopOrAnyExtend cannot truncate!");
3492 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3493 return V; // No conversion
3494 return getAnyExtendExpr(V, Ty);
3497 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3498 /// input value to the specified type. The conversion must not be widening.
3500 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3501 Type *SrcTy = V->getType();
3502 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3503 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3504 "Cannot truncate or noop with non-integer arguments!");
3505 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3506 "getTruncateOrNoop cannot extend!");
3507 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3508 return V; // No conversion
3509 return getTruncateExpr(V, Ty);
3512 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3513 /// the types using zero-extension, and then perform a umax operation
3515 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3517 const SCEV *PromotedLHS = LHS;
3518 const SCEV *PromotedRHS = RHS;
3520 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3521 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3523 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3525 return getUMaxExpr(PromotedLHS, PromotedRHS);
3528 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3529 /// the types using zero-extension, and then perform a umin operation
3531 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3533 const SCEV *PromotedLHS = LHS;
3534 const SCEV *PromotedRHS = RHS;
3536 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3537 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3539 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3541 return getUMinExpr(PromotedLHS, PromotedRHS);
3544 /// getPointerBase - Transitively follow the chain of pointer-type operands
3545 /// until reaching a SCEV that does not have a single pointer operand. This
3546 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3547 /// but corner cases do exist.
3548 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3549 // A pointer operand may evaluate to a nonpointer expression, such as null.
3550 if (!V->getType()->isPointerTy())
3553 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3554 return getPointerBase(Cast->getOperand());
3555 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3556 const SCEV *PtrOp = nullptr;
3557 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3559 if ((*I)->getType()->isPointerTy()) {
3560 // Cannot find the base of an expression with multiple pointer operands.
3568 return getPointerBase(PtrOp);
3573 /// PushDefUseChildren - Push users of the given Instruction
3574 /// onto the given Worklist.
3576 PushDefUseChildren(Instruction *I,
3577 SmallVectorImpl<Instruction *> &Worklist) {
3578 // Push the def-use children onto the Worklist stack.
3579 for (User *U : I->users())
3580 Worklist.push_back(cast<Instruction>(U));
3583 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3584 /// instructions that depend on the given instruction and removes them from
3585 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3588 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3589 SmallVector<Instruction *, 16> Worklist;
3590 PushDefUseChildren(PN, Worklist);
3592 SmallPtrSet<Instruction *, 8> Visited;
3594 while (!Worklist.empty()) {
3595 Instruction *I = Worklist.pop_back_val();
3596 if (!Visited.insert(I).second)
3599 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
3600 if (It != ValueExprMap.end()) {
3601 const SCEV *Old = It->second;
3603 // Short-circuit the def-use traversal if the symbolic name
3604 // ceases to appear in expressions.
3605 if (Old != SymName && !hasOperand(Old, SymName))
3608 // SCEVUnknown for a PHI either means that it has an unrecognized
3609 // structure, it's a PHI that's in the progress of being computed
3610 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3611 // additional loop trip count information isn't going to change anything.
3612 // In the second case, createNodeForPHI will perform the necessary
3613 // updates on its own when it gets to that point. In the third, we do
3614 // want to forget the SCEVUnknown.
3615 if (!isa<PHINode>(I) ||
3616 !isa<SCEVUnknown>(Old) ||
3617 (I != PN && Old == SymName)) {
3618 forgetMemoizedResults(Old);
3619 ValueExprMap.erase(It);
3623 PushDefUseChildren(I, Worklist);
3628 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
3630 static const SCEV *rewrite(const SCEV *Scev, const Loop *L,
3631 ScalarEvolution &SE) {
3632 SCEVInitRewriter Rewriter(L, SE);
3633 const SCEV *Result = Rewriter.visit(Scev);
3634 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3637 SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
3638 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3640 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3641 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3646 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3647 // Only allow AddRecExprs for this loop.
3648 if (Expr->getLoop() == L)
3649 return Expr->getStart();
3654 bool isValid() { return Valid; }
3661 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
3663 static const SCEV *rewrite(const SCEV *Scev, const Loop *L,
3664 ScalarEvolution &SE) {
3665 SCEVShiftRewriter Rewriter(L, SE);
3666 const SCEV *Result = Rewriter.visit(Scev);
3667 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3670 SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
3671 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3673 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3674 // Only allow AddRecExprs for this loop.
3675 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3680 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3681 if (Expr->getLoop() == L && Expr->isAffine())
3682 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
3686 bool isValid() { return Valid; }
3692 } // end anonymous namespace
3694 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
3695 const Loop *L = LI.getLoopFor(PN->getParent());
3696 if (!L || L->getHeader() != PN->getParent())
3699 // The loop may have multiple entrances or multiple exits; we can analyze
3700 // this phi as an addrec if it has a unique entry value and a unique
3702 Value *BEValueV = nullptr, *StartValueV = nullptr;
3703 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3704 Value *V = PN->getIncomingValue(i);
3705 if (L->contains(PN->getIncomingBlock(i))) {
3708 } else if (BEValueV != V) {
3712 } else if (!StartValueV) {
3714 } else if (StartValueV != V) {
3715 StartValueV = nullptr;
3719 if (BEValueV && StartValueV) {
3720 // While we are analyzing this PHI node, handle its value symbolically.
3721 const SCEV *SymbolicName = getUnknown(PN);
3722 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3723 "PHI node already processed?");
3724 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3726 // Using this symbolic name for the PHI, analyze the value coming around
3728 const SCEV *BEValue = getSCEV(BEValueV);
3730 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3731 // has a special value for the first iteration of the loop.
3733 // If the value coming around the backedge is an add with the symbolic
3734 // value we just inserted, then we found a simple induction variable!
3735 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3736 // If there is a single occurrence of the symbolic value, replace it
3737 // with a recurrence.
3738 unsigned FoundIndex = Add->getNumOperands();
3739 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3740 if (Add->getOperand(i) == SymbolicName)
3741 if (FoundIndex == e) {
3746 if (FoundIndex != Add->getNumOperands()) {
3747 // Create an add with everything but the specified operand.
3748 SmallVector<const SCEV *, 8> Ops;
3749 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3750 if (i != FoundIndex)
3751 Ops.push_back(Add->getOperand(i));
3752 const SCEV *Accum = getAddExpr(Ops);
3754 // This is not a valid addrec if the step amount is varying each
3755 // loop iteration, but is not itself an addrec in this loop.
3756 if (isLoopInvariant(Accum, L) ||
3757 (isa<SCEVAddRecExpr>(Accum) &&
3758 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3759 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3761 // If the increment doesn't overflow, then neither the addrec nor
3762 // the post-increment will overflow.
3763 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3764 if (OBO->getOperand(0) == PN) {
3765 if (OBO->hasNoUnsignedWrap())
3766 Flags = setFlags(Flags, SCEV::FlagNUW);
3767 if (OBO->hasNoSignedWrap())
3768 Flags = setFlags(Flags, SCEV::FlagNSW);
3770 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3771 // If the increment is an inbounds GEP, then we know the address
3772 // space cannot be wrapped around. We cannot make any guarantee
3773 // about signed or unsigned overflow because pointers are
3774 // unsigned but we may have a negative index from the base
3775 // pointer. We can guarantee that no unsigned wrap occurs if the
3776 // indices form a positive value.
3777 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3778 Flags = setFlags(Flags, SCEV::FlagNW);
3780 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3781 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3782 Flags = setFlags(Flags, SCEV::FlagNUW);
3785 // We cannot transfer nuw and nsw flags from subtraction
3786 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3790 const SCEV *StartVal = getSCEV(StartValueV);
3791 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3793 // Since the no-wrap flags are on the increment, they apply to the
3794 // post-incremented value as well.
3795 if (isLoopInvariant(Accum, L))
3796 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
3798 // Okay, for the entire analysis of this edge we assumed the PHI
3799 // to be symbolic. We now need to go back and purge all of the
3800 // entries for the scalars that use the symbolic expression.
3801 ForgetSymbolicName(PN, SymbolicName);
3802 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3807 // Otherwise, this could be a loop like this:
3808 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3809 // In this case, j = {1,+,1} and BEValue is j.
3810 // Because the other in-value of i (0) fits the evolution of BEValue
3811 // i really is an addrec evolution.
3813 // We can generalize this saying that i is the shifted value of BEValue
3814 // by one iteration:
3815 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
3816 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
3817 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
3818 if (Shifted != getCouldNotCompute() &&
3819 Start != getCouldNotCompute()) {
3820 const SCEV *StartVal = getSCEV(StartValueV);
3821 if (Start == StartVal) {
3822 // Okay, for the entire analysis of this edge we assumed the PHI
3823 // to be symbolic. We now need to go back and purge all of the
3824 // entries for the scalars that use the symbolic expression.
3825 ForgetSymbolicName(PN, SymbolicName);
3826 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
3836 // Checks if the SCEV S is available at BB. S is considered available at BB
3837 // if S can be materialized at BB without introducing a fault.
3838 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
3840 struct CheckAvailable {
3841 bool TraversalDone = false;
3842 bool Available = true;
3844 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
3845 BasicBlock *BB = nullptr;
3848 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
3849 : L(L), BB(BB), DT(DT) {}
3851 bool setUnavailable() {
3852 TraversalDone = true;
3857 bool follow(const SCEV *S) {
3858 switch (S->getSCEVType()) {
3859 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
3860 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
3861 // These expressions are available if their operand(s) is/are.
3864 case scAddRecExpr: {
3865 // We allow add recurrences that are on the loop BB is in, or some
3866 // outer loop. This guarantees availability because the value of the
3867 // add recurrence at BB is simply the "current" value of the induction
3868 // variable. We can relax this in the future; for instance an add
3869 // recurrence on a sibling dominating loop is also available at BB.
3870 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
3871 if (L && (ARLoop == L || ARLoop->contains(L)))
3874 return setUnavailable();
3878 // For SCEVUnknown, we check for simple dominance.
3879 const auto *SU = cast<SCEVUnknown>(S);
3880 Value *V = SU->getValue();
3882 if (isa<Argument>(V))
3885 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
3888 return setUnavailable();
3892 case scCouldNotCompute:
3893 // We do not try to smart about these at all.
3894 return setUnavailable();
3896 llvm_unreachable("switch should be fully covered!");
3899 bool isDone() { return TraversalDone; }
3902 CheckAvailable CA(L, BB, DT);
3903 SCEVTraversal<CheckAvailable> ST(CA);
3906 return CA.Available;
3909 // Try to match a control flow sequence that branches out at BI and merges back
3910 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
3912 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
3913 Value *&C, Value *&LHS, Value *&RHS) {
3914 C = BI->getCondition();
3916 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
3917 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
3919 if (!LeftEdge.isSingleEdge())
3922 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
3924 Use &LeftUse = Merge->getOperandUse(0);
3925 Use &RightUse = Merge->getOperandUse(1);
3927 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
3933 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
3942 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
3943 if (PN->getNumIncomingValues() == 2) {
3944 const Loop *L = LI.getLoopFor(PN->getParent());
3946 // We don't want to break LCSSA, even in a SCEV expression tree.
3947 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
3948 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
3953 // br %cond, label %left, label %right
3959 // V = phi [ %x, %left ], [ %y, %right ]
3961 // as "select %cond, %x, %y"
3963 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
3964 assert(IDom && "At least the entry block should dominate PN");
3966 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
3967 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
3969 if (BI && BI->isConditional() &&
3970 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
3971 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
3972 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
3973 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
3979 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3980 if (const SCEV *S = createAddRecFromPHI(PN))
3983 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
3986 // If the PHI has a single incoming value, follow that value, unless the
3987 // PHI's incoming blocks are in a different loop, in which case doing so
3988 // risks breaking LCSSA form. Instcombine would normally zap these, but
3989 // it doesn't have DominatorTree information, so it may miss cases.
3990 if (Value *V = SimplifyInstruction(PN, getDataLayout(), &TLI, &DT, &AC))
3991 if (LI.replacementPreservesLCSSAForm(PN, V))
3994 // If it's not a loop phi, we can't handle it yet.
3995 return getUnknown(PN);
3998 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
4002 // Handle "constant" branch or select. This can occur for instance when a
4003 // loop pass transforms an inner loop and moves on to process the outer loop.
4004 if (auto *CI = dyn_cast<ConstantInt>(Cond))
4005 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
4007 // Try to match some simple smax or umax patterns.
4008 auto *ICI = dyn_cast<ICmpInst>(Cond);
4010 return getUnknown(I);
4012 Value *LHS = ICI->getOperand(0);
4013 Value *RHS = ICI->getOperand(1);
4015 switch (ICI->getPredicate()) {
4016 case ICmpInst::ICMP_SLT:
4017 case ICmpInst::ICMP_SLE:
4018 std::swap(LHS, RHS);
4020 case ICmpInst::ICMP_SGT:
4021 case ICmpInst::ICMP_SGE:
4022 // a >s b ? a+x : b+x -> smax(a, b)+x
4023 // a >s b ? b+x : a+x -> smin(a, b)+x
4024 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4025 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
4026 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
4027 const SCEV *LA = getSCEV(TrueVal);
4028 const SCEV *RA = getSCEV(FalseVal);
4029 const SCEV *LDiff = getMinusSCEV(LA, LS);
4030 const SCEV *RDiff = getMinusSCEV(RA, RS);
4032 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4033 LDiff = getMinusSCEV(LA, RS);
4034 RDiff = getMinusSCEV(RA, LS);
4036 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4039 case ICmpInst::ICMP_ULT:
4040 case ICmpInst::ICMP_ULE:
4041 std::swap(LHS, RHS);
4043 case ICmpInst::ICMP_UGT:
4044 case ICmpInst::ICMP_UGE:
4045 // a >u b ? a+x : b+x -> umax(a, b)+x
4046 // a >u b ? b+x : a+x -> umin(a, b)+x
4047 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4048 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4049 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
4050 const SCEV *LA = getSCEV(TrueVal);
4051 const SCEV *RA = getSCEV(FalseVal);
4052 const SCEV *LDiff = getMinusSCEV(LA, LS);
4053 const SCEV *RDiff = getMinusSCEV(RA, RS);
4055 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4056 LDiff = getMinusSCEV(LA, RS);
4057 RDiff = getMinusSCEV(RA, LS);
4059 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4062 case ICmpInst::ICMP_NE:
4063 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4064 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4065 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4066 const SCEV *One = getOne(I->getType());
4067 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4068 const SCEV *LA = getSCEV(TrueVal);
4069 const SCEV *RA = getSCEV(FalseVal);
4070 const SCEV *LDiff = getMinusSCEV(LA, LS);
4071 const SCEV *RDiff = getMinusSCEV(RA, One);
4073 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4076 case ICmpInst::ICMP_EQ:
4077 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4078 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4079 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4080 const SCEV *One = getOne(I->getType());
4081 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4082 const SCEV *LA = getSCEV(TrueVal);
4083 const SCEV *RA = getSCEV(FalseVal);
4084 const SCEV *LDiff = getMinusSCEV(LA, One);
4085 const SCEV *RDiff = getMinusSCEV(RA, LS);
4087 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4094 return getUnknown(I);
4097 /// createNodeForGEP - Expand GEP instructions into add and multiply
4098 /// operations. This allows them to be analyzed by regular SCEV code.
4100 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
4101 Value *Base = GEP->getOperand(0);
4102 // Don't attempt to analyze GEPs over unsized objects.
4103 if (!Base->getType()->getPointerElementType()->isSized())
4104 return getUnknown(GEP);
4106 SmallVector<const SCEV *, 4> IndexExprs;
4107 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4108 IndexExprs.push_back(getSCEV(*Index));
4109 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
4113 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
4114 /// guaranteed to end in (at every loop iteration). It is, at the same time,
4115 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
4116 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
4118 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4119 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4120 return C->getValue()->getValue().countTrailingZeros();
4122 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4123 return std::min(GetMinTrailingZeros(T->getOperand()),
4124 (uint32_t)getTypeSizeInBits(T->getType()));
4126 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4127 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4128 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4129 getTypeSizeInBits(E->getType()) : OpRes;
4132 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4133 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4134 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4135 getTypeSizeInBits(E->getType()) : OpRes;
4138 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4139 // The result is the min of all operands results.
4140 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4141 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4142 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4146 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4147 // The result is the sum of all operands results.
4148 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4149 uint32_t BitWidth = getTypeSizeInBits(M->getType());
4150 for (unsigned i = 1, e = M->getNumOperands();
4151 SumOpRes != BitWidth && i != e; ++i)
4152 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4157 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4158 // The result is the min of all operands results.
4159 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4160 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4161 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4165 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4166 // The result is the min of all operands results.
4167 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4168 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4169 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4173 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4174 // The result is the min of all operands results.
4175 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4176 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4177 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4181 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4182 // For a SCEVUnknown, ask ValueTracking.
4183 unsigned BitWidth = getTypeSizeInBits(U->getType());
4184 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4185 computeKnownBits(U->getValue(), Zeros, Ones, getDataLayout(), 0, &AC,
4187 return Zeros.countTrailingOnes();
4194 /// GetRangeFromMetadata - Helper method to assign a range to V from
4195 /// metadata present in the IR.
4196 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4197 if (Instruction *I = dyn_cast<Instruction>(V))
4198 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
4199 return getConstantRangeFromMetadata(*MD);
4204 /// getRange - Determine the range for a particular SCEV. If SignHint is
4205 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4206 /// with a "cleaner" unsigned (resp. signed) representation.
4209 ScalarEvolution::getRange(const SCEV *S,
4210 ScalarEvolution::RangeSignHint SignHint) {
4211 DenseMap<const SCEV *, ConstantRange> &Cache =
4212 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4215 // See if we've computed this range already.
4216 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4217 if (I != Cache.end())
4220 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4221 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
4223 unsigned BitWidth = getTypeSizeInBits(S->getType());
4224 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4226 // If the value has known zeros, the maximum value will have those known zeros
4228 uint32_t TZ = GetMinTrailingZeros(S);
4230 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4231 ConservativeResult =
4232 ConstantRange(APInt::getMinValue(BitWidth),
4233 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4235 ConservativeResult = ConstantRange(
4236 APInt::getSignedMinValue(BitWidth),
4237 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4240 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4241 ConstantRange X = getRange(Add->getOperand(0), SignHint);
4242 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4243 X = X.add(getRange(Add->getOperand(i), SignHint));
4244 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4247 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4248 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4249 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4250 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4251 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4254 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4255 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4256 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4257 X = X.smax(getRange(SMax->getOperand(i), SignHint));
4258 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4261 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4262 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4263 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4264 X = X.umax(getRange(UMax->getOperand(i), SignHint));
4265 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4268 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4269 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4270 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4271 return setRange(UDiv, SignHint,
4272 ConservativeResult.intersectWith(X.udiv(Y)));
4275 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4276 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4277 return setRange(ZExt, SignHint,
4278 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4281 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4282 ConstantRange X = getRange(SExt->getOperand(), SignHint);
4283 return setRange(SExt, SignHint,
4284 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4287 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4288 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4289 return setRange(Trunc, SignHint,
4290 ConservativeResult.intersectWith(X.truncate(BitWidth)));
4293 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4294 // If there's no unsigned wrap, the value will never be less than its
4296 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
4297 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4298 if (!C->getValue()->isZero())
4299 ConservativeResult =
4300 ConservativeResult.intersectWith(
4301 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
4303 // If there's no signed wrap, and all the operands have the same sign or
4304 // zero, the value won't ever change sign.
4305 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
4306 bool AllNonNeg = true;
4307 bool AllNonPos = true;
4308 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4309 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4310 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4313 ConservativeResult = ConservativeResult.intersectWith(
4314 ConstantRange(APInt(BitWidth, 0),
4315 APInt::getSignedMinValue(BitWidth)));
4317 ConservativeResult = ConservativeResult.intersectWith(
4318 ConstantRange(APInt::getSignedMinValue(BitWidth),
4319 APInt(BitWidth, 1)));
4322 // TODO: non-affine addrec
4323 if (AddRec->isAffine()) {
4324 Type *Ty = AddRec->getType();
4325 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4326 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4327 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4329 // Check for overflow. This must be done with ConstantRange arithmetic
4330 // because we could be called from within the ScalarEvolution overflow
4333 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4334 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4335 ConstantRange ZExtMaxBECountRange =
4336 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4338 const SCEV *Start = AddRec->getStart();
4339 const SCEV *Step = AddRec->getStepRecurrence(*this);
4340 ConstantRange StepSRange = getSignedRange(Step);
4341 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4343 ConstantRange StartURange = getUnsignedRange(Start);
4344 ConstantRange EndURange =
4345 StartURange.add(MaxBECountRange.multiply(StepSRange));
4347 // Check for unsigned overflow.
4348 ConstantRange ZExtStartURange =
4349 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4350 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4351 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4353 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4354 EndURange.getUnsignedMin());
4355 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4356 EndURange.getUnsignedMax());
4357 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4359 ConservativeResult =
4360 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4363 ConstantRange StartSRange = getSignedRange(Start);
4364 ConstantRange EndSRange =
4365 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4367 // Check for signed overflow. This must be done with ConstantRange
4368 // arithmetic because we could be called from within the ScalarEvolution
4369 // overflow checking code.
4370 ConstantRange SExtStartSRange =
4371 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4372 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4373 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4375 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4376 EndSRange.getSignedMin());
4377 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4378 EndSRange.getSignedMax());
4379 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4381 ConservativeResult =
4382 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4387 return setRange(AddRec, SignHint, ConservativeResult);
4390 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4391 // Check if the IR explicitly contains !range metadata.
4392 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4393 if (MDRange.hasValue())
4394 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4396 // Split here to avoid paying the compile-time cost of calling both
4397 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4399 const DataLayout &DL = getDataLayout();
4400 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4401 // For a SCEVUnknown, ask ValueTracking.
4402 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4403 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4404 if (Ones != ~Zeros + 1)
4405 ConservativeResult =
4406 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4408 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4409 "generalize as needed!");
4410 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4412 ConservativeResult = ConservativeResult.intersectWith(
4413 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4414 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4417 return setRange(U, SignHint, ConservativeResult);
4420 return setRange(S, SignHint, ConservativeResult);
4423 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4424 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4425 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4427 // Return early if there are no flags to propagate to the SCEV.
4428 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4429 if (BinOp->hasNoUnsignedWrap())
4430 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4431 if (BinOp->hasNoSignedWrap())
4432 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4433 if (Flags == SCEV::FlagAnyWrap) {
4434 return SCEV::FlagAnyWrap;
4437 // Here we check that BinOp is in the header of the innermost loop
4438 // containing BinOp, since we only deal with instructions in the loop
4439 // header. The actual loop we need to check later will come from an add
4440 // recurrence, but getting that requires computing the SCEV of the operands,
4441 // which can be expensive. This check we can do cheaply to rule out some
4443 Loop *innermostContainingLoop = LI.getLoopFor(BinOp->getParent());
4444 if (innermostContainingLoop == nullptr ||
4445 innermostContainingLoop->getHeader() != BinOp->getParent())
4446 return SCEV::FlagAnyWrap;
4448 // Only proceed if we can prove that BinOp does not yield poison.
4449 if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
4451 // At this point we know that if V is executed, then it does not wrap
4452 // according to at least one of NSW or NUW. If V is not executed, then we do
4453 // not know if the calculation that V represents would wrap. Multiple
4454 // instructions can map to the same SCEV. If we apply NSW or NUW from V to
4455 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4456 // derived from other instructions that map to the same SCEV. We cannot make
4457 // that guarantee for cases where V is not executed. So we need to find the
4458 // loop that V is considered in relation to and prove that V is executed for
4459 // every iteration of that loop. That implies that the value that V
4460 // calculates does not wrap anywhere in the loop, so then we can apply the
4461 // flags to the SCEV.
4463 // We check isLoopInvariant to disambiguate in case we are adding two
4464 // recurrences from different loops, so that we know which loop to prove
4465 // that V is executed in.
4466 for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
4467 const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
4468 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4469 const int OtherOpIndex = 1 - OpIndex;
4470 const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
4471 if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
4472 isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
4476 return SCEV::FlagAnyWrap;
4479 /// createSCEV - We know that there is no SCEV for the specified value. Analyze
4482 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4483 if (!isSCEVable(V->getType()))
4484 return getUnknown(V);
4486 unsigned Opcode = Instruction::UserOp1;
4487 if (Instruction *I = dyn_cast<Instruction>(V)) {
4488 Opcode = I->getOpcode();
4490 // Don't attempt to analyze instructions in blocks that aren't
4491 // reachable. Such instructions don't matter, and they aren't required
4492 // to obey basic rules for definitions dominating uses which this
4493 // analysis depends on.
4494 if (!DT.isReachableFromEntry(I->getParent()))
4495 return getUnknown(V);
4496 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4497 Opcode = CE->getOpcode();
4498 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4499 return getConstant(CI);
4500 else if (isa<ConstantPointerNull>(V))
4501 return getZero(V->getType());
4502 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4503 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4505 return getUnknown(V);
4507 Operator *U = cast<Operator>(V);
4509 case Instruction::Add: {
4510 // The simple thing to do would be to just call getSCEV on both operands
4511 // and call getAddExpr with the result. However if we're looking at a
4512 // bunch of things all added together, this can be quite inefficient,
4513 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4514 // Instead, gather up all the operands and make a single getAddExpr call.
4515 // LLVM IR canonical form means we need only traverse the left operands.
4516 SmallVector<const SCEV *, 4> AddOps;
4517 for (Value *Op = U;; Op = U->getOperand(0)) {
4518 U = dyn_cast<Operator>(Op);
4519 unsigned Opcode = U ? U->getOpcode() : 0;
4520 if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
4521 assert(Op != V && "V should be an add");
4522 AddOps.push_back(getSCEV(Op));
4526 if (auto *OpSCEV = getExistingSCEV(U)) {
4527 AddOps.push_back(OpSCEV);
4531 // If a NUW or NSW flag can be applied to the SCEV for this
4532 // addition, then compute the SCEV for this addition by itself
4533 // with a separate call to getAddExpr. We need to do that
4534 // instead of pushing the operands of the addition onto AddOps,
4535 // since the flags are only known to apply to this particular
4536 // addition - they may not apply to other additions that can be
4537 // formed with operands from AddOps.
4538 const SCEV *RHS = getSCEV(U->getOperand(1));
4539 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4540 if (Flags != SCEV::FlagAnyWrap) {
4541 const SCEV *LHS = getSCEV(U->getOperand(0));
4542 if (Opcode == Instruction::Sub)
4543 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4545 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4549 if (Opcode == Instruction::Sub)
4550 AddOps.push_back(getNegativeSCEV(RHS));
4552 AddOps.push_back(RHS);
4554 return getAddExpr(AddOps);
4557 case Instruction::Mul: {
4558 SmallVector<const SCEV *, 4> MulOps;
4559 for (Value *Op = U;; Op = U->getOperand(0)) {
4560 U = dyn_cast<Operator>(Op);
4561 if (!U || U->getOpcode() != Instruction::Mul) {
4562 assert(Op != V && "V should be a mul");
4563 MulOps.push_back(getSCEV(Op));
4567 if (auto *OpSCEV = getExistingSCEV(U)) {
4568 MulOps.push_back(OpSCEV);
4572 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4573 if (Flags != SCEV::FlagAnyWrap) {
4574 MulOps.push_back(getMulExpr(getSCEV(U->getOperand(0)),
4575 getSCEV(U->getOperand(1)), Flags));
4579 MulOps.push_back(getSCEV(U->getOperand(1)));
4581 return getMulExpr(MulOps);
4583 case Instruction::UDiv:
4584 return getUDivExpr(getSCEV(U->getOperand(0)),
4585 getSCEV(U->getOperand(1)));
4586 case Instruction::Sub:
4587 return getMinusSCEV(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)),
4588 getNoWrapFlagsFromUB(U));
4589 case Instruction::And:
4590 // For an expression like x&255 that merely masks off the high bits,
4591 // use zext(trunc(x)) as the SCEV expression.
4592 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4593 if (CI->isNullValue())
4594 return getSCEV(U->getOperand(1));
4595 if (CI->isAllOnesValue())
4596 return getSCEV(U->getOperand(0));
4597 const APInt &A = CI->getValue();
4599 // Instcombine's ShrinkDemandedConstant may strip bits out of
4600 // constants, obscuring what would otherwise be a low-bits mask.
4601 // Use computeKnownBits to compute what ShrinkDemandedConstant
4602 // knew about to reconstruct a low-bits mask value.
4603 unsigned LZ = A.countLeadingZeros();
4604 unsigned TZ = A.countTrailingZeros();
4605 unsigned BitWidth = A.getBitWidth();
4606 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4607 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, getDataLayout(),
4608 0, &AC, nullptr, &DT);
4610 APInt EffectiveMask =
4611 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4612 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4613 const SCEV *MulCount = getConstant(
4614 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4618 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4619 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4626 case Instruction::Or:
4627 // If the RHS of the Or is a constant, we may have something like:
4628 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4629 // optimizations will transparently handle this case.
4631 // In order for this transformation to be safe, the LHS must be of the
4632 // form X*(2^n) and the Or constant must be less than 2^n.
4633 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4634 const SCEV *LHS = getSCEV(U->getOperand(0));
4635 const APInt &CIVal = CI->getValue();
4636 if (GetMinTrailingZeros(LHS) >=
4637 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4638 // Build a plain add SCEV.
4639 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4640 // If the LHS of the add was an addrec and it has no-wrap flags,
4641 // transfer the no-wrap flags, since an or won't introduce a wrap.
4642 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4643 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4644 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4645 OldAR->getNoWrapFlags());
4651 case Instruction::Xor:
4652 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4653 // If the RHS of the xor is a signbit, then this is just an add.
4654 // Instcombine turns add of signbit into xor as a strength reduction step.
4655 if (CI->getValue().isSignBit())
4656 return getAddExpr(getSCEV(U->getOperand(0)),
4657 getSCEV(U->getOperand(1)));
4659 // If the RHS of xor is -1, then this is a not operation.
4660 if (CI->isAllOnesValue())
4661 return getNotSCEV(getSCEV(U->getOperand(0)));
4663 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4664 // This is a variant of the check for xor with -1, and it handles
4665 // the case where instcombine has trimmed non-demanded bits out
4666 // of an xor with -1.
4667 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4668 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4669 if (BO->getOpcode() == Instruction::And &&
4670 LCI->getValue() == CI->getValue())
4671 if (const SCEVZeroExtendExpr *Z =
4672 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4673 Type *UTy = U->getType();
4674 const SCEV *Z0 = Z->getOperand();
4675 Type *Z0Ty = Z0->getType();
4676 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4678 // If C is a low-bits mask, the zero extend is serving to
4679 // mask off the high bits. Complement the operand and
4680 // re-apply the zext.
4681 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4682 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4684 // If C is a single bit, it may be in the sign-bit position
4685 // before the zero-extend. In this case, represent the xor
4686 // using an add, which is equivalent, and re-apply the zext.
4687 APInt Trunc = CI->getValue().trunc(Z0TySize);
4688 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4690 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4696 case Instruction::Shl:
4697 // Turn shift left of a constant amount into a multiply.
4698 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4699 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4701 // If the shift count is not less than the bitwidth, the result of
4702 // the shift is undefined. Don't try to analyze it, because the
4703 // resolution chosen here may differ from the resolution chosen in
4704 // other parts of the compiler.
4705 if (SA->getValue().uge(BitWidth))
4708 // It is currently not resolved how to interpret NSW for left
4709 // shift by BitWidth - 1, so we avoid applying flags in that
4710 // case. Remove this check (or this comment) once the situation
4712 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
4713 // and http://reviews.llvm.org/D8890 .
4714 auto Flags = SCEV::FlagAnyWrap;
4715 if (SA->getValue().ult(BitWidth - 1)) Flags = getNoWrapFlagsFromUB(U);
4717 Constant *X = ConstantInt::get(getContext(),
4718 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4719 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X), Flags);
4723 case Instruction::LShr:
4724 // Turn logical shift right of a constant into a unsigned divide.
4725 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4726 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4728 // If the shift count is not less than the bitwidth, the result of
4729 // the shift is undefined. Don't try to analyze it, because the
4730 // resolution chosen here may differ from the resolution chosen in
4731 // other parts of the compiler.
4732 if (SA->getValue().uge(BitWidth))
4735 Constant *X = ConstantInt::get(getContext(),
4736 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4737 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4741 case Instruction::AShr:
4742 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4743 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4744 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4745 if (L->getOpcode() == Instruction::Shl &&
4746 L->getOperand(1) == U->getOperand(1)) {
4747 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4749 // If the shift count is not less than the bitwidth, the result of
4750 // the shift is undefined. Don't try to analyze it, because the
4751 // resolution chosen here may differ from the resolution chosen in
4752 // other parts of the compiler.
4753 if (CI->getValue().uge(BitWidth))
4756 uint64_t Amt = BitWidth - CI->getZExtValue();
4757 if (Amt == BitWidth)
4758 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4760 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4761 IntegerType::get(getContext(),
4767 case Instruction::Trunc:
4768 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4770 case Instruction::ZExt:
4771 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4773 case Instruction::SExt:
4774 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4776 case Instruction::BitCast:
4777 // BitCasts are no-op casts so we just eliminate the cast.
4778 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4779 return getSCEV(U->getOperand(0));
4782 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4783 // lead to pointer expressions which cannot safely be expanded to GEPs,
4784 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4785 // simplifying integer expressions.
4787 case Instruction::GetElementPtr:
4788 return createNodeForGEP(cast<GEPOperator>(U));
4790 case Instruction::PHI:
4791 return createNodeForPHI(cast<PHINode>(U));
4793 case Instruction::Select:
4794 // U can also be a select constant expr, which let fall through. Since
4795 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
4796 // constant expressions cannot have instructions as operands, we'd have
4797 // returned getUnknown for a select constant expressions anyway.
4798 if (isa<Instruction>(U))
4799 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
4800 U->getOperand(1), U->getOperand(2));
4802 default: // We cannot analyze this expression.
4806 return getUnknown(V);
4811 //===----------------------------------------------------------------------===//
4812 // Iteration Count Computation Code
4815 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4816 if (BasicBlock *ExitingBB = L->getExitingBlock())
4817 return getSmallConstantTripCount(L, ExitingBB);
4819 // No trip count information for multiple exits.
4823 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4824 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4825 /// constant. Will also return 0 if the maximum trip count is very large (>=
4828 /// This "trip count" assumes that control exits via ExitingBlock. More
4829 /// precisely, it is the number of times that control may reach ExitingBlock
4830 /// before taking the branch. For loops with multiple exits, it may not be the
4831 /// number times that the loop header executes because the loop may exit
4832 /// prematurely via another branch.
4833 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4834 BasicBlock *ExitingBlock) {
4835 assert(ExitingBlock && "Must pass a non-null exiting block!");
4836 assert(L->isLoopExiting(ExitingBlock) &&
4837 "Exiting block must actually branch out of the loop!");
4838 const SCEVConstant *ExitCount =
4839 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4843 ConstantInt *ExitConst = ExitCount->getValue();
4845 // Guard against huge trip counts.
4846 if (ExitConst->getValue().getActiveBits() > 32)
4849 // In case of integer overflow, this returns 0, which is correct.
4850 return ((unsigned)ExitConst->getZExtValue()) + 1;
4853 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4854 if (BasicBlock *ExitingBB = L->getExitingBlock())
4855 return getSmallConstantTripMultiple(L, ExitingBB);
4857 // No trip multiple information for multiple exits.
4861 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4862 /// trip count of this loop as a normal unsigned value, if possible. This
4863 /// means that the actual trip count is always a multiple of the returned
4864 /// value (don't forget the trip count could very well be zero as well!).
4866 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4867 /// multiple of a constant (which is also the case if the trip count is simply
4868 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4869 /// if the trip count is very large (>= 2^32).
4871 /// As explained in the comments for getSmallConstantTripCount, this assumes
4872 /// that control exits the loop via ExitingBlock.
4874 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4875 BasicBlock *ExitingBlock) {
4876 assert(ExitingBlock && "Must pass a non-null exiting block!");
4877 assert(L->isLoopExiting(ExitingBlock) &&
4878 "Exiting block must actually branch out of the loop!");
4879 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4880 if (ExitCount == getCouldNotCompute())
4883 // Get the trip count from the BE count by adding 1.
4884 const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
4885 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4886 // to factor simple cases.
4887 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4888 TCMul = Mul->getOperand(0);
4890 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4894 ConstantInt *Result = MulC->getValue();
4896 // Guard against huge trip counts (this requires checking
4897 // for zero to handle the case where the trip count == -1 and the
4899 if (!Result || Result->getValue().getActiveBits() > 32 ||
4900 Result->getValue().getActiveBits() == 0)
4903 return (unsigned)Result->getZExtValue();
4906 // getExitCount - Get the expression for the number of loop iterations for which
4907 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4908 // SCEVCouldNotCompute.
4909 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4910 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4913 /// getBackedgeTakenCount - If the specified loop has a predictable
4914 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4915 /// object. The backedge-taken count is the number of times the loop header
4916 /// will be branched to from within the loop. This is one less than the
4917 /// trip count of the loop, since it doesn't count the first iteration,
4918 /// when the header is branched to from outside the loop.
4920 /// Note that it is not valid to call this method on a loop without a
4921 /// loop-invariant backedge-taken count (see
4922 /// hasLoopInvariantBackedgeTakenCount).
4924 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4925 return getBackedgeTakenInfo(L).getExact(this);
4928 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4929 /// return the least SCEV value that is known never to be less than the
4930 /// actual backedge taken count.
4931 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4932 return getBackedgeTakenInfo(L).getMax(this);
4935 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4936 /// onto the given Worklist.
4938 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4939 BasicBlock *Header = L->getHeader();
4941 // Push all Loop-header PHIs onto the Worklist stack.
4942 for (BasicBlock::iterator I = Header->begin();
4943 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4944 Worklist.push_back(PN);
4947 const ScalarEvolution::BackedgeTakenInfo &
4948 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4949 // Initially insert an invalid entry for this loop. If the insertion
4950 // succeeds, proceed to actually compute a backedge-taken count and
4951 // update the value. The temporary CouldNotCompute value tells SCEV
4952 // code elsewhere that it shouldn't attempt to request a new
4953 // backedge-taken count, which could result in infinite recursion.
4954 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4955 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4957 return Pair.first->second;
4959 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
4960 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4961 // must be cleared in this scope.
4962 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
4964 if (Result.getExact(this) != getCouldNotCompute()) {
4965 assert(isLoopInvariant(Result.getExact(this), L) &&
4966 isLoopInvariant(Result.getMax(this), L) &&
4967 "Computed backedge-taken count isn't loop invariant for loop!");
4968 ++NumTripCountsComputed;
4970 else if (Result.getMax(this) == getCouldNotCompute() &&
4971 isa<PHINode>(L->getHeader()->begin())) {
4972 // Only count loops that have phi nodes as not being computable.
4973 ++NumTripCountsNotComputed;
4976 // Now that we know more about the trip count for this loop, forget any
4977 // existing SCEV values for PHI nodes in this loop since they are only
4978 // conservative estimates made without the benefit of trip count
4979 // information. This is similar to the code in forgetLoop, except that
4980 // it handles SCEVUnknown PHI nodes specially.
4981 if (Result.hasAnyInfo()) {
4982 SmallVector<Instruction *, 16> Worklist;
4983 PushLoopPHIs(L, Worklist);
4985 SmallPtrSet<Instruction *, 8> Visited;
4986 while (!Worklist.empty()) {
4987 Instruction *I = Worklist.pop_back_val();
4988 if (!Visited.insert(I).second)
4991 ValueExprMapType::iterator It =
4992 ValueExprMap.find_as(static_cast<Value *>(I));
4993 if (It != ValueExprMap.end()) {
4994 const SCEV *Old = It->second;
4996 // SCEVUnknown for a PHI either means that it has an unrecognized
4997 // structure, or it's a PHI that's in the progress of being computed
4998 // by createNodeForPHI. In the former case, additional loop trip
4999 // count information isn't going to change anything. In the later
5000 // case, createNodeForPHI will perform the necessary updates on its
5001 // own when it gets to that point.
5002 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
5003 forgetMemoizedResults(Old);
5004 ValueExprMap.erase(It);
5006 if (PHINode *PN = dyn_cast<PHINode>(I))
5007 ConstantEvolutionLoopExitValue.erase(PN);
5010 PushDefUseChildren(I, Worklist);
5014 // Re-lookup the insert position, since the call to
5015 // computeBackedgeTakenCount above could result in a
5016 // recusive call to getBackedgeTakenInfo (on a different
5017 // loop), which would invalidate the iterator computed
5019 return BackedgeTakenCounts.find(L)->second = Result;
5022 /// forgetLoop - This method should be called by the client when it has
5023 /// changed a loop in a way that may effect ScalarEvolution's ability to
5024 /// compute a trip count, or if the loop is deleted.
5025 void ScalarEvolution::forgetLoop(const Loop *L) {
5026 // Drop any stored trip count value.
5027 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
5028 BackedgeTakenCounts.find(L);
5029 if (BTCPos != BackedgeTakenCounts.end()) {
5030 BTCPos->second.clear();
5031 BackedgeTakenCounts.erase(BTCPos);
5034 // Drop information about expressions based on loop-header PHIs.
5035 SmallVector<Instruction *, 16> Worklist;
5036 PushLoopPHIs(L, Worklist);
5038 SmallPtrSet<Instruction *, 8> Visited;
5039 while (!Worklist.empty()) {
5040 Instruction *I = Worklist.pop_back_val();
5041 if (!Visited.insert(I).second)
5044 ValueExprMapType::iterator It =
5045 ValueExprMap.find_as(static_cast<Value *>(I));
5046 if (It != ValueExprMap.end()) {
5047 forgetMemoizedResults(It->second);
5048 ValueExprMap.erase(It);
5049 if (PHINode *PN = dyn_cast<PHINode>(I))
5050 ConstantEvolutionLoopExitValue.erase(PN);
5053 PushDefUseChildren(I, Worklist);
5056 // Forget all contained loops too, to avoid dangling entries in the
5057 // ValuesAtScopes map.
5058 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5062 /// forgetValue - This method should be called by the client when it has
5063 /// changed a value in a way that may effect its value, or which may
5064 /// disconnect it from a def-use chain linking it to a loop.
5065 void ScalarEvolution::forgetValue(Value *V) {
5066 Instruction *I = dyn_cast<Instruction>(V);
5069 // Drop information about expressions based on loop-header PHIs.
5070 SmallVector<Instruction *, 16> Worklist;
5071 Worklist.push_back(I);
5073 SmallPtrSet<Instruction *, 8> Visited;
5074 while (!Worklist.empty()) {
5075 I = Worklist.pop_back_val();
5076 if (!Visited.insert(I).second)
5079 ValueExprMapType::iterator It =
5080 ValueExprMap.find_as(static_cast<Value *>(I));
5081 if (It != ValueExprMap.end()) {
5082 forgetMemoizedResults(It->second);
5083 ValueExprMap.erase(It);
5084 if (PHINode *PN = dyn_cast<PHINode>(I))
5085 ConstantEvolutionLoopExitValue.erase(PN);
5088 PushDefUseChildren(I, Worklist);
5092 /// getExact - Get the exact loop backedge taken count considering all loop
5093 /// exits. A computable result can only be returned for loops with a single
5094 /// exit. Returning the minimum taken count among all exits is incorrect
5095 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
5096 /// assumes that the limit of each loop test is never skipped. This is a valid
5097 /// assumption as long as the loop exits via that test. For precise results, it
5098 /// is the caller's responsibility to specify the relevant loop exit using
5099 /// getExact(ExitingBlock, SE).
5101 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
5102 // If any exits were not computable, the loop is not computable.
5103 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
5105 // We need exactly one computable exit.
5106 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
5107 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
5109 const SCEV *BECount = nullptr;
5110 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5111 ENT != nullptr; ENT = ENT->getNextExit()) {
5113 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5116 BECount = ENT->ExactNotTaken;
5117 else if (BECount != ENT->ExactNotTaken)
5118 return SE->getCouldNotCompute();
5120 assert(BECount && "Invalid not taken count for loop exit");
5124 /// getExact - Get the exact not taken count for this loop exit.
5126 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5127 ScalarEvolution *SE) const {
5128 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5129 ENT != nullptr; ENT = ENT->getNextExit()) {
5131 if (ENT->ExitingBlock == ExitingBlock)
5132 return ENT->ExactNotTaken;
5134 return SE->getCouldNotCompute();
5137 /// getMax - Get the max backedge taken count for the loop.
5139 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5140 return Max ? Max : SE->getCouldNotCompute();
5143 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5144 ScalarEvolution *SE) const {
5145 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
5148 if (!ExitNotTaken.ExitingBlock)
5151 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5152 ENT != nullptr; ENT = ENT->getNextExit()) {
5154 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
5155 && SE->hasOperand(ENT->ExactNotTaken, S)) {
5162 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5163 /// computable exit into a persistent ExitNotTakenInfo array.
5164 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5165 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
5166 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
5169 ExitNotTaken.setIncomplete();
5171 unsigned NumExits = ExitCounts.size();
5172 if (NumExits == 0) return;
5174 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
5175 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
5176 if (NumExits == 1) return;
5178 // Handle the rare case of multiple computable exits.
5179 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
5181 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
5182 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
5183 PrevENT->setNextExit(ENT);
5184 ENT->ExitingBlock = ExitCounts[i].first;
5185 ENT->ExactNotTaken = ExitCounts[i].second;
5189 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
5190 void ScalarEvolution::BackedgeTakenInfo::clear() {
5191 ExitNotTaken.ExitingBlock = nullptr;
5192 ExitNotTaken.ExactNotTaken = nullptr;
5193 delete[] ExitNotTaken.getNextExit();
5196 /// computeBackedgeTakenCount - Compute the number of times the backedge
5197 /// of the specified loop will execute.
5198 ScalarEvolution::BackedgeTakenInfo
5199 ScalarEvolution::computeBackedgeTakenCount(const Loop *L) {
5200 SmallVector<BasicBlock *, 8> ExitingBlocks;
5201 L->getExitingBlocks(ExitingBlocks);
5203 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
5204 bool CouldComputeBECount = true;
5205 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5206 const SCEV *MustExitMaxBECount = nullptr;
5207 const SCEV *MayExitMaxBECount = nullptr;
5209 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5210 // and compute maxBECount.
5211 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5212 BasicBlock *ExitBB = ExitingBlocks[i];
5213 ExitLimit EL = computeExitLimit(L, ExitBB);
5215 // 1. For each exit that can be computed, add an entry to ExitCounts.
5216 // CouldComputeBECount is true only if all exits can be computed.
5217 if (EL.Exact == getCouldNotCompute())
5218 // We couldn't compute an exact value for this exit, so
5219 // we won't be able to compute an exact value for the loop.
5220 CouldComputeBECount = false;
5222 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
5224 // 2. Derive the loop's MaxBECount from each exit's max number of
5225 // non-exiting iterations. Partition the loop exits into two kinds:
5226 // LoopMustExits and LoopMayExits.
5228 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5229 // is a LoopMayExit. If any computable LoopMustExit is found, then
5230 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
5231 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
5232 // considered greater than any computable EL.Max.
5233 if (EL.Max != getCouldNotCompute() && Latch &&
5234 DT.dominates(ExitBB, Latch)) {
5235 if (!MustExitMaxBECount)
5236 MustExitMaxBECount = EL.Max;
5238 MustExitMaxBECount =
5239 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5241 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5242 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5243 MayExitMaxBECount = EL.Max;
5246 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5250 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5251 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5252 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5255 ScalarEvolution::ExitLimit
5256 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
5258 // Okay, we've chosen an exiting block. See what condition causes us to exit
5259 // at this block and remember the exit block and whether all other targets
5260 // lead to the loop header.
5261 bool MustExecuteLoopHeader = true;
5262 BasicBlock *Exit = nullptr;
5263 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5265 if (!L->contains(*SI)) {
5266 if (Exit) // Multiple exit successors.
5267 return getCouldNotCompute();
5269 } else if (*SI != L->getHeader()) {
5270 MustExecuteLoopHeader = false;
5273 // At this point, we know we have a conditional branch that determines whether
5274 // the loop is exited. However, we don't know if the branch is executed each
5275 // time through the loop. If not, then the execution count of the branch will
5276 // not be equal to the trip count of the loop.
5278 // Currently we check for this by checking to see if the Exit branch goes to
5279 // the loop header. If so, we know it will always execute the same number of
5280 // times as the loop. We also handle the case where the exit block *is* the
5281 // loop header. This is common for un-rotated loops.
5283 // If both of those tests fail, walk up the unique predecessor chain to the
5284 // header, stopping if there is an edge that doesn't exit the loop. If the
5285 // header is reached, the execution count of the branch will be equal to the
5286 // trip count of the loop.
5288 // More extensive analysis could be done to handle more cases here.
5290 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5291 // The simple checks failed, try climbing the unique predecessor chain
5292 // up to the header.
5294 for (BasicBlock *BB = ExitingBlock; BB; ) {
5295 BasicBlock *Pred = BB->getUniquePredecessor();
5297 return getCouldNotCompute();
5298 TerminatorInst *PredTerm = Pred->getTerminator();
5299 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5302 // If the predecessor has a successor that isn't BB and isn't
5303 // outside the loop, assume the worst.
5304 if (L->contains(PredSucc))
5305 return getCouldNotCompute();
5307 if (Pred == L->getHeader()) {
5314 return getCouldNotCompute();
5317 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5318 TerminatorInst *Term = ExitingBlock->getTerminator();
5319 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5320 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5321 // Proceed to the next level to examine the exit condition expression.
5322 return computeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5323 BI->getSuccessor(1),
5324 /*ControlsExit=*/IsOnlyExit);
5327 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5328 return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
5329 /*ControlsExit=*/IsOnlyExit);
5331 return getCouldNotCompute();
5334 /// computeExitLimitFromCond - Compute the number of times the
5335 /// backedge of the specified loop will execute if its exit condition
5336 /// were a conditional branch of ExitCond, TBB, and FBB.
5338 /// @param ControlsExit is true if ExitCond directly controls the exit
5339 /// branch. In this case, we can assume that the loop exits only if the
5340 /// condition is true and can infer that failing to meet the condition prior to
5341 /// integer wraparound results in undefined behavior.
5342 ScalarEvolution::ExitLimit
5343 ScalarEvolution::computeExitLimitFromCond(const Loop *L,
5347 bool ControlsExit) {
5348 // Check if the controlling expression for this loop is an And or Or.
5349 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5350 if (BO->getOpcode() == Instruction::And) {
5351 // Recurse on the operands of the and.
5352 bool EitherMayExit = L->contains(TBB);
5353 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5354 ControlsExit && !EitherMayExit);
5355 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5356 ControlsExit && !EitherMayExit);
5357 const SCEV *BECount = getCouldNotCompute();
5358 const SCEV *MaxBECount = getCouldNotCompute();
5359 if (EitherMayExit) {
5360 // Both conditions must be true for the loop to continue executing.
5361 // Choose the less conservative count.
5362 if (EL0.Exact == getCouldNotCompute() ||
5363 EL1.Exact == getCouldNotCompute())
5364 BECount = getCouldNotCompute();
5366 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5367 if (EL0.Max == getCouldNotCompute())
5368 MaxBECount = EL1.Max;
5369 else if (EL1.Max == getCouldNotCompute())
5370 MaxBECount = EL0.Max;
5372 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5374 // Both conditions must be true at the same time for the loop to exit.
5375 // For now, be conservative.
5376 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5377 if (EL0.Max == EL1.Max)
5378 MaxBECount = EL0.Max;
5379 if (EL0.Exact == EL1.Exact)
5380 BECount = EL0.Exact;
5383 return ExitLimit(BECount, MaxBECount);
5385 if (BO->getOpcode() == Instruction::Or) {
5386 // Recurse on the operands of the or.
5387 bool EitherMayExit = L->contains(FBB);
5388 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5389 ControlsExit && !EitherMayExit);
5390 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5391 ControlsExit && !EitherMayExit);
5392 const SCEV *BECount = getCouldNotCompute();
5393 const SCEV *MaxBECount = getCouldNotCompute();
5394 if (EitherMayExit) {
5395 // Both conditions must be false for the loop to continue executing.
5396 // Choose the less conservative count.
5397 if (EL0.Exact == getCouldNotCompute() ||
5398 EL1.Exact == getCouldNotCompute())
5399 BECount = getCouldNotCompute();
5401 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5402 if (EL0.Max == getCouldNotCompute())
5403 MaxBECount = EL1.Max;
5404 else if (EL1.Max == getCouldNotCompute())
5405 MaxBECount = EL0.Max;
5407 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5409 // Both conditions must be false at the same time for the loop to exit.
5410 // For now, be conservative.
5411 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5412 if (EL0.Max == EL1.Max)
5413 MaxBECount = EL0.Max;
5414 if (EL0.Exact == EL1.Exact)
5415 BECount = EL0.Exact;
5418 return ExitLimit(BECount, MaxBECount);
5422 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5423 // Proceed to the next level to examine the icmp.
5424 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5425 return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5427 // Check for a constant condition. These are normally stripped out by
5428 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5429 // preserve the CFG and is temporarily leaving constant conditions
5431 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5432 if (L->contains(FBB) == !CI->getZExtValue())
5433 // The backedge is always taken.
5434 return getCouldNotCompute();
5436 // The backedge is never taken.
5437 return getZero(CI->getType());
5440 // If it's not an integer or pointer comparison then compute it the hard way.
5441 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5444 ScalarEvolution::ExitLimit
5445 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
5449 bool ControlsExit) {
5451 // If the condition was exit on true, convert the condition to exit on false
5452 ICmpInst::Predicate Cond;
5453 if (!L->contains(FBB))
5454 Cond = ExitCond->getPredicate();
5456 Cond = ExitCond->getInversePredicate();
5458 // Handle common loops like: for (X = "string"; *X; ++X)
5459 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5460 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5462 computeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5463 if (ItCnt.hasAnyInfo())
5467 ExitLimit ShiftEL = computeShiftCompareExitLimit(
5468 ExitCond->getOperand(0), ExitCond->getOperand(1), L, Cond);
5469 if (ShiftEL.hasAnyInfo())
5472 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5473 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5475 // Try to evaluate any dependencies out of the loop.
5476 LHS = getSCEVAtScope(LHS, L);
5477 RHS = getSCEVAtScope(RHS, L);
5479 // At this point, we would like to compute how many iterations of the
5480 // loop the predicate will return true for these inputs.
5481 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5482 // If there is a loop-invariant, force it into the RHS.
5483 std::swap(LHS, RHS);
5484 Cond = ICmpInst::getSwappedPredicate(Cond);
5487 // Simplify the operands before analyzing them.
5488 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5490 // If we have a comparison of a chrec against a constant, try to use value
5491 // ranges to answer this query.
5492 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5493 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5494 if (AddRec->getLoop() == L) {
5495 // Form the constant range.
5496 ConstantRange CompRange(
5497 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5499 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5500 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5504 case ICmpInst::ICMP_NE: { // while (X != Y)
5505 // Convert to: while (X-Y != 0)
5506 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5507 if (EL.hasAnyInfo()) return EL;
5510 case ICmpInst::ICMP_EQ: { // while (X == Y)
5511 // Convert to: while (X-Y == 0)
5512 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5513 if (EL.hasAnyInfo()) return EL;
5516 case ICmpInst::ICMP_SLT:
5517 case ICmpInst::ICMP_ULT: { // while (X < Y)
5518 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5519 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5520 if (EL.hasAnyInfo()) return EL;
5523 case ICmpInst::ICMP_SGT:
5524 case ICmpInst::ICMP_UGT: { // while (X > Y)
5525 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5526 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5527 if (EL.hasAnyInfo()) return EL;
5533 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5536 ScalarEvolution::ExitLimit
5537 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
5539 BasicBlock *ExitingBlock,
5540 bool ControlsExit) {
5541 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5543 // Give up if the exit is the default dest of a switch.
5544 if (Switch->getDefaultDest() == ExitingBlock)
5545 return getCouldNotCompute();
5547 assert(L->contains(Switch->getDefaultDest()) &&
5548 "Default case must not exit the loop!");
5549 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5550 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5552 // while (X != Y) --> while (X-Y != 0)
5553 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5554 if (EL.hasAnyInfo())
5557 return getCouldNotCompute();
5560 static ConstantInt *
5561 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5562 ScalarEvolution &SE) {
5563 const SCEV *InVal = SE.getConstant(C);
5564 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5565 assert(isa<SCEVConstant>(Val) &&
5566 "Evaluation of SCEV at constant didn't fold correctly?");
5567 return cast<SCEVConstant>(Val)->getValue();
5570 /// computeLoadConstantCompareExitLimit - Given an exit condition of
5571 /// 'icmp op load X, cst', try to see if we can compute the backedge
5572 /// execution count.
5573 ScalarEvolution::ExitLimit
5574 ScalarEvolution::computeLoadConstantCompareExitLimit(
5578 ICmpInst::Predicate predicate) {
5580 if (LI->isVolatile()) return getCouldNotCompute();
5582 // Check to see if the loaded pointer is a getelementptr of a global.
5583 // TODO: Use SCEV instead of manually grubbing with GEPs.
5584 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5585 if (!GEP) return getCouldNotCompute();
5587 // Make sure that it is really a constant global we are gepping, with an
5588 // initializer, and make sure the first IDX is really 0.
5589 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5590 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5591 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5592 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5593 return getCouldNotCompute();
5595 // Okay, we allow one non-constant index into the GEP instruction.
5596 Value *VarIdx = nullptr;
5597 std::vector<Constant*> Indexes;
5598 unsigned VarIdxNum = 0;
5599 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5600 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5601 Indexes.push_back(CI);
5602 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5603 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5604 VarIdx = GEP->getOperand(i);
5606 Indexes.push_back(nullptr);
5609 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5611 return getCouldNotCompute();
5613 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5614 // Check to see if X is a loop variant variable value now.
5615 const SCEV *Idx = getSCEV(VarIdx);
5616 Idx = getSCEVAtScope(Idx, L);
5618 // We can only recognize very limited forms of loop index expressions, in
5619 // particular, only affine AddRec's like {C1,+,C2}.
5620 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5621 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5622 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5623 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5624 return getCouldNotCompute();
5626 unsigned MaxSteps = MaxBruteForceIterations;
5627 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5628 ConstantInt *ItCst = ConstantInt::get(
5629 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5630 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5632 // Form the GEP offset.
5633 Indexes[VarIdxNum] = Val;
5635 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5637 if (!Result) break; // Cannot compute!
5639 // Evaluate the condition for this iteration.
5640 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5641 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5642 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5643 ++NumArrayLenItCounts;
5644 return getConstant(ItCst); // Found terminating iteration!
5647 return getCouldNotCompute();
5650 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
5651 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
5652 ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
5654 return getCouldNotCompute();
5656 const BasicBlock *Latch = L->getLoopLatch();
5658 return getCouldNotCompute();
5660 const BasicBlock *Predecessor = L->getLoopPredecessor();
5662 return getCouldNotCompute();
5664 // Return true if V is of the form "LHS `shift_op` <positive constant>".
5665 // Return LHS in OutLHS and shift_opt in OutOpCode.
5666 auto MatchPositiveShift =
5667 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
5669 using namespace PatternMatch;
5671 ConstantInt *ShiftAmt;
5672 if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
5673 OutOpCode = Instruction::LShr;
5674 else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
5675 OutOpCode = Instruction::AShr;
5676 else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
5677 OutOpCode = Instruction::Shl;
5681 return ShiftAmt->getValue().isStrictlyPositive();
5684 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
5687 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
5688 // %iv.shifted = lshr i32 %iv, <positive constant>
5690 // Return true on a succesful match. Return the corresponding PHI node (%iv
5691 // above) in PNOut and the opcode of the shift operation in OpCodeOut.
5692 auto MatchShiftRecurrence =
5693 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
5694 Optional<Instruction::BinaryOps> PostShiftOpCode;
5697 Instruction::BinaryOps OpC;
5700 // If we encounter a shift instruction, "peel off" the shift operation,
5701 // and remember that we did so. Later when we inspect %iv's backedge
5702 // value, we will make sure that the backedge value uses the same
5705 // Note: the peeled shift operation does not have to be the same
5706 // instruction as the one feeding into the PHI's backedge value. We only
5707 // really care about it being the same *kind* of shift instruction --
5708 // that's all that is required for our later inferences to hold.
5709 if (MatchPositiveShift(LHS, V, OpC)) {
5710 PostShiftOpCode = OpC;
5715 PNOut = dyn_cast<PHINode>(LHS);
5716 if (!PNOut || PNOut->getParent() != L->getHeader())
5719 Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
5723 // The backedge value for the PHI node must be a shift by a positive
5725 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
5727 // of the PHI node itself
5730 // and the kind of shift should be match the kind of shift we peeled
5732 (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
5736 Instruction::BinaryOps OpCode;
5737 if (!MatchShiftRecurrence(LHS, PN, OpCode))
5738 return getCouldNotCompute();
5740 const DataLayout &DL = getDataLayout();
5742 // The key rationale for this optimization is that for some kinds of shift
5743 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
5744 // within a finite number of iterations. If the condition guarding the
5745 // backedge (in the sense that the backedge is taken if the condition is true)
5746 // is false for the value the shift recurrence stabilizes to, then we know
5747 // that the backedge is taken only a finite number of times.
5749 ConstantInt *StableValue = nullptr;
5752 llvm_unreachable("Impossible case!");
5754 case Instruction::AShr: {
5755 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
5756 // bitwidth(K) iterations.
5757 Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
5758 bool KnownZero, KnownOne;
5759 ComputeSignBit(FirstValue, KnownZero, KnownOne, DL, 0, nullptr,
5760 Predecessor->getTerminator(), &DT);
5761 auto *Ty = cast<IntegerType>(RHS->getType());
5763 StableValue = ConstantInt::get(Ty, 0);
5765 StableValue = ConstantInt::get(Ty, -1, true);
5767 return getCouldNotCompute();
5771 case Instruction::LShr:
5772 case Instruction::Shl:
5773 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
5774 // stabilize to 0 in at most bitwidth(K) iterations.
5775 StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
5780 ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
5781 assert(Result->getType()->isIntegerTy(1) &&
5782 "Otherwise cannot be an operand to a branch instruction");
5784 if (Result->isZeroValue()) {
5785 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
5786 const SCEV *UpperBound =
5787 getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
5788 return ExitLimit(getCouldNotCompute(), UpperBound);
5791 return getCouldNotCompute();
5794 /// CanConstantFold - Return true if we can constant fold an instruction of the
5795 /// specified type, assuming that all operands were constants.
5796 static bool CanConstantFold(const Instruction *I) {
5797 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5798 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5802 if (const CallInst *CI = dyn_cast<CallInst>(I))
5803 if (const Function *F = CI->getCalledFunction())
5804 return canConstantFoldCallTo(F);
5808 /// Determine whether this instruction can constant evolve within this loop
5809 /// assuming its operands can all constant evolve.
5810 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5811 // An instruction outside of the loop can't be derived from a loop PHI.
5812 if (!L->contains(I)) return false;
5814 if (isa<PHINode>(I)) {
5815 // We don't currently keep track of the control flow needed to evaluate
5816 // PHIs, so we cannot handle PHIs inside of loops.
5817 return L->getHeader() == I->getParent();
5820 // If we won't be able to constant fold this expression even if the operands
5821 // are constants, bail early.
5822 return CanConstantFold(I);
5825 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5826 /// recursing through each instruction operand until reaching a loop header phi.
5828 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5829 DenseMap<Instruction *, PHINode *> &PHIMap) {
5831 // Otherwise, we can evaluate this instruction if all of its operands are
5832 // constant or derived from a PHI node themselves.
5833 PHINode *PHI = nullptr;
5834 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5835 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5837 if (isa<Constant>(*OpI)) continue;
5839 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5840 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5842 PHINode *P = dyn_cast<PHINode>(OpInst);
5844 // If this operand is already visited, reuse the prior result.
5845 // We may have P != PHI if this is the deepest point at which the
5846 // inconsistent paths meet.
5847 P = PHIMap.lookup(OpInst);
5849 // Recurse and memoize the results, whether a phi is found or not.
5850 // This recursive call invalidates pointers into PHIMap.
5851 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5855 return nullptr; // Not evolving from PHI
5856 if (PHI && PHI != P)
5857 return nullptr; // Evolving from multiple different PHIs.
5860 // This is a expression evolving from a constant PHI!
5864 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5865 /// in the loop that V is derived from. We allow arbitrary operations along the
5866 /// way, but the operands of an operation must either be constants or a value
5867 /// derived from a constant PHI. If this expression does not fit with these
5868 /// constraints, return null.
5869 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5870 Instruction *I = dyn_cast<Instruction>(V);
5871 if (!I || !canConstantEvolve(I, L)) return nullptr;
5873 if (PHINode *PN = dyn_cast<PHINode>(I))
5876 // Record non-constant instructions contained by the loop.
5877 DenseMap<Instruction *, PHINode *> PHIMap;
5878 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5881 /// EvaluateExpression - Given an expression that passes the
5882 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5883 /// in the loop has the value PHIVal. If we can't fold this expression for some
5884 /// reason, return null.
5885 static Constant *EvaluateExpression(Value *V, const Loop *L,
5886 DenseMap<Instruction *, Constant *> &Vals,
5887 const DataLayout &DL,
5888 const TargetLibraryInfo *TLI) {
5889 // Convenient constant check, but redundant for recursive calls.
5890 if (Constant *C = dyn_cast<Constant>(V)) return C;
5891 Instruction *I = dyn_cast<Instruction>(V);
5892 if (!I) return nullptr;
5894 if (Constant *C = Vals.lookup(I)) return C;
5896 // An instruction inside the loop depends on a value outside the loop that we
5897 // weren't given a mapping for, or a value such as a call inside the loop.
5898 if (!canConstantEvolve(I, L)) return nullptr;
5900 // An unmapped PHI can be due to a branch or another loop inside this loop,
5901 // or due to this not being the initial iteration through a loop where we
5902 // couldn't compute the evolution of this particular PHI last time.
5903 if (isa<PHINode>(I)) return nullptr;
5905 std::vector<Constant*> Operands(I->getNumOperands());
5907 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5908 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5910 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5911 if (!Operands[i]) return nullptr;
5914 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5916 if (!C) return nullptr;
5920 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5921 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5922 Operands[1], DL, TLI);
5923 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5924 if (!LI->isVolatile())
5925 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5927 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5932 // If every incoming value to PN except the one for BB is a specific Constant,
5933 // return that, else return nullptr.
5934 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
5935 Constant *IncomingVal = nullptr;
5937 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
5938 if (PN->getIncomingBlock(i) == BB)
5941 auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
5945 if (IncomingVal != CurrentVal) {
5948 IncomingVal = CurrentVal;
5955 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5956 /// in the header of its containing loop, we know the loop executes a
5957 /// constant number of times, and the PHI node is just a recurrence
5958 /// involving constants, fold it.
5960 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5963 auto I = ConstantEvolutionLoopExitValue.find(PN);
5964 if (I != ConstantEvolutionLoopExitValue.end())
5967 if (BEs.ugt(MaxBruteForceIterations))
5968 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5970 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5972 DenseMap<Instruction *, Constant *> CurrentIterVals;
5973 BasicBlock *Header = L->getHeader();
5974 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5976 BasicBlock *Latch = L->getLoopLatch();
5980 for (auto &I : *Header) {
5981 PHINode *PHI = dyn_cast<PHINode>(&I);
5983 auto *StartCST = getOtherIncomingValue(PHI, Latch);
5984 if (!StartCST) continue;
5985 CurrentIterVals[PHI] = StartCST;
5987 if (!CurrentIterVals.count(PN))
5988 return RetVal = nullptr;
5990 Value *BEValue = PN->getIncomingValueForBlock(Latch);
5992 // Execute the loop symbolically to determine the exit value.
5993 if (BEs.getActiveBits() >= 32)
5994 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5996 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5997 unsigned IterationNum = 0;
5998 const DataLayout &DL = getDataLayout();
5999 for (; ; ++IterationNum) {
6000 if (IterationNum == NumIterations)
6001 return RetVal = CurrentIterVals[PN]; // Got exit value!
6003 // Compute the value of the PHIs for the next iteration.
6004 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
6005 DenseMap<Instruction *, Constant *> NextIterVals;
6007 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6009 return nullptr; // Couldn't evaluate!
6010 NextIterVals[PN] = NextPHI;
6012 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
6014 // Also evaluate the other PHI nodes. However, we don't get to stop if we
6015 // cease to be able to evaluate one of them or if they stop evolving,
6016 // because that doesn't necessarily prevent us from computing PN.
6017 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
6018 for (const auto &I : CurrentIterVals) {
6019 PHINode *PHI = dyn_cast<PHINode>(I.first);
6020 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
6021 PHIsToCompute.emplace_back(PHI, I.second);
6023 // We use two distinct loops because EvaluateExpression may invalidate any
6024 // iterators into CurrentIterVals.
6025 for (const auto &I : PHIsToCompute) {
6026 PHINode *PHI = I.first;
6027 Constant *&NextPHI = NextIterVals[PHI];
6028 if (!NextPHI) { // Not already computed.
6029 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6030 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6032 if (NextPHI != I.second)
6033 StoppedEvolving = false;
6036 // If all entries in CurrentIterVals == NextIterVals then we can stop
6037 // iterating, the loop can't continue to change.
6038 if (StoppedEvolving)
6039 return RetVal = CurrentIterVals[PN];
6041 CurrentIterVals.swap(NextIterVals);
6045 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
6048 PHINode *PN = getConstantEvolvingPHI(Cond, L);
6049 if (!PN) return getCouldNotCompute();
6051 // If the loop is canonicalized, the PHI will have exactly two entries.
6052 // That's the only form we support here.
6053 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
6055 DenseMap<Instruction *, Constant *> CurrentIterVals;
6056 BasicBlock *Header = L->getHeader();
6057 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6059 BasicBlock *Latch = L->getLoopLatch();
6060 assert(Latch && "Should follow from NumIncomingValues == 2!");
6062 for (auto &I : *Header) {
6063 PHINode *PHI = dyn_cast<PHINode>(&I);
6066 auto *StartCST = getOtherIncomingValue(PHI, Latch);
6067 if (!StartCST) continue;
6068 CurrentIterVals[PHI] = StartCST;
6070 if (!CurrentIterVals.count(PN))
6071 return getCouldNotCompute();
6073 // Okay, we find a PHI node that defines the trip count of this loop. Execute
6074 // the loop symbolically to determine when the condition gets a value of
6076 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
6077 const DataLayout &DL = getDataLayout();
6078 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
6079 auto *CondVal = dyn_cast_or_null<ConstantInt>(
6080 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
6082 // Couldn't symbolically evaluate.
6083 if (!CondVal) return getCouldNotCompute();
6085 if (CondVal->getValue() == uint64_t(ExitWhen)) {
6086 ++NumBruteForceTripCountsComputed;
6087 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
6090 // Update all the PHI nodes for the next iteration.
6091 DenseMap<Instruction *, Constant *> NextIterVals;
6093 // Create a list of which PHIs we need to compute. We want to do this before
6094 // calling EvaluateExpression on them because that may invalidate iterators
6095 // into CurrentIterVals.
6096 SmallVector<PHINode *, 8> PHIsToCompute;
6097 for (const auto &I : CurrentIterVals) {
6098 PHINode *PHI = dyn_cast<PHINode>(I.first);
6099 if (!PHI || PHI->getParent() != Header) continue;
6100 PHIsToCompute.push_back(PHI);
6102 for (PHINode *PHI : PHIsToCompute) {
6103 Constant *&NextPHI = NextIterVals[PHI];
6104 if (NextPHI) continue; // Already computed!
6106 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6107 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6109 CurrentIterVals.swap(NextIterVals);
6112 // Too many iterations were needed to evaluate.
6113 return getCouldNotCompute();
6116 /// getSCEVAtScope - Return a SCEV expression for the specified value
6117 /// at the specified scope in the program. The L value specifies a loop
6118 /// nest to evaluate the expression at, where null is the top-level or a
6119 /// specified loop is immediately inside of the loop.
6121 /// This method can be used to compute the exit value for a variable defined
6122 /// in a loop by querying what the value will hold in the parent loop.
6124 /// In the case that a relevant loop exit value cannot be computed, the
6125 /// original value V is returned.
6126 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
6127 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
6129 // Check to see if we've folded this expression at this loop before.
6130 for (auto &LS : Values)
6132 return LS.second ? LS.second : V;
6134 Values.emplace_back(L, nullptr);
6136 // Otherwise compute it.
6137 const SCEV *C = computeSCEVAtScope(V, L);
6138 for (auto &LS : reverse(ValuesAtScopes[V]))
6139 if (LS.first == L) {
6146 /// This builds up a Constant using the ConstantExpr interface. That way, we
6147 /// will return Constants for objects which aren't represented by a
6148 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
6149 /// Returns NULL if the SCEV isn't representable as a Constant.
6150 static Constant *BuildConstantFromSCEV(const SCEV *V) {
6151 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
6152 case scCouldNotCompute:
6156 return cast<SCEVConstant>(V)->getValue();
6158 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
6159 case scSignExtend: {
6160 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
6161 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
6162 return ConstantExpr::getSExt(CastOp, SS->getType());
6165 case scZeroExtend: {
6166 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
6167 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
6168 return ConstantExpr::getZExt(CastOp, SZ->getType());
6172 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
6173 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
6174 return ConstantExpr::getTrunc(CastOp, ST->getType());
6178 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
6179 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
6180 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6181 unsigned AS = PTy->getAddressSpace();
6182 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6183 C = ConstantExpr::getBitCast(C, DestPtrTy);
6185 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
6186 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
6187 if (!C2) return nullptr;
6190 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
6191 unsigned AS = C2->getType()->getPointerAddressSpace();
6193 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6194 // The offsets have been converted to bytes. We can add bytes to an
6195 // i8* by GEP with the byte count in the first index.
6196 C = ConstantExpr::getBitCast(C, DestPtrTy);
6199 // Don't bother trying to sum two pointers. We probably can't
6200 // statically compute a load that results from it anyway.
6201 if (C2->getType()->isPointerTy())
6204 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6205 if (PTy->getElementType()->isStructTy())
6206 C2 = ConstantExpr::getIntegerCast(
6207 C2, Type::getInt32Ty(C->getContext()), true);
6208 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
6210 C = ConstantExpr::getAdd(C, C2);
6217 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
6218 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
6219 // Don't bother with pointers at all.
6220 if (C->getType()->isPointerTy()) return nullptr;
6221 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
6222 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
6223 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
6224 C = ConstantExpr::getMul(C, C2);
6231 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6232 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6233 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6234 if (LHS->getType() == RHS->getType())
6235 return ConstantExpr::getUDiv(LHS, RHS);
6240 break; // TODO: smax, umax.
6245 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6246 if (isa<SCEVConstant>(V)) return V;
6248 // If this instruction is evolved from a constant-evolving PHI, compute the
6249 // exit value from the loop without using SCEVs.
6250 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6251 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6252 const Loop *LI = this->LI[I->getParent()];
6253 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
6254 if (PHINode *PN = dyn_cast<PHINode>(I))
6255 if (PN->getParent() == LI->getHeader()) {
6256 // Okay, there is no closed form solution for the PHI node. Check
6257 // to see if the loop that contains it has a known backedge-taken
6258 // count. If so, we may be able to force computation of the exit
6260 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6261 if (const SCEVConstant *BTCC =
6262 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6263 // Okay, we know how many times the containing loop executes. If
6264 // this is a constant evolving PHI node, get the final value at
6265 // the specified iteration number.
6266 Constant *RV = getConstantEvolutionLoopExitValue(PN,
6267 BTCC->getValue()->getValue(),
6269 if (RV) return getSCEV(RV);
6273 // Okay, this is an expression that we cannot symbolically evaluate
6274 // into a SCEV. Check to see if it's possible to symbolically evaluate
6275 // the arguments into constants, and if so, try to constant propagate the
6276 // result. This is particularly useful for computing loop exit values.
6277 if (CanConstantFold(I)) {
6278 SmallVector<Constant *, 4> Operands;
6279 bool MadeImprovement = false;
6280 for (Value *Op : I->operands()) {
6281 if (Constant *C = dyn_cast<Constant>(Op)) {
6282 Operands.push_back(C);
6286 // If any of the operands is non-constant and if they are
6287 // non-integer and non-pointer, don't even try to analyze them
6288 // with scev techniques.
6289 if (!isSCEVable(Op->getType()))
6292 const SCEV *OrigV = getSCEV(Op);
6293 const SCEV *OpV = getSCEVAtScope(OrigV, L);
6294 MadeImprovement |= OrigV != OpV;
6296 Constant *C = BuildConstantFromSCEV(OpV);
6298 if (C->getType() != Op->getType())
6299 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6303 Operands.push_back(C);
6306 // Check to see if getSCEVAtScope actually made an improvement.
6307 if (MadeImprovement) {
6308 Constant *C = nullptr;
6309 const DataLayout &DL = getDataLayout();
6310 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6311 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6312 Operands[1], DL, &TLI);
6313 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6314 if (!LI->isVolatile())
6315 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
6317 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
6325 // This is some other type of SCEVUnknown, just return it.
6329 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6330 // Avoid performing the look-up in the common case where the specified
6331 // expression has no loop-variant portions.
6332 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6333 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6334 if (OpAtScope != Comm->getOperand(i)) {
6335 // Okay, at least one of these operands is loop variant but might be
6336 // foldable. Build a new instance of the folded commutative expression.
6337 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6338 Comm->op_begin()+i);
6339 NewOps.push_back(OpAtScope);
6341 for (++i; i != e; ++i) {
6342 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6343 NewOps.push_back(OpAtScope);
6345 if (isa<SCEVAddExpr>(Comm))
6346 return getAddExpr(NewOps);
6347 if (isa<SCEVMulExpr>(Comm))
6348 return getMulExpr(NewOps);
6349 if (isa<SCEVSMaxExpr>(Comm))
6350 return getSMaxExpr(NewOps);
6351 if (isa<SCEVUMaxExpr>(Comm))
6352 return getUMaxExpr(NewOps);
6353 llvm_unreachable("Unknown commutative SCEV type!");
6356 // If we got here, all operands are loop invariant.
6360 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6361 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6362 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6363 if (LHS == Div->getLHS() && RHS == Div->getRHS())
6364 return Div; // must be loop invariant
6365 return getUDivExpr(LHS, RHS);
6368 // If this is a loop recurrence for a loop that does not contain L, then we
6369 // are dealing with the final value computed by the loop.
6370 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6371 // First, attempt to evaluate each operand.
6372 // Avoid performing the look-up in the common case where the specified
6373 // expression has no loop-variant portions.
6374 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6375 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6376 if (OpAtScope == AddRec->getOperand(i))
6379 // Okay, at least one of these operands is loop variant but might be
6380 // foldable. Build a new instance of the folded commutative expression.
6381 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6382 AddRec->op_begin()+i);
6383 NewOps.push_back(OpAtScope);
6384 for (++i; i != e; ++i)
6385 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6387 const SCEV *FoldedRec =
6388 getAddRecExpr(NewOps, AddRec->getLoop(),
6389 AddRec->getNoWrapFlags(SCEV::FlagNW));
6390 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6391 // The addrec may be folded to a nonrecurrence, for example, if the
6392 // induction variable is multiplied by zero after constant folding. Go
6393 // ahead and return the folded value.
6399 // If the scope is outside the addrec's loop, evaluate it by using the
6400 // loop exit value of the addrec.
6401 if (!AddRec->getLoop()->contains(L)) {
6402 // To evaluate this recurrence, we need to know how many times the AddRec
6403 // loop iterates. Compute this now.
6404 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6405 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6407 // Then, evaluate the AddRec.
6408 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6414 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6415 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6416 if (Op == Cast->getOperand())
6417 return Cast; // must be loop invariant
6418 return getZeroExtendExpr(Op, Cast->getType());
6421 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6422 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6423 if (Op == Cast->getOperand())
6424 return Cast; // must be loop invariant
6425 return getSignExtendExpr(Op, Cast->getType());
6428 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6429 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6430 if (Op == Cast->getOperand())
6431 return Cast; // must be loop invariant
6432 return getTruncateExpr(Op, Cast->getType());
6435 llvm_unreachable("Unknown SCEV type!");
6438 /// getSCEVAtScope - This is a convenience function which does
6439 /// getSCEVAtScope(getSCEV(V), L).
6440 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6441 return getSCEVAtScope(getSCEV(V), L);
6444 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6445 /// following equation:
6447 /// A * X = B (mod N)
6449 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6450 /// A and B isn't important.
6452 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6453 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6454 ScalarEvolution &SE) {
6455 uint32_t BW = A.getBitWidth();
6456 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6457 assert(A != 0 && "A must be non-zero.");
6461 // The gcd of A and N may have only one prime factor: 2. The number of
6462 // trailing zeros in A is its multiplicity
6463 uint32_t Mult2 = A.countTrailingZeros();
6466 // 2. Check if B is divisible by D.
6468 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6469 // is not less than multiplicity of this prime factor for D.
6470 if (B.countTrailingZeros() < Mult2)
6471 return SE.getCouldNotCompute();
6473 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6476 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6477 // bit width during computations.
6478 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6479 APInt Mod(BW + 1, 0);
6480 Mod.setBit(BW - Mult2); // Mod = N / D
6481 APInt I = AD.multiplicativeInverse(Mod);
6483 // 4. Compute the minimum unsigned root of the equation:
6484 // I * (B / D) mod (N / D)
6485 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6487 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6489 return SE.getConstant(Result.trunc(BW));
6492 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6493 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6494 /// might be the same) or two SCEVCouldNotCompute objects.
6496 static std::pair<const SCEV *,const SCEV *>
6497 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6498 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6499 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6500 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6501 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6503 // We currently can only solve this if the coefficients are constants.
6504 if (!LC || !MC || !NC) {
6505 const SCEV *CNC = SE.getCouldNotCompute();
6506 return std::make_pair(CNC, CNC);
6509 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6510 const APInt &L = LC->getValue()->getValue();
6511 const APInt &M = MC->getValue()->getValue();
6512 const APInt &N = NC->getValue()->getValue();
6513 APInt Two(BitWidth, 2);
6514 APInt Four(BitWidth, 4);
6517 using namespace APIntOps;
6519 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6520 // The B coefficient is M-N/2
6524 // The A coefficient is N/2
6525 APInt A(N.sdiv(Two));
6527 // Compute the B^2-4ac term.
6530 SqrtTerm -= Four * (A * C);
6532 if (SqrtTerm.isNegative()) {
6533 // The loop is provably infinite.
6534 const SCEV *CNC = SE.getCouldNotCompute();
6535 return std::make_pair(CNC, CNC);
6538 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6539 // integer value or else APInt::sqrt() will assert.
6540 APInt SqrtVal(SqrtTerm.sqrt());
6542 // Compute the two solutions for the quadratic formula.
6543 // The divisions must be performed as signed divisions.
6546 if (TwoA.isMinValue()) {
6547 const SCEV *CNC = SE.getCouldNotCompute();
6548 return std::make_pair(CNC, CNC);
6551 LLVMContext &Context = SE.getContext();
6553 ConstantInt *Solution1 =
6554 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6555 ConstantInt *Solution2 =
6556 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6558 return std::make_pair(SE.getConstant(Solution1),
6559 SE.getConstant(Solution2));
6560 } // end APIntOps namespace
6563 /// HowFarToZero - Return the number of times a backedge comparing the specified
6564 /// value to zero will execute. If not computable, return CouldNotCompute.
6566 /// This is only used for loops with a "x != y" exit test. The exit condition is
6567 /// now expressed as a single expression, V = x-y. So the exit test is
6568 /// effectively V != 0. We know and take advantage of the fact that this
6569 /// expression only being used in a comparison by zero context.
6570 ScalarEvolution::ExitLimit
6571 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6572 // If the value is a constant
6573 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6574 // If the value is already zero, the branch will execute zero times.
6575 if (C->getValue()->isZero()) return C;
6576 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6579 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6580 if (!AddRec || AddRec->getLoop() != L)
6581 return getCouldNotCompute();
6583 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6584 // the quadratic equation to solve it.
6585 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6586 std::pair<const SCEV *,const SCEV *> Roots =
6587 SolveQuadraticEquation(AddRec, *this);
6588 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6589 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6591 // Pick the smallest positive root value.
6592 if (ConstantInt *CB =
6593 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6596 if (!CB->getZExtValue())
6597 std::swap(R1, R2); // R1 is the minimum root now.
6599 // We can only use this value if the chrec ends up with an exact zero
6600 // value at this index. When solving for "X*X != 5", for example, we
6601 // should not accept a root of 2.
6602 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6604 return R1; // We found a quadratic root!
6607 return getCouldNotCompute();
6610 // Otherwise we can only handle this if it is affine.
6611 if (!AddRec->isAffine())
6612 return getCouldNotCompute();
6614 // If this is an affine expression, the execution count of this branch is
6615 // the minimum unsigned root of the following equation:
6617 // Start + Step*N = 0 (mod 2^BW)
6621 // Step*N = -Start (mod 2^BW)
6623 // where BW is the common bit width of Start and Step.
6625 // Get the initial value for the loop.
6626 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6627 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6629 // For now we handle only constant steps.
6631 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6632 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6633 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6634 // We have not yet seen any such cases.
6635 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6636 if (!StepC || StepC->getValue()->equalsInt(0))
6637 return getCouldNotCompute();
6639 // For positive steps (counting up until unsigned overflow):
6640 // N = -Start/Step (as unsigned)
6641 // For negative steps (counting down to zero):
6643 // First compute the unsigned distance from zero in the direction of Step.
6644 bool CountDown = StepC->getValue()->getValue().isNegative();
6645 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6647 // Handle unitary steps, which cannot wraparound.
6648 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6649 // N = Distance (as unsigned)
6650 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6651 ConstantRange CR = getUnsignedRange(Start);
6652 const SCEV *MaxBECount;
6653 if (!CountDown && CR.getUnsignedMin().isMinValue())
6654 // When counting up, the worst starting value is 1, not 0.
6655 MaxBECount = CR.getUnsignedMax().isMinValue()
6656 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6657 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6659 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6660 : -CR.getUnsignedMin());
6661 return ExitLimit(Distance, MaxBECount);
6664 // As a special case, handle the instance where Step is a positive power of
6665 // two. In this case, determining whether Step divides Distance evenly can be
6666 // done by counting and comparing the number of trailing zeros of Step and
6669 const APInt &StepV = StepC->getValue()->getValue();
6670 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6671 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6672 // case is not handled as this code is guarded by !CountDown.
6673 if (StepV.isPowerOf2() &&
6674 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
6675 // Here we've constrained the equation to be of the form
6677 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
6679 // where we're operating on a W bit wide integer domain and k is
6680 // non-negative. The smallest unsigned solution for X is the trip count.
6682 // (0) is equivalent to:
6684 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
6685 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
6686 // <=> 2^k * Distance' - X = L * 2^(W - N)
6687 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
6689 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
6692 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
6694 // E.g. say we're solving
6696 // 2 * Val = 2 * X (in i8) ... (3)
6698 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
6700 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
6701 // necessarily the smallest unsigned value of X that satisfies (3).
6702 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
6703 // is i8 1, not i8 -127
6705 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
6707 // Since SCEV does not have a URem node, we construct one using a truncate
6708 // and a zero extend.
6710 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
6711 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
6712 auto *WideTy = Distance->getType();
6714 return getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
6718 // If the condition controls loop exit (the loop exits only if the expression
6719 // is true) and the addition is no-wrap we can use unsigned divide to
6720 // compute the backedge count. In this case, the step may not divide the
6721 // distance, but we don't care because if the condition is "missed" the loop
6722 // will have undefined behavior due to wrapping.
6723 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6725 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6726 return ExitLimit(Exact, Exact);
6729 // Then, try to solve the above equation provided that Start is constant.
6730 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6731 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6732 -StartC->getValue()->getValue(),
6734 return getCouldNotCompute();
6737 /// HowFarToNonZero - Return the number of times a backedge checking the
6738 /// specified value for nonzero will execute. If not computable, return
6740 ScalarEvolution::ExitLimit
6741 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6742 // Loops that look like: while (X == 0) are very strange indeed. We don't
6743 // handle them yet except for the trivial case. This could be expanded in the
6744 // future as needed.
6746 // If the value is a constant, check to see if it is known to be non-zero
6747 // already. If so, the backedge will execute zero times.
6748 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6749 if (!C->getValue()->isNullValue())
6750 return getZero(C->getType());
6751 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6754 // We could implement others, but I really doubt anyone writes loops like
6755 // this, and if they did, they would already be constant folded.
6756 return getCouldNotCompute();
6759 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6760 /// (which may not be an immediate predecessor) which has exactly one
6761 /// successor from which BB is reachable, or null if no such block is
6764 std::pair<BasicBlock *, BasicBlock *>
6765 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6766 // If the block has a unique predecessor, then there is no path from the
6767 // predecessor to the block that does not go through the direct edge
6768 // from the predecessor to the block.
6769 if (BasicBlock *Pred = BB->getSinglePredecessor())
6770 return std::make_pair(Pred, BB);
6772 // A loop's header is defined to be a block that dominates the loop.
6773 // If the header has a unique predecessor outside the loop, it must be
6774 // a block that has exactly one successor that can reach the loop.
6775 if (Loop *L = LI.getLoopFor(BB))
6776 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6778 return std::pair<BasicBlock *, BasicBlock *>();
6781 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6782 /// testing whether two expressions are equal, however for the purposes of
6783 /// looking for a condition guarding a loop, it can be useful to be a little
6784 /// more general, since a front-end may have replicated the controlling
6787 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6788 // Quick check to see if they are the same SCEV.
6789 if (A == B) return true;
6791 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
6792 // Not all instructions that are "identical" compute the same value. For
6793 // instance, two distinct alloca instructions allocating the same type are
6794 // identical and do not read memory; but compute distinct values.
6795 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
6798 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6799 // two different instructions with the same value. Check for this case.
6800 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6801 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6802 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6803 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6804 if (ComputesEqualValues(AI, BI))
6807 // Otherwise assume they may have a different value.
6811 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6812 /// predicate Pred. Return true iff any changes were made.
6814 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6815 const SCEV *&LHS, const SCEV *&RHS,
6817 bool Changed = false;
6819 // If we hit the max recursion limit bail out.
6823 // Canonicalize a constant to the right side.
6824 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6825 // Check for both operands constant.
6826 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6827 if (ConstantExpr::getICmp(Pred,
6829 RHSC->getValue())->isNullValue())
6830 goto trivially_false;
6832 goto trivially_true;
6834 // Otherwise swap the operands to put the constant on the right.
6835 std::swap(LHS, RHS);
6836 Pred = ICmpInst::getSwappedPredicate(Pred);
6840 // If we're comparing an addrec with a value which is loop-invariant in the
6841 // addrec's loop, put the addrec on the left. Also make a dominance check,
6842 // as both operands could be addrecs loop-invariant in each other's loop.
6843 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6844 const Loop *L = AR->getLoop();
6845 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6846 std::swap(LHS, RHS);
6847 Pred = ICmpInst::getSwappedPredicate(Pred);
6852 // If there's a constant operand, canonicalize comparisons with boundary
6853 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6854 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6855 const APInt &RA = RC->getValue()->getValue();
6857 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6858 case ICmpInst::ICMP_EQ:
6859 case ICmpInst::ICMP_NE:
6860 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6862 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6863 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6864 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6865 ME->getOperand(0)->isAllOnesValue()) {
6866 RHS = AE->getOperand(1);
6867 LHS = ME->getOperand(1);
6871 case ICmpInst::ICMP_UGE:
6872 if ((RA - 1).isMinValue()) {
6873 Pred = ICmpInst::ICMP_NE;
6874 RHS = getConstant(RA - 1);
6878 if (RA.isMaxValue()) {
6879 Pred = ICmpInst::ICMP_EQ;
6883 if (RA.isMinValue()) goto trivially_true;
6885 Pred = ICmpInst::ICMP_UGT;
6886 RHS = getConstant(RA - 1);
6889 case ICmpInst::ICMP_ULE:
6890 if ((RA + 1).isMaxValue()) {
6891 Pred = ICmpInst::ICMP_NE;
6892 RHS = getConstant(RA + 1);
6896 if (RA.isMinValue()) {
6897 Pred = ICmpInst::ICMP_EQ;
6901 if (RA.isMaxValue()) goto trivially_true;
6903 Pred = ICmpInst::ICMP_ULT;
6904 RHS = getConstant(RA + 1);
6907 case ICmpInst::ICMP_SGE:
6908 if ((RA - 1).isMinSignedValue()) {
6909 Pred = ICmpInst::ICMP_NE;
6910 RHS = getConstant(RA - 1);
6914 if (RA.isMaxSignedValue()) {
6915 Pred = ICmpInst::ICMP_EQ;
6919 if (RA.isMinSignedValue()) goto trivially_true;
6921 Pred = ICmpInst::ICMP_SGT;
6922 RHS = getConstant(RA - 1);
6925 case ICmpInst::ICMP_SLE:
6926 if ((RA + 1).isMaxSignedValue()) {
6927 Pred = ICmpInst::ICMP_NE;
6928 RHS = getConstant(RA + 1);
6932 if (RA.isMinSignedValue()) {
6933 Pred = ICmpInst::ICMP_EQ;
6937 if (RA.isMaxSignedValue()) goto trivially_true;
6939 Pred = ICmpInst::ICMP_SLT;
6940 RHS = getConstant(RA + 1);
6943 case ICmpInst::ICMP_UGT:
6944 if (RA.isMinValue()) {
6945 Pred = ICmpInst::ICMP_NE;
6949 if ((RA + 1).isMaxValue()) {
6950 Pred = ICmpInst::ICMP_EQ;
6951 RHS = getConstant(RA + 1);
6955 if (RA.isMaxValue()) goto trivially_false;
6957 case ICmpInst::ICMP_ULT:
6958 if (RA.isMaxValue()) {
6959 Pred = ICmpInst::ICMP_NE;
6963 if ((RA - 1).isMinValue()) {
6964 Pred = ICmpInst::ICMP_EQ;
6965 RHS = getConstant(RA - 1);
6969 if (RA.isMinValue()) goto trivially_false;
6971 case ICmpInst::ICMP_SGT:
6972 if (RA.isMinSignedValue()) {
6973 Pred = ICmpInst::ICMP_NE;
6977 if ((RA + 1).isMaxSignedValue()) {
6978 Pred = ICmpInst::ICMP_EQ;
6979 RHS = getConstant(RA + 1);
6983 if (RA.isMaxSignedValue()) goto trivially_false;
6985 case ICmpInst::ICMP_SLT:
6986 if (RA.isMaxSignedValue()) {
6987 Pred = ICmpInst::ICMP_NE;
6991 if ((RA - 1).isMinSignedValue()) {
6992 Pred = ICmpInst::ICMP_EQ;
6993 RHS = getConstant(RA - 1);
6997 if (RA.isMinSignedValue()) goto trivially_false;
7002 // Check for obvious equality.
7003 if (HasSameValue(LHS, RHS)) {
7004 if (ICmpInst::isTrueWhenEqual(Pred))
7005 goto trivially_true;
7006 if (ICmpInst::isFalseWhenEqual(Pred))
7007 goto trivially_false;
7010 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
7011 // adding or subtracting 1 from one of the operands.
7013 case ICmpInst::ICMP_SLE:
7014 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
7015 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7017 Pred = ICmpInst::ICMP_SLT;
7019 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
7020 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
7022 Pred = ICmpInst::ICMP_SLT;
7026 case ICmpInst::ICMP_SGE:
7027 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
7028 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
7030 Pred = ICmpInst::ICMP_SGT;
7032 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
7033 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7035 Pred = ICmpInst::ICMP_SGT;
7039 case ICmpInst::ICMP_ULE:
7040 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
7041 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7043 Pred = ICmpInst::ICMP_ULT;
7045 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
7046 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
7047 Pred = ICmpInst::ICMP_ULT;
7051 case ICmpInst::ICMP_UGE:
7052 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
7053 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
7054 Pred = ICmpInst::ICMP_UGT;
7056 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
7057 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7059 Pred = ICmpInst::ICMP_UGT;
7067 // TODO: More simplifications are possible here.
7069 // Recursively simplify until we either hit a recursion limit or nothing
7072 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
7078 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7079 Pred = ICmpInst::ICMP_EQ;
7084 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7085 Pred = ICmpInst::ICMP_NE;
7089 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
7090 return getSignedRange(S).getSignedMax().isNegative();
7093 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
7094 return getSignedRange(S).getSignedMin().isStrictlyPositive();
7097 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
7098 return !getSignedRange(S).getSignedMin().isNegative();
7101 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
7102 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
7105 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
7106 return isKnownNegative(S) || isKnownPositive(S);
7109 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
7110 const SCEV *LHS, const SCEV *RHS) {
7111 // Canonicalize the inputs first.
7112 (void)SimplifyICmpOperands(Pred, LHS, RHS);
7114 // If LHS or RHS is an addrec, check to see if the condition is true in
7115 // every iteration of the loop.
7116 // If LHS and RHS are both addrec, both conditions must be true in
7117 // every iteration of the loop.
7118 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7119 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7120 bool LeftGuarded = false;
7121 bool RightGuarded = false;
7123 const Loop *L = LAR->getLoop();
7124 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
7125 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
7126 if (!RAR) return true;
7131 const Loop *L = RAR->getLoop();
7132 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
7133 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
7134 if (!LAR) return true;
7135 RightGuarded = true;
7138 if (LeftGuarded && RightGuarded)
7141 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
7144 // Otherwise see what can be done with known constant ranges.
7145 return isKnownPredicateWithRanges(Pred, LHS, RHS);
7148 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
7149 ICmpInst::Predicate Pred,
7151 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
7154 // Verify an invariant: inverting the predicate should turn a monotonically
7155 // increasing change to a monotonically decreasing one, and vice versa.
7156 bool IncreasingSwapped;
7157 bool ResultSwapped = isMonotonicPredicateImpl(
7158 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
7160 assert(Result == ResultSwapped && "should be able to analyze both!");
7162 assert(Increasing == !IncreasingSwapped &&
7163 "monotonicity should flip as we flip the predicate");
7169 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
7170 ICmpInst::Predicate Pred,
7173 // A zero step value for LHS means the induction variable is essentially a
7174 // loop invariant value. We don't really depend on the predicate actually
7175 // flipping from false to true (for increasing predicates, and the other way
7176 // around for decreasing predicates), all we care about is that *if* the
7177 // predicate changes then it only changes from false to true.
7179 // A zero step value in itself is not very useful, but there may be places
7180 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
7181 // as general as possible.
7185 return false; // Conservative answer
7187 case ICmpInst::ICMP_UGT:
7188 case ICmpInst::ICMP_UGE:
7189 case ICmpInst::ICMP_ULT:
7190 case ICmpInst::ICMP_ULE:
7191 if (!LHS->getNoWrapFlags(SCEV::FlagNUW))
7194 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
7197 case ICmpInst::ICMP_SGT:
7198 case ICmpInst::ICMP_SGE:
7199 case ICmpInst::ICMP_SLT:
7200 case ICmpInst::ICMP_SLE: {
7201 if (!LHS->getNoWrapFlags(SCEV::FlagNSW))
7204 const SCEV *Step = LHS->getStepRecurrence(*this);
7206 if (isKnownNonNegative(Step)) {
7207 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
7211 if (isKnownNonPositive(Step)) {
7212 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7221 llvm_unreachable("switch has default clause!");
7224 bool ScalarEvolution::isLoopInvariantPredicate(
7225 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7226 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7227 const SCEV *&InvariantRHS) {
7229 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7230 if (!isLoopInvariant(RHS, L)) {
7231 if (!isLoopInvariant(LHS, L))
7234 std::swap(LHS, RHS);
7235 Pred = ICmpInst::getSwappedPredicate(Pred);
7238 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7239 if (!ArLHS || ArLHS->getLoop() != L)
7243 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7246 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7247 // true as the loop iterates, and the backedge is control dependent on
7248 // "ArLHS `Pred` RHS" == true then we can reason as follows:
7250 // * if the predicate was false in the first iteration then the predicate
7251 // is never evaluated again, since the loop exits without taking the
7253 // * if the predicate was true in the first iteration then it will
7254 // continue to be true for all future iterations since it is
7255 // monotonically increasing.
7257 // For both the above possibilities, we can replace the loop varying
7258 // predicate with its value on the first iteration of the loop (which is
7261 // A similar reasoning applies for a monotonically decreasing predicate, by
7262 // replacing true with false and false with true in the above two bullets.
7264 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7266 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7269 InvariantPred = Pred;
7270 InvariantLHS = ArLHS->getStart();
7276 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
7277 const SCEV *LHS, const SCEV *RHS) {
7278 if (HasSameValue(LHS, RHS))
7279 return ICmpInst::isTrueWhenEqual(Pred);
7281 // This code is split out from isKnownPredicate because it is called from
7282 // within isLoopEntryGuardedByCond.
7285 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7286 case ICmpInst::ICMP_SGT:
7287 std::swap(LHS, RHS);
7288 case ICmpInst::ICMP_SLT: {
7289 ConstantRange LHSRange = getSignedRange(LHS);
7290 ConstantRange RHSRange = getSignedRange(RHS);
7291 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
7293 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
7297 case ICmpInst::ICMP_SGE:
7298 std::swap(LHS, RHS);
7299 case ICmpInst::ICMP_SLE: {
7300 ConstantRange LHSRange = getSignedRange(LHS);
7301 ConstantRange RHSRange = getSignedRange(RHS);
7302 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
7304 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
7308 case ICmpInst::ICMP_UGT:
7309 std::swap(LHS, RHS);
7310 case ICmpInst::ICMP_ULT: {
7311 ConstantRange LHSRange = getUnsignedRange(LHS);
7312 ConstantRange RHSRange = getUnsignedRange(RHS);
7313 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
7315 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
7319 case ICmpInst::ICMP_UGE:
7320 std::swap(LHS, RHS);
7321 case ICmpInst::ICMP_ULE: {
7322 ConstantRange LHSRange = getUnsignedRange(LHS);
7323 ConstantRange RHSRange = getUnsignedRange(RHS);
7324 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
7326 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
7330 case ICmpInst::ICMP_NE: {
7331 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
7333 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
7336 const SCEV *Diff = getMinusSCEV(LHS, RHS);
7337 if (isKnownNonZero(Diff))
7341 case ICmpInst::ICMP_EQ:
7342 // The check at the top of the function catches the case where
7343 // the values are known to be equal.
7349 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
7353 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
7354 // Return Y via OutY.
7355 auto MatchBinaryAddToConst =
7356 [this](const SCEV *Result, const SCEV *X, APInt &OutY,
7357 SCEV::NoWrapFlags ExpectedFlags) {
7358 const SCEV *NonConstOp, *ConstOp;
7359 SCEV::NoWrapFlags FlagsPresent;
7361 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
7362 !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
7365 OutY = cast<SCEVConstant>(ConstOp)->getValue()->getValue();
7366 return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
7375 case ICmpInst::ICMP_SGE:
7376 std::swap(LHS, RHS);
7377 case ICmpInst::ICMP_SLE:
7378 // X s<= (X + C)<nsw> if C >= 0
7379 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
7382 // (X + C)<nsw> s<= X if C <= 0
7383 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
7384 !C.isStrictlyPositive())
7388 case ICmpInst::ICMP_SGT:
7389 std::swap(LHS, RHS);
7390 case ICmpInst::ICMP_SLT:
7391 // X s< (X + C)<nsw> if C > 0
7392 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
7393 C.isStrictlyPositive())
7396 // (X + C)<nsw> s< X if C < 0
7397 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
7405 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7408 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
7411 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7412 // the stack can result in exponential time complexity.
7413 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7415 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7417 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7418 // isKnownPredicate. isKnownPredicate is more powerful, but also more
7419 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7420 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
7421 // use isKnownPredicate later if needed.
7422 return isKnownNonNegative(RHS) &&
7423 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7424 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
7427 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7428 /// protected by a conditional between LHS and RHS. This is used to
7429 /// to eliminate casts.
7431 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7432 ICmpInst::Predicate Pred,
7433 const SCEV *LHS, const SCEV *RHS) {
7434 // Interpret a null as meaning no loop, where there is obviously no guard
7435 // (interprocedural conditions notwithstanding).
7436 if (!L) return true;
7438 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7440 BasicBlock *Latch = L->getLoopLatch();
7444 BranchInst *LoopContinuePredicate =
7445 dyn_cast<BranchInst>(Latch->getTerminator());
7446 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7447 isImpliedCond(Pred, LHS, RHS,
7448 LoopContinuePredicate->getCondition(),
7449 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7452 // We don't want more than one activation of the following loops on the stack
7453 // -- that can lead to O(n!) time complexity.
7454 if (WalkingBEDominatingConds)
7457 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7459 // See if we can exploit a trip count to prove the predicate.
7460 const auto &BETakenInfo = getBackedgeTakenInfo(L);
7461 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7462 if (LatchBECount != getCouldNotCompute()) {
7463 // We know that Latch branches back to the loop header exactly
7464 // LatchBECount times. This means the backdege condition at Latch is
7465 // equivalent to "{0,+,1} u< LatchBECount".
7466 Type *Ty = LatchBECount->getType();
7467 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7468 const SCEV *LoopCounter =
7469 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7470 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7475 // Check conditions due to any @llvm.assume intrinsics.
7476 for (auto &AssumeVH : AC.assumptions()) {
7479 auto *CI = cast<CallInst>(AssumeVH);
7480 if (!DT.dominates(CI, Latch->getTerminator()))
7483 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7487 // If the loop is not reachable from the entry block, we risk running into an
7488 // infinite loop as we walk up into the dom tree. These loops do not matter
7489 // anyway, so we just return a conservative answer when we see them.
7490 if (!DT.isReachableFromEntry(L->getHeader()))
7493 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7494 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7496 assert(DTN && "should reach the loop header before reaching the root!");
7498 BasicBlock *BB = DTN->getBlock();
7499 BasicBlock *PBB = BB->getSinglePredecessor();
7503 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7504 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7507 Value *Condition = ContinuePredicate->getCondition();
7509 // If we have an edge `E` within the loop body that dominates the only
7510 // latch, the condition guarding `E` also guards the backedge. This
7511 // reasoning works only for loops with a single latch.
7513 BasicBlockEdge DominatingEdge(PBB, BB);
7514 if (DominatingEdge.isSingleEdge()) {
7515 // We're constructively (and conservatively) enumerating edges within the
7516 // loop body that dominate the latch. The dominator tree better agree
7518 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7520 if (isImpliedCond(Pred, LHS, RHS, Condition,
7521 BB != ContinuePredicate->getSuccessor(0)))
7529 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7530 /// by a conditional between LHS and RHS. This is used to help avoid max
7531 /// expressions in loop trip counts, and to eliminate casts.
7533 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7534 ICmpInst::Predicate Pred,
7535 const SCEV *LHS, const SCEV *RHS) {
7536 // Interpret a null as meaning no loop, where there is obviously no guard
7537 // (interprocedural conditions notwithstanding).
7538 if (!L) return false;
7540 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7542 // Starting at the loop predecessor, climb up the predecessor chain, as long
7543 // as there are predecessors that can be found that have unique successors
7544 // leading to the original header.
7545 for (std::pair<BasicBlock *, BasicBlock *>
7546 Pair(L->getLoopPredecessor(), L->getHeader());
7548 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7550 BranchInst *LoopEntryPredicate =
7551 dyn_cast<BranchInst>(Pair.first->getTerminator());
7552 if (!LoopEntryPredicate ||
7553 LoopEntryPredicate->isUnconditional())
7556 if (isImpliedCond(Pred, LHS, RHS,
7557 LoopEntryPredicate->getCondition(),
7558 LoopEntryPredicate->getSuccessor(0) != Pair.second))
7562 // Check conditions due to any @llvm.assume intrinsics.
7563 for (auto &AssumeVH : AC.assumptions()) {
7566 auto *CI = cast<CallInst>(AssumeVH);
7567 if (!DT.dominates(CI, L->getHeader()))
7570 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7578 /// RAII wrapper to prevent recursive application of isImpliedCond.
7579 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7580 /// currently evaluating isImpliedCond.
7581 struct MarkPendingLoopPredicate {
7583 DenseSet<Value*> &LoopPreds;
7586 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7587 : Cond(C), LoopPreds(LP) {
7588 Pending = !LoopPreds.insert(Cond).second;
7590 ~MarkPendingLoopPredicate() {
7592 LoopPreds.erase(Cond);
7595 } // end anonymous namespace
7597 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7598 /// and RHS is true whenever the given Cond value evaluates to true.
7599 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7600 const SCEV *LHS, const SCEV *RHS,
7601 Value *FoundCondValue,
7603 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7607 // Recursively handle And and Or conditions.
7608 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7609 if (BO->getOpcode() == Instruction::And) {
7611 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7612 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7613 } else if (BO->getOpcode() == Instruction::Or) {
7615 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7616 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7620 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
7621 if (!ICI) return false;
7623 // Now that we found a conditional branch that dominates the loop or controls
7624 // the loop latch. Check to see if it is the comparison we are looking for.
7625 ICmpInst::Predicate FoundPred;
7627 FoundPred = ICI->getInversePredicate();
7629 FoundPred = ICI->getPredicate();
7631 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
7632 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
7634 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
7637 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
7639 ICmpInst::Predicate FoundPred,
7640 const SCEV *FoundLHS,
7641 const SCEV *FoundRHS) {
7642 // Balance the types.
7643 if (getTypeSizeInBits(LHS->getType()) <
7644 getTypeSizeInBits(FoundLHS->getType())) {
7645 if (CmpInst::isSigned(Pred)) {
7646 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
7647 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
7649 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
7650 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
7652 } else if (getTypeSizeInBits(LHS->getType()) >
7653 getTypeSizeInBits(FoundLHS->getType())) {
7654 if (CmpInst::isSigned(FoundPred)) {
7655 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
7656 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
7658 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
7659 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
7663 // Canonicalize the query to match the way instcombine will have
7664 // canonicalized the comparison.
7665 if (SimplifyICmpOperands(Pred, LHS, RHS))
7667 return CmpInst::isTrueWhenEqual(Pred);
7668 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
7669 if (FoundLHS == FoundRHS)
7670 return CmpInst::isFalseWhenEqual(FoundPred);
7672 // Check to see if we can make the LHS or RHS match.
7673 if (LHS == FoundRHS || RHS == FoundLHS) {
7674 if (isa<SCEVConstant>(RHS)) {
7675 std::swap(FoundLHS, FoundRHS);
7676 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
7678 std::swap(LHS, RHS);
7679 Pred = ICmpInst::getSwappedPredicate(Pred);
7683 // Check whether the found predicate is the same as the desired predicate.
7684 if (FoundPred == Pred)
7685 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7687 // Check whether swapping the found predicate makes it the same as the
7688 // desired predicate.
7689 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
7690 if (isa<SCEVConstant>(RHS))
7691 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
7693 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
7694 RHS, LHS, FoundLHS, FoundRHS);
7697 // Unsigned comparison is the same as signed comparison when both the operands
7698 // are non-negative.
7699 if (CmpInst::isUnsigned(FoundPred) &&
7700 CmpInst::getSignedPredicate(FoundPred) == Pred &&
7701 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
7702 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7704 // Check if we can make progress by sharpening ranges.
7705 if (FoundPred == ICmpInst::ICMP_NE &&
7706 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
7708 const SCEVConstant *C = nullptr;
7709 const SCEV *V = nullptr;
7711 if (isa<SCEVConstant>(FoundLHS)) {
7712 C = cast<SCEVConstant>(FoundLHS);
7715 C = cast<SCEVConstant>(FoundRHS);
7719 // The guarding predicate tells us that C != V. If the known range
7720 // of V is [C, t), we can sharpen the range to [C + 1, t). The
7721 // range we consider has to correspond to same signedness as the
7722 // predicate we're interested in folding.
7724 APInt Min = ICmpInst::isSigned(Pred) ?
7725 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7727 if (Min == C->getValue()->getValue()) {
7728 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7729 // This is true even if (Min + 1) wraps around -- in case of
7730 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7732 APInt SharperMin = Min + 1;
7735 case ICmpInst::ICMP_SGE:
7736 case ICmpInst::ICMP_UGE:
7737 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7739 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7740 getConstant(SharperMin)))
7743 case ICmpInst::ICMP_SGT:
7744 case ICmpInst::ICMP_UGT:
7745 // We know from the range information that (V `Pred` Min ||
7746 // V == Min). We know from the guarding condition that !(V
7747 // == Min). This gives us
7749 // V `Pred` Min || V == Min && !(V == Min)
7752 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7754 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7764 // Check whether the actual condition is beyond sufficient.
7765 if (FoundPred == ICmpInst::ICMP_EQ)
7766 if (ICmpInst::isTrueWhenEqual(Pred))
7767 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7769 if (Pred == ICmpInst::ICMP_NE)
7770 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7771 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7774 // Otherwise assume the worst.
7778 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
7779 const SCEV *&L, const SCEV *&R,
7780 SCEV::NoWrapFlags &Flags) {
7781 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
7782 if (!AE || AE->getNumOperands() != 2)
7785 L = AE->getOperand(0);
7786 R = AE->getOperand(1);
7787 Flags = AE->getNoWrapFlags();
7791 bool ScalarEvolution::computeConstantDifference(const SCEV *Less,
7794 // We avoid subtracting expressions here because this function is usually
7795 // fairly deep in the call stack (i.e. is called many times).
7797 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
7798 const auto *LAR = cast<SCEVAddRecExpr>(Less);
7799 const auto *MAR = cast<SCEVAddRecExpr>(More);
7801 if (LAR->getLoop() != MAR->getLoop())
7804 // We look at affine expressions only; not for correctness but to keep
7805 // getStepRecurrence cheap.
7806 if (!LAR->isAffine() || !MAR->isAffine())
7809 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
7812 Less = LAR->getStart();
7813 More = MAR->getStart();
7818 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
7819 const auto &M = cast<SCEVConstant>(More)->getValue()->getValue();
7820 const auto &L = cast<SCEVConstant>(Less)->getValue()->getValue();
7826 SCEV::NoWrapFlags Flags;
7827 if (splitBinaryAdd(Less, L, R, Flags))
7828 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7830 C = -(LC->getValue()->getValue());
7834 if (splitBinaryAdd(More, L, R, Flags))
7835 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7837 C = LC->getValue()->getValue();
7844 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
7845 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
7846 const SCEV *FoundLHS, const SCEV *FoundRHS) {
7847 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
7850 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7854 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
7855 if (!AddRecFoundLHS)
7858 // We'd like to let SCEV reason about control dependencies, so we constrain
7859 // both the inequalities to be about add recurrences on the same loop. This
7860 // way we can use isLoopEntryGuardedByCond later.
7862 const Loop *L = AddRecFoundLHS->getLoop();
7863 if (L != AddRecLHS->getLoop())
7866 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
7868 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
7871 // Informal proof for (2), assuming (1) [*]:
7873 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
7877 // FoundLHS s< FoundRHS s< INT_MIN - C
7878 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
7879 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
7880 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
7881 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
7882 // <=> FoundLHS + C s< FoundRHS + C
7884 // [*]: (1) can be proved by ruling out overflow.
7886 // [**]: This can be proved by analyzing all the four possibilities:
7887 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
7888 // (A s>= 0, B s>= 0).
7891 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
7892 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
7893 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
7894 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
7895 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
7899 if (!computeConstantDifference(FoundLHS, LHS, LDiff) ||
7900 !computeConstantDifference(FoundRHS, RHS, RDiff) ||
7907 APInt FoundRHSLimit;
7909 if (Pred == CmpInst::ICMP_ULT) {
7910 FoundRHSLimit = -RDiff;
7912 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
7913 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - RDiff;
7916 // Try to prove (1) or (2), as needed.
7917 return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
7918 getConstant(FoundRHSLimit));
7921 /// isImpliedCondOperands - Test whether the condition described by Pred,
7922 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7923 /// and FoundRHS is true.
7924 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7925 const SCEV *LHS, const SCEV *RHS,
7926 const SCEV *FoundLHS,
7927 const SCEV *FoundRHS) {
7928 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7931 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
7934 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7935 FoundLHS, FoundRHS) ||
7936 // ~x < ~y --> x > y
7937 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7938 getNotSCEV(FoundRHS),
7939 getNotSCEV(FoundLHS));
7943 /// If Expr computes ~A, return A else return nullptr
7944 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7945 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7946 if (!Add || Add->getNumOperands() != 2 ||
7947 !Add->getOperand(0)->isAllOnesValue())
7950 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7951 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
7952 !AddRHS->getOperand(0)->isAllOnesValue())
7955 return AddRHS->getOperand(1);
7959 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7960 template<typename MaxExprType>
7961 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7962 const SCEV *Candidate) {
7963 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7964 if (!MaxExpr) return false;
7966 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7967 return It != MaxExpr->op_end();
7971 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7972 template<typename MaxExprType>
7973 static bool IsMinConsistingOf(ScalarEvolution &SE,
7974 const SCEV *MaybeMinExpr,
7975 const SCEV *Candidate) {
7976 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7980 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7983 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
7984 ICmpInst::Predicate Pred,
7985 const SCEV *LHS, const SCEV *RHS) {
7987 // If both sides are affine addrecs for the same loop, with equal
7988 // steps, and we know the recurrences don't wrap, then we only
7989 // need to check the predicate on the starting values.
7991 if (!ICmpInst::isRelational(Pred))
7994 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7997 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
8000 if (LAR->getLoop() != RAR->getLoop())
8002 if (!LAR->isAffine() || !RAR->isAffine())
8005 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
8008 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
8009 SCEV::FlagNSW : SCEV::FlagNUW;
8010 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
8013 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
8016 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
8018 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
8019 ICmpInst::Predicate Pred,
8020 const SCEV *LHS, const SCEV *RHS) {
8025 case ICmpInst::ICMP_SGE:
8026 std::swap(LHS, RHS);
8028 case ICmpInst::ICMP_SLE:
8031 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
8033 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
8035 case ICmpInst::ICMP_UGE:
8036 std::swap(LHS, RHS);
8038 case ICmpInst::ICMP_ULE:
8041 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
8043 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
8046 llvm_unreachable("covered switch fell through?!");
8049 /// isImpliedCondOperandsHelper - Test whether the condition described by
8050 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
8051 /// FoundLHS, and FoundRHS is true.
8053 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
8054 const SCEV *LHS, const SCEV *RHS,
8055 const SCEV *FoundLHS,
8056 const SCEV *FoundRHS) {
8057 auto IsKnownPredicateFull =
8058 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
8059 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
8060 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
8061 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
8062 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
8066 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
8067 case ICmpInst::ICMP_EQ:
8068 case ICmpInst::ICMP_NE:
8069 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
8072 case ICmpInst::ICMP_SLT:
8073 case ICmpInst::ICMP_SLE:
8074 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
8075 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
8078 case ICmpInst::ICMP_SGT:
8079 case ICmpInst::ICMP_SGE:
8080 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
8081 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
8084 case ICmpInst::ICMP_ULT:
8085 case ICmpInst::ICMP_ULE:
8086 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
8087 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
8090 case ICmpInst::ICMP_UGT:
8091 case ICmpInst::ICMP_UGE:
8092 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
8093 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
8101 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
8102 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
8103 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
8106 const SCEV *FoundLHS,
8107 const SCEV *FoundRHS) {
8108 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
8109 // The restriction on `FoundRHS` be lifted easily -- it exists only to
8110 // reduce the compile time impact of this optimization.
8113 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
8114 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
8115 !isa<SCEVConstant>(AddLHS->getOperand(0)))
8118 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
8120 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
8121 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
8122 ConstantRange FoundLHSRange =
8123 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
8125 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
8128 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
8129 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
8131 // We can also compute the range of values for `LHS` that satisfy the
8132 // consequent, "`LHS` `Pred` `RHS`":
8133 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
8134 ConstantRange SatisfyingLHSRange =
8135 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
8137 // The antecedent implies the consequent if every value of `LHS` that
8138 // satisfies the antecedent also satisfies the consequent.
8139 return SatisfyingLHSRange.contains(LHSRange);
8142 // Verify if an linear IV with positive stride can overflow when in a
8143 // less-than comparison, knowing the invariant term of the comparison, the
8144 // stride and the knowledge of NSW/NUW flags on the recurrence.
8145 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
8146 bool IsSigned, bool NoWrap) {
8147 if (NoWrap) return false;
8149 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8150 const SCEV *One = getOne(Stride->getType());
8153 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
8154 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
8155 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8158 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
8159 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
8162 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
8163 APInt MaxValue = APInt::getMaxValue(BitWidth);
8164 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8167 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
8168 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
8171 // Verify if an linear IV with negative stride can overflow when in a
8172 // greater-than comparison, knowing the invariant term of the comparison,
8173 // the stride and the knowledge of NSW/NUW flags on the recurrence.
8174 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
8175 bool IsSigned, bool NoWrap) {
8176 if (NoWrap) return false;
8178 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8179 const SCEV *One = getOne(Stride->getType());
8182 APInt MinRHS = getSignedRange(RHS).getSignedMin();
8183 APInt MinValue = APInt::getSignedMinValue(BitWidth);
8184 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8187 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
8188 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
8191 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
8192 APInt MinValue = APInt::getMinValue(BitWidth);
8193 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8196 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
8197 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
8200 // Compute the backedge taken count knowing the interval difference, the
8201 // stride and presence of the equality in the comparison.
8202 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
8204 const SCEV *One = getOne(Step->getType());
8205 Delta = Equality ? getAddExpr(Delta, Step)
8206 : getAddExpr(Delta, getMinusSCEV(Step, One));
8207 return getUDivExpr(Delta, Step);
8210 /// HowManyLessThans - Return the number of times a backedge containing the
8211 /// specified less-than comparison will execute. If not computable, return
8212 /// CouldNotCompute.
8214 /// @param ControlsExit is true when the LHS < RHS condition directly controls
8215 /// the branch (loops exits only if condition is true). In this case, we can use
8216 /// NoWrapFlags to skip overflow checks.
8217 ScalarEvolution::ExitLimit
8218 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
8219 const Loop *L, bool IsSigned,
8220 bool ControlsExit) {
8221 // We handle only IV < Invariant
8222 if (!isLoopInvariant(RHS, L))
8223 return getCouldNotCompute();
8225 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8227 // Avoid weird loops
8228 if (!IV || IV->getLoop() != L || !IV->isAffine())
8229 return getCouldNotCompute();
8231 bool NoWrap = ControlsExit &&
8232 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8234 const SCEV *Stride = IV->getStepRecurrence(*this);
8236 // Avoid negative or zero stride values
8237 if (!isKnownPositive(Stride))
8238 return getCouldNotCompute();
8240 // Avoid proven overflow cases: this will ensure that the backedge taken count
8241 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8242 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8243 // behaviors like the case of C language.
8244 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
8245 return getCouldNotCompute();
8247 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
8248 : ICmpInst::ICMP_ULT;
8249 const SCEV *Start = IV->getStart();
8250 const SCEV *End = RHS;
8251 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
8252 const SCEV *Diff = getMinusSCEV(RHS, Start);
8253 // If we have NoWrap set, then we can assume that the increment won't
8254 // overflow, in which case if RHS - Start is a constant, we don't need to
8255 // do a max operation since we can just figure it out statically
8256 if (NoWrap && isa<SCEVConstant>(Diff)) {
8257 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
8261 End = IsSigned ? getSMaxExpr(RHS, Start)
8262 : getUMaxExpr(RHS, Start);
8265 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
8267 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
8268 : getUnsignedRange(Start).getUnsignedMin();
8270 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8271 : getUnsignedRange(Stride).getUnsignedMin();
8273 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8274 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
8275 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
8277 // Although End can be a MAX expression we estimate MaxEnd considering only
8278 // the case End = RHS. This is safe because in the other case (End - Start)
8279 // is zero, leading to a zero maximum backedge taken count.
8281 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8282 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8284 const SCEV *MaxBECount;
8285 if (isa<SCEVConstant>(BECount))
8286 MaxBECount = BECount;
8288 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8289 getConstant(MinStride), false);
8291 if (isa<SCEVCouldNotCompute>(MaxBECount))
8292 MaxBECount = BECount;
8294 return ExitLimit(BECount, MaxBECount);
8297 ScalarEvolution::ExitLimit
8298 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8299 const Loop *L, bool IsSigned,
8300 bool ControlsExit) {
8301 // We handle only IV > Invariant
8302 if (!isLoopInvariant(RHS, L))
8303 return getCouldNotCompute();
8305 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8307 // Avoid weird loops
8308 if (!IV || IV->getLoop() != L || !IV->isAffine())
8309 return getCouldNotCompute();
8311 bool NoWrap = ControlsExit &&
8312 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8314 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8316 // Avoid negative or zero stride values
8317 if (!isKnownPositive(Stride))
8318 return getCouldNotCompute();
8320 // Avoid proven overflow cases: this will ensure that the backedge taken count
8321 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8322 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8323 // behaviors like the case of C language.
8324 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8325 return getCouldNotCompute();
8327 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8328 : ICmpInst::ICMP_UGT;
8330 const SCEV *Start = IV->getStart();
8331 const SCEV *End = RHS;
8332 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
8333 const SCEV *Diff = getMinusSCEV(RHS, Start);
8334 // If we have NoWrap set, then we can assume that the increment won't
8335 // overflow, in which case if RHS - Start is a constant, we don't need to
8336 // do a max operation since we can just figure it out statically
8337 if (NoWrap && isa<SCEVConstant>(Diff)) {
8338 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
8339 if (!D.isNegative())
8342 End = IsSigned ? getSMinExpr(RHS, Start)
8343 : getUMinExpr(RHS, Start);
8346 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8348 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8349 : getUnsignedRange(Start).getUnsignedMax();
8351 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8352 : getUnsignedRange(Stride).getUnsignedMin();
8354 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8355 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8356 : APInt::getMinValue(BitWidth) + (MinStride - 1);
8358 // Although End can be a MIN expression we estimate MinEnd considering only
8359 // the case End = RHS. This is safe because in the other case (Start - End)
8360 // is zero, leading to a zero maximum backedge taken count.
8362 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8363 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8366 const SCEV *MaxBECount = getCouldNotCompute();
8367 if (isa<SCEVConstant>(BECount))
8368 MaxBECount = BECount;
8370 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8371 getConstant(MinStride), false);
8373 if (isa<SCEVCouldNotCompute>(MaxBECount))
8374 MaxBECount = BECount;
8376 return ExitLimit(BECount, MaxBECount);
8379 /// getNumIterationsInRange - Return the number of iterations of this loop that
8380 /// produce values in the specified constant range. Another way of looking at
8381 /// this is that it returns the first iteration number where the value is not in
8382 /// the condition, thus computing the exit count. If the iteration count can't
8383 /// be computed, an instance of SCEVCouldNotCompute is returned.
8384 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
8385 ScalarEvolution &SE) const {
8386 if (Range.isFullSet()) // Infinite loop.
8387 return SE.getCouldNotCompute();
8389 // If the start is a non-zero constant, shift the range to simplify things.
8390 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8391 if (!SC->getValue()->isZero()) {
8392 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8393 Operands[0] = SE.getZero(SC->getType());
8394 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8395 getNoWrapFlags(FlagNW));
8396 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
8397 return ShiftedAddRec->getNumIterationsInRange(
8398 Range.subtract(SC->getValue()->getValue()), SE);
8399 // This is strange and shouldn't happen.
8400 return SE.getCouldNotCompute();
8403 // The only time we can solve this is when we have all constant indices.
8404 // Otherwise, we cannot determine the overflow conditions.
8405 if (std::any_of(op_begin(), op_end(),
8406 [](const SCEV *Op) { return !isa<SCEVConstant>(Op);}))
8407 return SE.getCouldNotCompute();
8409 // Okay at this point we know that all elements of the chrec are constants and
8410 // that the start element is zero.
8412 // First check to see if the range contains zero. If not, the first
8414 unsigned BitWidth = SE.getTypeSizeInBits(getType());
8415 if (!Range.contains(APInt(BitWidth, 0)))
8416 return SE.getZero(getType());
8419 // If this is an affine expression then we have this situation:
8420 // Solve {0,+,A} in Range === Ax in Range
8422 // We know that zero is in the range. If A is positive then we know that
8423 // the upper value of the range must be the first possible exit value.
8424 // If A is negative then the lower of the range is the last possible loop
8425 // value. Also note that we already checked for a full range.
8426 APInt One(BitWidth,1);
8427 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
8428 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8430 // The exit value should be (End+A)/A.
8431 APInt ExitVal = (End + A).udiv(A);
8432 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8434 // Evaluate at the exit value. If we really did fall out of the valid
8435 // range, then we computed our trip count, otherwise wrap around or other
8436 // things must have happened.
8437 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8438 if (Range.contains(Val->getValue()))
8439 return SE.getCouldNotCompute(); // Something strange happened
8441 // Ensure that the previous value is in the range. This is a sanity check.
8442 assert(Range.contains(
8443 EvaluateConstantChrecAtConstant(this,
8444 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8445 "Linear scev computation is off in a bad way!");
8446 return SE.getConstant(ExitValue);
8447 } else if (isQuadratic()) {
8448 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8449 // quadratic equation to solve it. To do this, we must frame our problem in
8450 // terms of figuring out when zero is crossed, instead of when
8451 // Range.getUpper() is crossed.
8452 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8453 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8454 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
8455 // getNoWrapFlags(FlagNW)
8458 // Next, solve the constructed addrec
8459 auto Roots = SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
8460 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
8461 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
8463 // Pick the smallest positive root value.
8464 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
8465 ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
8466 if (!CB->getZExtValue())
8467 std::swap(R1, R2); // R1 is the minimum root now.
8469 // Make sure the root is not off by one. The returned iteration should
8470 // not be in the range, but the previous one should be. When solving
8471 // for "X*X < 5", for example, we should not return a root of 2.
8472 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
8475 if (Range.contains(R1Val->getValue())) {
8476 // The next iteration must be out of the range...
8477 ConstantInt *NextVal =
8478 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
8480 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8481 if (!Range.contains(R1Val->getValue()))
8482 return SE.getConstant(NextVal);
8483 return SE.getCouldNotCompute(); // Something strange happened
8486 // If R1 was not in the range, then it is a good return value. Make
8487 // sure that R1-1 WAS in the range though, just in case.
8488 ConstantInt *NextVal =
8489 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
8490 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8491 if (Range.contains(R1Val->getValue()))
8493 return SE.getCouldNotCompute(); // Something strange happened
8498 return SE.getCouldNotCompute();
8504 FindUndefs() : Found(false) {}
8506 bool follow(const SCEV *S) {
8507 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
8508 if (isa<UndefValue>(C->getValue()))
8510 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
8511 if (isa<UndefValue>(C->getValue()))
8515 // Keep looking if we haven't found it yet.
8518 bool isDone() const {
8519 // Stop recursion if we have found an undef.
8525 // Return true when S contains at least an undef value.
8527 containsUndefs(const SCEV *S) {
8529 SCEVTraversal<FindUndefs> ST(F);
8536 // Collect all steps of SCEV expressions.
8537 struct SCEVCollectStrides {
8538 ScalarEvolution &SE;
8539 SmallVectorImpl<const SCEV *> &Strides;
8541 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
8542 : SE(SE), Strides(S) {}
8544 bool follow(const SCEV *S) {
8545 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
8546 Strides.push_back(AR->getStepRecurrence(SE));
8549 bool isDone() const { return false; }
8552 // Collect all SCEVUnknown and SCEVMulExpr expressions.
8553 struct SCEVCollectTerms {
8554 SmallVectorImpl<const SCEV *> &Terms;
8556 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
8559 bool follow(const SCEV *S) {
8560 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
8561 if (!containsUndefs(S))
8564 // Stop recursion: once we collected a term, do not walk its operands.
8571 bool isDone() const { return false; }
8574 // Check if a SCEV contains an AddRecExpr.
8575 struct SCEVHasAddRec {
8576 bool &ContainsAddRec;
8578 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
8579 ContainsAddRec = false;
8582 bool follow(const SCEV *S) {
8583 if (isa<SCEVAddRecExpr>(S)) {
8584 ContainsAddRec = true;
8586 // Stop recursion: once we collected a term, do not walk its operands.
8593 bool isDone() const { return false; }
8596 // Find factors that are multiplied with an expression that (possibly as a
8597 // subexpression) contains an AddRecExpr. In the expression:
8599 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
8601 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
8602 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
8603 // parameters as they form a product with an induction variable.
8605 // This collector expects all array size parameters to be in the same MulExpr.
8606 // It might be necessary to later add support for collecting parameters that are
8607 // spread over different nested MulExpr.
8608 struct SCEVCollectAddRecMultiplies {
8609 SmallVectorImpl<const SCEV *> &Terms;
8610 ScalarEvolution &SE;
8612 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
8613 : Terms(T), SE(SE) {}
8615 bool follow(const SCEV *S) {
8616 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
8617 bool HasAddRec = false;
8618 SmallVector<const SCEV *, 0> Operands;
8619 for (auto Op : Mul->operands()) {
8620 if (isa<SCEVUnknown>(Op)) {
8621 Operands.push_back(Op);
8623 bool ContainsAddRec;
8624 SCEVHasAddRec ContiansAddRec(ContainsAddRec);
8625 visitAll(Op, ContiansAddRec);
8626 HasAddRec |= ContainsAddRec;
8629 if (Operands.size() == 0)
8635 Terms.push_back(SE.getMulExpr(Operands));
8636 // Stop recursion: once we collected a term, do not walk its operands.
8643 bool isDone() const { return false; }
8647 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
8649 /// 1) The strides of AddRec expressions.
8650 /// 2) Unknowns that are multiplied with AddRec expressions.
8651 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
8652 SmallVectorImpl<const SCEV *> &Terms) {
8653 SmallVector<const SCEV *, 4> Strides;
8654 SCEVCollectStrides StrideCollector(*this, Strides);
8655 visitAll(Expr, StrideCollector);
8658 dbgs() << "Strides:\n";
8659 for (const SCEV *S : Strides)
8660 dbgs() << *S << "\n";
8663 for (const SCEV *S : Strides) {
8664 SCEVCollectTerms TermCollector(Terms);
8665 visitAll(S, TermCollector);
8669 dbgs() << "Terms:\n";
8670 for (const SCEV *T : Terms)
8671 dbgs() << *T << "\n";
8674 SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
8675 visitAll(Expr, MulCollector);
8678 static bool findArrayDimensionsRec(ScalarEvolution &SE,
8679 SmallVectorImpl<const SCEV *> &Terms,
8680 SmallVectorImpl<const SCEV *> &Sizes) {
8681 int Last = Terms.size() - 1;
8682 const SCEV *Step = Terms[Last];
8684 // End of recursion.
8686 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
8687 SmallVector<const SCEV *, 2> Qs;
8688 for (const SCEV *Op : M->operands())
8689 if (!isa<SCEVConstant>(Op))
8692 Step = SE.getMulExpr(Qs);
8695 Sizes.push_back(Step);
8699 for (const SCEV *&Term : Terms) {
8700 // Normalize the terms before the next call to findArrayDimensionsRec.
8702 SCEVDivision::divide(SE, Term, Step, &Q, &R);
8704 // Bail out when GCD does not evenly divide one of the terms.
8711 // Remove all SCEVConstants.
8712 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
8713 return isa<SCEVConstant>(E);
8717 if (Terms.size() > 0)
8718 if (!findArrayDimensionsRec(SE, Terms, Sizes))
8721 Sizes.push_back(Step);
8726 struct FindParameter {
8727 bool FoundParameter;
8728 FindParameter() : FoundParameter(false) {}
8730 bool follow(const SCEV *S) {
8731 if (isa<SCEVUnknown>(S)) {
8732 FoundParameter = true;
8733 // Stop recursion: we found a parameter.
8739 bool isDone() const {
8740 // Stop recursion if we have found a parameter.
8741 return FoundParameter;
8746 // Returns true when S contains at least a SCEVUnknown parameter.
8748 containsParameters(const SCEV *S) {
8750 SCEVTraversal<FindParameter> ST(F);
8753 return F.FoundParameter;
8756 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
8758 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
8759 for (const SCEV *T : Terms)
8760 if (containsParameters(T))
8765 // Return the number of product terms in S.
8766 static inline int numberOfTerms(const SCEV *S) {
8767 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
8768 return Expr->getNumOperands();
8772 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
8773 if (isa<SCEVConstant>(T))
8776 if (isa<SCEVUnknown>(T))
8779 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
8780 SmallVector<const SCEV *, 2> Factors;
8781 for (const SCEV *Op : M->operands())
8782 if (!isa<SCEVConstant>(Op))
8783 Factors.push_back(Op);
8785 return SE.getMulExpr(Factors);
8791 /// Return the size of an element read or written by Inst.
8792 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
8794 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
8795 Ty = Store->getValueOperand()->getType();
8796 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
8797 Ty = Load->getType();
8801 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
8802 return getSizeOfExpr(ETy, Ty);
8805 /// Second step of delinearization: compute the array dimensions Sizes from the
8806 /// set of Terms extracted from the memory access function of this SCEVAddRec.
8807 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
8808 SmallVectorImpl<const SCEV *> &Sizes,
8809 const SCEV *ElementSize) const {
8811 if (Terms.size() < 1 || !ElementSize)
8814 // Early return when Terms do not contain parameters: we do not delinearize
8815 // non parametric SCEVs.
8816 if (!containsParameters(Terms))
8820 dbgs() << "Terms:\n";
8821 for (const SCEV *T : Terms)
8822 dbgs() << *T << "\n";
8825 // Remove duplicates.
8826 std::sort(Terms.begin(), Terms.end());
8827 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
8829 // Put larger terms first.
8830 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
8831 return numberOfTerms(LHS) > numberOfTerms(RHS);
8834 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8836 // Try to divide all terms by the element size. If term is not divisible by
8837 // element size, proceed with the original term.
8838 for (const SCEV *&Term : Terms) {
8840 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
8845 SmallVector<const SCEV *, 4> NewTerms;
8847 // Remove constant factors.
8848 for (const SCEV *T : Terms)
8849 if (const SCEV *NewT = removeConstantFactors(SE, T))
8850 NewTerms.push_back(NewT);
8853 dbgs() << "Terms after sorting:\n";
8854 for (const SCEV *T : NewTerms)
8855 dbgs() << *T << "\n";
8858 if (NewTerms.empty() ||
8859 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
8864 // The last element to be pushed into Sizes is the size of an element.
8865 Sizes.push_back(ElementSize);
8868 dbgs() << "Sizes:\n";
8869 for (const SCEV *S : Sizes)
8870 dbgs() << *S << "\n";
8874 /// Third step of delinearization: compute the access functions for the
8875 /// Subscripts based on the dimensions in Sizes.
8876 void ScalarEvolution::computeAccessFunctions(
8877 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
8878 SmallVectorImpl<const SCEV *> &Sizes) {
8880 // Early exit in case this SCEV is not an affine multivariate function.
8884 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
8885 if (!AR->isAffine())
8888 const SCEV *Res = Expr;
8889 int Last = Sizes.size() - 1;
8890 for (int i = Last; i >= 0; i--) {
8892 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
8895 dbgs() << "Res: " << *Res << "\n";
8896 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
8897 dbgs() << "Res divided by Sizes[i]:\n";
8898 dbgs() << "Quotient: " << *Q << "\n";
8899 dbgs() << "Remainder: " << *R << "\n";
8904 // Do not record the last subscript corresponding to the size of elements in
8908 // Bail out if the remainder is too complex.
8909 if (isa<SCEVAddRecExpr>(R)) {
8918 // Record the access function for the current subscript.
8919 Subscripts.push_back(R);
8922 // Also push in last position the remainder of the last division: it will be
8923 // the access function of the innermost dimension.
8924 Subscripts.push_back(Res);
8926 std::reverse(Subscripts.begin(), Subscripts.end());
8929 dbgs() << "Subscripts:\n";
8930 for (const SCEV *S : Subscripts)
8931 dbgs() << *S << "\n";
8935 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
8936 /// sizes of an array access. Returns the remainder of the delinearization that
8937 /// is the offset start of the array. The SCEV->delinearize algorithm computes
8938 /// the multiples of SCEV coefficients: that is a pattern matching of sub
8939 /// expressions in the stride and base of a SCEV corresponding to the
8940 /// computation of a GCD (greatest common divisor) of base and stride. When
8941 /// SCEV->delinearize fails, it returns the SCEV unchanged.
8943 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
8945 /// void foo(long n, long m, long o, double A[n][m][o]) {
8947 /// for (long i = 0; i < n; i++)
8948 /// for (long j = 0; j < m; j++)
8949 /// for (long k = 0; k < o; k++)
8950 /// A[i][j][k] = 1.0;
8953 /// the delinearization input is the following AddRec SCEV:
8955 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
8957 /// From this SCEV, we are able to say that the base offset of the access is %A
8958 /// because it appears as an offset that does not divide any of the strides in
8961 /// CHECK: Base offset: %A
8963 /// and then SCEV->delinearize determines the size of some of the dimensions of
8964 /// the array as these are the multiples by which the strides are happening:
8966 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
8968 /// Note that the outermost dimension remains of UnknownSize because there are
8969 /// no strides that would help identifying the size of the last dimension: when
8970 /// the array has been statically allocated, one could compute the size of that
8971 /// dimension by dividing the overall size of the array by the size of the known
8972 /// dimensions: %m * %o * 8.
8974 /// Finally delinearize provides the access functions for the array reference
8975 /// that does correspond to A[i][j][k] of the above C testcase:
8977 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
8979 /// The testcases are checking the output of a function pass:
8980 /// DelinearizationPass that walks through all loads and stores of a function
8981 /// asking for the SCEV of the memory access with respect to all enclosing
8982 /// loops, calling SCEV->delinearize on that and printing the results.
8984 void ScalarEvolution::delinearize(const SCEV *Expr,
8985 SmallVectorImpl<const SCEV *> &Subscripts,
8986 SmallVectorImpl<const SCEV *> &Sizes,
8987 const SCEV *ElementSize) {
8988 // First step: collect parametric terms.
8989 SmallVector<const SCEV *, 4> Terms;
8990 collectParametricTerms(Expr, Terms);
8995 // Second step: find subscript sizes.
8996 findArrayDimensions(Terms, Sizes, ElementSize);
9001 // Third step: compute the access functions for each subscript.
9002 computeAccessFunctions(Expr, Subscripts, Sizes);
9004 if (Subscripts.empty())
9008 dbgs() << "succeeded to delinearize " << *Expr << "\n";
9009 dbgs() << "ArrayDecl[UnknownSize]";
9010 for (const SCEV *S : Sizes)
9011 dbgs() << "[" << *S << "]";
9013 dbgs() << "\nArrayRef";
9014 for (const SCEV *S : Subscripts)
9015 dbgs() << "[" << *S << "]";
9020 //===----------------------------------------------------------------------===//
9021 // SCEVCallbackVH Class Implementation
9022 //===----------------------------------------------------------------------===//
9024 void ScalarEvolution::SCEVCallbackVH::deleted() {
9025 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9026 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
9027 SE->ConstantEvolutionLoopExitValue.erase(PN);
9028 SE->ValueExprMap.erase(getValPtr());
9029 // this now dangles!
9032 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
9033 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9035 // Forget all the expressions associated with users of the old value,
9036 // so that future queries will recompute the expressions using the new
9038 Value *Old = getValPtr();
9039 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
9040 SmallPtrSet<User *, 8> Visited;
9041 while (!Worklist.empty()) {
9042 User *U = Worklist.pop_back_val();
9043 // Deleting the Old value will cause this to dangle. Postpone
9044 // that until everything else is done.
9047 if (!Visited.insert(U).second)
9049 if (PHINode *PN = dyn_cast<PHINode>(U))
9050 SE->ConstantEvolutionLoopExitValue.erase(PN);
9051 SE->ValueExprMap.erase(U);
9052 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
9054 // Delete the Old value.
9055 if (PHINode *PN = dyn_cast<PHINode>(Old))
9056 SE->ConstantEvolutionLoopExitValue.erase(PN);
9057 SE->ValueExprMap.erase(Old);
9058 // this now dangles!
9061 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
9062 : CallbackVH(V), SE(se) {}
9064 //===----------------------------------------------------------------------===//
9065 // ScalarEvolution Class Implementation
9066 //===----------------------------------------------------------------------===//
9068 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
9069 AssumptionCache &AC, DominatorTree &DT,
9071 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
9072 CouldNotCompute(new SCEVCouldNotCompute()),
9073 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9074 ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
9075 FirstUnknown(nullptr) {}
9077 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
9078 : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
9079 CouldNotCompute(std::move(Arg.CouldNotCompute)),
9080 ValueExprMap(std::move(Arg.ValueExprMap)),
9081 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9082 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
9083 ConstantEvolutionLoopExitValue(
9084 std::move(Arg.ConstantEvolutionLoopExitValue)),
9085 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
9086 LoopDispositions(std::move(Arg.LoopDispositions)),
9087 BlockDispositions(std::move(Arg.BlockDispositions)),
9088 UnsignedRanges(std::move(Arg.UnsignedRanges)),
9089 SignedRanges(std::move(Arg.SignedRanges)),
9090 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
9091 UniquePreds(std::move(Arg.UniquePreds)),
9092 SCEVAllocator(std::move(Arg.SCEVAllocator)),
9093 FirstUnknown(Arg.FirstUnknown) {
9094 Arg.FirstUnknown = nullptr;
9097 ScalarEvolution::~ScalarEvolution() {
9098 // Iterate through all the SCEVUnknown instances and call their
9099 // destructors, so that they release their references to their values.
9100 for (SCEVUnknown *U = FirstUnknown; U;) {
9101 SCEVUnknown *Tmp = U;
9103 Tmp->~SCEVUnknown();
9105 FirstUnknown = nullptr;
9107 ValueExprMap.clear();
9109 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
9110 // that a loop had multiple computable exits.
9111 for (auto &BTCI : BackedgeTakenCounts)
9112 BTCI.second.clear();
9114 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
9115 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
9116 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
9119 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
9120 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
9123 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
9125 // Print all inner loops first
9126 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
9127 PrintLoopInfo(OS, SE, *I);
9130 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9133 SmallVector<BasicBlock *, 8> ExitBlocks;
9134 L->getExitBlocks(ExitBlocks);
9135 if (ExitBlocks.size() != 1)
9136 OS << "<multiple exits> ";
9138 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
9139 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
9141 OS << "Unpredictable backedge-taken count. ";
9146 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9149 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
9150 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
9152 OS << "Unpredictable max backedge-taken count. ";
9158 void ScalarEvolution::print(raw_ostream &OS) const {
9159 // ScalarEvolution's implementation of the print method is to print
9160 // out SCEV values of all instructions that are interesting. Doing
9161 // this potentially causes it to create new SCEV objects though,
9162 // which technically conflicts with the const qualifier. This isn't
9163 // observable from outside the class though, so casting away the
9164 // const isn't dangerous.
9165 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9167 OS << "Classifying expressions for: ";
9168 F.printAsOperand(OS, /*PrintType=*/false);
9170 for (Instruction &I : instructions(F))
9171 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
9174 const SCEV *SV = SE.getSCEV(&I);
9176 if (!isa<SCEVCouldNotCompute>(SV)) {
9178 SE.getUnsignedRange(SV).print(OS);
9180 SE.getSignedRange(SV).print(OS);
9183 const Loop *L = LI.getLoopFor(I.getParent());
9185 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
9189 if (!isa<SCEVCouldNotCompute>(AtUse)) {
9191 SE.getUnsignedRange(AtUse).print(OS);
9193 SE.getSignedRange(AtUse).print(OS);
9198 OS << "\t\t" "Exits: ";
9199 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
9200 if (!SE.isLoopInvariant(ExitValue, L)) {
9201 OS << "<<Unknown>>";
9210 OS << "Determining loop execution counts for: ";
9211 F.printAsOperand(OS, /*PrintType=*/false);
9213 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
9214 PrintLoopInfo(OS, &SE, *I);
9217 ScalarEvolution::LoopDisposition
9218 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
9219 auto &Values = LoopDispositions[S];
9220 for (auto &V : Values) {
9221 if (V.getPointer() == L)
9224 Values.emplace_back(L, LoopVariant);
9225 LoopDisposition D = computeLoopDisposition(S, L);
9226 auto &Values2 = LoopDispositions[S];
9227 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9228 if (V.getPointer() == L) {
9236 ScalarEvolution::LoopDisposition
9237 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
9238 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9240 return LoopInvariant;
9244 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
9245 case scAddRecExpr: {
9246 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9248 // If L is the addrec's loop, it's computable.
9249 if (AR->getLoop() == L)
9250 return LoopComputable;
9252 // Add recurrences are never invariant in the function-body (null loop).
9256 // This recurrence is variant w.r.t. L if L contains AR's loop.
9257 if (L->contains(AR->getLoop()))
9260 // This recurrence is invariant w.r.t. L if AR's loop contains L.
9261 if (AR->getLoop()->contains(L))
9262 return LoopInvariant;
9264 // This recurrence is variant w.r.t. L if any of its operands
9266 for (auto *Op : AR->operands())
9267 if (!isLoopInvariant(Op, L))
9270 // Otherwise it's loop-invariant.
9271 return LoopInvariant;
9277 bool HasVarying = false;
9278 for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
9279 LoopDisposition D = getLoopDisposition(Op, L);
9280 if (D == LoopVariant)
9282 if (D == LoopComputable)
9285 return HasVarying ? LoopComputable : LoopInvariant;
9288 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9289 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
9290 if (LD == LoopVariant)
9292 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
9293 if (RD == LoopVariant)
9295 return (LD == LoopInvariant && RD == LoopInvariant) ?
9296 LoopInvariant : LoopComputable;
9299 // All non-instruction values are loop invariant. All instructions are loop
9300 // invariant if they are not contained in the specified loop.
9301 // Instructions are never considered invariant in the function body
9302 // (null loop) because they are defined within the "loop".
9303 if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
9304 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
9305 return LoopInvariant;
9306 case scCouldNotCompute:
9307 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9309 llvm_unreachable("Unknown SCEV kind!");
9312 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
9313 return getLoopDisposition(S, L) == LoopInvariant;
9316 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
9317 return getLoopDisposition(S, L) == LoopComputable;
9320 ScalarEvolution::BlockDisposition
9321 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9322 auto &Values = BlockDispositions[S];
9323 for (auto &V : Values) {
9324 if (V.getPointer() == BB)
9327 Values.emplace_back(BB, DoesNotDominateBlock);
9328 BlockDisposition D = computeBlockDisposition(S, BB);
9329 auto &Values2 = BlockDispositions[S];
9330 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9331 if (V.getPointer() == BB) {
9339 ScalarEvolution::BlockDisposition
9340 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9341 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9343 return ProperlyDominatesBlock;
9347 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
9348 case scAddRecExpr: {
9349 // This uses a "dominates" query instead of "properly dominates" query
9350 // to test for proper dominance too, because the instruction which
9351 // produces the addrec's value is a PHI, and a PHI effectively properly
9352 // dominates its entire containing block.
9353 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9354 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9355 return DoesNotDominateBlock;
9357 // FALL THROUGH into SCEVNAryExpr handling.
9362 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9364 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
9366 BlockDisposition D = getBlockDisposition(*I, BB);
9367 if (D == DoesNotDominateBlock)
9368 return DoesNotDominateBlock;
9369 if (D == DominatesBlock)
9372 return Proper ? ProperlyDominatesBlock : DominatesBlock;
9375 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9376 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9377 BlockDisposition LD = getBlockDisposition(LHS, BB);
9378 if (LD == DoesNotDominateBlock)
9379 return DoesNotDominateBlock;
9380 BlockDisposition RD = getBlockDisposition(RHS, BB);
9381 if (RD == DoesNotDominateBlock)
9382 return DoesNotDominateBlock;
9383 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9384 ProperlyDominatesBlock : DominatesBlock;
9387 if (Instruction *I =
9388 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9389 if (I->getParent() == BB)
9390 return DominatesBlock;
9391 if (DT.properlyDominates(I->getParent(), BB))
9392 return ProperlyDominatesBlock;
9393 return DoesNotDominateBlock;
9395 return ProperlyDominatesBlock;
9396 case scCouldNotCompute:
9397 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9399 llvm_unreachable("Unknown SCEV kind!");
9402 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9403 return getBlockDisposition(S, BB) >= DominatesBlock;
9406 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9407 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9411 // Search for a SCEV expression node within an expression tree.
9412 // Implements SCEVTraversal::Visitor.
9417 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
9419 bool follow(const SCEV *S) {
9420 IsFound |= (S == Node);
9423 bool isDone() const { return IsFound; }
9427 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9428 SCEVSearch Search(Op);
9429 visitAll(S, Search);
9430 return Search.IsFound;
9433 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9434 ValuesAtScopes.erase(S);
9435 LoopDispositions.erase(S);
9436 BlockDispositions.erase(S);
9437 UnsignedRanges.erase(S);
9438 SignedRanges.erase(S);
9440 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
9441 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
9442 BackedgeTakenInfo &BEInfo = I->second;
9443 if (BEInfo.hasOperand(S, this)) {
9445 BackedgeTakenCounts.erase(I++);
9452 typedef DenseMap<const Loop *, std::string> VerifyMap;
9454 /// replaceSubString - Replaces all occurrences of From in Str with To.
9455 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9457 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9458 Str.replace(Pos, From.size(), To.data(), To.size());
9463 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9465 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9466 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
9467 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
9469 std::string &S = Map[L];
9471 raw_string_ostream OS(S);
9472 SE.getBackedgeTakenCount(L)->print(OS);
9474 // false and 0 are semantically equivalent. This can happen in dead loops.
9475 replaceSubString(OS.str(), "false", "0");
9476 // Remove wrap flags, their use in SCEV is highly fragile.
9477 // FIXME: Remove this when SCEV gets smarter about them.
9478 replaceSubString(OS.str(), "<nw>", "");
9479 replaceSubString(OS.str(), "<nsw>", "");
9480 replaceSubString(OS.str(), "<nuw>", "");
9485 void ScalarEvolution::verify() const {
9486 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9488 // Gather stringified backedge taken counts for all loops using SCEV's caches.
9489 // FIXME: It would be much better to store actual values instead of strings,
9490 // but SCEV pointers will change if we drop the caches.
9491 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9492 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9493 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9495 // Gather stringified backedge taken counts for all loops using a fresh
9496 // ScalarEvolution object.
9497 ScalarEvolution SE2(F, TLI, AC, DT, LI);
9498 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9499 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9501 // Now compare whether they're the same with and without caches. This allows
9502 // verifying that no pass changed the cache.
9503 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
9504 "New loops suddenly appeared!");
9506 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
9507 OldE = BackedgeDumpsOld.end(),
9508 NewI = BackedgeDumpsNew.begin();
9509 OldI != OldE; ++OldI, ++NewI) {
9510 assert(OldI->first == NewI->first && "Loop order changed!");
9512 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
9514 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
9515 // means that a pass is buggy or SCEV has to learn a new pattern but is
9516 // usually not harmful.
9517 if (OldI->second != NewI->second &&
9518 OldI->second.find("undef") == std::string::npos &&
9519 NewI->second.find("undef") == std::string::npos &&
9520 OldI->second != "***COULDNOTCOMPUTE***" &&
9521 NewI->second != "***COULDNOTCOMPUTE***") {
9522 dbgs() << "SCEVValidator: SCEV for loop '"
9523 << OldI->first->getHeader()->getName()
9524 << "' changed from '" << OldI->second
9525 << "' to '" << NewI->second << "'!\n";
9530 // TODO: Verify more things.
9533 char ScalarEvolutionAnalysis::PassID;
9535 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
9536 AnalysisManager<Function> *AM) {
9537 return ScalarEvolution(F, AM->getResult<TargetLibraryAnalysis>(F),
9538 AM->getResult<AssumptionAnalysis>(F),
9539 AM->getResult<DominatorTreeAnalysis>(F),
9540 AM->getResult<LoopAnalysis>(F));
9544 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> *AM) {
9545 AM->getResult<ScalarEvolutionAnalysis>(F).print(OS);
9546 return PreservedAnalyses::all();
9549 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
9550 "Scalar Evolution Analysis", false, true)
9551 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
9552 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
9553 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
9554 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
9555 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
9556 "Scalar Evolution Analysis", false, true)
9557 char ScalarEvolutionWrapperPass::ID = 0;
9559 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
9560 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
9563 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
9564 SE.reset(new ScalarEvolution(
9565 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
9566 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
9567 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
9568 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
9572 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
9574 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
9578 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
9585 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
9586 AU.setPreservesAll();
9587 AU.addRequiredTransitive<AssumptionCacheTracker>();
9588 AU.addRequiredTransitive<LoopInfoWrapperPass>();
9589 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
9590 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
9593 const SCEVPredicate *
9594 ScalarEvolution::getEqualPredicate(const SCEVUnknown *LHS,
9595 const SCEVConstant *RHS) {
9596 FoldingSetNodeID ID;
9597 // Unique this node based on the arguments
9598 ID.AddInteger(SCEVPredicate::P_Equal);
9602 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
9604 SCEVEqualPredicate *Eq = new (SCEVAllocator)
9605 SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
9606 UniquePreds.InsertNode(Eq, IP);
9611 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
9613 static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE,
9614 SCEVUnionPredicate &A) {
9615 SCEVPredicateRewriter Rewriter(SE, A);
9616 return Rewriter.visit(Scev);
9619 SCEVPredicateRewriter(ScalarEvolution &SE, SCEVUnionPredicate &P)
9620 : SCEVRewriteVisitor(SE), P(P) {}
9622 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
9623 auto ExprPreds = P.getPredicatesForExpr(Expr);
9624 for (auto *Pred : ExprPreds)
9625 if (const auto *IPred = dyn_cast<const SCEVEqualPredicate>(Pred))
9626 if (IPred->getLHS() == Expr)
9627 return IPred->getRHS();
9633 SCEVUnionPredicate &P;
9635 } // end anonymous namespace
9637 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *Scev,
9638 SCEVUnionPredicate &Preds) {
9639 return SCEVPredicateRewriter::rewrite(Scev, *this, Preds);
9643 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
9644 SCEVPredicateKind Kind)
9645 : FastID(ID), Kind(Kind) {}
9647 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
9648 const SCEVUnknown *LHS,
9649 const SCEVConstant *RHS)
9650 : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {}
9652 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
9653 const auto *Op = dyn_cast<const SCEVEqualPredicate>(N);
9658 return Op->LHS == LHS && Op->RHS == RHS;
9661 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
9663 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
9665 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
9666 OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
9669 /// Union predicates don't get cached so create a dummy set ID for it.
9670 SCEVUnionPredicate::SCEVUnionPredicate()
9671 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
9673 bool SCEVUnionPredicate::isAlwaysTrue() const {
9674 return all_of(Preds,
9675 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
9678 ArrayRef<const SCEVPredicate *>
9679 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
9680 auto I = SCEVToPreds.find(Expr);
9681 if (I == SCEVToPreds.end())
9682 return ArrayRef<const SCEVPredicate *>();
9686 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
9687 if (const auto *Set = dyn_cast<const SCEVUnionPredicate>(N))
9688 return all_of(Set->Preds,
9689 [this](const SCEVPredicate *I) { return this->implies(I); });
9691 auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
9692 if (ScevPredsIt == SCEVToPreds.end())
9694 auto &SCEVPreds = ScevPredsIt->second;
9696 return std::any_of(SCEVPreds.begin(), SCEVPreds.end(),
9697 [N](const SCEVPredicate *I) { return I->implies(N); });
9700 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
9702 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
9703 for (auto Pred : Preds)
9704 Pred->print(OS, Depth);
9707 void SCEVUnionPredicate::add(const SCEVPredicate *N) {
9708 if (const auto *Set = dyn_cast<const SCEVUnionPredicate>(N)) {
9709 for (auto Pred : Set->Preds)
9717 const SCEV *Key = N->getExpr();
9718 assert(Key && "Only SCEVUnionPredicate doesn't have an "
9719 " associated expression!");
9721 SCEVToPreds[Key].push_back(N);