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 &&
1964 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1966 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1968 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1970 if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
1971 Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
1973 // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
1974 // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
1976 const APInt &C = cast<SCEVConstant>(Ops[0])->getValue()->getValue();
1977 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
1979 ConstantRange::makeNoWrapRegion(Instruction::Add, C, OBO::NoSignedWrap);
1980 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
1981 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
1983 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
1985 ConstantRange::makeNoWrapRegion(Instruction::Add, C,
1986 OBO::NoUnsignedWrap);
1987 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
1988 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
1995 /// getAddExpr - Get a canonical add expression, or something simpler if
1997 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1998 SCEV::NoWrapFlags Flags) {
1999 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2000 "only nuw or nsw allowed");
2001 assert(!Ops.empty() && "Cannot get empty add!");
2002 if (Ops.size() == 1) return Ops[0];
2004 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2005 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2006 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2007 "SCEVAddExpr operand types don't match!");
2010 // Sort by complexity, this groups all similar expression types together.
2011 GroupByComplexity(Ops, &LI);
2013 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2015 // If there are any constants, fold them together.
2017 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2019 assert(Idx < Ops.size());
2020 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2021 // We found two constants, fold them together!
2022 Ops[0] = getConstant(LHSC->getValue()->getValue() +
2023 RHSC->getValue()->getValue());
2024 if (Ops.size() == 2) return Ops[0];
2025 Ops.erase(Ops.begin()+1); // Erase the folded element
2026 LHSC = cast<SCEVConstant>(Ops[0]);
2029 // If we are left with a constant zero being added, strip it off.
2030 if (LHSC->getValue()->isZero()) {
2031 Ops.erase(Ops.begin());
2035 if (Ops.size() == 1) return Ops[0];
2038 // Okay, check to see if the same value occurs in the operand list more than
2039 // once. If so, merge them together into an multiply expression. Since we
2040 // sorted the list, these values are required to be adjacent.
2041 Type *Ty = Ops[0]->getType();
2042 bool FoundMatch = false;
2043 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2044 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2045 // Scan ahead to count how many equal operands there are.
2047 while (i+Count != e && Ops[i+Count] == Ops[i])
2049 // Merge the values into a multiply.
2050 const SCEV *Scale = getConstant(Ty, Count);
2051 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2052 if (Ops.size() == Count)
2055 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2056 --i; e -= Count - 1;
2060 return getAddExpr(Ops, Flags);
2062 // Check for truncates. If all the operands are truncated from the same
2063 // type, see if factoring out the truncate would permit the result to be
2064 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2065 // if the contents of the resulting outer trunc fold to something simple.
2066 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2067 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2068 Type *DstType = Trunc->getType();
2069 Type *SrcType = Trunc->getOperand()->getType();
2070 SmallVector<const SCEV *, 8> LargeOps;
2072 // Check all the operands to see if they can be represented in the
2073 // source type of the truncate.
2074 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2075 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2076 if (T->getOperand()->getType() != SrcType) {
2080 LargeOps.push_back(T->getOperand());
2081 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2082 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2083 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2084 SmallVector<const SCEV *, 8> LargeMulOps;
2085 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2086 if (const SCEVTruncateExpr *T =
2087 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2088 if (T->getOperand()->getType() != SrcType) {
2092 LargeMulOps.push_back(T->getOperand());
2093 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2094 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2101 LargeOps.push_back(getMulExpr(LargeMulOps));
2108 // Evaluate the expression in the larger type.
2109 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2110 // If it folds to something simple, use it. Otherwise, don't.
2111 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2112 return getTruncateExpr(Fold, DstType);
2116 // Skip past any other cast SCEVs.
2117 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2120 // If there are add operands they would be next.
2121 if (Idx < Ops.size()) {
2122 bool DeletedAdd = false;
2123 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2124 // If we have an add, expand the add operands onto the end of the operands
2126 Ops.erase(Ops.begin()+Idx);
2127 Ops.append(Add->op_begin(), Add->op_end());
2131 // If we deleted at least one add, we added operands to the end of the list,
2132 // and they are not necessarily sorted. Recurse to resort and resimplify
2133 // any operands we just acquired.
2135 return getAddExpr(Ops);
2138 // Skip over the add expression until we get to a multiply.
2139 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2142 // Check to see if there are any folding opportunities present with
2143 // operands multiplied by constant values.
2144 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2145 uint64_t BitWidth = getTypeSizeInBits(Ty);
2146 DenseMap<const SCEV *, APInt> M;
2147 SmallVector<const SCEV *, 8> NewOps;
2148 APInt AccumulatedConstant(BitWidth, 0);
2149 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2150 Ops.data(), Ops.size(),
2151 APInt(BitWidth, 1), *this)) {
2152 // Some interesting folding opportunity is present, so its worthwhile to
2153 // re-generate the operands list. Group the operands by constant scale,
2154 // to avoid multiplying by the same constant scale multiple times.
2155 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2156 for (const SCEV *NewOp : NewOps)
2157 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2158 // Re-generate the operands list.
2160 if (AccumulatedConstant != 0)
2161 Ops.push_back(getConstant(AccumulatedConstant));
2162 for (auto &MulOp : MulOpLists)
2163 if (MulOp.first != 0)
2164 Ops.push_back(getMulExpr(getConstant(MulOp.first),
2165 getAddExpr(MulOp.second)));
2168 if (Ops.size() == 1)
2170 return getAddExpr(Ops);
2174 // If we are adding something to a multiply expression, make sure the
2175 // something is not already an operand of the multiply. If so, merge it into
2177 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2178 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2179 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2180 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2181 if (isa<SCEVConstant>(MulOpSCEV))
2183 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2184 if (MulOpSCEV == Ops[AddOp]) {
2185 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2186 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2187 if (Mul->getNumOperands() != 2) {
2188 // If the multiply has more than two operands, we must get the
2190 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2191 Mul->op_begin()+MulOp);
2192 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2193 InnerMul = getMulExpr(MulOps);
2195 const SCEV *One = getOne(Ty);
2196 const SCEV *AddOne = getAddExpr(One, InnerMul);
2197 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2198 if (Ops.size() == 2) return OuterMul;
2200 Ops.erase(Ops.begin()+AddOp);
2201 Ops.erase(Ops.begin()+Idx-1);
2203 Ops.erase(Ops.begin()+Idx);
2204 Ops.erase(Ops.begin()+AddOp-1);
2206 Ops.push_back(OuterMul);
2207 return getAddExpr(Ops);
2210 // Check this multiply against other multiplies being added together.
2211 for (unsigned OtherMulIdx = Idx+1;
2212 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2214 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2215 // If MulOp occurs in OtherMul, we can fold the two multiplies
2217 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2218 OMulOp != e; ++OMulOp)
2219 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2220 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2221 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2222 if (Mul->getNumOperands() != 2) {
2223 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2224 Mul->op_begin()+MulOp);
2225 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2226 InnerMul1 = getMulExpr(MulOps);
2228 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2229 if (OtherMul->getNumOperands() != 2) {
2230 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2231 OtherMul->op_begin()+OMulOp);
2232 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2233 InnerMul2 = getMulExpr(MulOps);
2235 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2236 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2237 if (Ops.size() == 2) return OuterMul;
2238 Ops.erase(Ops.begin()+Idx);
2239 Ops.erase(Ops.begin()+OtherMulIdx-1);
2240 Ops.push_back(OuterMul);
2241 return getAddExpr(Ops);
2247 // If there are any add recurrences in the operands list, see if any other
2248 // added values are loop invariant. If so, we can fold them into the
2250 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2253 // Scan over all recurrences, trying to fold loop invariants into them.
2254 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2255 // Scan all of the other operands to this add and add them to the vector if
2256 // they are loop invariant w.r.t. the recurrence.
2257 SmallVector<const SCEV *, 8> LIOps;
2258 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2259 const Loop *AddRecLoop = AddRec->getLoop();
2260 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2261 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2262 LIOps.push_back(Ops[i]);
2263 Ops.erase(Ops.begin()+i);
2267 // If we found some loop invariants, fold them into the recurrence.
2268 if (!LIOps.empty()) {
2269 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2270 LIOps.push_back(AddRec->getStart());
2272 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2274 AddRecOps[0] = getAddExpr(LIOps);
2276 // Build the new addrec. Propagate the NUW and NSW flags if both the
2277 // outer add and the inner addrec are guaranteed to have no overflow.
2278 // Always propagate NW.
2279 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2280 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2282 // If all of the other operands were loop invariant, we are done.
2283 if (Ops.size() == 1) return NewRec;
2285 // Otherwise, add the folded AddRec by the non-invariant parts.
2286 for (unsigned i = 0;; ++i)
2287 if (Ops[i] == AddRec) {
2291 return getAddExpr(Ops);
2294 // Okay, if there weren't any loop invariants to be folded, check to see if
2295 // there are multiple AddRec's with the same loop induction variable being
2296 // added together. If so, we can fold them.
2297 for (unsigned OtherIdx = Idx+1;
2298 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2300 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2301 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2302 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2304 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2306 if (const auto *OtherAddRec = dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2307 if (OtherAddRec->getLoop() == AddRecLoop) {
2308 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2310 if (i >= AddRecOps.size()) {
2311 AddRecOps.append(OtherAddRec->op_begin()+i,
2312 OtherAddRec->op_end());
2315 AddRecOps[i] = getAddExpr(AddRecOps[i],
2316 OtherAddRec->getOperand(i));
2318 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2320 // Step size has changed, so we cannot guarantee no self-wraparound.
2321 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2322 return getAddExpr(Ops);
2325 // Otherwise couldn't fold anything into this recurrence. Move onto the
2329 // Okay, it looks like we really DO need an add expr. Check to see if we
2330 // already have one, otherwise create a new one.
2331 FoldingSetNodeID ID;
2332 ID.AddInteger(scAddExpr);
2333 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2334 ID.AddPointer(Ops[i]);
2337 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2339 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2340 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2341 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2343 UniqueSCEVs.InsertNode(S, IP);
2345 S->setNoWrapFlags(Flags);
2349 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2351 if (j > 1 && k / j != i) Overflow = true;
2355 /// Compute the result of "n choose k", the binomial coefficient. If an
2356 /// intermediate computation overflows, Overflow will be set and the return will
2357 /// be garbage. Overflow is not cleared on absence of overflow.
2358 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2359 // We use the multiplicative formula:
2360 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2361 // At each iteration, we take the n-th term of the numeral and divide by the
2362 // (k-n)th term of the denominator. This division will always produce an
2363 // integral result, and helps reduce the chance of overflow in the
2364 // intermediate computations. However, we can still overflow even when the
2365 // final result would fit.
2367 if (n == 0 || n == k) return 1;
2368 if (k > n) return 0;
2374 for (uint64_t i = 1; i <= k; ++i) {
2375 r = umul_ov(r, n-(i-1), Overflow);
2381 /// Determine if any of the operands in this SCEV are a constant or if
2382 /// any of the add or multiply expressions in this SCEV contain a constant.
2383 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2384 SmallVector<const SCEV *, 4> Ops;
2385 Ops.push_back(StartExpr);
2386 while (!Ops.empty()) {
2387 const SCEV *CurrentExpr = Ops.pop_back_val();
2388 if (isa<SCEVConstant>(*CurrentExpr))
2391 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2392 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2393 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2399 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2401 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2402 SCEV::NoWrapFlags Flags) {
2403 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2404 "only nuw or nsw allowed");
2405 assert(!Ops.empty() && "Cannot get empty mul!");
2406 if (Ops.size() == 1) return Ops[0];
2408 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2409 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2410 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2411 "SCEVMulExpr operand types don't match!");
2414 // Sort by complexity, this groups all similar expression types together.
2415 GroupByComplexity(Ops, &LI);
2417 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2419 // If there are any constants, fold them together.
2421 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2423 // C1*(C2+V) -> C1*C2 + C1*V
2424 if (Ops.size() == 2)
2425 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2426 // If any of Add's ops are Adds or Muls with a constant,
2427 // apply this transformation as well.
2428 if (Add->getNumOperands() == 2)
2429 if (containsConstantSomewhere(Add))
2430 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2431 getMulExpr(LHSC, Add->getOperand(1)));
2434 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2435 // We found two constants, fold them together!
2436 ConstantInt *Fold = ConstantInt::get(getContext(),
2437 LHSC->getValue()->getValue() *
2438 RHSC->getValue()->getValue());
2439 Ops[0] = getConstant(Fold);
2440 Ops.erase(Ops.begin()+1); // Erase the folded element
2441 if (Ops.size() == 1) return Ops[0];
2442 LHSC = cast<SCEVConstant>(Ops[0]);
2445 // If we are left with a constant one being multiplied, strip it off.
2446 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2447 Ops.erase(Ops.begin());
2449 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2450 // If we have a multiply of zero, it will always be zero.
2452 } else if (Ops[0]->isAllOnesValue()) {
2453 // If we have a mul by -1 of an add, try distributing the -1 among the
2455 if (Ops.size() == 2) {
2456 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2457 SmallVector<const SCEV *, 4> NewOps;
2458 bool AnyFolded = false;
2459 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2460 E = Add->op_end(); I != E; ++I) {
2461 const SCEV *Mul = getMulExpr(Ops[0], *I);
2462 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2463 NewOps.push_back(Mul);
2466 return getAddExpr(NewOps);
2467 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2468 // Negation preserves a recurrence's no self-wrap property.
2469 SmallVector<const SCEV *, 4> Operands;
2470 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2471 E = AddRec->op_end(); I != E; ++I) {
2472 Operands.push_back(getMulExpr(Ops[0], *I));
2474 return getAddRecExpr(Operands, AddRec->getLoop(),
2475 AddRec->getNoWrapFlags(SCEV::FlagNW));
2480 if (Ops.size() == 1)
2484 // Skip over the add expression until we get to a multiply.
2485 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2488 // If there are mul operands inline them all into this expression.
2489 if (Idx < Ops.size()) {
2490 bool DeletedMul = false;
2491 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2492 // If we have an mul, expand the mul operands onto the end of the operands
2494 Ops.erase(Ops.begin()+Idx);
2495 Ops.append(Mul->op_begin(), Mul->op_end());
2499 // If we deleted at least one mul, we added operands to the end of the list,
2500 // and they are not necessarily sorted. Recurse to resort and resimplify
2501 // any operands we just acquired.
2503 return getMulExpr(Ops);
2506 // If there are any add recurrences in the operands list, see if any other
2507 // added values are loop invariant. If so, we can fold them into the
2509 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2512 // Scan over all recurrences, trying to fold loop invariants into them.
2513 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2514 // Scan all of the other operands to this mul and add them to the vector if
2515 // they are loop invariant w.r.t. the recurrence.
2516 SmallVector<const SCEV *, 8> LIOps;
2517 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2518 const Loop *AddRecLoop = AddRec->getLoop();
2519 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2520 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2521 LIOps.push_back(Ops[i]);
2522 Ops.erase(Ops.begin()+i);
2526 // If we found some loop invariants, fold them into the recurrence.
2527 if (!LIOps.empty()) {
2528 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2529 SmallVector<const SCEV *, 4> NewOps;
2530 NewOps.reserve(AddRec->getNumOperands());
2531 const SCEV *Scale = getMulExpr(LIOps);
2532 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2533 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2535 // Build the new addrec. Propagate the NUW and NSW flags if both the
2536 // outer mul and the inner addrec are guaranteed to have no overflow.
2538 // No self-wrap cannot be guaranteed after changing the step size, but
2539 // will be inferred if either NUW or NSW is true.
2540 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2541 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2543 // If all of the other operands were loop invariant, we are done.
2544 if (Ops.size() == 1) return NewRec;
2546 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2547 for (unsigned i = 0;; ++i)
2548 if (Ops[i] == AddRec) {
2552 return getMulExpr(Ops);
2555 // Okay, if there weren't any loop invariants to be folded, check to see if
2556 // there are multiple AddRec's with the same loop induction variable being
2557 // multiplied together. If so, we can fold them.
2559 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2560 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2561 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2562 // ]]],+,...up to x=2n}.
2563 // Note that the arguments to choose() are always integers with values
2564 // known at compile time, never SCEV objects.
2566 // The implementation avoids pointless extra computations when the two
2567 // addrec's are of different length (mathematically, it's equivalent to
2568 // an infinite stream of zeros on the right).
2569 bool OpsModified = false;
2570 for (unsigned OtherIdx = Idx+1;
2571 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2573 const SCEVAddRecExpr *OtherAddRec =
2574 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2575 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2578 bool Overflow = false;
2579 Type *Ty = AddRec->getType();
2580 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2581 SmallVector<const SCEV*, 7> AddRecOps;
2582 for (int x = 0, xe = AddRec->getNumOperands() +
2583 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2584 const SCEV *Term = getZero(Ty);
2585 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2586 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2587 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2588 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2589 z < ze && !Overflow; ++z) {
2590 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2592 if (LargerThan64Bits)
2593 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2595 Coeff = Coeff1*Coeff2;
2596 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2597 const SCEV *Term1 = AddRec->getOperand(y-z);
2598 const SCEV *Term2 = OtherAddRec->getOperand(z);
2599 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2602 AddRecOps.push_back(Term);
2605 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2607 if (Ops.size() == 2) return NewAddRec;
2608 Ops[Idx] = NewAddRec;
2609 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2611 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2617 return getMulExpr(Ops);
2619 // Otherwise couldn't fold anything into this recurrence. Move onto the
2623 // Okay, it looks like we really DO need an mul expr. Check to see if we
2624 // already have one, otherwise create a new one.
2625 FoldingSetNodeID ID;
2626 ID.AddInteger(scMulExpr);
2627 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2628 ID.AddPointer(Ops[i]);
2631 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2633 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2634 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2635 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2637 UniqueSCEVs.InsertNode(S, IP);
2639 S->setNoWrapFlags(Flags);
2643 /// getUDivExpr - Get a canonical unsigned division expression, or something
2644 /// simpler if possible.
2645 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2647 assert(getEffectiveSCEVType(LHS->getType()) ==
2648 getEffectiveSCEVType(RHS->getType()) &&
2649 "SCEVUDivExpr operand types don't match!");
2651 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2652 if (RHSC->getValue()->equalsInt(1))
2653 return LHS; // X udiv 1 --> x
2654 // If the denominator is zero, the result of the udiv is undefined. Don't
2655 // try to analyze it, because the resolution chosen here may differ from
2656 // the resolution chosen in other parts of the compiler.
2657 if (!RHSC->getValue()->isZero()) {
2658 // Determine if the division can be folded into the operands of
2660 // TODO: Generalize this to non-constants by using known-bits information.
2661 Type *Ty = LHS->getType();
2662 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2663 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2664 // For non-power-of-two values, effectively round the value up to the
2665 // nearest power of two.
2666 if (!RHSC->getValue()->getValue().isPowerOf2())
2668 IntegerType *ExtTy =
2669 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2670 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2671 if (const SCEVConstant *Step =
2672 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2673 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2674 const APInt &StepInt = Step->getValue()->getValue();
2675 const APInt &DivInt = RHSC->getValue()->getValue();
2676 if (!StepInt.urem(DivInt) &&
2677 getZeroExtendExpr(AR, ExtTy) ==
2678 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2679 getZeroExtendExpr(Step, ExtTy),
2680 AR->getLoop(), SCEV::FlagAnyWrap)) {
2681 SmallVector<const SCEV *, 4> Operands;
2682 for (const SCEV *Op : AR->operands())
2683 Operands.push_back(getUDivExpr(Op, RHS));
2684 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
2686 /// Get a canonical UDivExpr for a recurrence.
2687 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2688 // We can currently only fold X%N if X is constant.
2689 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2690 if (StartC && !DivInt.urem(StepInt) &&
2691 getZeroExtendExpr(AR, ExtTy) ==
2692 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2693 getZeroExtendExpr(Step, ExtTy),
2694 AR->getLoop(), SCEV::FlagAnyWrap)) {
2695 const APInt &StartInt = StartC->getValue()->getValue();
2696 const APInt &StartRem = StartInt.urem(StepInt);
2698 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2699 AR->getLoop(), SCEV::FlagNW);
2702 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2703 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2704 SmallVector<const SCEV *, 4> Operands;
2705 for (const SCEV *Op : M->operands())
2706 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2707 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2708 // Find an operand that's safely divisible.
2709 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2710 const SCEV *Op = M->getOperand(i);
2711 const SCEV *Div = getUDivExpr(Op, RHSC);
2712 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2713 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2716 return getMulExpr(Operands);
2720 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2721 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2722 SmallVector<const SCEV *, 4> Operands;
2723 for (const SCEV *Op : A->operands())
2724 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2725 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2727 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2728 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2729 if (isa<SCEVUDivExpr>(Op) ||
2730 getMulExpr(Op, RHS) != A->getOperand(i))
2732 Operands.push_back(Op);
2734 if (Operands.size() == A->getNumOperands())
2735 return getAddExpr(Operands);
2739 // Fold if both operands are constant.
2740 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2741 Constant *LHSCV = LHSC->getValue();
2742 Constant *RHSCV = RHSC->getValue();
2743 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2749 FoldingSetNodeID ID;
2750 ID.AddInteger(scUDivExpr);
2754 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2755 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2757 UniqueSCEVs.InsertNode(S, IP);
2761 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2762 APInt A = C1->getValue()->getValue().abs();
2763 APInt B = C2->getValue()->getValue().abs();
2764 uint32_t ABW = A.getBitWidth();
2765 uint32_t BBW = B.getBitWidth();
2772 return APIntOps::GreatestCommonDivisor(A, B);
2775 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2776 /// something simpler if possible. There is no representation for an exact udiv
2777 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2778 /// We can't do this when it's not exact because the udiv may be clearing bits.
2779 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2781 // TODO: we could try to find factors in all sorts of things, but for now we
2782 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2783 // end of this file for inspiration.
2785 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2787 return getUDivExpr(LHS, RHS);
2789 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2790 // If the mulexpr multiplies by a constant, then that constant must be the
2791 // first element of the mulexpr.
2792 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2793 if (LHSCst == RHSCst) {
2794 SmallVector<const SCEV *, 2> Operands;
2795 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2796 return getMulExpr(Operands);
2799 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2800 // that there's a factor provided by one of the other terms. We need to
2802 APInt Factor = gcd(LHSCst, RHSCst);
2803 if (!Factor.isIntN(1)) {
2804 LHSCst = cast<SCEVConstant>(
2805 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2806 RHSCst = cast<SCEVConstant>(
2807 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2808 SmallVector<const SCEV *, 2> Operands;
2809 Operands.push_back(LHSCst);
2810 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2811 LHS = getMulExpr(Operands);
2813 Mul = dyn_cast<SCEVMulExpr>(LHS);
2815 return getUDivExactExpr(LHS, RHS);
2820 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2821 if (Mul->getOperand(i) == RHS) {
2822 SmallVector<const SCEV *, 2> Operands;
2823 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2824 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2825 return getMulExpr(Operands);
2829 return getUDivExpr(LHS, RHS);
2832 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2833 /// Simplify the expression as much as possible.
2834 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2836 SCEV::NoWrapFlags Flags) {
2837 SmallVector<const SCEV *, 4> Operands;
2838 Operands.push_back(Start);
2839 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2840 if (StepChrec->getLoop() == L) {
2841 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2842 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2845 Operands.push_back(Step);
2846 return getAddRecExpr(Operands, L, Flags);
2849 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2850 /// Simplify the expression as much as possible.
2852 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2853 const Loop *L, SCEV::NoWrapFlags Flags) {
2854 if (Operands.size() == 1) return Operands[0];
2856 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2857 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2858 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2859 "SCEVAddRecExpr operand types don't match!");
2860 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2861 assert(isLoopInvariant(Operands[i], L) &&
2862 "SCEVAddRecExpr operand is not loop-invariant!");
2865 if (Operands.back()->isZero()) {
2866 Operands.pop_back();
2867 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2870 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2871 // use that information to infer NUW and NSW flags. However, computing a
2872 // BE count requires calling getAddRecExpr, so we may not yet have a
2873 // meaningful BE count at this point (and if we don't, we'd be stuck
2874 // with a SCEVCouldNotCompute as the cached BE count).
2876 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2878 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2879 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2880 const Loop *NestedLoop = NestedAR->getLoop();
2881 if (L->contains(NestedLoop)
2882 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2883 : (!NestedLoop->contains(L) &&
2884 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2885 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2886 NestedAR->op_end());
2887 Operands[0] = NestedAR->getStart();
2888 // AddRecs require their operands be loop-invariant with respect to their
2889 // loops. Don't perform this transformation if it would break this
2892 std::all_of(Operands.begin(), Operands.end(),
2893 [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
2896 // Create a recurrence for the outer loop with the same step size.
2898 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2899 // inner recurrence has the same property.
2900 SCEV::NoWrapFlags OuterFlags =
2901 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2903 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2904 AllInvariant = std::all_of(
2905 NestedOperands.begin(), NestedOperands.end(),
2906 [&](const SCEV *Op) { return isLoopInvariant(Op, NestedLoop); });
2909 // Ok, both add recurrences are valid after the transformation.
2911 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2912 // the outer recurrence has the same property.
2913 SCEV::NoWrapFlags InnerFlags =
2914 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2915 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2918 // Reset Operands to its original state.
2919 Operands[0] = NestedAR;
2923 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2924 // already have one, otherwise create a new one.
2925 FoldingSetNodeID ID;
2926 ID.AddInteger(scAddRecExpr);
2927 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2928 ID.AddPointer(Operands[i]);
2932 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2934 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2935 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2936 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2937 O, Operands.size(), L);
2938 UniqueSCEVs.InsertNode(S, IP);
2940 S->setNoWrapFlags(Flags);
2945 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2946 const SmallVectorImpl<const SCEV *> &IndexExprs,
2948 // getSCEV(Base)->getType() has the same address space as Base->getType()
2949 // because SCEV::getType() preserves the address space.
2950 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2951 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2952 // instruction to its SCEV, because the Instruction may be guarded by control
2953 // flow and the no-overflow bits may not be valid for the expression in any
2954 // context. This can be fixed similarly to how these flags are handled for
2956 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2958 const SCEV *TotalOffset = getZero(IntPtrTy);
2959 // The address space is unimportant. The first thing we do on CurTy is getting
2960 // its element type.
2961 Type *CurTy = PointerType::getUnqual(PointeeType);
2962 for (const SCEV *IndexExpr : IndexExprs) {
2963 // Compute the (potentially symbolic) offset in bytes for this index.
2964 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2965 // For a struct, add the member offset.
2966 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2967 unsigned FieldNo = Index->getZExtValue();
2968 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2970 // Add the field offset to the running total offset.
2971 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2973 // Update CurTy to the type of the field at Index.
2974 CurTy = STy->getTypeAtIndex(Index);
2976 // Update CurTy to its element type.
2977 CurTy = cast<SequentialType>(CurTy)->getElementType();
2978 // For an array, add the element offset, explicitly scaled.
2979 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2980 // Getelementptr indices are signed.
2981 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2983 // Multiply the index by the element size to compute the element offset.
2984 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2986 // Add the element offset to the running total offset.
2987 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2991 // Add the total offset from all the GEP indices to the base.
2992 return getAddExpr(BaseExpr, TotalOffset, Wrap);
2995 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2997 SmallVector<const SCEV *, 2> Ops;
3000 return getSMaxExpr(Ops);
3004 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3005 assert(!Ops.empty() && "Cannot get empty smax!");
3006 if (Ops.size() == 1) return Ops[0];
3008 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3009 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3010 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3011 "SCEVSMaxExpr operand types don't match!");
3014 // Sort by complexity, this groups all similar expression types together.
3015 GroupByComplexity(Ops, &LI);
3017 // If there are any constants, fold them together.
3019 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3021 assert(Idx < Ops.size());
3022 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3023 // We found two constants, fold them together!
3024 ConstantInt *Fold = ConstantInt::get(getContext(),
3025 APIntOps::smax(LHSC->getValue()->getValue(),
3026 RHSC->getValue()->getValue()));
3027 Ops[0] = getConstant(Fold);
3028 Ops.erase(Ops.begin()+1); // Erase the folded element
3029 if (Ops.size() == 1) return Ops[0];
3030 LHSC = cast<SCEVConstant>(Ops[0]);
3033 // If we are left with a constant minimum-int, strip it off.
3034 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3035 Ops.erase(Ops.begin());
3037 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3038 // If we have an smax with a constant maximum-int, it will always be
3043 if (Ops.size() == 1) return Ops[0];
3046 // Find the first SMax
3047 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3050 // Check to see if one of the operands is an SMax. If so, expand its operands
3051 // onto our operand list, and recurse to simplify.
3052 if (Idx < Ops.size()) {
3053 bool DeletedSMax = false;
3054 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3055 Ops.erase(Ops.begin()+Idx);
3056 Ops.append(SMax->op_begin(), SMax->op_end());
3061 return getSMaxExpr(Ops);
3064 // Okay, check to see if the same value occurs in the operand list twice. If
3065 // so, delete one. Since we sorted the list, these values are required to
3067 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3068 // X smax Y smax Y --> X smax Y
3069 // X smax Y --> X, if X is always greater than Y
3070 if (Ops[i] == Ops[i+1] ||
3071 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3072 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3074 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3075 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3079 if (Ops.size() == 1) return Ops[0];
3081 assert(!Ops.empty() && "Reduced smax down to nothing!");
3083 // Okay, it looks like we really DO need an smax expr. Check to see if we
3084 // already have one, otherwise create a new one.
3085 FoldingSetNodeID ID;
3086 ID.AddInteger(scSMaxExpr);
3087 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3088 ID.AddPointer(Ops[i]);
3090 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3091 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3092 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3093 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3095 UniqueSCEVs.InsertNode(S, IP);
3099 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3101 SmallVector<const SCEV *, 2> Ops;
3104 return getUMaxExpr(Ops);
3108 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3109 assert(!Ops.empty() && "Cannot get empty umax!");
3110 if (Ops.size() == 1) return Ops[0];
3112 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3113 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3114 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3115 "SCEVUMaxExpr operand types don't match!");
3118 // Sort by complexity, this groups all similar expression types together.
3119 GroupByComplexity(Ops, &LI);
3121 // If there are any constants, fold them together.
3123 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3125 assert(Idx < Ops.size());
3126 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3127 // We found two constants, fold them together!
3128 ConstantInt *Fold = ConstantInt::get(getContext(),
3129 APIntOps::umax(LHSC->getValue()->getValue(),
3130 RHSC->getValue()->getValue()));
3131 Ops[0] = getConstant(Fold);
3132 Ops.erase(Ops.begin()+1); // Erase the folded element
3133 if (Ops.size() == 1) return Ops[0];
3134 LHSC = cast<SCEVConstant>(Ops[0]);
3137 // If we are left with a constant minimum-int, strip it off.
3138 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3139 Ops.erase(Ops.begin());
3141 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3142 // If we have an umax with a constant maximum-int, it will always be
3147 if (Ops.size() == 1) return Ops[0];
3150 // Find the first UMax
3151 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3154 // Check to see if one of the operands is a UMax. If so, expand its operands
3155 // onto our operand list, and recurse to simplify.
3156 if (Idx < Ops.size()) {
3157 bool DeletedUMax = false;
3158 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3159 Ops.erase(Ops.begin()+Idx);
3160 Ops.append(UMax->op_begin(), UMax->op_end());
3165 return getUMaxExpr(Ops);
3168 // Okay, check to see if the same value occurs in the operand list twice. If
3169 // so, delete one. Since we sorted the list, these values are required to
3171 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3172 // X umax Y umax Y --> X umax Y
3173 // X umax Y --> X, if X is always greater than Y
3174 if (Ops[i] == Ops[i+1] ||
3175 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3176 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3178 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3179 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3183 if (Ops.size() == 1) return Ops[0];
3185 assert(!Ops.empty() && "Reduced umax down to nothing!");
3187 // Okay, it looks like we really DO need a umax expr. Check to see if we
3188 // already have one, otherwise create a new one.
3189 FoldingSetNodeID ID;
3190 ID.AddInteger(scUMaxExpr);
3191 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3192 ID.AddPointer(Ops[i]);
3194 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3195 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3196 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3197 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3199 UniqueSCEVs.InsertNode(S, IP);
3203 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3205 // ~smax(~x, ~y) == smin(x, y).
3206 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3209 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3211 // ~umax(~x, ~y) == umin(x, y)
3212 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3215 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3216 // We can bypass creating a target-independent
3217 // constant expression and then folding it back into a ConstantInt.
3218 // This is just a compile-time optimization.
3219 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3222 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3225 // We can bypass creating a target-independent
3226 // constant expression and then folding it back into a ConstantInt.
3227 // This is just a compile-time optimization.
3229 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3232 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3233 // Don't attempt to do anything other than create a SCEVUnknown object
3234 // here. createSCEV only calls getUnknown after checking for all other
3235 // interesting possibilities, and any other code that calls getUnknown
3236 // is doing so in order to hide a value from SCEV canonicalization.
3238 FoldingSetNodeID ID;
3239 ID.AddInteger(scUnknown);
3242 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3243 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3244 "Stale SCEVUnknown in uniquing map!");
3247 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3249 FirstUnknown = cast<SCEVUnknown>(S);
3250 UniqueSCEVs.InsertNode(S, IP);
3254 //===----------------------------------------------------------------------===//
3255 // Basic SCEV Analysis and PHI Idiom Recognition Code
3258 /// isSCEVable - Test if values of the given type are analyzable within
3259 /// the SCEV framework. This primarily includes integer types, and it
3260 /// can optionally include pointer types if the ScalarEvolution class
3261 /// has access to target-specific information.
3262 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3263 // Integers and pointers are always SCEVable.
3264 return Ty->isIntegerTy() || Ty->isPointerTy();
3267 /// getTypeSizeInBits - Return the size in bits of the specified type,
3268 /// for which isSCEVable must return true.
3269 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3270 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3271 return getDataLayout().getTypeSizeInBits(Ty);
3274 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3275 /// the given type and which represents how SCEV will treat the given
3276 /// type, for which isSCEVable must return true. For pointer types,
3277 /// this is the pointer-sized integer type.
3278 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3279 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3281 if (Ty->isIntegerTy())
3284 // The only other support type is pointer.
3285 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3286 return getDataLayout().getIntPtrType(Ty);
3289 const SCEV *ScalarEvolution::getCouldNotCompute() {
3290 return CouldNotCompute.get();
3294 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3295 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3296 // is set iff if find such SCEVUnknown.
3298 struct FindInvalidSCEVUnknown {
3300 FindInvalidSCEVUnknown() { FindOne = false; }
3301 bool follow(const SCEV *S) {
3302 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3306 if (!cast<SCEVUnknown>(S)->getValue())
3313 bool isDone() const { return FindOne; }
3317 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3318 FindInvalidSCEVUnknown F;
3319 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3325 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3326 /// expression and create a new one.
3327 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3328 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3330 const SCEV *S = getExistingSCEV(V);
3333 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3338 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3339 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3341 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3342 if (I != ValueExprMap.end()) {
3343 const SCEV *S = I->second;
3344 if (checkValidity(S))
3346 ValueExprMap.erase(I);
3351 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3353 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3354 SCEV::NoWrapFlags Flags) {
3355 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3357 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3359 Type *Ty = V->getType();
3360 Ty = getEffectiveSCEVType(Ty);
3362 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3365 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3366 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3367 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3369 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3371 Type *Ty = V->getType();
3372 Ty = getEffectiveSCEVType(Ty);
3373 const SCEV *AllOnes =
3374 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3375 return getMinusSCEV(AllOnes, V);
3378 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3379 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3380 SCEV::NoWrapFlags Flags) {
3381 // Fast path: X - X --> 0.
3383 return getZero(LHS->getType());
3385 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3386 // makes it so that we cannot make much use of NUW.
3387 auto AddFlags = SCEV::FlagAnyWrap;
3388 const bool RHSIsNotMinSigned =
3389 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3390 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3391 // Let M be the minimum representable signed value. Then (-1)*RHS
3392 // signed-wraps if and only if RHS is M. That can happen even for
3393 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3394 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3395 // (-1)*RHS, we need to prove that RHS != M.
3397 // If LHS is non-negative and we know that LHS - RHS does not
3398 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3399 // either by proving that RHS > M or that LHS >= 0.
3400 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3401 AddFlags = SCEV::FlagNSW;
3405 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3406 // RHS is NSW and LHS >= 0.
3408 // The difficulty here is that the NSW flag may have been proven
3409 // relative to a loop that is to be found in a recurrence in LHS and
3410 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3411 // larger scope than intended.
3412 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3414 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3417 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3418 /// input value to the specified type. If the type must be extended, it is zero
3421 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3422 Type *SrcTy = V->getType();
3423 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3424 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3425 "Cannot truncate or zero extend with non-integer arguments!");
3426 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3427 return V; // No conversion
3428 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3429 return getTruncateExpr(V, Ty);
3430 return getZeroExtendExpr(V, Ty);
3433 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3434 /// input value to the specified type. If the type must be extended, it is sign
3437 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3439 Type *SrcTy = V->getType();
3440 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3441 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3442 "Cannot truncate or zero extend with non-integer arguments!");
3443 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3444 return V; // No conversion
3445 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3446 return getTruncateExpr(V, Ty);
3447 return getSignExtendExpr(V, Ty);
3450 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3451 /// input value to the specified type. If the type must be extended, it is zero
3452 /// extended. The conversion must not be narrowing.
3454 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3455 Type *SrcTy = V->getType();
3456 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3457 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3458 "Cannot noop or zero extend with non-integer arguments!");
3459 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3460 "getNoopOrZeroExtend cannot truncate!");
3461 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3462 return V; // No conversion
3463 return getZeroExtendExpr(V, Ty);
3466 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3467 /// input value to the specified type. If the type must be extended, it is sign
3468 /// extended. The conversion must not be narrowing.
3470 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3471 Type *SrcTy = V->getType();
3472 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3473 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3474 "Cannot noop or sign extend with non-integer arguments!");
3475 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3476 "getNoopOrSignExtend cannot truncate!");
3477 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3478 return V; // No conversion
3479 return getSignExtendExpr(V, Ty);
3482 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3483 /// the input value to the specified type. If the type must be extended,
3484 /// it is extended with unspecified bits. The conversion must not be
3487 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3488 Type *SrcTy = V->getType();
3489 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3490 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3491 "Cannot noop or any extend with non-integer arguments!");
3492 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3493 "getNoopOrAnyExtend cannot truncate!");
3494 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3495 return V; // No conversion
3496 return getAnyExtendExpr(V, Ty);
3499 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3500 /// input value to the specified type. The conversion must not be widening.
3502 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3503 Type *SrcTy = V->getType();
3504 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3505 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3506 "Cannot truncate or noop with non-integer arguments!");
3507 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3508 "getTruncateOrNoop cannot extend!");
3509 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3510 return V; // No conversion
3511 return getTruncateExpr(V, Ty);
3514 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3515 /// the types using zero-extension, and then perform a umax operation
3517 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3519 const SCEV *PromotedLHS = LHS;
3520 const SCEV *PromotedRHS = RHS;
3522 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3523 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3525 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3527 return getUMaxExpr(PromotedLHS, PromotedRHS);
3530 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3531 /// the types using zero-extension, and then perform a umin operation
3533 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3535 const SCEV *PromotedLHS = LHS;
3536 const SCEV *PromotedRHS = RHS;
3538 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3539 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3541 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3543 return getUMinExpr(PromotedLHS, PromotedRHS);
3546 /// getPointerBase - Transitively follow the chain of pointer-type operands
3547 /// until reaching a SCEV that does not have a single pointer operand. This
3548 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3549 /// but corner cases do exist.
3550 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3551 // A pointer operand may evaluate to a nonpointer expression, such as null.
3552 if (!V->getType()->isPointerTy())
3555 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3556 return getPointerBase(Cast->getOperand());
3557 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3558 const SCEV *PtrOp = nullptr;
3559 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3561 if ((*I)->getType()->isPointerTy()) {
3562 // Cannot find the base of an expression with multiple pointer operands.
3570 return getPointerBase(PtrOp);
3575 /// PushDefUseChildren - Push users of the given Instruction
3576 /// onto the given Worklist.
3578 PushDefUseChildren(Instruction *I,
3579 SmallVectorImpl<Instruction *> &Worklist) {
3580 // Push the def-use children onto the Worklist stack.
3581 for (User *U : I->users())
3582 Worklist.push_back(cast<Instruction>(U));
3585 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3586 /// instructions that depend on the given instruction and removes them from
3587 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3590 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3591 SmallVector<Instruction *, 16> Worklist;
3592 PushDefUseChildren(PN, Worklist);
3594 SmallPtrSet<Instruction *, 8> Visited;
3596 while (!Worklist.empty()) {
3597 Instruction *I = Worklist.pop_back_val();
3598 if (!Visited.insert(I).second)
3601 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
3602 if (It != ValueExprMap.end()) {
3603 const SCEV *Old = It->second;
3605 // Short-circuit the def-use traversal if the symbolic name
3606 // ceases to appear in expressions.
3607 if (Old != SymName && !hasOperand(Old, SymName))
3610 // SCEVUnknown for a PHI either means that it has an unrecognized
3611 // structure, it's a PHI that's in the progress of being computed
3612 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3613 // additional loop trip count information isn't going to change anything.
3614 // In the second case, createNodeForPHI will perform the necessary
3615 // updates on its own when it gets to that point. In the third, we do
3616 // want to forget the SCEVUnknown.
3617 if (!isa<PHINode>(I) ||
3618 !isa<SCEVUnknown>(Old) ||
3619 (I != PN && Old == SymName)) {
3620 forgetMemoizedResults(Old);
3621 ValueExprMap.erase(It);
3625 PushDefUseChildren(I, Worklist);
3630 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
3632 static const SCEV *rewrite(const SCEV *Scev, const Loop *L,
3633 ScalarEvolution &SE) {
3634 SCEVInitRewriter Rewriter(L, SE);
3635 const SCEV *Result = Rewriter.visit(Scev);
3636 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3639 SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
3640 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3642 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3643 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3648 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3649 // Only allow AddRecExprs for this loop.
3650 if (Expr->getLoop() == L)
3651 return Expr->getStart();
3656 bool isValid() { return Valid; }
3663 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
3665 static const SCEV *rewrite(const SCEV *Scev, const Loop *L,
3666 ScalarEvolution &SE) {
3667 SCEVShiftRewriter Rewriter(L, SE);
3668 const SCEV *Result = Rewriter.visit(Scev);
3669 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3672 SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
3673 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3675 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3676 // Only allow AddRecExprs for this loop.
3677 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3682 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3683 if (Expr->getLoop() == L && Expr->isAffine())
3684 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
3688 bool isValid() { return Valid; }
3694 } // end anonymous namespace
3696 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
3697 const Loop *L = LI.getLoopFor(PN->getParent());
3698 if (!L || L->getHeader() != PN->getParent())
3701 // The loop may have multiple entrances or multiple exits; we can analyze
3702 // this phi as an addrec if it has a unique entry value and a unique
3704 Value *BEValueV = nullptr, *StartValueV = nullptr;
3705 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3706 Value *V = PN->getIncomingValue(i);
3707 if (L->contains(PN->getIncomingBlock(i))) {
3710 } else if (BEValueV != V) {
3714 } else if (!StartValueV) {
3716 } else if (StartValueV != V) {
3717 StartValueV = nullptr;
3721 if (BEValueV && StartValueV) {
3722 // While we are analyzing this PHI node, handle its value symbolically.
3723 const SCEV *SymbolicName = getUnknown(PN);
3724 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3725 "PHI node already processed?");
3726 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3728 // Using this symbolic name for the PHI, analyze the value coming around
3730 const SCEV *BEValue = getSCEV(BEValueV);
3732 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3733 // has a special value for the first iteration of the loop.
3735 // If the value coming around the backedge is an add with the symbolic
3736 // value we just inserted, then we found a simple induction variable!
3737 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3738 // If there is a single occurrence of the symbolic value, replace it
3739 // with a recurrence.
3740 unsigned FoundIndex = Add->getNumOperands();
3741 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3742 if (Add->getOperand(i) == SymbolicName)
3743 if (FoundIndex == e) {
3748 if (FoundIndex != Add->getNumOperands()) {
3749 // Create an add with everything but the specified operand.
3750 SmallVector<const SCEV *, 8> Ops;
3751 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3752 if (i != FoundIndex)
3753 Ops.push_back(Add->getOperand(i));
3754 const SCEV *Accum = getAddExpr(Ops);
3756 // This is not a valid addrec if the step amount is varying each
3757 // loop iteration, but is not itself an addrec in this loop.
3758 if (isLoopInvariant(Accum, L) ||
3759 (isa<SCEVAddRecExpr>(Accum) &&
3760 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3761 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3763 // If the increment doesn't overflow, then neither the addrec nor
3764 // the post-increment will overflow.
3765 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3766 if (OBO->getOperand(0) == PN) {
3767 if (OBO->hasNoUnsignedWrap())
3768 Flags = setFlags(Flags, SCEV::FlagNUW);
3769 if (OBO->hasNoSignedWrap())
3770 Flags = setFlags(Flags, SCEV::FlagNSW);
3772 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3773 // If the increment is an inbounds GEP, then we know the address
3774 // space cannot be wrapped around. We cannot make any guarantee
3775 // about signed or unsigned overflow because pointers are
3776 // unsigned but we may have a negative index from the base
3777 // pointer. We can guarantee that no unsigned wrap occurs if the
3778 // indices form a positive value.
3779 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3780 Flags = setFlags(Flags, SCEV::FlagNW);
3782 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3783 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3784 Flags = setFlags(Flags, SCEV::FlagNUW);
3787 // We cannot transfer nuw and nsw flags from subtraction
3788 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3792 const SCEV *StartVal = getSCEV(StartValueV);
3793 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3795 // Since the no-wrap flags are on the increment, they apply to the
3796 // post-incremented value as well.
3797 if (isLoopInvariant(Accum, L))
3798 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
3800 // Okay, for the entire analysis of this edge we assumed the PHI
3801 // to be symbolic. We now need to go back and purge all of the
3802 // entries for the scalars that use the symbolic expression.
3803 ForgetSymbolicName(PN, SymbolicName);
3804 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3809 // Otherwise, this could be a loop like this:
3810 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3811 // In this case, j = {1,+,1} and BEValue is j.
3812 // Because the other in-value of i (0) fits the evolution of BEValue
3813 // i really is an addrec evolution.
3815 // We can generalize this saying that i is the shifted value of BEValue
3816 // by one iteration:
3817 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
3818 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
3819 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
3820 if (Shifted != getCouldNotCompute() &&
3821 Start != getCouldNotCompute()) {
3822 const SCEV *StartVal = getSCEV(StartValueV);
3823 if (Start == StartVal) {
3824 // Okay, for the entire analysis of this edge we assumed the PHI
3825 // to be symbolic. We now need to go back and purge all of the
3826 // entries for the scalars that use the symbolic expression.
3827 ForgetSymbolicName(PN, SymbolicName);
3828 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
3838 // Checks if the SCEV S is available at BB. S is considered available at BB
3839 // if S can be materialized at BB without introducing a fault.
3840 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
3842 struct CheckAvailable {
3843 bool TraversalDone = false;
3844 bool Available = true;
3846 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
3847 BasicBlock *BB = nullptr;
3850 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
3851 : L(L), BB(BB), DT(DT) {}
3853 bool setUnavailable() {
3854 TraversalDone = true;
3859 bool follow(const SCEV *S) {
3860 switch (S->getSCEVType()) {
3861 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
3862 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
3863 // These expressions are available if their operand(s) is/are.
3866 case scAddRecExpr: {
3867 // We allow add recurrences that are on the loop BB is in, or some
3868 // outer loop. This guarantees availability because the value of the
3869 // add recurrence at BB is simply the "current" value of the induction
3870 // variable. We can relax this in the future; for instance an add
3871 // recurrence on a sibling dominating loop is also available at BB.
3872 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
3873 if (L && (ARLoop == L || ARLoop->contains(L)))
3876 return setUnavailable();
3880 // For SCEVUnknown, we check for simple dominance.
3881 const auto *SU = cast<SCEVUnknown>(S);
3882 Value *V = SU->getValue();
3884 if (isa<Argument>(V))
3887 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
3890 return setUnavailable();
3894 case scCouldNotCompute:
3895 // We do not try to smart about these at all.
3896 return setUnavailable();
3898 llvm_unreachable("switch should be fully covered!");
3901 bool isDone() { return TraversalDone; }
3904 CheckAvailable CA(L, BB, DT);
3905 SCEVTraversal<CheckAvailable> ST(CA);
3908 return CA.Available;
3911 // Try to match a control flow sequence that branches out at BI and merges back
3912 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
3914 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
3915 Value *&C, Value *&LHS, Value *&RHS) {
3916 C = BI->getCondition();
3918 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
3919 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
3921 if (!LeftEdge.isSingleEdge())
3924 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
3926 Use &LeftUse = Merge->getOperandUse(0);
3927 Use &RightUse = Merge->getOperandUse(1);
3929 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
3935 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
3944 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
3945 if (PN->getNumIncomingValues() == 2) {
3946 const Loop *L = LI.getLoopFor(PN->getParent());
3948 // We don't want to break LCSSA, even in a SCEV expression tree.
3949 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
3950 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
3955 // br %cond, label %left, label %right
3961 // V = phi [ %x, %left ], [ %y, %right ]
3963 // as "select %cond, %x, %y"
3965 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
3966 assert(IDom && "At least the entry block should dominate PN");
3968 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
3969 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
3971 if (BI && BI->isConditional() &&
3972 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
3973 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
3974 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
3975 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
3981 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3982 if (const SCEV *S = createAddRecFromPHI(PN))
3985 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
3988 // If the PHI has a single incoming value, follow that value, unless the
3989 // PHI's incoming blocks are in a different loop, in which case doing so
3990 // risks breaking LCSSA form. Instcombine would normally zap these, but
3991 // it doesn't have DominatorTree information, so it may miss cases.
3992 if (Value *V = SimplifyInstruction(PN, getDataLayout(), &TLI, &DT, &AC))
3993 if (LI.replacementPreservesLCSSAForm(PN, V))
3996 // If it's not a loop phi, we can't handle it yet.
3997 return getUnknown(PN);
4000 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
4004 // Handle "constant" branch or select. This can occur for instance when a
4005 // loop pass transforms an inner loop and moves on to process the outer loop.
4006 if (auto *CI = dyn_cast<ConstantInt>(Cond))
4007 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
4009 // Try to match some simple smax or umax patterns.
4010 auto *ICI = dyn_cast<ICmpInst>(Cond);
4012 return getUnknown(I);
4014 Value *LHS = ICI->getOperand(0);
4015 Value *RHS = ICI->getOperand(1);
4017 switch (ICI->getPredicate()) {
4018 case ICmpInst::ICMP_SLT:
4019 case ICmpInst::ICMP_SLE:
4020 std::swap(LHS, RHS);
4022 case ICmpInst::ICMP_SGT:
4023 case ICmpInst::ICMP_SGE:
4024 // a >s b ? a+x : b+x -> smax(a, b)+x
4025 // a >s b ? b+x : a+x -> smin(a, b)+x
4026 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4027 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
4028 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
4029 const SCEV *LA = getSCEV(TrueVal);
4030 const SCEV *RA = getSCEV(FalseVal);
4031 const SCEV *LDiff = getMinusSCEV(LA, LS);
4032 const SCEV *RDiff = getMinusSCEV(RA, RS);
4034 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4035 LDiff = getMinusSCEV(LA, RS);
4036 RDiff = getMinusSCEV(RA, LS);
4038 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4041 case ICmpInst::ICMP_ULT:
4042 case ICmpInst::ICMP_ULE:
4043 std::swap(LHS, RHS);
4045 case ICmpInst::ICMP_UGT:
4046 case ICmpInst::ICMP_UGE:
4047 // a >u b ? a+x : b+x -> umax(a, b)+x
4048 // a >u b ? b+x : a+x -> umin(a, b)+x
4049 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4050 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4051 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
4052 const SCEV *LA = getSCEV(TrueVal);
4053 const SCEV *RA = getSCEV(FalseVal);
4054 const SCEV *LDiff = getMinusSCEV(LA, LS);
4055 const SCEV *RDiff = getMinusSCEV(RA, RS);
4057 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4058 LDiff = getMinusSCEV(LA, RS);
4059 RDiff = getMinusSCEV(RA, LS);
4061 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4064 case ICmpInst::ICMP_NE:
4065 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4066 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4067 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4068 const SCEV *One = getOne(I->getType());
4069 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4070 const SCEV *LA = getSCEV(TrueVal);
4071 const SCEV *RA = getSCEV(FalseVal);
4072 const SCEV *LDiff = getMinusSCEV(LA, LS);
4073 const SCEV *RDiff = getMinusSCEV(RA, One);
4075 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4078 case ICmpInst::ICMP_EQ:
4079 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4080 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4081 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4082 const SCEV *One = getOne(I->getType());
4083 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4084 const SCEV *LA = getSCEV(TrueVal);
4085 const SCEV *RA = getSCEV(FalseVal);
4086 const SCEV *LDiff = getMinusSCEV(LA, One);
4087 const SCEV *RDiff = getMinusSCEV(RA, LS);
4089 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4096 return getUnknown(I);
4099 /// createNodeForGEP - Expand GEP instructions into add and multiply
4100 /// operations. This allows them to be analyzed by regular SCEV code.
4102 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
4103 Value *Base = GEP->getOperand(0);
4104 // Don't attempt to analyze GEPs over unsized objects.
4105 if (!Base->getType()->getPointerElementType()->isSized())
4106 return getUnknown(GEP);
4108 SmallVector<const SCEV *, 4> IndexExprs;
4109 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4110 IndexExprs.push_back(getSCEV(*Index));
4111 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
4115 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
4116 /// guaranteed to end in (at every loop iteration). It is, at the same time,
4117 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
4118 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
4120 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4121 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4122 return C->getValue()->getValue().countTrailingZeros();
4124 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4125 return std::min(GetMinTrailingZeros(T->getOperand()),
4126 (uint32_t)getTypeSizeInBits(T->getType()));
4128 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4129 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4130 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4131 getTypeSizeInBits(E->getType()) : OpRes;
4134 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4135 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4136 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4137 getTypeSizeInBits(E->getType()) : OpRes;
4140 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4141 // The result is the min of all operands results.
4142 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4143 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4144 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4148 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4149 // The result is the sum of all operands results.
4150 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4151 uint32_t BitWidth = getTypeSizeInBits(M->getType());
4152 for (unsigned i = 1, e = M->getNumOperands();
4153 SumOpRes != BitWidth && i != e; ++i)
4154 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4159 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4160 // The result is the min of all operands results.
4161 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4162 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4163 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4167 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4168 // The result is the min of all operands results.
4169 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4170 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4171 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4175 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4176 // The result is the min of all operands results.
4177 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4178 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4179 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4183 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4184 // For a SCEVUnknown, ask ValueTracking.
4185 unsigned BitWidth = getTypeSizeInBits(U->getType());
4186 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4187 computeKnownBits(U->getValue(), Zeros, Ones, getDataLayout(), 0, &AC,
4189 return Zeros.countTrailingOnes();
4196 /// GetRangeFromMetadata - Helper method to assign a range to V from
4197 /// metadata present in the IR.
4198 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4199 if (Instruction *I = dyn_cast<Instruction>(V))
4200 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
4201 return getConstantRangeFromMetadata(*MD);
4206 /// getRange - Determine the range for a particular SCEV. If SignHint is
4207 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4208 /// with a "cleaner" unsigned (resp. signed) representation.
4211 ScalarEvolution::getRange(const SCEV *S,
4212 ScalarEvolution::RangeSignHint SignHint) {
4213 DenseMap<const SCEV *, ConstantRange> &Cache =
4214 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4217 // See if we've computed this range already.
4218 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4219 if (I != Cache.end())
4222 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4223 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
4225 unsigned BitWidth = getTypeSizeInBits(S->getType());
4226 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4228 // If the value has known zeros, the maximum value will have those known zeros
4230 uint32_t TZ = GetMinTrailingZeros(S);
4232 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4233 ConservativeResult =
4234 ConstantRange(APInt::getMinValue(BitWidth),
4235 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4237 ConservativeResult = ConstantRange(
4238 APInt::getSignedMinValue(BitWidth),
4239 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4242 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4243 ConstantRange X = getRange(Add->getOperand(0), SignHint);
4244 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4245 X = X.add(getRange(Add->getOperand(i), SignHint));
4246 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4249 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4250 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4251 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4252 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4253 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4256 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4257 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4258 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4259 X = X.smax(getRange(SMax->getOperand(i), SignHint));
4260 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4263 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4264 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4265 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4266 X = X.umax(getRange(UMax->getOperand(i), SignHint));
4267 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4270 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4271 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4272 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4273 return setRange(UDiv, SignHint,
4274 ConservativeResult.intersectWith(X.udiv(Y)));
4277 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4278 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4279 return setRange(ZExt, SignHint,
4280 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4283 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4284 ConstantRange X = getRange(SExt->getOperand(), SignHint);
4285 return setRange(SExt, SignHint,
4286 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4289 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4290 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4291 return setRange(Trunc, SignHint,
4292 ConservativeResult.intersectWith(X.truncate(BitWidth)));
4295 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4296 // If there's no unsigned wrap, the value will never be less than its
4298 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
4299 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4300 if (!C->getValue()->isZero())
4301 ConservativeResult =
4302 ConservativeResult.intersectWith(
4303 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
4305 // If there's no signed wrap, and all the operands have the same sign or
4306 // zero, the value won't ever change sign.
4307 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
4308 bool AllNonNeg = true;
4309 bool AllNonPos = true;
4310 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4311 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4312 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4315 ConservativeResult = ConservativeResult.intersectWith(
4316 ConstantRange(APInt(BitWidth, 0),
4317 APInt::getSignedMinValue(BitWidth)));
4319 ConservativeResult = ConservativeResult.intersectWith(
4320 ConstantRange(APInt::getSignedMinValue(BitWidth),
4321 APInt(BitWidth, 1)));
4324 // TODO: non-affine addrec
4325 if (AddRec->isAffine()) {
4326 Type *Ty = AddRec->getType();
4327 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4328 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4329 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4331 // Check for overflow. This must be done with ConstantRange arithmetic
4332 // because we could be called from within the ScalarEvolution overflow
4335 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4336 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4337 ConstantRange ZExtMaxBECountRange =
4338 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4340 const SCEV *Start = AddRec->getStart();
4341 const SCEV *Step = AddRec->getStepRecurrence(*this);
4342 ConstantRange StepSRange = getSignedRange(Step);
4343 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4345 ConstantRange StartURange = getUnsignedRange(Start);
4346 ConstantRange EndURange =
4347 StartURange.add(MaxBECountRange.multiply(StepSRange));
4349 // Check for unsigned overflow.
4350 ConstantRange ZExtStartURange =
4351 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4352 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4353 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4355 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4356 EndURange.getUnsignedMin());
4357 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4358 EndURange.getUnsignedMax());
4359 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4361 ConservativeResult =
4362 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4365 ConstantRange StartSRange = getSignedRange(Start);
4366 ConstantRange EndSRange =
4367 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4369 // Check for signed overflow. This must be done with ConstantRange
4370 // arithmetic because we could be called from within the ScalarEvolution
4371 // overflow checking code.
4372 ConstantRange SExtStartSRange =
4373 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4374 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4375 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4377 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4378 EndSRange.getSignedMin());
4379 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4380 EndSRange.getSignedMax());
4381 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4383 ConservativeResult =
4384 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4389 return setRange(AddRec, SignHint, ConservativeResult);
4392 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4393 // Check if the IR explicitly contains !range metadata.
4394 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4395 if (MDRange.hasValue())
4396 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4398 // Split here to avoid paying the compile-time cost of calling both
4399 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4401 const DataLayout &DL = getDataLayout();
4402 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4403 // For a SCEVUnknown, ask ValueTracking.
4404 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4405 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4406 if (Ones != ~Zeros + 1)
4407 ConservativeResult =
4408 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4410 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4411 "generalize as needed!");
4412 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4414 ConservativeResult = ConservativeResult.intersectWith(
4415 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4416 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4419 return setRange(U, SignHint, ConservativeResult);
4422 return setRange(S, SignHint, ConservativeResult);
4425 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4426 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4427 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4429 // Return early if there are no flags to propagate to the SCEV.
4430 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4431 if (BinOp->hasNoUnsignedWrap())
4432 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4433 if (BinOp->hasNoSignedWrap())
4434 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4435 if (Flags == SCEV::FlagAnyWrap) {
4436 return SCEV::FlagAnyWrap;
4439 // Here we check that BinOp is in the header of the innermost loop
4440 // containing BinOp, since we only deal with instructions in the loop
4441 // header. The actual loop we need to check later will come from an add
4442 // recurrence, but getting that requires computing the SCEV of the operands,
4443 // which can be expensive. This check we can do cheaply to rule out some
4445 Loop *innermostContainingLoop = LI.getLoopFor(BinOp->getParent());
4446 if (innermostContainingLoop == nullptr ||
4447 innermostContainingLoop->getHeader() != BinOp->getParent())
4448 return SCEV::FlagAnyWrap;
4450 // Only proceed if we can prove that BinOp does not yield poison.
4451 if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
4453 // At this point we know that if V is executed, then it does not wrap
4454 // according to at least one of NSW or NUW. If V is not executed, then we do
4455 // not know if the calculation that V represents would wrap. Multiple
4456 // instructions can map to the same SCEV. If we apply NSW or NUW from V to
4457 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4458 // derived from other instructions that map to the same SCEV. We cannot make
4459 // that guarantee for cases where V is not executed. So we need to find the
4460 // loop that V is considered in relation to and prove that V is executed for
4461 // every iteration of that loop. That implies that the value that V
4462 // calculates does not wrap anywhere in the loop, so then we can apply the
4463 // flags to the SCEV.
4465 // We check isLoopInvariant to disambiguate in case we are adding two
4466 // recurrences from different loops, so that we know which loop to prove
4467 // that V is executed in.
4468 for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
4469 const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
4470 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4471 const int OtherOpIndex = 1 - OpIndex;
4472 const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
4473 if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
4474 isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
4478 return SCEV::FlagAnyWrap;
4481 /// createSCEV - We know that there is no SCEV for the specified value. Analyze
4484 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4485 if (!isSCEVable(V->getType()))
4486 return getUnknown(V);
4488 unsigned Opcode = Instruction::UserOp1;
4489 if (Instruction *I = dyn_cast<Instruction>(V)) {
4490 Opcode = I->getOpcode();
4492 // Don't attempt to analyze instructions in blocks that aren't
4493 // reachable. Such instructions don't matter, and they aren't required
4494 // to obey basic rules for definitions dominating uses which this
4495 // analysis depends on.
4496 if (!DT.isReachableFromEntry(I->getParent()))
4497 return getUnknown(V);
4498 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4499 Opcode = CE->getOpcode();
4500 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4501 return getConstant(CI);
4502 else if (isa<ConstantPointerNull>(V))
4503 return getZero(V->getType());
4504 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4505 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4507 return getUnknown(V);
4509 Operator *U = cast<Operator>(V);
4511 case Instruction::Add: {
4512 // The simple thing to do would be to just call getSCEV on both operands
4513 // and call getAddExpr with the result. However if we're looking at a
4514 // bunch of things all added together, this can be quite inefficient,
4515 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4516 // Instead, gather up all the operands and make a single getAddExpr call.
4517 // LLVM IR canonical form means we need only traverse the left operands.
4518 SmallVector<const SCEV *, 4> AddOps;
4519 for (Value *Op = U;; Op = U->getOperand(0)) {
4520 U = dyn_cast<Operator>(Op);
4521 unsigned Opcode = U ? U->getOpcode() : 0;
4522 if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
4523 assert(Op != V && "V should be an add");
4524 AddOps.push_back(getSCEV(Op));
4528 if (auto *OpSCEV = getExistingSCEV(U)) {
4529 AddOps.push_back(OpSCEV);
4533 // If a NUW or NSW flag can be applied to the SCEV for this
4534 // addition, then compute the SCEV for this addition by itself
4535 // with a separate call to getAddExpr. We need to do that
4536 // instead of pushing the operands of the addition onto AddOps,
4537 // since the flags are only known to apply to this particular
4538 // addition - they may not apply to other additions that can be
4539 // formed with operands from AddOps.
4540 const SCEV *RHS = getSCEV(U->getOperand(1));
4541 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4542 if (Flags != SCEV::FlagAnyWrap) {
4543 const SCEV *LHS = getSCEV(U->getOperand(0));
4544 if (Opcode == Instruction::Sub)
4545 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4547 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4551 if (Opcode == Instruction::Sub)
4552 AddOps.push_back(getNegativeSCEV(RHS));
4554 AddOps.push_back(RHS);
4556 return getAddExpr(AddOps);
4559 case Instruction::Mul: {
4560 SmallVector<const SCEV *, 4> MulOps;
4561 for (Value *Op = U;; Op = U->getOperand(0)) {
4562 U = dyn_cast<Operator>(Op);
4563 if (!U || U->getOpcode() != Instruction::Mul) {
4564 assert(Op != V && "V should be a mul");
4565 MulOps.push_back(getSCEV(Op));
4569 if (auto *OpSCEV = getExistingSCEV(U)) {
4570 MulOps.push_back(OpSCEV);
4574 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4575 if (Flags != SCEV::FlagAnyWrap) {
4576 MulOps.push_back(getMulExpr(getSCEV(U->getOperand(0)),
4577 getSCEV(U->getOperand(1)), Flags));
4581 MulOps.push_back(getSCEV(U->getOperand(1)));
4583 return getMulExpr(MulOps);
4585 case Instruction::UDiv:
4586 return getUDivExpr(getSCEV(U->getOperand(0)),
4587 getSCEV(U->getOperand(1)));
4588 case Instruction::Sub:
4589 return getMinusSCEV(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)),
4590 getNoWrapFlagsFromUB(U));
4591 case Instruction::And:
4592 // For an expression like x&255 that merely masks off the high bits,
4593 // use zext(trunc(x)) as the SCEV expression.
4594 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4595 if (CI->isNullValue())
4596 return getSCEV(U->getOperand(1));
4597 if (CI->isAllOnesValue())
4598 return getSCEV(U->getOperand(0));
4599 const APInt &A = CI->getValue();
4601 // Instcombine's ShrinkDemandedConstant may strip bits out of
4602 // constants, obscuring what would otherwise be a low-bits mask.
4603 // Use computeKnownBits to compute what ShrinkDemandedConstant
4604 // knew about to reconstruct a low-bits mask value.
4605 unsigned LZ = A.countLeadingZeros();
4606 unsigned TZ = A.countTrailingZeros();
4607 unsigned BitWidth = A.getBitWidth();
4608 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4609 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, getDataLayout(),
4610 0, &AC, nullptr, &DT);
4612 APInt EffectiveMask =
4613 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4614 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4615 const SCEV *MulCount = getConstant(
4616 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4620 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4621 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4628 case Instruction::Or:
4629 // If the RHS of the Or is a constant, we may have something like:
4630 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4631 // optimizations will transparently handle this case.
4633 // In order for this transformation to be safe, the LHS must be of the
4634 // form X*(2^n) and the Or constant must be less than 2^n.
4635 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4636 const SCEV *LHS = getSCEV(U->getOperand(0));
4637 const APInt &CIVal = CI->getValue();
4638 if (GetMinTrailingZeros(LHS) >=
4639 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4640 // Build a plain add SCEV.
4641 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4642 // If the LHS of the add was an addrec and it has no-wrap flags,
4643 // transfer the no-wrap flags, since an or won't introduce a wrap.
4644 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4645 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4646 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4647 OldAR->getNoWrapFlags());
4653 case Instruction::Xor:
4654 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4655 // If the RHS of the xor is a signbit, then this is just an add.
4656 // Instcombine turns add of signbit into xor as a strength reduction step.
4657 if (CI->getValue().isSignBit())
4658 return getAddExpr(getSCEV(U->getOperand(0)),
4659 getSCEV(U->getOperand(1)));
4661 // If the RHS of xor is -1, then this is a not operation.
4662 if (CI->isAllOnesValue())
4663 return getNotSCEV(getSCEV(U->getOperand(0)));
4665 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4666 // This is a variant of the check for xor with -1, and it handles
4667 // the case where instcombine has trimmed non-demanded bits out
4668 // of an xor with -1.
4669 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4670 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4671 if (BO->getOpcode() == Instruction::And &&
4672 LCI->getValue() == CI->getValue())
4673 if (const SCEVZeroExtendExpr *Z =
4674 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4675 Type *UTy = U->getType();
4676 const SCEV *Z0 = Z->getOperand();
4677 Type *Z0Ty = Z0->getType();
4678 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4680 // If C is a low-bits mask, the zero extend is serving to
4681 // mask off the high bits. Complement the operand and
4682 // re-apply the zext.
4683 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4684 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4686 // If C is a single bit, it may be in the sign-bit position
4687 // before the zero-extend. In this case, represent the xor
4688 // using an add, which is equivalent, and re-apply the zext.
4689 APInt Trunc = CI->getValue().trunc(Z0TySize);
4690 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4692 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4698 case Instruction::Shl:
4699 // Turn shift left of a constant amount into a multiply.
4700 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4701 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4703 // If the shift count is not less than the bitwidth, the result of
4704 // the shift is undefined. Don't try to analyze it, because the
4705 // resolution chosen here may differ from the resolution chosen in
4706 // other parts of the compiler.
4707 if (SA->getValue().uge(BitWidth))
4710 // It is currently not resolved how to interpret NSW for left
4711 // shift by BitWidth - 1, so we avoid applying flags in that
4712 // case. Remove this check (or this comment) once the situation
4714 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
4715 // and http://reviews.llvm.org/D8890 .
4716 auto Flags = SCEV::FlagAnyWrap;
4717 if (SA->getValue().ult(BitWidth - 1)) Flags = getNoWrapFlagsFromUB(U);
4719 Constant *X = ConstantInt::get(getContext(),
4720 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4721 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X), Flags);
4725 case Instruction::LShr:
4726 // Turn logical shift right of a constant into a unsigned divide.
4727 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4728 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4730 // If the shift count is not less than the bitwidth, the result of
4731 // the shift is undefined. Don't try to analyze it, because the
4732 // resolution chosen here may differ from the resolution chosen in
4733 // other parts of the compiler.
4734 if (SA->getValue().uge(BitWidth))
4737 Constant *X = ConstantInt::get(getContext(),
4738 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4739 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4743 case Instruction::AShr:
4744 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4745 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4746 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4747 if (L->getOpcode() == Instruction::Shl &&
4748 L->getOperand(1) == U->getOperand(1)) {
4749 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4751 // If the shift count is not less than the bitwidth, the result of
4752 // the shift is undefined. Don't try to analyze it, because the
4753 // resolution chosen here may differ from the resolution chosen in
4754 // other parts of the compiler.
4755 if (CI->getValue().uge(BitWidth))
4758 uint64_t Amt = BitWidth - CI->getZExtValue();
4759 if (Amt == BitWidth)
4760 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4762 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4763 IntegerType::get(getContext(),
4769 case Instruction::Trunc:
4770 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4772 case Instruction::ZExt:
4773 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4775 case Instruction::SExt:
4776 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4778 case Instruction::BitCast:
4779 // BitCasts are no-op casts so we just eliminate the cast.
4780 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4781 return getSCEV(U->getOperand(0));
4784 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4785 // lead to pointer expressions which cannot safely be expanded to GEPs,
4786 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4787 // simplifying integer expressions.
4789 case Instruction::GetElementPtr:
4790 return createNodeForGEP(cast<GEPOperator>(U));
4792 case Instruction::PHI:
4793 return createNodeForPHI(cast<PHINode>(U));
4795 case Instruction::Select:
4796 // U can also be a select constant expr, which let fall through. Since
4797 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
4798 // constant expressions cannot have instructions as operands, we'd have
4799 // returned getUnknown for a select constant expressions anyway.
4800 if (isa<Instruction>(U))
4801 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
4802 U->getOperand(1), U->getOperand(2));
4804 default: // We cannot analyze this expression.
4808 return getUnknown(V);
4813 //===----------------------------------------------------------------------===//
4814 // Iteration Count Computation Code
4817 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4818 if (BasicBlock *ExitingBB = L->getExitingBlock())
4819 return getSmallConstantTripCount(L, ExitingBB);
4821 // No trip count information for multiple exits.
4825 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4826 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4827 /// constant. Will also return 0 if the maximum trip count is very large (>=
4830 /// This "trip count" assumes that control exits via ExitingBlock. More
4831 /// precisely, it is the number of times that control may reach ExitingBlock
4832 /// before taking the branch. For loops with multiple exits, it may not be the
4833 /// number times that the loop header executes because the loop may exit
4834 /// prematurely via another branch.
4835 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4836 BasicBlock *ExitingBlock) {
4837 assert(ExitingBlock && "Must pass a non-null exiting block!");
4838 assert(L->isLoopExiting(ExitingBlock) &&
4839 "Exiting block must actually branch out of the loop!");
4840 const SCEVConstant *ExitCount =
4841 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4845 ConstantInt *ExitConst = ExitCount->getValue();
4847 // Guard against huge trip counts.
4848 if (ExitConst->getValue().getActiveBits() > 32)
4851 // In case of integer overflow, this returns 0, which is correct.
4852 return ((unsigned)ExitConst->getZExtValue()) + 1;
4855 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4856 if (BasicBlock *ExitingBB = L->getExitingBlock())
4857 return getSmallConstantTripMultiple(L, ExitingBB);
4859 // No trip multiple information for multiple exits.
4863 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4864 /// trip count of this loop as a normal unsigned value, if possible. This
4865 /// means that the actual trip count is always a multiple of the returned
4866 /// value (don't forget the trip count could very well be zero as well!).
4868 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4869 /// multiple of a constant (which is also the case if the trip count is simply
4870 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4871 /// if the trip count is very large (>= 2^32).
4873 /// As explained in the comments for getSmallConstantTripCount, this assumes
4874 /// that control exits the loop via ExitingBlock.
4876 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4877 BasicBlock *ExitingBlock) {
4878 assert(ExitingBlock && "Must pass a non-null exiting block!");
4879 assert(L->isLoopExiting(ExitingBlock) &&
4880 "Exiting block must actually branch out of the loop!");
4881 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4882 if (ExitCount == getCouldNotCompute())
4885 // Get the trip count from the BE count by adding 1.
4886 const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
4887 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4888 // to factor simple cases.
4889 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4890 TCMul = Mul->getOperand(0);
4892 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4896 ConstantInt *Result = MulC->getValue();
4898 // Guard against huge trip counts (this requires checking
4899 // for zero to handle the case where the trip count == -1 and the
4901 if (!Result || Result->getValue().getActiveBits() > 32 ||
4902 Result->getValue().getActiveBits() == 0)
4905 return (unsigned)Result->getZExtValue();
4908 // getExitCount - Get the expression for the number of loop iterations for which
4909 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4910 // SCEVCouldNotCompute.
4911 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4912 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4915 /// getBackedgeTakenCount - If the specified loop has a predictable
4916 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4917 /// object. The backedge-taken count is the number of times the loop header
4918 /// will be branched to from within the loop. This is one less than the
4919 /// trip count of the loop, since it doesn't count the first iteration,
4920 /// when the header is branched to from outside the loop.
4922 /// Note that it is not valid to call this method on a loop without a
4923 /// loop-invariant backedge-taken count (see
4924 /// hasLoopInvariantBackedgeTakenCount).
4926 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4927 return getBackedgeTakenInfo(L).getExact(this);
4930 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4931 /// return the least SCEV value that is known never to be less than the
4932 /// actual backedge taken count.
4933 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4934 return getBackedgeTakenInfo(L).getMax(this);
4937 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4938 /// onto the given Worklist.
4940 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4941 BasicBlock *Header = L->getHeader();
4943 // Push all Loop-header PHIs onto the Worklist stack.
4944 for (BasicBlock::iterator I = Header->begin();
4945 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4946 Worklist.push_back(PN);
4949 const ScalarEvolution::BackedgeTakenInfo &
4950 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4951 // Initially insert an invalid entry for this loop. If the insertion
4952 // succeeds, proceed to actually compute a backedge-taken count and
4953 // update the value. The temporary CouldNotCompute value tells SCEV
4954 // code elsewhere that it shouldn't attempt to request a new
4955 // backedge-taken count, which could result in infinite recursion.
4956 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4957 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4959 return Pair.first->second;
4961 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
4962 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4963 // must be cleared in this scope.
4964 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
4966 if (Result.getExact(this) != getCouldNotCompute()) {
4967 assert(isLoopInvariant(Result.getExact(this), L) &&
4968 isLoopInvariant(Result.getMax(this), L) &&
4969 "Computed backedge-taken count isn't loop invariant for loop!");
4970 ++NumTripCountsComputed;
4972 else if (Result.getMax(this) == getCouldNotCompute() &&
4973 isa<PHINode>(L->getHeader()->begin())) {
4974 // Only count loops that have phi nodes as not being computable.
4975 ++NumTripCountsNotComputed;
4978 // Now that we know more about the trip count for this loop, forget any
4979 // existing SCEV values for PHI nodes in this loop since they are only
4980 // conservative estimates made without the benefit of trip count
4981 // information. This is similar to the code in forgetLoop, except that
4982 // it handles SCEVUnknown PHI nodes specially.
4983 if (Result.hasAnyInfo()) {
4984 SmallVector<Instruction *, 16> Worklist;
4985 PushLoopPHIs(L, Worklist);
4987 SmallPtrSet<Instruction *, 8> Visited;
4988 while (!Worklist.empty()) {
4989 Instruction *I = Worklist.pop_back_val();
4990 if (!Visited.insert(I).second)
4993 ValueExprMapType::iterator It =
4994 ValueExprMap.find_as(static_cast<Value *>(I));
4995 if (It != ValueExprMap.end()) {
4996 const SCEV *Old = It->second;
4998 // SCEVUnknown for a PHI either means that it has an unrecognized
4999 // structure, or it's a PHI that's in the progress of being computed
5000 // by createNodeForPHI. In the former case, additional loop trip
5001 // count information isn't going to change anything. In the later
5002 // case, createNodeForPHI will perform the necessary updates on its
5003 // own when it gets to that point.
5004 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
5005 forgetMemoizedResults(Old);
5006 ValueExprMap.erase(It);
5008 if (PHINode *PN = dyn_cast<PHINode>(I))
5009 ConstantEvolutionLoopExitValue.erase(PN);
5012 PushDefUseChildren(I, Worklist);
5016 // Re-lookup the insert position, since the call to
5017 // computeBackedgeTakenCount above could result in a
5018 // recusive call to getBackedgeTakenInfo (on a different
5019 // loop), which would invalidate the iterator computed
5021 return BackedgeTakenCounts.find(L)->second = Result;
5024 /// forgetLoop - This method should be called by the client when it has
5025 /// changed a loop in a way that may effect ScalarEvolution's ability to
5026 /// compute a trip count, or if the loop is deleted.
5027 void ScalarEvolution::forgetLoop(const Loop *L) {
5028 // Drop any stored trip count value.
5029 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
5030 BackedgeTakenCounts.find(L);
5031 if (BTCPos != BackedgeTakenCounts.end()) {
5032 BTCPos->second.clear();
5033 BackedgeTakenCounts.erase(BTCPos);
5036 // Drop information about expressions based on loop-header PHIs.
5037 SmallVector<Instruction *, 16> Worklist;
5038 PushLoopPHIs(L, Worklist);
5040 SmallPtrSet<Instruction *, 8> Visited;
5041 while (!Worklist.empty()) {
5042 Instruction *I = Worklist.pop_back_val();
5043 if (!Visited.insert(I).second)
5046 ValueExprMapType::iterator It =
5047 ValueExprMap.find_as(static_cast<Value *>(I));
5048 if (It != ValueExprMap.end()) {
5049 forgetMemoizedResults(It->second);
5050 ValueExprMap.erase(It);
5051 if (PHINode *PN = dyn_cast<PHINode>(I))
5052 ConstantEvolutionLoopExitValue.erase(PN);
5055 PushDefUseChildren(I, Worklist);
5058 // Forget all contained loops too, to avoid dangling entries in the
5059 // ValuesAtScopes map.
5060 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5064 /// forgetValue - This method should be called by the client when it has
5065 /// changed a value in a way that may effect its value, or which may
5066 /// disconnect it from a def-use chain linking it to a loop.
5067 void ScalarEvolution::forgetValue(Value *V) {
5068 Instruction *I = dyn_cast<Instruction>(V);
5071 // Drop information about expressions based on loop-header PHIs.
5072 SmallVector<Instruction *, 16> Worklist;
5073 Worklist.push_back(I);
5075 SmallPtrSet<Instruction *, 8> Visited;
5076 while (!Worklist.empty()) {
5077 I = Worklist.pop_back_val();
5078 if (!Visited.insert(I).second)
5081 ValueExprMapType::iterator It =
5082 ValueExprMap.find_as(static_cast<Value *>(I));
5083 if (It != ValueExprMap.end()) {
5084 forgetMemoizedResults(It->second);
5085 ValueExprMap.erase(It);
5086 if (PHINode *PN = dyn_cast<PHINode>(I))
5087 ConstantEvolutionLoopExitValue.erase(PN);
5090 PushDefUseChildren(I, Worklist);
5094 /// getExact - Get the exact loop backedge taken count considering all loop
5095 /// exits. A computable result can only be returned for loops with a single
5096 /// exit. Returning the minimum taken count among all exits is incorrect
5097 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
5098 /// assumes that the limit of each loop test is never skipped. This is a valid
5099 /// assumption as long as the loop exits via that test. For precise results, it
5100 /// is the caller's responsibility to specify the relevant loop exit using
5101 /// getExact(ExitingBlock, SE).
5103 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
5104 // If any exits were not computable, the loop is not computable.
5105 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
5107 // We need exactly one computable exit.
5108 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
5109 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
5111 const SCEV *BECount = nullptr;
5112 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5113 ENT != nullptr; ENT = ENT->getNextExit()) {
5115 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5118 BECount = ENT->ExactNotTaken;
5119 else if (BECount != ENT->ExactNotTaken)
5120 return SE->getCouldNotCompute();
5122 assert(BECount && "Invalid not taken count for loop exit");
5126 /// getExact - Get the exact not taken count for this loop exit.
5128 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5129 ScalarEvolution *SE) const {
5130 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5131 ENT != nullptr; ENT = ENT->getNextExit()) {
5133 if (ENT->ExitingBlock == ExitingBlock)
5134 return ENT->ExactNotTaken;
5136 return SE->getCouldNotCompute();
5139 /// getMax - Get the max backedge taken count for the loop.
5141 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5142 return Max ? Max : SE->getCouldNotCompute();
5145 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5146 ScalarEvolution *SE) const {
5147 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
5150 if (!ExitNotTaken.ExitingBlock)
5153 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5154 ENT != nullptr; ENT = ENT->getNextExit()) {
5156 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
5157 && SE->hasOperand(ENT->ExactNotTaken, S)) {
5164 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5165 /// computable exit into a persistent ExitNotTakenInfo array.
5166 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5167 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
5168 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
5171 ExitNotTaken.setIncomplete();
5173 unsigned NumExits = ExitCounts.size();
5174 if (NumExits == 0) return;
5176 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
5177 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
5178 if (NumExits == 1) return;
5180 // Handle the rare case of multiple computable exits.
5181 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
5183 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
5184 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
5185 PrevENT->setNextExit(ENT);
5186 ENT->ExitingBlock = ExitCounts[i].first;
5187 ENT->ExactNotTaken = ExitCounts[i].second;
5191 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
5192 void ScalarEvolution::BackedgeTakenInfo::clear() {
5193 ExitNotTaken.ExitingBlock = nullptr;
5194 ExitNotTaken.ExactNotTaken = nullptr;
5195 delete[] ExitNotTaken.getNextExit();
5198 /// computeBackedgeTakenCount - Compute the number of times the backedge
5199 /// of the specified loop will execute.
5200 ScalarEvolution::BackedgeTakenInfo
5201 ScalarEvolution::computeBackedgeTakenCount(const Loop *L) {
5202 SmallVector<BasicBlock *, 8> ExitingBlocks;
5203 L->getExitingBlocks(ExitingBlocks);
5205 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
5206 bool CouldComputeBECount = true;
5207 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5208 const SCEV *MustExitMaxBECount = nullptr;
5209 const SCEV *MayExitMaxBECount = nullptr;
5211 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5212 // and compute maxBECount.
5213 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5214 BasicBlock *ExitBB = ExitingBlocks[i];
5215 ExitLimit EL = computeExitLimit(L, ExitBB);
5217 // 1. For each exit that can be computed, add an entry to ExitCounts.
5218 // CouldComputeBECount is true only if all exits can be computed.
5219 if (EL.Exact == getCouldNotCompute())
5220 // We couldn't compute an exact value for this exit, so
5221 // we won't be able to compute an exact value for the loop.
5222 CouldComputeBECount = false;
5224 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
5226 // 2. Derive the loop's MaxBECount from each exit's max number of
5227 // non-exiting iterations. Partition the loop exits into two kinds:
5228 // LoopMustExits and LoopMayExits.
5230 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5231 // is a LoopMayExit. If any computable LoopMustExit is found, then
5232 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
5233 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
5234 // considered greater than any computable EL.Max.
5235 if (EL.Max != getCouldNotCompute() && Latch &&
5236 DT.dominates(ExitBB, Latch)) {
5237 if (!MustExitMaxBECount)
5238 MustExitMaxBECount = EL.Max;
5240 MustExitMaxBECount =
5241 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5243 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5244 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5245 MayExitMaxBECount = EL.Max;
5248 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5252 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5253 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5254 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5257 ScalarEvolution::ExitLimit
5258 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
5260 // Okay, we've chosen an exiting block. See what condition causes us to exit
5261 // at this block and remember the exit block and whether all other targets
5262 // lead to the loop header.
5263 bool MustExecuteLoopHeader = true;
5264 BasicBlock *Exit = nullptr;
5265 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5267 if (!L->contains(*SI)) {
5268 if (Exit) // Multiple exit successors.
5269 return getCouldNotCompute();
5271 } else if (*SI != L->getHeader()) {
5272 MustExecuteLoopHeader = false;
5275 // At this point, we know we have a conditional branch that determines whether
5276 // the loop is exited. However, we don't know if the branch is executed each
5277 // time through the loop. If not, then the execution count of the branch will
5278 // not be equal to the trip count of the loop.
5280 // Currently we check for this by checking to see if the Exit branch goes to
5281 // the loop header. If so, we know it will always execute the same number of
5282 // times as the loop. We also handle the case where the exit block *is* the
5283 // loop header. This is common for un-rotated loops.
5285 // If both of those tests fail, walk up the unique predecessor chain to the
5286 // header, stopping if there is an edge that doesn't exit the loop. If the
5287 // header is reached, the execution count of the branch will be equal to the
5288 // trip count of the loop.
5290 // More extensive analysis could be done to handle more cases here.
5292 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5293 // The simple checks failed, try climbing the unique predecessor chain
5294 // up to the header.
5296 for (BasicBlock *BB = ExitingBlock; BB; ) {
5297 BasicBlock *Pred = BB->getUniquePredecessor();
5299 return getCouldNotCompute();
5300 TerminatorInst *PredTerm = Pred->getTerminator();
5301 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5304 // If the predecessor has a successor that isn't BB and isn't
5305 // outside the loop, assume the worst.
5306 if (L->contains(PredSucc))
5307 return getCouldNotCompute();
5309 if (Pred == L->getHeader()) {
5316 return getCouldNotCompute();
5319 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5320 TerminatorInst *Term = ExitingBlock->getTerminator();
5321 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5322 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5323 // Proceed to the next level to examine the exit condition expression.
5324 return computeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5325 BI->getSuccessor(1),
5326 /*ControlsExit=*/IsOnlyExit);
5329 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5330 return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
5331 /*ControlsExit=*/IsOnlyExit);
5333 return getCouldNotCompute();
5336 /// computeExitLimitFromCond - Compute the number of times the
5337 /// backedge of the specified loop will execute if its exit condition
5338 /// were a conditional branch of ExitCond, TBB, and FBB.
5340 /// @param ControlsExit is true if ExitCond directly controls the exit
5341 /// branch. In this case, we can assume that the loop exits only if the
5342 /// condition is true and can infer that failing to meet the condition prior to
5343 /// integer wraparound results in undefined behavior.
5344 ScalarEvolution::ExitLimit
5345 ScalarEvolution::computeExitLimitFromCond(const Loop *L,
5349 bool ControlsExit) {
5350 // Check if the controlling expression for this loop is an And or Or.
5351 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5352 if (BO->getOpcode() == Instruction::And) {
5353 // Recurse on the operands of the and.
5354 bool EitherMayExit = L->contains(TBB);
5355 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5356 ControlsExit && !EitherMayExit);
5357 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5358 ControlsExit && !EitherMayExit);
5359 const SCEV *BECount = getCouldNotCompute();
5360 const SCEV *MaxBECount = getCouldNotCompute();
5361 if (EitherMayExit) {
5362 // Both conditions must be true for the loop to continue executing.
5363 // Choose the less conservative count.
5364 if (EL0.Exact == getCouldNotCompute() ||
5365 EL1.Exact == getCouldNotCompute())
5366 BECount = getCouldNotCompute();
5368 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5369 if (EL0.Max == getCouldNotCompute())
5370 MaxBECount = EL1.Max;
5371 else if (EL1.Max == getCouldNotCompute())
5372 MaxBECount = EL0.Max;
5374 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5376 // Both conditions must be true at the same time for the loop to exit.
5377 // For now, be conservative.
5378 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5379 if (EL0.Max == EL1.Max)
5380 MaxBECount = EL0.Max;
5381 if (EL0.Exact == EL1.Exact)
5382 BECount = EL0.Exact;
5385 return ExitLimit(BECount, MaxBECount);
5387 if (BO->getOpcode() == Instruction::Or) {
5388 // Recurse on the operands of the or.
5389 bool EitherMayExit = L->contains(FBB);
5390 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5391 ControlsExit && !EitherMayExit);
5392 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5393 ControlsExit && !EitherMayExit);
5394 const SCEV *BECount = getCouldNotCompute();
5395 const SCEV *MaxBECount = getCouldNotCompute();
5396 if (EitherMayExit) {
5397 // Both conditions must be false for the loop to continue executing.
5398 // Choose the less conservative count.
5399 if (EL0.Exact == getCouldNotCompute() ||
5400 EL1.Exact == getCouldNotCompute())
5401 BECount = getCouldNotCompute();
5403 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5404 if (EL0.Max == getCouldNotCompute())
5405 MaxBECount = EL1.Max;
5406 else if (EL1.Max == getCouldNotCompute())
5407 MaxBECount = EL0.Max;
5409 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5411 // Both conditions must be false at the same time for the loop to exit.
5412 // For now, be conservative.
5413 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5414 if (EL0.Max == EL1.Max)
5415 MaxBECount = EL0.Max;
5416 if (EL0.Exact == EL1.Exact)
5417 BECount = EL0.Exact;
5420 return ExitLimit(BECount, MaxBECount);
5424 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5425 // Proceed to the next level to examine the icmp.
5426 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5427 return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5429 // Check for a constant condition. These are normally stripped out by
5430 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5431 // preserve the CFG and is temporarily leaving constant conditions
5433 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5434 if (L->contains(FBB) == !CI->getZExtValue())
5435 // The backedge is always taken.
5436 return getCouldNotCompute();
5438 // The backedge is never taken.
5439 return getZero(CI->getType());
5442 // If it's not an integer or pointer comparison then compute it the hard way.
5443 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5446 ScalarEvolution::ExitLimit
5447 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
5451 bool ControlsExit) {
5453 // If the condition was exit on true, convert the condition to exit on false
5454 ICmpInst::Predicate Cond;
5455 if (!L->contains(FBB))
5456 Cond = ExitCond->getPredicate();
5458 Cond = ExitCond->getInversePredicate();
5460 // Handle common loops like: for (X = "string"; *X; ++X)
5461 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5462 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5464 computeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5465 if (ItCnt.hasAnyInfo())
5469 ExitLimit ShiftEL = computeShiftCompareExitLimit(
5470 ExitCond->getOperand(0), ExitCond->getOperand(1), L, Cond);
5471 if (ShiftEL.hasAnyInfo())
5474 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5475 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5477 // Try to evaluate any dependencies out of the loop.
5478 LHS = getSCEVAtScope(LHS, L);
5479 RHS = getSCEVAtScope(RHS, L);
5481 // At this point, we would like to compute how many iterations of the
5482 // loop the predicate will return true for these inputs.
5483 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5484 // If there is a loop-invariant, force it into the RHS.
5485 std::swap(LHS, RHS);
5486 Cond = ICmpInst::getSwappedPredicate(Cond);
5489 // Simplify the operands before analyzing them.
5490 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5492 // If we have a comparison of a chrec against a constant, try to use value
5493 // ranges to answer this query.
5494 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5495 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5496 if (AddRec->getLoop() == L) {
5497 // Form the constant range.
5498 ConstantRange CompRange(
5499 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5501 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5502 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5506 case ICmpInst::ICMP_NE: { // while (X != Y)
5507 // Convert to: while (X-Y != 0)
5508 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5509 if (EL.hasAnyInfo()) return EL;
5512 case ICmpInst::ICMP_EQ: { // while (X == Y)
5513 // Convert to: while (X-Y == 0)
5514 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5515 if (EL.hasAnyInfo()) return EL;
5518 case ICmpInst::ICMP_SLT:
5519 case ICmpInst::ICMP_ULT: { // while (X < Y)
5520 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5521 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5522 if (EL.hasAnyInfo()) return EL;
5525 case ICmpInst::ICMP_SGT:
5526 case ICmpInst::ICMP_UGT: { // while (X > Y)
5527 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5528 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5529 if (EL.hasAnyInfo()) return EL;
5535 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5538 ScalarEvolution::ExitLimit
5539 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
5541 BasicBlock *ExitingBlock,
5542 bool ControlsExit) {
5543 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5545 // Give up if the exit is the default dest of a switch.
5546 if (Switch->getDefaultDest() == ExitingBlock)
5547 return getCouldNotCompute();
5549 assert(L->contains(Switch->getDefaultDest()) &&
5550 "Default case must not exit the loop!");
5551 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5552 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5554 // while (X != Y) --> while (X-Y != 0)
5555 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5556 if (EL.hasAnyInfo())
5559 return getCouldNotCompute();
5562 static ConstantInt *
5563 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5564 ScalarEvolution &SE) {
5565 const SCEV *InVal = SE.getConstant(C);
5566 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5567 assert(isa<SCEVConstant>(Val) &&
5568 "Evaluation of SCEV at constant didn't fold correctly?");
5569 return cast<SCEVConstant>(Val)->getValue();
5572 /// computeLoadConstantCompareExitLimit - Given an exit condition of
5573 /// 'icmp op load X, cst', try to see if we can compute the backedge
5574 /// execution count.
5575 ScalarEvolution::ExitLimit
5576 ScalarEvolution::computeLoadConstantCompareExitLimit(
5580 ICmpInst::Predicate predicate) {
5582 if (LI->isVolatile()) return getCouldNotCompute();
5584 // Check to see if the loaded pointer is a getelementptr of a global.
5585 // TODO: Use SCEV instead of manually grubbing with GEPs.
5586 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5587 if (!GEP) return getCouldNotCompute();
5589 // Make sure that it is really a constant global we are gepping, with an
5590 // initializer, and make sure the first IDX is really 0.
5591 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5592 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5593 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5594 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5595 return getCouldNotCompute();
5597 // Okay, we allow one non-constant index into the GEP instruction.
5598 Value *VarIdx = nullptr;
5599 std::vector<Constant*> Indexes;
5600 unsigned VarIdxNum = 0;
5601 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5602 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5603 Indexes.push_back(CI);
5604 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5605 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5606 VarIdx = GEP->getOperand(i);
5608 Indexes.push_back(nullptr);
5611 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5613 return getCouldNotCompute();
5615 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5616 // Check to see if X is a loop variant variable value now.
5617 const SCEV *Idx = getSCEV(VarIdx);
5618 Idx = getSCEVAtScope(Idx, L);
5620 // We can only recognize very limited forms of loop index expressions, in
5621 // particular, only affine AddRec's like {C1,+,C2}.
5622 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5623 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5624 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5625 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5626 return getCouldNotCompute();
5628 unsigned MaxSteps = MaxBruteForceIterations;
5629 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5630 ConstantInt *ItCst = ConstantInt::get(
5631 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5632 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5634 // Form the GEP offset.
5635 Indexes[VarIdxNum] = Val;
5637 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5639 if (!Result) break; // Cannot compute!
5641 // Evaluate the condition for this iteration.
5642 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5643 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5644 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5645 ++NumArrayLenItCounts;
5646 return getConstant(ItCst); // Found terminating iteration!
5649 return getCouldNotCompute();
5652 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
5653 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
5654 ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
5656 return getCouldNotCompute();
5658 const BasicBlock *Latch = L->getLoopLatch();
5660 return getCouldNotCompute();
5662 const BasicBlock *Predecessor = L->getLoopPredecessor();
5664 return getCouldNotCompute();
5666 // Return true if V is of the form "LHS `shift_op` <positive constant>".
5667 // Return LHS in OutLHS and shift_opt in OutOpCode.
5668 auto MatchPositiveShift =
5669 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
5671 using namespace PatternMatch;
5673 ConstantInt *ShiftAmt;
5674 if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
5675 OutOpCode = Instruction::LShr;
5676 else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
5677 OutOpCode = Instruction::AShr;
5678 else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
5679 OutOpCode = Instruction::Shl;
5683 return ShiftAmt->getValue().isStrictlyPositive();
5686 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
5689 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
5690 // %iv.shifted = lshr i32 %iv, <positive constant>
5692 // Return true on a succesful match. Return the corresponding PHI node (%iv
5693 // above) in PNOut and the opcode of the shift operation in OpCodeOut.
5694 auto MatchShiftRecurrence =
5695 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
5696 Optional<Instruction::BinaryOps> PostShiftOpCode;
5699 Instruction::BinaryOps OpC;
5702 // If we encounter a shift instruction, "peel off" the shift operation,
5703 // and remember that we did so. Later when we inspect %iv's backedge
5704 // value, we will make sure that the backedge value uses the same
5707 // Note: the peeled shift operation does not have to be the same
5708 // instruction as the one feeding into the PHI's backedge value. We only
5709 // really care about it being the same *kind* of shift instruction --
5710 // that's all that is required for our later inferences to hold.
5711 if (MatchPositiveShift(LHS, V, OpC)) {
5712 PostShiftOpCode = OpC;
5717 PNOut = dyn_cast<PHINode>(LHS);
5718 if (!PNOut || PNOut->getParent() != L->getHeader())
5721 Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
5725 // The backedge value for the PHI node must be a shift by a positive
5727 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
5729 // of the PHI node itself
5732 // and the kind of shift should be match the kind of shift we peeled
5734 (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
5738 Instruction::BinaryOps OpCode;
5739 if (!MatchShiftRecurrence(LHS, PN, OpCode))
5740 return getCouldNotCompute();
5742 const DataLayout &DL = getDataLayout();
5744 // The key rationale for this optimization is that for some kinds of shift
5745 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
5746 // within a finite number of iterations. If the condition guarding the
5747 // backedge (in the sense that the backedge is taken if the condition is true)
5748 // is false for the value the shift recurrence stabilizes to, then we know
5749 // that the backedge is taken only a finite number of times.
5751 ConstantInt *StableValue = nullptr;
5754 llvm_unreachable("Impossible case!");
5756 case Instruction::AShr: {
5757 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
5758 // bitwidth(K) iterations.
5759 Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
5760 bool KnownZero, KnownOne;
5761 ComputeSignBit(FirstValue, KnownZero, KnownOne, DL, 0, nullptr,
5762 Predecessor->getTerminator(), &DT);
5763 auto *Ty = cast<IntegerType>(RHS->getType());
5765 StableValue = ConstantInt::get(Ty, 0);
5767 StableValue = ConstantInt::get(Ty, -1, true);
5769 return getCouldNotCompute();
5773 case Instruction::LShr:
5774 case Instruction::Shl:
5775 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
5776 // stabilize to 0 in at most bitwidth(K) iterations.
5777 StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
5782 ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
5783 assert(Result->getType()->isIntegerTy(1) &&
5784 "Otherwise cannot be an operand to a branch instruction");
5786 if (Result->isZeroValue()) {
5787 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
5788 const SCEV *UpperBound =
5789 getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
5790 return ExitLimit(getCouldNotCompute(), UpperBound);
5793 return getCouldNotCompute();
5796 /// CanConstantFold - Return true if we can constant fold an instruction of the
5797 /// specified type, assuming that all operands were constants.
5798 static bool CanConstantFold(const Instruction *I) {
5799 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5800 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5804 if (const CallInst *CI = dyn_cast<CallInst>(I))
5805 if (const Function *F = CI->getCalledFunction())
5806 return canConstantFoldCallTo(F);
5810 /// Determine whether this instruction can constant evolve within this loop
5811 /// assuming its operands can all constant evolve.
5812 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5813 // An instruction outside of the loop can't be derived from a loop PHI.
5814 if (!L->contains(I)) return false;
5816 if (isa<PHINode>(I)) {
5817 // We don't currently keep track of the control flow needed to evaluate
5818 // PHIs, so we cannot handle PHIs inside of loops.
5819 return L->getHeader() == I->getParent();
5822 // If we won't be able to constant fold this expression even if the operands
5823 // are constants, bail early.
5824 return CanConstantFold(I);
5827 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5828 /// recursing through each instruction operand until reaching a loop header phi.
5830 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5831 DenseMap<Instruction *, PHINode *> &PHIMap) {
5833 // Otherwise, we can evaluate this instruction if all of its operands are
5834 // constant or derived from a PHI node themselves.
5835 PHINode *PHI = nullptr;
5836 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5837 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5839 if (isa<Constant>(*OpI)) continue;
5841 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5842 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5844 PHINode *P = dyn_cast<PHINode>(OpInst);
5846 // If this operand is already visited, reuse the prior result.
5847 // We may have P != PHI if this is the deepest point at which the
5848 // inconsistent paths meet.
5849 P = PHIMap.lookup(OpInst);
5851 // Recurse and memoize the results, whether a phi is found or not.
5852 // This recursive call invalidates pointers into PHIMap.
5853 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5857 return nullptr; // Not evolving from PHI
5858 if (PHI && PHI != P)
5859 return nullptr; // Evolving from multiple different PHIs.
5862 // This is a expression evolving from a constant PHI!
5866 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5867 /// in the loop that V is derived from. We allow arbitrary operations along the
5868 /// way, but the operands of an operation must either be constants or a value
5869 /// derived from a constant PHI. If this expression does not fit with these
5870 /// constraints, return null.
5871 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5872 Instruction *I = dyn_cast<Instruction>(V);
5873 if (!I || !canConstantEvolve(I, L)) return nullptr;
5875 if (PHINode *PN = dyn_cast<PHINode>(I))
5878 // Record non-constant instructions contained by the loop.
5879 DenseMap<Instruction *, PHINode *> PHIMap;
5880 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5883 /// EvaluateExpression - Given an expression that passes the
5884 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5885 /// in the loop has the value PHIVal. If we can't fold this expression for some
5886 /// reason, return null.
5887 static Constant *EvaluateExpression(Value *V, const Loop *L,
5888 DenseMap<Instruction *, Constant *> &Vals,
5889 const DataLayout &DL,
5890 const TargetLibraryInfo *TLI) {
5891 // Convenient constant check, but redundant for recursive calls.
5892 if (Constant *C = dyn_cast<Constant>(V)) return C;
5893 Instruction *I = dyn_cast<Instruction>(V);
5894 if (!I) return nullptr;
5896 if (Constant *C = Vals.lookup(I)) return C;
5898 // An instruction inside the loop depends on a value outside the loop that we
5899 // weren't given a mapping for, or a value such as a call inside the loop.
5900 if (!canConstantEvolve(I, L)) return nullptr;
5902 // An unmapped PHI can be due to a branch or another loop inside this loop,
5903 // or due to this not being the initial iteration through a loop where we
5904 // couldn't compute the evolution of this particular PHI last time.
5905 if (isa<PHINode>(I)) return nullptr;
5907 std::vector<Constant*> Operands(I->getNumOperands());
5909 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5910 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5912 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5913 if (!Operands[i]) return nullptr;
5916 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5918 if (!C) return nullptr;
5922 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5923 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5924 Operands[1], DL, TLI);
5925 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5926 if (!LI->isVolatile())
5927 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5929 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5934 // If every incoming value to PN except the one for BB is a specific Constant,
5935 // return that, else return nullptr.
5936 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
5937 Constant *IncomingVal = nullptr;
5939 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
5940 if (PN->getIncomingBlock(i) == BB)
5943 auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
5947 if (IncomingVal != CurrentVal) {
5950 IncomingVal = CurrentVal;
5957 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5958 /// in the header of its containing loop, we know the loop executes a
5959 /// constant number of times, and the PHI node is just a recurrence
5960 /// involving constants, fold it.
5962 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5965 auto I = ConstantEvolutionLoopExitValue.find(PN);
5966 if (I != ConstantEvolutionLoopExitValue.end())
5969 if (BEs.ugt(MaxBruteForceIterations))
5970 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5972 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5974 DenseMap<Instruction *, Constant *> CurrentIterVals;
5975 BasicBlock *Header = L->getHeader();
5976 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5978 BasicBlock *Latch = L->getLoopLatch();
5982 for (auto &I : *Header) {
5983 PHINode *PHI = dyn_cast<PHINode>(&I);
5985 auto *StartCST = getOtherIncomingValue(PHI, Latch);
5986 if (!StartCST) continue;
5987 CurrentIterVals[PHI] = StartCST;
5989 if (!CurrentIterVals.count(PN))
5990 return RetVal = nullptr;
5992 Value *BEValue = PN->getIncomingValueForBlock(Latch);
5994 // Execute the loop symbolically to determine the exit value.
5995 if (BEs.getActiveBits() >= 32)
5996 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5998 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5999 unsigned IterationNum = 0;
6000 const DataLayout &DL = getDataLayout();
6001 for (; ; ++IterationNum) {
6002 if (IterationNum == NumIterations)
6003 return RetVal = CurrentIterVals[PN]; // Got exit value!
6005 // Compute the value of the PHIs for the next iteration.
6006 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
6007 DenseMap<Instruction *, Constant *> NextIterVals;
6009 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6011 return nullptr; // Couldn't evaluate!
6012 NextIterVals[PN] = NextPHI;
6014 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
6016 // Also evaluate the other PHI nodes. However, we don't get to stop if we
6017 // cease to be able to evaluate one of them or if they stop evolving,
6018 // because that doesn't necessarily prevent us from computing PN.
6019 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
6020 for (const auto &I : CurrentIterVals) {
6021 PHINode *PHI = dyn_cast<PHINode>(I.first);
6022 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
6023 PHIsToCompute.emplace_back(PHI, I.second);
6025 // We use two distinct loops because EvaluateExpression may invalidate any
6026 // iterators into CurrentIterVals.
6027 for (const auto &I : PHIsToCompute) {
6028 PHINode *PHI = I.first;
6029 Constant *&NextPHI = NextIterVals[PHI];
6030 if (!NextPHI) { // Not already computed.
6031 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6032 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6034 if (NextPHI != I.second)
6035 StoppedEvolving = false;
6038 // If all entries in CurrentIterVals == NextIterVals then we can stop
6039 // iterating, the loop can't continue to change.
6040 if (StoppedEvolving)
6041 return RetVal = CurrentIterVals[PN];
6043 CurrentIterVals.swap(NextIterVals);
6047 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
6050 PHINode *PN = getConstantEvolvingPHI(Cond, L);
6051 if (!PN) return getCouldNotCompute();
6053 // If the loop is canonicalized, the PHI will have exactly two entries.
6054 // That's the only form we support here.
6055 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
6057 DenseMap<Instruction *, Constant *> CurrentIterVals;
6058 BasicBlock *Header = L->getHeader();
6059 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6061 BasicBlock *Latch = L->getLoopLatch();
6062 assert(Latch && "Should follow from NumIncomingValues == 2!");
6064 for (auto &I : *Header) {
6065 PHINode *PHI = dyn_cast<PHINode>(&I);
6068 auto *StartCST = getOtherIncomingValue(PHI, Latch);
6069 if (!StartCST) continue;
6070 CurrentIterVals[PHI] = StartCST;
6072 if (!CurrentIterVals.count(PN))
6073 return getCouldNotCompute();
6075 // Okay, we find a PHI node that defines the trip count of this loop. Execute
6076 // the loop symbolically to determine when the condition gets a value of
6078 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
6079 const DataLayout &DL = getDataLayout();
6080 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
6081 auto *CondVal = dyn_cast_or_null<ConstantInt>(
6082 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
6084 // Couldn't symbolically evaluate.
6085 if (!CondVal) return getCouldNotCompute();
6087 if (CondVal->getValue() == uint64_t(ExitWhen)) {
6088 ++NumBruteForceTripCountsComputed;
6089 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
6092 // Update all the PHI nodes for the next iteration.
6093 DenseMap<Instruction *, Constant *> NextIterVals;
6095 // Create a list of which PHIs we need to compute. We want to do this before
6096 // calling EvaluateExpression on them because that may invalidate iterators
6097 // into CurrentIterVals.
6098 SmallVector<PHINode *, 8> PHIsToCompute;
6099 for (const auto &I : CurrentIterVals) {
6100 PHINode *PHI = dyn_cast<PHINode>(I.first);
6101 if (!PHI || PHI->getParent() != Header) continue;
6102 PHIsToCompute.push_back(PHI);
6104 for (PHINode *PHI : PHIsToCompute) {
6105 Constant *&NextPHI = NextIterVals[PHI];
6106 if (NextPHI) continue; // Already computed!
6108 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6109 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6111 CurrentIterVals.swap(NextIterVals);
6114 // Too many iterations were needed to evaluate.
6115 return getCouldNotCompute();
6118 /// getSCEVAtScope - Return a SCEV expression for the specified value
6119 /// at the specified scope in the program. The L value specifies a loop
6120 /// nest to evaluate the expression at, where null is the top-level or a
6121 /// specified loop is immediately inside of the loop.
6123 /// This method can be used to compute the exit value for a variable defined
6124 /// in a loop by querying what the value will hold in the parent loop.
6126 /// In the case that a relevant loop exit value cannot be computed, the
6127 /// original value V is returned.
6128 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
6129 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
6131 // Check to see if we've folded this expression at this loop before.
6132 for (auto &LS : Values)
6134 return LS.second ? LS.second : V;
6136 Values.emplace_back(L, nullptr);
6138 // Otherwise compute it.
6139 const SCEV *C = computeSCEVAtScope(V, L);
6140 for (auto &LS : reverse(ValuesAtScopes[V]))
6141 if (LS.first == L) {
6148 /// This builds up a Constant using the ConstantExpr interface. That way, we
6149 /// will return Constants for objects which aren't represented by a
6150 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
6151 /// Returns NULL if the SCEV isn't representable as a Constant.
6152 static Constant *BuildConstantFromSCEV(const SCEV *V) {
6153 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
6154 case scCouldNotCompute:
6158 return cast<SCEVConstant>(V)->getValue();
6160 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
6161 case scSignExtend: {
6162 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
6163 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
6164 return ConstantExpr::getSExt(CastOp, SS->getType());
6167 case scZeroExtend: {
6168 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
6169 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
6170 return ConstantExpr::getZExt(CastOp, SZ->getType());
6174 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
6175 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
6176 return ConstantExpr::getTrunc(CastOp, ST->getType());
6180 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
6181 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
6182 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6183 unsigned AS = PTy->getAddressSpace();
6184 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6185 C = ConstantExpr::getBitCast(C, DestPtrTy);
6187 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
6188 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
6189 if (!C2) return nullptr;
6192 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
6193 unsigned AS = C2->getType()->getPointerAddressSpace();
6195 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6196 // The offsets have been converted to bytes. We can add bytes to an
6197 // i8* by GEP with the byte count in the first index.
6198 C = ConstantExpr::getBitCast(C, DestPtrTy);
6201 // Don't bother trying to sum two pointers. We probably can't
6202 // statically compute a load that results from it anyway.
6203 if (C2->getType()->isPointerTy())
6206 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6207 if (PTy->getElementType()->isStructTy())
6208 C2 = ConstantExpr::getIntegerCast(
6209 C2, Type::getInt32Ty(C->getContext()), true);
6210 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
6212 C = ConstantExpr::getAdd(C, C2);
6219 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
6220 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
6221 // Don't bother with pointers at all.
6222 if (C->getType()->isPointerTy()) return nullptr;
6223 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
6224 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
6225 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
6226 C = ConstantExpr::getMul(C, C2);
6233 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6234 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6235 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6236 if (LHS->getType() == RHS->getType())
6237 return ConstantExpr::getUDiv(LHS, RHS);
6242 break; // TODO: smax, umax.
6247 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6248 if (isa<SCEVConstant>(V)) return V;
6250 // If this instruction is evolved from a constant-evolving PHI, compute the
6251 // exit value from the loop without using SCEVs.
6252 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6253 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6254 const Loop *LI = this->LI[I->getParent()];
6255 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
6256 if (PHINode *PN = dyn_cast<PHINode>(I))
6257 if (PN->getParent() == LI->getHeader()) {
6258 // Okay, there is no closed form solution for the PHI node. Check
6259 // to see if the loop that contains it has a known backedge-taken
6260 // count. If so, we may be able to force computation of the exit
6262 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6263 if (const SCEVConstant *BTCC =
6264 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6265 // Okay, we know how many times the containing loop executes. If
6266 // this is a constant evolving PHI node, get the final value at
6267 // the specified iteration number.
6268 Constant *RV = getConstantEvolutionLoopExitValue(PN,
6269 BTCC->getValue()->getValue(),
6271 if (RV) return getSCEV(RV);
6275 // Okay, this is an expression that we cannot symbolically evaluate
6276 // into a SCEV. Check to see if it's possible to symbolically evaluate
6277 // the arguments into constants, and if so, try to constant propagate the
6278 // result. This is particularly useful for computing loop exit values.
6279 if (CanConstantFold(I)) {
6280 SmallVector<Constant *, 4> Operands;
6281 bool MadeImprovement = false;
6282 for (Value *Op : I->operands()) {
6283 if (Constant *C = dyn_cast<Constant>(Op)) {
6284 Operands.push_back(C);
6288 // If any of the operands is non-constant and if they are
6289 // non-integer and non-pointer, don't even try to analyze them
6290 // with scev techniques.
6291 if (!isSCEVable(Op->getType()))
6294 const SCEV *OrigV = getSCEV(Op);
6295 const SCEV *OpV = getSCEVAtScope(OrigV, L);
6296 MadeImprovement |= OrigV != OpV;
6298 Constant *C = BuildConstantFromSCEV(OpV);
6300 if (C->getType() != Op->getType())
6301 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6305 Operands.push_back(C);
6308 // Check to see if getSCEVAtScope actually made an improvement.
6309 if (MadeImprovement) {
6310 Constant *C = nullptr;
6311 const DataLayout &DL = getDataLayout();
6312 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6313 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6314 Operands[1], DL, &TLI);
6315 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6316 if (!LI->isVolatile())
6317 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
6319 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
6327 // This is some other type of SCEVUnknown, just return it.
6331 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6332 // Avoid performing the look-up in the common case where the specified
6333 // expression has no loop-variant portions.
6334 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6335 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6336 if (OpAtScope != Comm->getOperand(i)) {
6337 // Okay, at least one of these operands is loop variant but might be
6338 // foldable. Build a new instance of the folded commutative expression.
6339 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6340 Comm->op_begin()+i);
6341 NewOps.push_back(OpAtScope);
6343 for (++i; i != e; ++i) {
6344 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6345 NewOps.push_back(OpAtScope);
6347 if (isa<SCEVAddExpr>(Comm))
6348 return getAddExpr(NewOps);
6349 if (isa<SCEVMulExpr>(Comm))
6350 return getMulExpr(NewOps);
6351 if (isa<SCEVSMaxExpr>(Comm))
6352 return getSMaxExpr(NewOps);
6353 if (isa<SCEVUMaxExpr>(Comm))
6354 return getUMaxExpr(NewOps);
6355 llvm_unreachable("Unknown commutative SCEV type!");
6358 // If we got here, all operands are loop invariant.
6362 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6363 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6364 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6365 if (LHS == Div->getLHS() && RHS == Div->getRHS())
6366 return Div; // must be loop invariant
6367 return getUDivExpr(LHS, RHS);
6370 // If this is a loop recurrence for a loop that does not contain L, then we
6371 // are dealing with the final value computed by the loop.
6372 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6373 // First, attempt to evaluate each operand.
6374 // Avoid performing the look-up in the common case where the specified
6375 // expression has no loop-variant portions.
6376 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6377 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6378 if (OpAtScope == AddRec->getOperand(i))
6381 // Okay, at least one of these operands is loop variant but might be
6382 // foldable. Build a new instance of the folded commutative expression.
6383 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6384 AddRec->op_begin()+i);
6385 NewOps.push_back(OpAtScope);
6386 for (++i; i != e; ++i)
6387 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6389 const SCEV *FoldedRec =
6390 getAddRecExpr(NewOps, AddRec->getLoop(),
6391 AddRec->getNoWrapFlags(SCEV::FlagNW));
6392 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6393 // The addrec may be folded to a nonrecurrence, for example, if the
6394 // induction variable is multiplied by zero after constant folding. Go
6395 // ahead and return the folded value.
6401 // If the scope is outside the addrec's loop, evaluate it by using the
6402 // loop exit value of the addrec.
6403 if (!AddRec->getLoop()->contains(L)) {
6404 // To evaluate this recurrence, we need to know how many times the AddRec
6405 // loop iterates. Compute this now.
6406 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6407 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6409 // Then, evaluate the AddRec.
6410 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6416 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6417 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6418 if (Op == Cast->getOperand())
6419 return Cast; // must be loop invariant
6420 return getZeroExtendExpr(Op, Cast->getType());
6423 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6424 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6425 if (Op == Cast->getOperand())
6426 return Cast; // must be loop invariant
6427 return getSignExtendExpr(Op, Cast->getType());
6430 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6431 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6432 if (Op == Cast->getOperand())
6433 return Cast; // must be loop invariant
6434 return getTruncateExpr(Op, Cast->getType());
6437 llvm_unreachable("Unknown SCEV type!");
6440 /// getSCEVAtScope - This is a convenience function which does
6441 /// getSCEVAtScope(getSCEV(V), L).
6442 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6443 return getSCEVAtScope(getSCEV(V), L);
6446 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6447 /// following equation:
6449 /// A * X = B (mod N)
6451 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6452 /// A and B isn't important.
6454 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6455 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6456 ScalarEvolution &SE) {
6457 uint32_t BW = A.getBitWidth();
6458 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6459 assert(A != 0 && "A must be non-zero.");
6463 // The gcd of A and N may have only one prime factor: 2. The number of
6464 // trailing zeros in A is its multiplicity
6465 uint32_t Mult2 = A.countTrailingZeros();
6468 // 2. Check if B is divisible by D.
6470 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6471 // is not less than multiplicity of this prime factor for D.
6472 if (B.countTrailingZeros() < Mult2)
6473 return SE.getCouldNotCompute();
6475 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6478 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6479 // bit width during computations.
6480 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6481 APInt Mod(BW + 1, 0);
6482 Mod.setBit(BW - Mult2); // Mod = N / D
6483 APInt I = AD.multiplicativeInverse(Mod);
6485 // 4. Compute the minimum unsigned root of the equation:
6486 // I * (B / D) mod (N / D)
6487 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6489 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6491 return SE.getConstant(Result.trunc(BW));
6494 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6495 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6496 /// might be the same) or two SCEVCouldNotCompute objects.
6498 static std::pair<const SCEV *,const SCEV *>
6499 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6500 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6501 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6502 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6503 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6505 // We currently can only solve this if the coefficients are constants.
6506 if (!LC || !MC || !NC) {
6507 const SCEV *CNC = SE.getCouldNotCompute();
6508 return std::make_pair(CNC, CNC);
6511 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6512 const APInt &L = LC->getValue()->getValue();
6513 const APInt &M = MC->getValue()->getValue();
6514 const APInt &N = NC->getValue()->getValue();
6515 APInt Two(BitWidth, 2);
6516 APInt Four(BitWidth, 4);
6519 using namespace APIntOps;
6521 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6522 // The B coefficient is M-N/2
6526 // The A coefficient is N/2
6527 APInt A(N.sdiv(Two));
6529 // Compute the B^2-4ac term.
6532 SqrtTerm -= Four * (A * C);
6534 if (SqrtTerm.isNegative()) {
6535 // The loop is provably infinite.
6536 const SCEV *CNC = SE.getCouldNotCompute();
6537 return std::make_pair(CNC, CNC);
6540 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6541 // integer value or else APInt::sqrt() will assert.
6542 APInt SqrtVal(SqrtTerm.sqrt());
6544 // Compute the two solutions for the quadratic formula.
6545 // The divisions must be performed as signed divisions.
6548 if (TwoA.isMinValue()) {
6549 const SCEV *CNC = SE.getCouldNotCompute();
6550 return std::make_pair(CNC, CNC);
6553 LLVMContext &Context = SE.getContext();
6555 ConstantInt *Solution1 =
6556 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6557 ConstantInt *Solution2 =
6558 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6560 return std::make_pair(SE.getConstant(Solution1),
6561 SE.getConstant(Solution2));
6562 } // end APIntOps namespace
6565 /// HowFarToZero - Return the number of times a backedge comparing the specified
6566 /// value to zero will execute. If not computable, return CouldNotCompute.
6568 /// This is only used for loops with a "x != y" exit test. The exit condition is
6569 /// now expressed as a single expression, V = x-y. So the exit test is
6570 /// effectively V != 0. We know and take advantage of the fact that this
6571 /// expression only being used in a comparison by zero context.
6572 ScalarEvolution::ExitLimit
6573 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6574 // If the value is a constant
6575 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6576 // If the value is already zero, the branch will execute zero times.
6577 if (C->getValue()->isZero()) return C;
6578 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6581 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6582 if (!AddRec || AddRec->getLoop() != L)
6583 return getCouldNotCompute();
6585 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6586 // the quadratic equation to solve it.
6587 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6588 std::pair<const SCEV *,const SCEV *> Roots =
6589 SolveQuadraticEquation(AddRec, *this);
6590 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6591 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6593 // Pick the smallest positive root value.
6594 if (ConstantInt *CB =
6595 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6598 if (!CB->getZExtValue())
6599 std::swap(R1, R2); // R1 is the minimum root now.
6601 // We can only use this value if the chrec ends up with an exact zero
6602 // value at this index. When solving for "X*X != 5", for example, we
6603 // should not accept a root of 2.
6604 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6606 return R1; // We found a quadratic root!
6609 return getCouldNotCompute();
6612 // Otherwise we can only handle this if it is affine.
6613 if (!AddRec->isAffine())
6614 return getCouldNotCompute();
6616 // If this is an affine expression, the execution count of this branch is
6617 // the minimum unsigned root of the following equation:
6619 // Start + Step*N = 0 (mod 2^BW)
6623 // Step*N = -Start (mod 2^BW)
6625 // where BW is the common bit width of Start and Step.
6627 // Get the initial value for the loop.
6628 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6629 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6631 // For now we handle only constant steps.
6633 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6634 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6635 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6636 // We have not yet seen any such cases.
6637 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6638 if (!StepC || StepC->getValue()->equalsInt(0))
6639 return getCouldNotCompute();
6641 // For positive steps (counting up until unsigned overflow):
6642 // N = -Start/Step (as unsigned)
6643 // For negative steps (counting down to zero):
6645 // First compute the unsigned distance from zero in the direction of Step.
6646 bool CountDown = StepC->getValue()->getValue().isNegative();
6647 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6649 // Handle unitary steps, which cannot wraparound.
6650 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6651 // N = Distance (as unsigned)
6652 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6653 ConstantRange CR = getUnsignedRange(Start);
6654 const SCEV *MaxBECount;
6655 if (!CountDown && CR.getUnsignedMin().isMinValue())
6656 // When counting up, the worst starting value is 1, not 0.
6657 MaxBECount = CR.getUnsignedMax().isMinValue()
6658 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6659 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6661 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6662 : -CR.getUnsignedMin());
6663 return ExitLimit(Distance, MaxBECount);
6666 // As a special case, handle the instance where Step is a positive power of
6667 // two. In this case, determining whether Step divides Distance evenly can be
6668 // done by counting and comparing the number of trailing zeros of Step and
6671 const APInt &StepV = StepC->getValue()->getValue();
6672 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6673 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6674 // case is not handled as this code is guarded by !CountDown.
6675 if (StepV.isPowerOf2() &&
6676 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
6677 // Here we've constrained the equation to be of the form
6679 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
6681 // where we're operating on a W bit wide integer domain and k is
6682 // non-negative. The smallest unsigned solution for X is the trip count.
6684 // (0) is equivalent to:
6686 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
6687 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
6688 // <=> 2^k * Distance' - X = L * 2^(W - N)
6689 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
6691 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
6694 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
6696 // E.g. say we're solving
6698 // 2 * Val = 2 * X (in i8) ... (3)
6700 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
6702 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
6703 // necessarily the smallest unsigned value of X that satisfies (3).
6704 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
6705 // is i8 1, not i8 -127
6707 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
6709 // Since SCEV does not have a URem node, we construct one using a truncate
6710 // and a zero extend.
6712 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
6713 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
6714 auto *WideTy = Distance->getType();
6716 return getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
6720 // If the condition controls loop exit (the loop exits only if the expression
6721 // is true) and the addition is no-wrap we can use unsigned divide to
6722 // compute the backedge count. In this case, the step may not divide the
6723 // distance, but we don't care because if the condition is "missed" the loop
6724 // will have undefined behavior due to wrapping.
6725 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6727 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6728 return ExitLimit(Exact, Exact);
6731 // Then, try to solve the above equation provided that Start is constant.
6732 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6733 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6734 -StartC->getValue()->getValue(),
6736 return getCouldNotCompute();
6739 /// HowFarToNonZero - Return the number of times a backedge checking the
6740 /// specified value for nonzero will execute. If not computable, return
6742 ScalarEvolution::ExitLimit
6743 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6744 // Loops that look like: while (X == 0) are very strange indeed. We don't
6745 // handle them yet except for the trivial case. This could be expanded in the
6746 // future as needed.
6748 // If the value is a constant, check to see if it is known to be non-zero
6749 // already. If so, the backedge will execute zero times.
6750 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6751 if (!C->getValue()->isNullValue())
6752 return getZero(C->getType());
6753 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6756 // We could implement others, but I really doubt anyone writes loops like
6757 // this, and if they did, they would already be constant folded.
6758 return getCouldNotCompute();
6761 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6762 /// (which may not be an immediate predecessor) which has exactly one
6763 /// successor from which BB is reachable, or null if no such block is
6766 std::pair<BasicBlock *, BasicBlock *>
6767 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6768 // If the block has a unique predecessor, then there is no path from the
6769 // predecessor to the block that does not go through the direct edge
6770 // from the predecessor to the block.
6771 if (BasicBlock *Pred = BB->getSinglePredecessor())
6772 return std::make_pair(Pred, BB);
6774 // A loop's header is defined to be a block that dominates the loop.
6775 // If the header has a unique predecessor outside the loop, it must be
6776 // a block that has exactly one successor that can reach the loop.
6777 if (Loop *L = LI.getLoopFor(BB))
6778 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6780 return std::pair<BasicBlock *, BasicBlock *>();
6783 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6784 /// testing whether two expressions are equal, however for the purposes of
6785 /// looking for a condition guarding a loop, it can be useful to be a little
6786 /// more general, since a front-end may have replicated the controlling
6789 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6790 // Quick check to see if they are the same SCEV.
6791 if (A == B) return true;
6793 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
6794 // Not all instructions that are "identical" compute the same value. For
6795 // instance, two distinct alloca instructions allocating the same type are
6796 // identical and do not read memory; but compute distinct values.
6797 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
6800 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6801 // two different instructions with the same value. Check for this case.
6802 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6803 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6804 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6805 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6806 if (ComputesEqualValues(AI, BI))
6809 // Otherwise assume they may have a different value.
6813 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6814 /// predicate Pred. Return true iff any changes were made.
6816 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6817 const SCEV *&LHS, const SCEV *&RHS,
6819 bool Changed = false;
6821 // If we hit the max recursion limit bail out.
6825 // Canonicalize a constant to the right side.
6826 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6827 // Check for both operands constant.
6828 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6829 if (ConstantExpr::getICmp(Pred,
6831 RHSC->getValue())->isNullValue())
6832 goto trivially_false;
6834 goto trivially_true;
6836 // Otherwise swap the operands to put the constant on the right.
6837 std::swap(LHS, RHS);
6838 Pred = ICmpInst::getSwappedPredicate(Pred);
6842 // If we're comparing an addrec with a value which is loop-invariant in the
6843 // addrec's loop, put the addrec on the left. Also make a dominance check,
6844 // as both operands could be addrecs loop-invariant in each other's loop.
6845 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6846 const Loop *L = AR->getLoop();
6847 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6848 std::swap(LHS, RHS);
6849 Pred = ICmpInst::getSwappedPredicate(Pred);
6854 // If there's a constant operand, canonicalize comparisons with boundary
6855 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6856 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6857 const APInt &RA = RC->getValue()->getValue();
6859 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6860 case ICmpInst::ICMP_EQ:
6861 case ICmpInst::ICMP_NE:
6862 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6864 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6865 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6866 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6867 ME->getOperand(0)->isAllOnesValue()) {
6868 RHS = AE->getOperand(1);
6869 LHS = ME->getOperand(1);
6873 case ICmpInst::ICMP_UGE:
6874 if ((RA - 1).isMinValue()) {
6875 Pred = ICmpInst::ICMP_NE;
6876 RHS = getConstant(RA - 1);
6880 if (RA.isMaxValue()) {
6881 Pred = ICmpInst::ICMP_EQ;
6885 if (RA.isMinValue()) goto trivially_true;
6887 Pred = ICmpInst::ICMP_UGT;
6888 RHS = getConstant(RA - 1);
6891 case ICmpInst::ICMP_ULE:
6892 if ((RA + 1).isMaxValue()) {
6893 Pred = ICmpInst::ICMP_NE;
6894 RHS = getConstant(RA + 1);
6898 if (RA.isMinValue()) {
6899 Pred = ICmpInst::ICMP_EQ;
6903 if (RA.isMaxValue()) goto trivially_true;
6905 Pred = ICmpInst::ICMP_ULT;
6906 RHS = getConstant(RA + 1);
6909 case ICmpInst::ICMP_SGE:
6910 if ((RA - 1).isMinSignedValue()) {
6911 Pred = ICmpInst::ICMP_NE;
6912 RHS = getConstant(RA - 1);
6916 if (RA.isMaxSignedValue()) {
6917 Pred = ICmpInst::ICMP_EQ;
6921 if (RA.isMinSignedValue()) goto trivially_true;
6923 Pred = ICmpInst::ICMP_SGT;
6924 RHS = getConstant(RA - 1);
6927 case ICmpInst::ICMP_SLE:
6928 if ((RA + 1).isMaxSignedValue()) {
6929 Pred = ICmpInst::ICMP_NE;
6930 RHS = getConstant(RA + 1);
6934 if (RA.isMinSignedValue()) {
6935 Pred = ICmpInst::ICMP_EQ;
6939 if (RA.isMaxSignedValue()) goto trivially_true;
6941 Pred = ICmpInst::ICMP_SLT;
6942 RHS = getConstant(RA + 1);
6945 case ICmpInst::ICMP_UGT:
6946 if (RA.isMinValue()) {
6947 Pred = ICmpInst::ICMP_NE;
6951 if ((RA + 1).isMaxValue()) {
6952 Pred = ICmpInst::ICMP_EQ;
6953 RHS = getConstant(RA + 1);
6957 if (RA.isMaxValue()) goto trivially_false;
6959 case ICmpInst::ICMP_ULT:
6960 if (RA.isMaxValue()) {
6961 Pred = ICmpInst::ICMP_NE;
6965 if ((RA - 1).isMinValue()) {
6966 Pred = ICmpInst::ICMP_EQ;
6967 RHS = getConstant(RA - 1);
6971 if (RA.isMinValue()) goto trivially_false;
6973 case ICmpInst::ICMP_SGT:
6974 if (RA.isMinSignedValue()) {
6975 Pred = ICmpInst::ICMP_NE;
6979 if ((RA + 1).isMaxSignedValue()) {
6980 Pred = ICmpInst::ICMP_EQ;
6981 RHS = getConstant(RA + 1);
6985 if (RA.isMaxSignedValue()) goto trivially_false;
6987 case ICmpInst::ICMP_SLT:
6988 if (RA.isMaxSignedValue()) {
6989 Pred = ICmpInst::ICMP_NE;
6993 if ((RA - 1).isMinSignedValue()) {
6994 Pred = ICmpInst::ICMP_EQ;
6995 RHS = getConstant(RA - 1);
6999 if (RA.isMinSignedValue()) goto trivially_false;
7004 // Check for obvious equality.
7005 if (HasSameValue(LHS, RHS)) {
7006 if (ICmpInst::isTrueWhenEqual(Pred))
7007 goto trivially_true;
7008 if (ICmpInst::isFalseWhenEqual(Pred))
7009 goto trivially_false;
7012 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
7013 // adding or subtracting 1 from one of the operands.
7015 case ICmpInst::ICMP_SLE:
7016 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
7017 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7019 Pred = ICmpInst::ICMP_SLT;
7021 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
7022 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
7024 Pred = ICmpInst::ICMP_SLT;
7028 case ICmpInst::ICMP_SGE:
7029 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
7030 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
7032 Pred = ICmpInst::ICMP_SGT;
7034 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
7035 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7037 Pred = ICmpInst::ICMP_SGT;
7041 case ICmpInst::ICMP_ULE:
7042 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
7043 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7045 Pred = ICmpInst::ICMP_ULT;
7047 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
7048 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
7049 Pred = ICmpInst::ICMP_ULT;
7053 case ICmpInst::ICMP_UGE:
7054 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
7055 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
7056 Pred = ICmpInst::ICMP_UGT;
7058 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
7059 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7061 Pred = ICmpInst::ICMP_UGT;
7069 // TODO: More simplifications are possible here.
7071 // Recursively simplify until we either hit a recursion limit or nothing
7074 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
7080 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7081 Pred = ICmpInst::ICMP_EQ;
7086 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7087 Pred = ICmpInst::ICMP_NE;
7091 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
7092 return getSignedRange(S).getSignedMax().isNegative();
7095 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
7096 return getSignedRange(S).getSignedMin().isStrictlyPositive();
7099 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
7100 return !getSignedRange(S).getSignedMin().isNegative();
7103 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
7104 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
7107 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
7108 return isKnownNegative(S) || isKnownPositive(S);
7111 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
7112 const SCEV *LHS, const SCEV *RHS) {
7113 // Canonicalize the inputs first.
7114 (void)SimplifyICmpOperands(Pred, LHS, RHS);
7116 // If LHS or RHS is an addrec, check to see if the condition is true in
7117 // every iteration of the loop.
7118 // If LHS and RHS are both addrec, both conditions must be true in
7119 // every iteration of the loop.
7120 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7121 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7122 bool LeftGuarded = false;
7123 bool RightGuarded = false;
7125 const Loop *L = LAR->getLoop();
7126 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
7127 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
7128 if (!RAR) return true;
7133 const Loop *L = RAR->getLoop();
7134 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
7135 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
7136 if (!LAR) return true;
7137 RightGuarded = true;
7140 if (LeftGuarded && RightGuarded)
7143 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
7146 // Otherwise see what can be done with known constant ranges.
7147 return isKnownPredicateWithRanges(Pred, LHS, RHS);
7150 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
7151 ICmpInst::Predicate Pred,
7153 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
7156 // Verify an invariant: inverting the predicate should turn a monotonically
7157 // increasing change to a monotonically decreasing one, and vice versa.
7158 bool IncreasingSwapped;
7159 bool ResultSwapped = isMonotonicPredicateImpl(
7160 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
7162 assert(Result == ResultSwapped && "should be able to analyze both!");
7164 assert(Increasing == !IncreasingSwapped &&
7165 "monotonicity should flip as we flip the predicate");
7171 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
7172 ICmpInst::Predicate Pred,
7175 // A zero step value for LHS means the induction variable is essentially a
7176 // loop invariant value. We don't really depend on the predicate actually
7177 // flipping from false to true (for increasing predicates, and the other way
7178 // around for decreasing predicates), all we care about is that *if* the
7179 // predicate changes then it only changes from false to true.
7181 // A zero step value in itself is not very useful, but there may be places
7182 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
7183 // as general as possible.
7187 return false; // Conservative answer
7189 case ICmpInst::ICMP_UGT:
7190 case ICmpInst::ICMP_UGE:
7191 case ICmpInst::ICMP_ULT:
7192 case ICmpInst::ICMP_ULE:
7193 if (!LHS->getNoWrapFlags(SCEV::FlagNUW))
7196 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
7199 case ICmpInst::ICMP_SGT:
7200 case ICmpInst::ICMP_SGE:
7201 case ICmpInst::ICMP_SLT:
7202 case ICmpInst::ICMP_SLE: {
7203 if (!LHS->getNoWrapFlags(SCEV::FlagNSW))
7206 const SCEV *Step = LHS->getStepRecurrence(*this);
7208 if (isKnownNonNegative(Step)) {
7209 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
7213 if (isKnownNonPositive(Step)) {
7214 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7223 llvm_unreachable("switch has default clause!");
7226 bool ScalarEvolution::isLoopInvariantPredicate(
7227 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7228 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7229 const SCEV *&InvariantRHS) {
7231 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7232 if (!isLoopInvariant(RHS, L)) {
7233 if (!isLoopInvariant(LHS, L))
7236 std::swap(LHS, RHS);
7237 Pred = ICmpInst::getSwappedPredicate(Pred);
7240 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7241 if (!ArLHS || ArLHS->getLoop() != L)
7245 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7248 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7249 // true as the loop iterates, and the backedge is control dependent on
7250 // "ArLHS `Pred` RHS" == true then we can reason as follows:
7252 // * if the predicate was false in the first iteration then the predicate
7253 // is never evaluated again, since the loop exits without taking the
7255 // * if the predicate was true in the first iteration then it will
7256 // continue to be true for all future iterations since it is
7257 // monotonically increasing.
7259 // For both the above possibilities, we can replace the loop varying
7260 // predicate with its value on the first iteration of the loop (which is
7263 // A similar reasoning applies for a monotonically decreasing predicate, by
7264 // replacing true with false and false with true in the above two bullets.
7266 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7268 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7271 InvariantPred = Pred;
7272 InvariantLHS = ArLHS->getStart();
7278 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
7279 const SCEV *LHS, const SCEV *RHS) {
7280 if (HasSameValue(LHS, RHS))
7281 return ICmpInst::isTrueWhenEqual(Pred);
7283 // This code is split out from isKnownPredicate because it is called from
7284 // within isLoopEntryGuardedByCond.
7287 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7288 case ICmpInst::ICMP_SGT:
7289 std::swap(LHS, RHS);
7290 case ICmpInst::ICMP_SLT: {
7291 ConstantRange LHSRange = getSignedRange(LHS);
7292 ConstantRange RHSRange = getSignedRange(RHS);
7293 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
7295 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
7299 case ICmpInst::ICMP_SGE:
7300 std::swap(LHS, RHS);
7301 case ICmpInst::ICMP_SLE: {
7302 ConstantRange LHSRange = getSignedRange(LHS);
7303 ConstantRange RHSRange = getSignedRange(RHS);
7304 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
7306 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
7310 case ICmpInst::ICMP_UGT:
7311 std::swap(LHS, RHS);
7312 case ICmpInst::ICMP_ULT: {
7313 ConstantRange LHSRange = getUnsignedRange(LHS);
7314 ConstantRange RHSRange = getUnsignedRange(RHS);
7315 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
7317 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
7321 case ICmpInst::ICMP_UGE:
7322 std::swap(LHS, RHS);
7323 case ICmpInst::ICMP_ULE: {
7324 ConstantRange LHSRange = getUnsignedRange(LHS);
7325 ConstantRange RHSRange = getUnsignedRange(RHS);
7326 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
7328 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
7332 case ICmpInst::ICMP_NE: {
7333 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
7335 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
7338 const SCEV *Diff = getMinusSCEV(LHS, RHS);
7339 if (isKnownNonZero(Diff))
7343 case ICmpInst::ICMP_EQ:
7344 // The check at the top of the function catches the case where
7345 // the values are known to be equal.
7351 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
7355 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
7356 // Return Y via OutY.
7357 auto MatchBinaryAddToConst =
7358 [this](const SCEV *Result, const SCEV *X, APInt &OutY,
7359 SCEV::NoWrapFlags ExpectedFlags) {
7360 const SCEV *NonConstOp, *ConstOp;
7361 SCEV::NoWrapFlags FlagsPresent;
7363 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
7364 !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
7367 OutY = cast<SCEVConstant>(ConstOp)->getValue()->getValue();
7368 return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
7377 case ICmpInst::ICMP_SGE:
7378 std::swap(LHS, RHS);
7379 case ICmpInst::ICMP_SLE:
7380 // X s<= (X + C)<nsw> if C >= 0
7381 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
7384 // (X + C)<nsw> s<= X if C <= 0
7385 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
7386 !C.isStrictlyPositive())
7390 case ICmpInst::ICMP_SGT:
7391 std::swap(LHS, RHS);
7392 case ICmpInst::ICMP_SLT:
7393 // X s< (X + C)<nsw> if C > 0
7394 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
7395 C.isStrictlyPositive())
7398 // (X + C)<nsw> s< X if C < 0
7399 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
7407 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7410 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
7413 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7414 // the stack can result in exponential time complexity.
7415 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7417 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7419 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7420 // isKnownPredicate. isKnownPredicate is more powerful, but also more
7421 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7422 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
7423 // use isKnownPredicate later if needed.
7424 return isKnownNonNegative(RHS) &&
7425 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7426 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
7429 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7430 /// protected by a conditional between LHS and RHS. This is used to
7431 /// to eliminate casts.
7433 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7434 ICmpInst::Predicate Pred,
7435 const SCEV *LHS, const SCEV *RHS) {
7436 // Interpret a null as meaning no loop, where there is obviously no guard
7437 // (interprocedural conditions notwithstanding).
7438 if (!L) return true;
7440 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7442 BasicBlock *Latch = L->getLoopLatch();
7446 BranchInst *LoopContinuePredicate =
7447 dyn_cast<BranchInst>(Latch->getTerminator());
7448 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7449 isImpliedCond(Pred, LHS, RHS,
7450 LoopContinuePredicate->getCondition(),
7451 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7454 // We don't want more than one activation of the following loops on the stack
7455 // -- that can lead to O(n!) time complexity.
7456 if (WalkingBEDominatingConds)
7459 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7461 // See if we can exploit a trip count to prove the predicate.
7462 const auto &BETakenInfo = getBackedgeTakenInfo(L);
7463 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7464 if (LatchBECount != getCouldNotCompute()) {
7465 // We know that Latch branches back to the loop header exactly
7466 // LatchBECount times. This means the backdege condition at Latch is
7467 // equivalent to "{0,+,1} u< LatchBECount".
7468 Type *Ty = LatchBECount->getType();
7469 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7470 const SCEV *LoopCounter =
7471 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7472 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7477 // Check conditions due to any @llvm.assume intrinsics.
7478 for (auto &AssumeVH : AC.assumptions()) {
7481 auto *CI = cast<CallInst>(AssumeVH);
7482 if (!DT.dominates(CI, Latch->getTerminator()))
7485 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7489 // If the loop is not reachable from the entry block, we risk running into an
7490 // infinite loop as we walk up into the dom tree. These loops do not matter
7491 // anyway, so we just return a conservative answer when we see them.
7492 if (!DT.isReachableFromEntry(L->getHeader()))
7495 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7496 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7498 assert(DTN && "should reach the loop header before reaching the root!");
7500 BasicBlock *BB = DTN->getBlock();
7501 BasicBlock *PBB = BB->getSinglePredecessor();
7505 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7506 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7509 Value *Condition = ContinuePredicate->getCondition();
7511 // If we have an edge `E` within the loop body that dominates the only
7512 // latch, the condition guarding `E` also guards the backedge. This
7513 // reasoning works only for loops with a single latch.
7515 BasicBlockEdge DominatingEdge(PBB, BB);
7516 if (DominatingEdge.isSingleEdge()) {
7517 // We're constructively (and conservatively) enumerating edges within the
7518 // loop body that dominate the latch. The dominator tree better agree
7520 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7522 if (isImpliedCond(Pred, LHS, RHS, Condition,
7523 BB != ContinuePredicate->getSuccessor(0)))
7531 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7532 /// by a conditional between LHS and RHS. This is used to help avoid max
7533 /// expressions in loop trip counts, and to eliminate casts.
7535 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7536 ICmpInst::Predicate Pred,
7537 const SCEV *LHS, const SCEV *RHS) {
7538 // Interpret a null as meaning no loop, where there is obviously no guard
7539 // (interprocedural conditions notwithstanding).
7540 if (!L) return false;
7542 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7544 // Starting at the loop predecessor, climb up the predecessor chain, as long
7545 // as there are predecessors that can be found that have unique successors
7546 // leading to the original header.
7547 for (std::pair<BasicBlock *, BasicBlock *>
7548 Pair(L->getLoopPredecessor(), L->getHeader());
7550 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7552 BranchInst *LoopEntryPredicate =
7553 dyn_cast<BranchInst>(Pair.first->getTerminator());
7554 if (!LoopEntryPredicate ||
7555 LoopEntryPredicate->isUnconditional())
7558 if (isImpliedCond(Pred, LHS, RHS,
7559 LoopEntryPredicate->getCondition(),
7560 LoopEntryPredicate->getSuccessor(0) != Pair.second))
7564 // Check conditions due to any @llvm.assume intrinsics.
7565 for (auto &AssumeVH : AC.assumptions()) {
7568 auto *CI = cast<CallInst>(AssumeVH);
7569 if (!DT.dominates(CI, L->getHeader()))
7572 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7580 /// RAII wrapper to prevent recursive application of isImpliedCond.
7581 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7582 /// currently evaluating isImpliedCond.
7583 struct MarkPendingLoopPredicate {
7585 DenseSet<Value*> &LoopPreds;
7588 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7589 : Cond(C), LoopPreds(LP) {
7590 Pending = !LoopPreds.insert(Cond).second;
7592 ~MarkPendingLoopPredicate() {
7594 LoopPreds.erase(Cond);
7597 } // end anonymous namespace
7599 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7600 /// and RHS is true whenever the given Cond value evaluates to true.
7601 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7602 const SCEV *LHS, const SCEV *RHS,
7603 Value *FoundCondValue,
7605 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7609 // Recursively handle And and Or conditions.
7610 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7611 if (BO->getOpcode() == Instruction::And) {
7613 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7614 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7615 } else if (BO->getOpcode() == Instruction::Or) {
7617 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7618 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7622 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
7623 if (!ICI) return false;
7625 // Now that we found a conditional branch that dominates the loop or controls
7626 // the loop latch. Check to see if it is the comparison we are looking for.
7627 ICmpInst::Predicate FoundPred;
7629 FoundPred = ICI->getInversePredicate();
7631 FoundPred = ICI->getPredicate();
7633 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
7634 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
7636 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
7639 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
7641 ICmpInst::Predicate FoundPred,
7642 const SCEV *FoundLHS,
7643 const SCEV *FoundRHS) {
7644 // Balance the types.
7645 if (getTypeSizeInBits(LHS->getType()) <
7646 getTypeSizeInBits(FoundLHS->getType())) {
7647 if (CmpInst::isSigned(Pred)) {
7648 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
7649 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
7651 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
7652 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
7654 } else if (getTypeSizeInBits(LHS->getType()) >
7655 getTypeSizeInBits(FoundLHS->getType())) {
7656 if (CmpInst::isSigned(FoundPred)) {
7657 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
7658 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
7660 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
7661 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
7665 // Canonicalize the query to match the way instcombine will have
7666 // canonicalized the comparison.
7667 if (SimplifyICmpOperands(Pred, LHS, RHS))
7669 return CmpInst::isTrueWhenEqual(Pred);
7670 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
7671 if (FoundLHS == FoundRHS)
7672 return CmpInst::isFalseWhenEqual(FoundPred);
7674 // Check to see if we can make the LHS or RHS match.
7675 if (LHS == FoundRHS || RHS == FoundLHS) {
7676 if (isa<SCEVConstant>(RHS)) {
7677 std::swap(FoundLHS, FoundRHS);
7678 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
7680 std::swap(LHS, RHS);
7681 Pred = ICmpInst::getSwappedPredicate(Pred);
7685 // Check whether the found predicate is the same as the desired predicate.
7686 if (FoundPred == Pred)
7687 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7689 // Check whether swapping the found predicate makes it the same as the
7690 // desired predicate.
7691 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
7692 if (isa<SCEVConstant>(RHS))
7693 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
7695 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
7696 RHS, LHS, FoundLHS, FoundRHS);
7699 // Unsigned comparison is the same as signed comparison when both the operands
7700 // are non-negative.
7701 if (CmpInst::isUnsigned(FoundPred) &&
7702 CmpInst::getSignedPredicate(FoundPred) == Pred &&
7703 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
7704 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7706 // Check if we can make progress by sharpening ranges.
7707 if (FoundPred == ICmpInst::ICMP_NE &&
7708 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
7710 const SCEVConstant *C = nullptr;
7711 const SCEV *V = nullptr;
7713 if (isa<SCEVConstant>(FoundLHS)) {
7714 C = cast<SCEVConstant>(FoundLHS);
7717 C = cast<SCEVConstant>(FoundRHS);
7721 // The guarding predicate tells us that C != V. If the known range
7722 // of V is [C, t), we can sharpen the range to [C + 1, t). The
7723 // range we consider has to correspond to same signedness as the
7724 // predicate we're interested in folding.
7726 APInt Min = ICmpInst::isSigned(Pred) ?
7727 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7729 if (Min == C->getValue()->getValue()) {
7730 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7731 // This is true even if (Min + 1) wraps around -- in case of
7732 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7734 APInt SharperMin = Min + 1;
7737 case ICmpInst::ICMP_SGE:
7738 case ICmpInst::ICMP_UGE:
7739 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7741 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7742 getConstant(SharperMin)))
7745 case ICmpInst::ICMP_SGT:
7746 case ICmpInst::ICMP_UGT:
7747 // We know from the range information that (V `Pred` Min ||
7748 // V == Min). We know from the guarding condition that !(V
7749 // == Min). This gives us
7751 // V `Pred` Min || V == Min && !(V == Min)
7754 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7756 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7766 // Check whether the actual condition is beyond sufficient.
7767 if (FoundPred == ICmpInst::ICMP_EQ)
7768 if (ICmpInst::isTrueWhenEqual(Pred))
7769 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7771 if (Pred == ICmpInst::ICMP_NE)
7772 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7773 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7776 // Otherwise assume the worst.
7780 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
7781 const SCEV *&L, const SCEV *&R,
7782 SCEV::NoWrapFlags &Flags) {
7783 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
7784 if (!AE || AE->getNumOperands() != 2)
7787 L = AE->getOperand(0);
7788 R = AE->getOperand(1);
7789 Flags = AE->getNoWrapFlags();
7793 bool ScalarEvolution::computeConstantDifference(const SCEV *Less,
7796 // We avoid subtracting expressions here because this function is usually
7797 // fairly deep in the call stack (i.e. is called many times).
7799 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
7800 const auto *LAR = cast<SCEVAddRecExpr>(Less);
7801 const auto *MAR = cast<SCEVAddRecExpr>(More);
7803 if (LAR->getLoop() != MAR->getLoop())
7806 // We look at affine expressions only; not for correctness but to keep
7807 // getStepRecurrence cheap.
7808 if (!LAR->isAffine() || !MAR->isAffine())
7811 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
7814 Less = LAR->getStart();
7815 More = MAR->getStart();
7820 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
7821 const auto &M = cast<SCEVConstant>(More)->getValue()->getValue();
7822 const auto &L = cast<SCEVConstant>(Less)->getValue()->getValue();
7828 SCEV::NoWrapFlags Flags;
7829 if (splitBinaryAdd(Less, L, R, Flags))
7830 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7832 C = -(LC->getValue()->getValue());
7836 if (splitBinaryAdd(More, L, R, Flags))
7837 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7839 C = LC->getValue()->getValue();
7846 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
7847 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
7848 const SCEV *FoundLHS, const SCEV *FoundRHS) {
7849 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
7852 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7856 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
7857 if (!AddRecFoundLHS)
7860 // We'd like to let SCEV reason about control dependencies, so we constrain
7861 // both the inequalities to be about add recurrences on the same loop. This
7862 // way we can use isLoopEntryGuardedByCond later.
7864 const Loop *L = AddRecFoundLHS->getLoop();
7865 if (L != AddRecLHS->getLoop())
7868 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
7870 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
7873 // Informal proof for (2), assuming (1) [*]:
7875 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
7879 // FoundLHS s< FoundRHS s< INT_MIN - C
7880 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
7881 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
7882 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
7883 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
7884 // <=> FoundLHS + C s< FoundRHS + C
7886 // [*]: (1) can be proved by ruling out overflow.
7888 // [**]: This can be proved by analyzing all the four possibilities:
7889 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
7890 // (A s>= 0, B s>= 0).
7893 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
7894 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
7895 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
7896 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
7897 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
7901 if (!computeConstantDifference(FoundLHS, LHS, LDiff) ||
7902 !computeConstantDifference(FoundRHS, RHS, RDiff) ||
7909 APInt FoundRHSLimit;
7911 if (Pred == CmpInst::ICMP_ULT) {
7912 FoundRHSLimit = -RDiff;
7914 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
7915 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - RDiff;
7918 // Try to prove (1) or (2), as needed.
7919 return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
7920 getConstant(FoundRHSLimit));
7923 /// isImpliedCondOperands - Test whether the condition described by Pred,
7924 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7925 /// and FoundRHS is true.
7926 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7927 const SCEV *LHS, const SCEV *RHS,
7928 const SCEV *FoundLHS,
7929 const SCEV *FoundRHS) {
7930 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7933 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
7936 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7937 FoundLHS, FoundRHS) ||
7938 // ~x < ~y --> x > y
7939 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7940 getNotSCEV(FoundRHS),
7941 getNotSCEV(FoundLHS));
7945 /// If Expr computes ~A, return A else return nullptr
7946 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7947 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7948 if (!Add || Add->getNumOperands() != 2 ||
7949 !Add->getOperand(0)->isAllOnesValue())
7952 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7953 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
7954 !AddRHS->getOperand(0)->isAllOnesValue())
7957 return AddRHS->getOperand(1);
7961 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7962 template<typename MaxExprType>
7963 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7964 const SCEV *Candidate) {
7965 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7966 if (!MaxExpr) return false;
7968 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7969 return It != MaxExpr->op_end();
7973 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7974 template<typename MaxExprType>
7975 static bool IsMinConsistingOf(ScalarEvolution &SE,
7976 const SCEV *MaybeMinExpr,
7977 const SCEV *Candidate) {
7978 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7982 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7985 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
7986 ICmpInst::Predicate Pred,
7987 const SCEV *LHS, const SCEV *RHS) {
7989 // If both sides are affine addrecs for the same loop, with equal
7990 // steps, and we know the recurrences don't wrap, then we only
7991 // need to check the predicate on the starting values.
7993 if (!ICmpInst::isRelational(Pred))
7996 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7999 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
8002 if (LAR->getLoop() != RAR->getLoop())
8004 if (!LAR->isAffine() || !RAR->isAffine())
8007 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
8010 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
8011 SCEV::FlagNSW : SCEV::FlagNUW;
8012 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
8015 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
8018 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
8020 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
8021 ICmpInst::Predicate Pred,
8022 const SCEV *LHS, const SCEV *RHS) {
8027 case ICmpInst::ICMP_SGE:
8028 std::swap(LHS, RHS);
8030 case ICmpInst::ICMP_SLE:
8033 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
8035 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
8037 case ICmpInst::ICMP_UGE:
8038 std::swap(LHS, RHS);
8040 case ICmpInst::ICMP_ULE:
8043 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
8045 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
8048 llvm_unreachable("covered switch fell through?!");
8051 /// isImpliedCondOperandsHelper - Test whether the condition described by
8052 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
8053 /// FoundLHS, and FoundRHS is true.
8055 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
8056 const SCEV *LHS, const SCEV *RHS,
8057 const SCEV *FoundLHS,
8058 const SCEV *FoundRHS) {
8059 auto IsKnownPredicateFull =
8060 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
8061 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
8062 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
8063 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
8064 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
8068 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
8069 case ICmpInst::ICMP_EQ:
8070 case ICmpInst::ICMP_NE:
8071 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
8074 case ICmpInst::ICMP_SLT:
8075 case ICmpInst::ICMP_SLE:
8076 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
8077 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
8080 case ICmpInst::ICMP_SGT:
8081 case ICmpInst::ICMP_SGE:
8082 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
8083 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
8086 case ICmpInst::ICMP_ULT:
8087 case ICmpInst::ICMP_ULE:
8088 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
8089 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
8092 case ICmpInst::ICMP_UGT:
8093 case ICmpInst::ICMP_UGE:
8094 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
8095 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
8103 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
8104 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
8105 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
8108 const SCEV *FoundLHS,
8109 const SCEV *FoundRHS) {
8110 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
8111 // The restriction on `FoundRHS` be lifted easily -- it exists only to
8112 // reduce the compile time impact of this optimization.
8115 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
8116 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
8117 !isa<SCEVConstant>(AddLHS->getOperand(0)))
8120 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
8122 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
8123 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
8124 ConstantRange FoundLHSRange =
8125 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
8127 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
8130 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
8131 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
8133 // We can also compute the range of values for `LHS` that satisfy the
8134 // consequent, "`LHS` `Pred` `RHS`":
8135 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
8136 ConstantRange SatisfyingLHSRange =
8137 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
8139 // The antecedent implies the consequent if every value of `LHS` that
8140 // satisfies the antecedent also satisfies the consequent.
8141 return SatisfyingLHSRange.contains(LHSRange);
8144 // Verify if an linear IV with positive stride can overflow when in a
8145 // less-than comparison, knowing the invariant term of the comparison, the
8146 // stride and the knowledge of NSW/NUW flags on the recurrence.
8147 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
8148 bool IsSigned, bool NoWrap) {
8149 if (NoWrap) return false;
8151 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8152 const SCEV *One = getOne(Stride->getType());
8155 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
8156 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
8157 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8160 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
8161 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
8164 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
8165 APInt MaxValue = APInt::getMaxValue(BitWidth);
8166 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8169 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
8170 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
8173 // Verify if an linear IV with negative stride can overflow when in a
8174 // greater-than comparison, knowing the invariant term of the comparison,
8175 // the stride and the knowledge of NSW/NUW flags on the recurrence.
8176 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
8177 bool IsSigned, bool NoWrap) {
8178 if (NoWrap) return false;
8180 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8181 const SCEV *One = getOne(Stride->getType());
8184 APInt MinRHS = getSignedRange(RHS).getSignedMin();
8185 APInt MinValue = APInt::getSignedMinValue(BitWidth);
8186 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8189 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
8190 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
8193 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
8194 APInt MinValue = APInt::getMinValue(BitWidth);
8195 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8198 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
8199 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
8202 // Compute the backedge taken count knowing the interval difference, the
8203 // stride and presence of the equality in the comparison.
8204 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
8206 const SCEV *One = getOne(Step->getType());
8207 Delta = Equality ? getAddExpr(Delta, Step)
8208 : getAddExpr(Delta, getMinusSCEV(Step, One));
8209 return getUDivExpr(Delta, Step);
8212 /// HowManyLessThans - Return the number of times a backedge containing the
8213 /// specified less-than comparison will execute. If not computable, return
8214 /// CouldNotCompute.
8216 /// @param ControlsExit is true when the LHS < RHS condition directly controls
8217 /// the branch (loops exits only if condition is true). In this case, we can use
8218 /// NoWrapFlags to skip overflow checks.
8219 ScalarEvolution::ExitLimit
8220 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
8221 const Loop *L, bool IsSigned,
8222 bool ControlsExit) {
8223 // We handle only IV < Invariant
8224 if (!isLoopInvariant(RHS, L))
8225 return getCouldNotCompute();
8227 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8229 // Avoid weird loops
8230 if (!IV || IV->getLoop() != L || !IV->isAffine())
8231 return getCouldNotCompute();
8233 bool NoWrap = ControlsExit &&
8234 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8236 const SCEV *Stride = IV->getStepRecurrence(*this);
8238 // Avoid negative or zero stride values
8239 if (!isKnownPositive(Stride))
8240 return getCouldNotCompute();
8242 // Avoid proven overflow cases: this will ensure that the backedge taken count
8243 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8244 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8245 // behaviors like the case of C language.
8246 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
8247 return getCouldNotCompute();
8249 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
8250 : ICmpInst::ICMP_ULT;
8251 const SCEV *Start = IV->getStart();
8252 const SCEV *End = RHS;
8253 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
8254 const SCEV *Diff = getMinusSCEV(RHS, Start);
8255 // If we have NoWrap set, then we can assume that the increment won't
8256 // overflow, in which case if RHS - Start is a constant, we don't need to
8257 // do a max operation since we can just figure it out statically
8258 if (NoWrap && isa<SCEVConstant>(Diff)) {
8259 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
8263 End = IsSigned ? getSMaxExpr(RHS, Start)
8264 : getUMaxExpr(RHS, Start);
8267 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
8269 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
8270 : getUnsignedRange(Start).getUnsignedMin();
8272 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8273 : getUnsignedRange(Stride).getUnsignedMin();
8275 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8276 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
8277 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
8279 // Although End can be a MAX expression we estimate MaxEnd considering only
8280 // the case End = RHS. This is safe because in the other case (End - Start)
8281 // is zero, leading to a zero maximum backedge taken count.
8283 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8284 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8286 const SCEV *MaxBECount;
8287 if (isa<SCEVConstant>(BECount))
8288 MaxBECount = BECount;
8290 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8291 getConstant(MinStride), false);
8293 if (isa<SCEVCouldNotCompute>(MaxBECount))
8294 MaxBECount = BECount;
8296 return ExitLimit(BECount, MaxBECount);
8299 ScalarEvolution::ExitLimit
8300 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8301 const Loop *L, bool IsSigned,
8302 bool ControlsExit) {
8303 // We handle only IV > Invariant
8304 if (!isLoopInvariant(RHS, L))
8305 return getCouldNotCompute();
8307 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8309 // Avoid weird loops
8310 if (!IV || IV->getLoop() != L || !IV->isAffine())
8311 return getCouldNotCompute();
8313 bool NoWrap = ControlsExit &&
8314 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8316 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8318 // Avoid negative or zero stride values
8319 if (!isKnownPositive(Stride))
8320 return getCouldNotCompute();
8322 // Avoid proven overflow cases: this will ensure that the backedge taken count
8323 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8324 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8325 // behaviors like the case of C language.
8326 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8327 return getCouldNotCompute();
8329 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8330 : ICmpInst::ICMP_UGT;
8332 const SCEV *Start = IV->getStart();
8333 const SCEV *End = RHS;
8334 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
8335 const SCEV *Diff = getMinusSCEV(RHS, Start);
8336 // If we have NoWrap set, then we can assume that the increment won't
8337 // overflow, in which case if RHS - Start is a constant, we don't need to
8338 // do a max operation since we can just figure it out statically
8339 if (NoWrap && isa<SCEVConstant>(Diff)) {
8340 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
8341 if (!D.isNegative())
8344 End = IsSigned ? getSMinExpr(RHS, Start)
8345 : getUMinExpr(RHS, Start);
8348 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8350 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8351 : getUnsignedRange(Start).getUnsignedMax();
8353 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8354 : getUnsignedRange(Stride).getUnsignedMin();
8356 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8357 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8358 : APInt::getMinValue(BitWidth) + (MinStride - 1);
8360 // Although End can be a MIN expression we estimate MinEnd considering only
8361 // the case End = RHS. This is safe because in the other case (Start - End)
8362 // is zero, leading to a zero maximum backedge taken count.
8364 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8365 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8368 const SCEV *MaxBECount = getCouldNotCompute();
8369 if (isa<SCEVConstant>(BECount))
8370 MaxBECount = BECount;
8372 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8373 getConstant(MinStride), false);
8375 if (isa<SCEVCouldNotCompute>(MaxBECount))
8376 MaxBECount = BECount;
8378 return ExitLimit(BECount, MaxBECount);
8381 /// getNumIterationsInRange - Return the number of iterations of this loop that
8382 /// produce values in the specified constant range. Another way of looking at
8383 /// this is that it returns the first iteration number where the value is not in
8384 /// the condition, thus computing the exit count. If the iteration count can't
8385 /// be computed, an instance of SCEVCouldNotCompute is returned.
8386 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
8387 ScalarEvolution &SE) const {
8388 if (Range.isFullSet()) // Infinite loop.
8389 return SE.getCouldNotCompute();
8391 // If the start is a non-zero constant, shift the range to simplify things.
8392 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8393 if (!SC->getValue()->isZero()) {
8394 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8395 Operands[0] = SE.getZero(SC->getType());
8396 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8397 getNoWrapFlags(FlagNW));
8398 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
8399 return ShiftedAddRec->getNumIterationsInRange(
8400 Range.subtract(SC->getValue()->getValue()), SE);
8401 // This is strange and shouldn't happen.
8402 return SE.getCouldNotCompute();
8405 // The only time we can solve this is when we have all constant indices.
8406 // Otherwise, we cannot determine the overflow conditions.
8407 if (std::any_of(op_begin(), op_end(),
8408 [](const SCEV *Op) { return !isa<SCEVConstant>(Op);}))
8409 return SE.getCouldNotCompute();
8411 // Okay at this point we know that all elements of the chrec are constants and
8412 // that the start element is zero.
8414 // First check to see if the range contains zero. If not, the first
8416 unsigned BitWidth = SE.getTypeSizeInBits(getType());
8417 if (!Range.contains(APInt(BitWidth, 0)))
8418 return SE.getZero(getType());
8421 // If this is an affine expression then we have this situation:
8422 // Solve {0,+,A} in Range === Ax in Range
8424 // We know that zero is in the range. If A is positive then we know that
8425 // the upper value of the range must be the first possible exit value.
8426 // If A is negative then the lower of the range is the last possible loop
8427 // value. Also note that we already checked for a full range.
8428 APInt One(BitWidth,1);
8429 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
8430 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8432 // The exit value should be (End+A)/A.
8433 APInt ExitVal = (End + A).udiv(A);
8434 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8436 // Evaluate at the exit value. If we really did fall out of the valid
8437 // range, then we computed our trip count, otherwise wrap around or other
8438 // things must have happened.
8439 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8440 if (Range.contains(Val->getValue()))
8441 return SE.getCouldNotCompute(); // Something strange happened
8443 // Ensure that the previous value is in the range. This is a sanity check.
8444 assert(Range.contains(
8445 EvaluateConstantChrecAtConstant(this,
8446 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8447 "Linear scev computation is off in a bad way!");
8448 return SE.getConstant(ExitValue);
8449 } else if (isQuadratic()) {
8450 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8451 // quadratic equation to solve it. To do this, we must frame our problem in
8452 // terms of figuring out when zero is crossed, instead of when
8453 // Range.getUpper() is crossed.
8454 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8455 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8456 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
8457 // getNoWrapFlags(FlagNW)
8460 // Next, solve the constructed addrec
8461 auto Roots = SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
8462 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
8463 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
8465 // Pick the smallest positive root value.
8466 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
8467 ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
8468 if (!CB->getZExtValue())
8469 std::swap(R1, R2); // R1 is the minimum root now.
8471 // Make sure the root is not off by one. The returned iteration should
8472 // not be in the range, but the previous one should be. When solving
8473 // for "X*X < 5", for example, we should not return a root of 2.
8474 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
8477 if (Range.contains(R1Val->getValue())) {
8478 // The next iteration must be out of the range...
8479 ConstantInt *NextVal =
8480 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
8482 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8483 if (!Range.contains(R1Val->getValue()))
8484 return SE.getConstant(NextVal);
8485 return SE.getCouldNotCompute(); // Something strange happened
8488 // If R1 was not in the range, then it is a good return value. Make
8489 // sure that R1-1 WAS in the range though, just in case.
8490 ConstantInt *NextVal =
8491 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
8492 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8493 if (Range.contains(R1Val->getValue()))
8495 return SE.getCouldNotCompute(); // Something strange happened
8500 return SE.getCouldNotCompute();
8506 FindUndefs() : Found(false) {}
8508 bool follow(const SCEV *S) {
8509 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
8510 if (isa<UndefValue>(C->getValue()))
8512 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
8513 if (isa<UndefValue>(C->getValue()))
8517 // Keep looking if we haven't found it yet.
8520 bool isDone() const {
8521 // Stop recursion if we have found an undef.
8527 // Return true when S contains at least an undef value.
8529 containsUndefs(const SCEV *S) {
8531 SCEVTraversal<FindUndefs> ST(F);
8538 // Collect all steps of SCEV expressions.
8539 struct SCEVCollectStrides {
8540 ScalarEvolution &SE;
8541 SmallVectorImpl<const SCEV *> &Strides;
8543 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
8544 : SE(SE), Strides(S) {}
8546 bool follow(const SCEV *S) {
8547 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
8548 Strides.push_back(AR->getStepRecurrence(SE));
8551 bool isDone() const { return false; }
8554 // Collect all SCEVUnknown and SCEVMulExpr expressions.
8555 struct SCEVCollectTerms {
8556 SmallVectorImpl<const SCEV *> &Terms;
8558 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
8561 bool follow(const SCEV *S) {
8562 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
8563 if (!containsUndefs(S))
8566 // Stop recursion: once we collected a term, do not walk its operands.
8573 bool isDone() const { return false; }
8576 // Check if a SCEV contains an AddRecExpr.
8577 struct SCEVHasAddRec {
8578 bool &ContainsAddRec;
8580 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
8581 ContainsAddRec = false;
8584 bool follow(const SCEV *S) {
8585 if (isa<SCEVAddRecExpr>(S)) {
8586 ContainsAddRec = true;
8588 // Stop recursion: once we collected a term, do not walk its operands.
8595 bool isDone() const { return false; }
8598 // Find factors that are multiplied with an expression that (possibly as a
8599 // subexpression) contains an AddRecExpr. In the expression:
8601 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
8603 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
8604 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
8605 // parameters as they form a product with an induction variable.
8607 // This collector expects all array size parameters to be in the same MulExpr.
8608 // It might be necessary to later add support for collecting parameters that are
8609 // spread over different nested MulExpr.
8610 struct SCEVCollectAddRecMultiplies {
8611 SmallVectorImpl<const SCEV *> &Terms;
8612 ScalarEvolution &SE;
8614 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
8615 : Terms(T), SE(SE) {}
8617 bool follow(const SCEV *S) {
8618 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
8619 bool HasAddRec = false;
8620 SmallVector<const SCEV *, 0> Operands;
8621 for (auto Op : Mul->operands()) {
8622 if (isa<SCEVUnknown>(Op)) {
8623 Operands.push_back(Op);
8625 bool ContainsAddRec;
8626 SCEVHasAddRec ContiansAddRec(ContainsAddRec);
8627 visitAll(Op, ContiansAddRec);
8628 HasAddRec |= ContainsAddRec;
8631 if (Operands.size() == 0)
8637 Terms.push_back(SE.getMulExpr(Operands));
8638 // Stop recursion: once we collected a term, do not walk its operands.
8645 bool isDone() const { return false; }
8649 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
8651 /// 1) The strides of AddRec expressions.
8652 /// 2) Unknowns that are multiplied with AddRec expressions.
8653 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
8654 SmallVectorImpl<const SCEV *> &Terms) {
8655 SmallVector<const SCEV *, 4> Strides;
8656 SCEVCollectStrides StrideCollector(*this, Strides);
8657 visitAll(Expr, StrideCollector);
8660 dbgs() << "Strides:\n";
8661 for (const SCEV *S : Strides)
8662 dbgs() << *S << "\n";
8665 for (const SCEV *S : Strides) {
8666 SCEVCollectTerms TermCollector(Terms);
8667 visitAll(S, TermCollector);
8671 dbgs() << "Terms:\n";
8672 for (const SCEV *T : Terms)
8673 dbgs() << *T << "\n";
8676 SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
8677 visitAll(Expr, MulCollector);
8680 static bool findArrayDimensionsRec(ScalarEvolution &SE,
8681 SmallVectorImpl<const SCEV *> &Terms,
8682 SmallVectorImpl<const SCEV *> &Sizes) {
8683 int Last = Terms.size() - 1;
8684 const SCEV *Step = Terms[Last];
8686 // End of recursion.
8688 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
8689 SmallVector<const SCEV *, 2> Qs;
8690 for (const SCEV *Op : M->operands())
8691 if (!isa<SCEVConstant>(Op))
8694 Step = SE.getMulExpr(Qs);
8697 Sizes.push_back(Step);
8701 for (const SCEV *&Term : Terms) {
8702 // Normalize the terms before the next call to findArrayDimensionsRec.
8704 SCEVDivision::divide(SE, Term, Step, &Q, &R);
8706 // Bail out when GCD does not evenly divide one of the terms.
8713 // Remove all SCEVConstants.
8714 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
8715 return isa<SCEVConstant>(E);
8719 if (Terms.size() > 0)
8720 if (!findArrayDimensionsRec(SE, Terms, Sizes))
8723 Sizes.push_back(Step);
8728 struct FindParameter {
8729 bool FoundParameter;
8730 FindParameter() : FoundParameter(false) {}
8732 bool follow(const SCEV *S) {
8733 if (isa<SCEVUnknown>(S)) {
8734 FoundParameter = true;
8735 // Stop recursion: we found a parameter.
8741 bool isDone() const {
8742 // Stop recursion if we have found a parameter.
8743 return FoundParameter;
8748 // Returns true when S contains at least a SCEVUnknown parameter.
8750 containsParameters(const SCEV *S) {
8752 SCEVTraversal<FindParameter> ST(F);
8755 return F.FoundParameter;
8758 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
8760 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
8761 for (const SCEV *T : Terms)
8762 if (containsParameters(T))
8767 // Return the number of product terms in S.
8768 static inline int numberOfTerms(const SCEV *S) {
8769 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
8770 return Expr->getNumOperands();
8774 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
8775 if (isa<SCEVConstant>(T))
8778 if (isa<SCEVUnknown>(T))
8781 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
8782 SmallVector<const SCEV *, 2> Factors;
8783 for (const SCEV *Op : M->operands())
8784 if (!isa<SCEVConstant>(Op))
8785 Factors.push_back(Op);
8787 return SE.getMulExpr(Factors);
8793 /// Return the size of an element read or written by Inst.
8794 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
8796 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
8797 Ty = Store->getValueOperand()->getType();
8798 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
8799 Ty = Load->getType();
8803 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
8804 return getSizeOfExpr(ETy, Ty);
8807 /// Second step of delinearization: compute the array dimensions Sizes from the
8808 /// set of Terms extracted from the memory access function of this SCEVAddRec.
8809 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
8810 SmallVectorImpl<const SCEV *> &Sizes,
8811 const SCEV *ElementSize) const {
8813 if (Terms.size() < 1 || !ElementSize)
8816 // Early return when Terms do not contain parameters: we do not delinearize
8817 // non parametric SCEVs.
8818 if (!containsParameters(Terms))
8822 dbgs() << "Terms:\n";
8823 for (const SCEV *T : Terms)
8824 dbgs() << *T << "\n";
8827 // Remove duplicates.
8828 std::sort(Terms.begin(), Terms.end());
8829 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
8831 // Put larger terms first.
8832 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
8833 return numberOfTerms(LHS) > numberOfTerms(RHS);
8836 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8838 // Try to divide all terms by the element size. If term is not divisible by
8839 // element size, proceed with the original term.
8840 for (const SCEV *&Term : Terms) {
8842 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
8847 SmallVector<const SCEV *, 4> NewTerms;
8849 // Remove constant factors.
8850 for (const SCEV *T : Terms)
8851 if (const SCEV *NewT = removeConstantFactors(SE, T))
8852 NewTerms.push_back(NewT);
8855 dbgs() << "Terms after sorting:\n";
8856 for (const SCEV *T : NewTerms)
8857 dbgs() << *T << "\n";
8860 if (NewTerms.empty() ||
8861 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
8866 // The last element to be pushed into Sizes is the size of an element.
8867 Sizes.push_back(ElementSize);
8870 dbgs() << "Sizes:\n";
8871 for (const SCEV *S : Sizes)
8872 dbgs() << *S << "\n";
8876 /// Third step of delinearization: compute the access functions for the
8877 /// Subscripts based on the dimensions in Sizes.
8878 void ScalarEvolution::computeAccessFunctions(
8879 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
8880 SmallVectorImpl<const SCEV *> &Sizes) {
8882 // Early exit in case this SCEV is not an affine multivariate function.
8886 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
8887 if (!AR->isAffine())
8890 const SCEV *Res = Expr;
8891 int Last = Sizes.size() - 1;
8892 for (int i = Last; i >= 0; i--) {
8894 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
8897 dbgs() << "Res: " << *Res << "\n";
8898 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
8899 dbgs() << "Res divided by Sizes[i]:\n";
8900 dbgs() << "Quotient: " << *Q << "\n";
8901 dbgs() << "Remainder: " << *R << "\n";
8906 // Do not record the last subscript corresponding to the size of elements in
8910 // Bail out if the remainder is too complex.
8911 if (isa<SCEVAddRecExpr>(R)) {
8920 // Record the access function for the current subscript.
8921 Subscripts.push_back(R);
8924 // Also push in last position the remainder of the last division: it will be
8925 // the access function of the innermost dimension.
8926 Subscripts.push_back(Res);
8928 std::reverse(Subscripts.begin(), Subscripts.end());
8931 dbgs() << "Subscripts:\n";
8932 for (const SCEV *S : Subscripts)
8933 dbgs() << *S << "\n";
8937 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
8938 /// sizes of an array access. Returns the remainder of the delinearization that
8939 /// is the offset start of the array. The SCEV->delinearize algorithm computes
8940 /// the multiples of SCEV coefficients: that is a pattern matching of sub
8941 /// expressions in the stride and base of a SCEV corresponding to the
8942 /// computation of a GCD (greatest common divisor) of base and stride. When
8943 /// SCEV->delinearize fails, it returns the SCEV unchanged.
8945 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
8947 /// void foo(long n, long m, long o, double A[n][m][o]) {
8949 /// for (long i = 0; i < n; i++)
8950 /// for (long j = 0; j < m; j++)
8951 /// for (long k = 0; k < o; k++)
8952 /// A[i][j][k] = 1.0;
8955 /// the delinearization input is the following AddRec SCEV:
8957 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
8959 /// From this SCEV, we are able to say that the base offset of the access is %A
8960 /// because it appears as an offset that does not divide any of the strides in
8963 /// CHECK: Base offset: %A
8965 /// and then SCEV->delinearize determines the size of some of the dimensions of
8966 /// the array as these are the multiples by which the strides are happening:
8968 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
8970 /// Note that the outermost dimension remains of UnknownSize because there are
8971 /// no strides that would help identifying the size of the last dimension: when
8972 /// the array has been statically allocated, one could compute the size of that
8973 /// dimension by dividing the overall size of the array by the size of the known
8974 /// dimensions: %m * %o * 8.
8976 /// Finally delinearize provides the access functions for the array reference
8977 /// that does correspond to A[i][j][k] of the above C testcase:
8979 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
8981 /// The testcases are checking the output of a function pass:
8982 /// DelinearizationPass that walks through all loads and stores of a function
8983 /// asking for the SCEV of the memory access with respect to all enclosing
8984 /// loops, calling SCEV->delinearize on that and printing the results.
8986 void ScalarEvolution::delinearize(const SCEV *Expr,
8987 SmallVectorImpl<const SCEV *> &Subscripts,
8988 SmallVectorImpl<const SCEV *> &Sizes,
8989 const SCEV *ElementSize) {
8990 // First step: collect parametric terms.
8991 SmallVector<const SCEV *, 4> Terms;
8992 collectParametricTerms(Expr, Terms);
8997 // Second step: find subscript sizes.
8998 findArrayDimensions(Terms, Sizes, ElementSize);
9003 // Third step: compute the access functions for each subscript.
9004 computeAccessFunctions(Expr, Subscripts, Sizes);
9006 if (Subscripts.empty())
9010 dbgs() << "succeeded to delinearize " << *Expr << "\n";
9011 dbgs() << "ArrayDecl[UnknownSize]";
9012 for (const SCEV *S : Sizes)
9013 dbgs() << "[" << *S << "]";
9015 dbgs() << "\nArrayRef";
9016 for (const SCEV *S : Subscripts)
9017 dbgs() << "[" << *S << "]";
9022 //===----------------------------------------------------------------------===//
9023 // SCEVCallbackVH Class Implementation
9024 //===----------------------------------------------------------------------===//
9026 void ScalarEvolution::SCEVCallbackVH::deleted() {
9027 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9028 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
9029 SE->ConstantEvolutionLoopExitValue.erase(PN);
9030 SE->ValueExprMap.erase(getValPtr());
9031 // this now dangles!
9034 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
9035 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9037 // Forget all the expressions associated with users of the old value,
9038 // so that future queries will recompute the expressions using the new
9040 Value *Old = getValPtr();
9041 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
9042 SmallPtrSet<User *, 8> Visited;
9043 while (!Worklist.empty()) {
9044 User *U = Worklist.pop_back_val();
9045 // Deleting the Old value will cause this to dangle. Postpone
9046 // that until everything else is done.
9049 if (!Visited.insert(U).second)
9051 if (PHINode *PN = dyn_cast<PHINode>(U))
9052 SE->ConstantEvolutionLoopExitValue.erase(PN);
9053 SE->ValueExprMap.erase(U);
9054 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
9056 // Delete the Old value.
9057 if (PHINode *PN = dyn_cast<PHINode>(Old))
9058 SE->ConstantEvolutionLoopExitValue.erase(PN);
9059 SE->ValueExprMap.erase(Old);
9060 // this now dangles!
9063 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
9064 : CallbackVH(V), SE(se) {}
9066 //===----------------------------------------------------------------------===//
9067 // ScalarEvolution Class Implementation
9068 //===----------------------------------------------------------------------===//
9070 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
9071 AssumptionCache &AC, DominatorTree &DT,
9073 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
9074 CouldNotCompute(new SCEVCouldNotCompute()),
9075 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9076 ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
9077 FirstUnknown(nullptr) {}
9079 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
9080 : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
9081 CouldNotCompute(std::move(Arg.CouldNotCompute)),
9082 ValueExprMap(std::move(Arg.ValueExprMap)),
9083 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9084 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
9085 ConstantEvolutionLoopExitValue(
9086 std::move(Arg.ConstantEvolutionLoopExitValue)),
9087 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
9088 LoopDispositions(std::move(Arg.LoopDispositions)),
9089 BlockDispositions(std::move(Arg.BlockDispositions)),
9090 UnsignedRanges(std::move(Arg.UnsignedRanges)),
9091 SignedRanges(std::move(Arg.SignedRanges)),
9092 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
9093 UniquePreds(std::move(Arg.UniquePreds)),
9094 SCEVAllocator(std::move(Arg.SCEVAllocator)),
9095 FirstUnknown(Arg.FirstUnknown) {
9096 Arg.FirstUnknown = nullptr;
9099 ScalarEvolution::~ScalarEvolution() {
9100 // Iterate through all the SCEVUnknown instances and call their
9101 // destructors, so that they release their references to their values.
9102 for (SCEVUnknown *U = FirstUnknown; U;) {
9103 SCEVUnknown *Tmp = U;
9105 Tmp->~SCEVUnknown();
9107 FirstUnknown = nullptr;
9109 ValueExprMap.clear();
9111 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
9112 // that a loop had multiple computable exits.
9113 for (auto &BTCI : BackedgeTakenCounts)
9114 BTCI.second.clear();
9116 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
9117 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
9118 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
9121 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
9122 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
9125 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
9127 // Print all inner loops first
9128 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
9129 PrintLoopInfo(OS, SE, *I);
9132 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9135 SmallVector<BasicBlock *, 8> ExitBlocks;
9136 L->getExitBlocks(ExitBlocks);
9137 if (ExitBlocks.size() != 1)
9138 OS << "<multiple exits> ";
9140 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
9141 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
9143 OS << "Unpredictable backedge-taken count. ";
9148 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9151 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
9152 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
9154 OS << "Unpredictable max backedge-taken count. ";
9160 void ScalarEvolution::print(raw_ostream &OS) const {
9161 // ScalarEvolution's implementation of the print method is to print
9162 // out SCEV values of all instructions that are interesting. Doing
9163 // this potentially causes it to create new SCEV objects though,
9164 // which technically conflicts with the const qualifier. This isn't
9165 // observable from outside the class though, so casting away the
9166 // const isn't dangerous.
9167 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9169 OS << "Classifying expressions for: ";
9170 F.printAsOperand(OS, /*PrintType=*/false);
9172 for (Instruction &I : instructions(F))
9173 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
9176 const SCEV *SV = SE.getSCEV(&I);
9178 if (!isa<SCEVCouldNotCompute>(SV)) {
9180 SE.getUnsignedRange(SV).print(OS);
9182 SE.getSignedRange(SV).print(OS);
9185 const Loop *L = LI.getLoopFor(I.getParent());
9187 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
9191 if (!isa<SCEVCouldNotCompute>(AtUse)) {
9193 SE.getUnsignedRange(AtUse).print(OS);
9195 SE.getSignedRange(AtUse).print(OS);
9200 OS << "\t\t" "Exits: ";
9201 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
9202 if (!SE.isLoopInvariant(ExitValue, L)) {
9203 OS << "<<Unknown>>";
9212 OS << "Determining loop execution counts for: ";
9213 F.printAsOperand(OS, /*PrintType=*/false);
9215 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
9216 PrintLoopInfo(OS, &SE, *I);
9219 ScalarEvolution::LoopDisposition
9220 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
9221 auto &Values = LoopDispositions[S];
9222 for (auto &V : Values) {
9223 if (V.getPointer() == L)
9226 Values.emplace_back(L, LoopVariant);
9227 LoopDisposition D = computeLoopDisposition(S, L);
9228 auto &Values2 = LoopDispositions[S];
9229 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9230 if (V.getPointer() == L) {
9238 ScalarEvolution::LoopDisposition
9239 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
9240 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9242 return LoopInvariant;
9246 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
9247 case scAddRecExpr: {
9248 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9250 // If L is the addrec's loop, it's computable.
9251 if (AR->getLoop() == L)
9252 return LoopComputable;
9254 // Add recurrences are never invariant in the function-body (null loop).
9258 // This recurrence is variant w.r.t. L if L contains AR's loop.
9259 if (L->contains(AR->getLoop()))
9262 // This recurrence is invariant w.r.t. L if AR's loop contains L.
9263 if (AR->getLoop()->contains(L))
9264 return LoopInvariant;
9266 // This recurrence is variant w.r.t. L if any of its operands
9268 for (auto *Op : AR->operands())
9269 if (!isLoopInvariant(Op, L))
9272 // Otherwise it's loop-invariant.
9273 return LoopInvariant;
9279 bool HasVarying = false;
9280 for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
9281 LoopDisposition D = getLoopDisposition(Op, L);
9282 if (D == LoopVariant)
9284 if (D == LoopComputable)
9287 return HasVarying ? LoopComputable : LoopInvariant;
9290 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9291 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
9292 if (LD == LoopVariant)
9294 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
9295 if (RD == LoopVariant)
9297 return (LD == LoopInvariant && RD == LoopInvariant) ?
9298 LoopInvariant : LoopComputable;
9301 // All non-instruction values are loop invariant. All instructions are loop
9302 // invariant if they are not contained in the specified loop.
9303 // Instructions are never considered invariant in the function body
9304 // (null loop) because they are defined within the "loop".
9305 if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
9306 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
9307 return LoopInvariant;
9308 case scCouldNotCompute:
9309 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9311 llvm_unreachable("Unknown SCEV kind!");
9314 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
9315 return getLoopDisposition(S, L) == LoopInvariant;
9318 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
9319 return getLoopDisposition(S, L) == LoopComputable;
9322 ScalarEvolution::BlockDisposition
9323 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9324 auto &Values = BlockDispositions[S];
9325 for (auto &V : Values) {
9326 if (V.getPointer() == BB)
9329 Values.emplace_back(BB, DoesNotDominateBlock);
9330 BlockDisposition D = computeBlockDisposition(S, BB);
9331 auto &Values2 = BlockDispositions[S];
9332 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9333 if (V.getPointer() == BB) {
9341 ScalarEvolution::BlockDisposition
9342 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9343 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9345 return ProperlyDominatesBlock;
9349 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
9350 case scAddRecExpr: {
9351 // This uses a "dominates" query instead of "properly dominates" query
9352 // to test for proper dominance too, because the instruction which
9353 // produces the addrec's value is a PHI, and a PHI effectively properly
9354 // dominates its entire containing block.
9355 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9356 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9357 return DoesNotDominateBlock;
9359 // FALL THROUGH into SCEVNAryExpr handling.
9364 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9366 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
9368 BlockDisposition D = getBlockDisposition(*I, BB);
9369 if (D == DoesNotDominateBlock)
9370 return DoesNotDominateBlock;
9371 if (D == DominatesBlock)
9374 return Proper ? ProperlyDominatesBlock : DominatesBlock;
9377 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9378 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9379 BlockDisposition LD = getBlockDisposition(LHS, BB);
9380 if (LD == DoesNotDominateBlock)
9381 return DoesNotDominateBlock;
9382 BlockDisposition RD = getBlockDisposition(RHS, BB);
9383 if (RD == DoesNotDominateBlock)
9384 return DoesNotDominateBlock;
9385 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9386 ProperlyDominatesBlock : DominatesBlock;
9389 if (Instruction *I =
9390 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9391 if (I->getParent() == BB)
9392 return DominatesBlock;
9393 if (DT.properlyDominates(I->getParent(), BB))
9394 return ProperlyDominatesBlock;
9395 return DoesNotDominateBlock;
9397 return ProperlyDominatesBlock;
9398 case scCouldNotCompute:
9399 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9401 llvm_unreachable("Unknown SCEV kind!");
9404 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9405 return getBlockDisposition(S, BB) >= DominatesBlock;
9408 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9409 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9413 // Search for a SCEV expression node within an expression tree.
9414 // Implements SCEVTraversal::Visitor.
9419 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
9421 bool follow(const SCEV *S) {
9422 IsFound |= (S == Node);
9425 bool isDone() const { return IsFound; }
9429 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9430 SCEVSearch Search(Op);
9431 visitAll(S, Search);
9432 return Search.IsFound;
9435 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9436 ValuesAtScopes.erase(S);
9437 LoopDispositions.erase(S);
9438 BlockDispositions.erase(S);
9439 UnsignedRanges.erase(S);
9440 SignedRanges.erase(S);
9442 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
9443 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
9444 BackedgeTakenInfo &BEInfo = I->second;
9445 if (BEInfo.hasOperand(S, this)) {
9447 BackedgeTakenCounts.erase(I++);
9454 typedef DenseMap<const Loop *, std::string> VerifyMap;
9456 /// replaceSubString - Replaces all occurrences of From in Str with To.
9457 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9459 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9460 Str.replace(Pos, From.size(), To.data(), To.size());
9465 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9467 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9468 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
9469 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
9471 std::string &S = Map[L];
9473 raw_string_ostream OS(S);
9474 SE.getBackedgeTakenCount(L)->print(OS);
9476 // false and 0 are semantically equivalent. This can happen in dead loops.
9477 replaceSubString(OS.str(), "false", "0");
9478 // Remove wrap flags, their use in SCEV is highly fragile.
9479 // FIXME: Remove this when SCEV gets smarter about them.
9480 replaceSubString(OS.str(), "<nw>", "");
9481 replaceSubString(OS.str(), "<nsw>", "");
9482 replaceSubString(OS.str(), "<nuw>", "");
9487 void ScalarEvolution::verify() const {
9488 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9490 // Gather stringified backedge taken counts for all loops using SCEV's caches.
9491 // FIXME: It would be much better to store actual values instead of strings,
9492 // but SCEV pointers will change if we drop the caches.
9493 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9494 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9495 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9497 // Gather stringified backedge taken counts for all loops using a fresh
9498 // ScalarEvolution object.
9499 ScalarEvolution SE2(F, TLI, AC, DT, LI);
9500 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9501 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9503 // Now compare whether they're the same with and without caches. This allows
9504 // verifying that no pass changed the cache.
9505 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
9506 "New loops suddenly appeared!");
9508 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
9509 OldE = BackedgeDumpsOld.end(),
9510 NewI = BackedgeDumpsNew.begin();
9511 OldI != OldE; ++OldI, ++NewI) {
9512 assert(OldI->first == NewI->first && "Loop order changed!");
9514 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
9516 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
9517 // means that a pass is buggy or SCEV has to learn a new pattern but is
9518 // usually not harmful.
9519 if (OldI->second != NewI->second &&
9520 OldI->second.find("undef") == std::string::npos &&
9521 NewI->second.find("undef") == std::string::npos &&
9522 OldI->second != "***COULDNOTCOMPUTE***" &&
9523 NewI->second != "***COULDNOTCOMPUTE***") {
9524 dbgs() << "SCEVValidator: SCEV for loop '"
9525 << OldI->first->getHeader()->getName()
9526 << "' changed from '" << OldI->second
9527 << "' to '" << NewI->second << "'!\n";
9532 // TODO: Verify more things.
9535 char ScalarEvolutionAnalysis::PassID;
9537 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
9538 AnalysisManager<Function> *AM) {
9539 return ScalarEvolution(F, AM->getResult<TargetLibraryAnalysis>(F),
9540 AM->getResult<AssumptionAnalysis>(F),
9541 AM->getResult<DominatorTreeAnalysis>(F),
9542 AM->getResult<LoopAnalysis>(F));
9546 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> *AM) {
9547 AM->getResult<ScalarEvolutionAnalysis>(F).print(OS);
9548 return PreservedAnalyses::all();
9551 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
9552 "Scalar Evolution Analysis", false, true)
9553 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
9554 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
9555 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
9556 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
9557 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
9558 "Scalar Evolution Analysis", false, true)
9559 char ScalarEvolutionWrapperPass::ID = 0;
9561 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
9562 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
9565 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
9566 SE.reset(new ScalarEvolution(
9567 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
9568 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
9569 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
9570 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
9574 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
9576 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
9580 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
9587 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
9588 AU.setPreservesAll();
9589 AU.addRequiredTransitive<AssumptionCacheTracker>();
9590 AU.addRequiredTransitive<LoopInfoWrapperPass>();
9591 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
9592 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
9595 const SCEVPredicate *
9596 ScalarEvolution::getEqualPredicate(const SCEVUnknown *LHS,
9597 const SCEVConstant *RHS) {
9598 FoldingSetNodeID ID;
9599 // Unique this node based on the arguments
9600 ID.AddInteger(SCEVPredicate::P_Equal);
9604 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
9606 SCEVEqualPredicate *Eq = new (SCEVAllocator)
9607 SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
9608 UniquePreds.InsertNode(Eq, IP);
9613 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
9615 static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE,
9616 SCEVUnionPredicate &A) {
9617 SCEVPredicateRewriter Rewriter(SE, A);
9618 return Rewriter.visit(Scev);
9621 SCEVPredicateRewriter(ScalarEvolution &SE, SCEVUnionPredicate &P)
9622 : SCEVRewriteVisitor(SE), P(P) {}
9624 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
9625 auto ExprPreds = P.getPredicatesForExpr(Expr);
9626 for (auto *Pred : ExprPreds)
9627 if (const auto *IPred = dyn_cast<const SCEVEqualPredicate>(Pred))
9628 if (IPred->getLHS() == Expr)
9629 return IPred->getRHS();
9635 SCEVUnionPredicate &P;
9637 } // end anonymous namespace
9639 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *Scev,
9640 SCEVUnionPredicate &Preds) {
9641 return SCEVPredicateRewriter::rewrite(Scev, *this, Preds);
9645 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
9646 SCEVPredicateKind Kind)
9647 : FastID(ID), Kind(Kind) {}
9649 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
9650 const SCEVUnknown *LHS,
9651 const SCEVConstant *RHS)
9652 : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {}
9654 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
9655 const auto *Op = dyn_cast<const SCEVEqualPredicate>(N);
9660 return Op->LHS == LHS && Op->RHS == RHS;
9663 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
9665 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
9667 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
9668 OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
9671 /// Union predicates don't get cached so create a dummy set ID for it.
9672 SCEVUnionPredicate::SCEVUnionPredicate()
9673 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
9675 bool SCEVUnionPredicate::isAlwaysTrue() const {
9676 return std::all_of(Preds.begin(), Preds.end(),
9677 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
9680 ArrayRef<const SCEVPredicate *>
9681 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
9682 auto I = SCEVToPreds.find(Expr);
9683 if (I == SCEVToPreds.end())
9684 return ArrayRef<const SCEVPredicate *>();
9688 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
9689 if (const auto *Set = dyn_cast<const SCEVUnionPredicate>(N))
9691 Set->Preds.begin(), Set->Preds.end(),
9692 [this](const SCEVPredicate *I) { return this->implies(I); });
9694 auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
9695 if (ScevPredsIt == SCEVToPreds.end())
9697 auto &SCEVPreds = ScevPredsIt->second;
9699 return std::any_of(SCEVPreds.begin(), SCEVPreds.end(),
9700 [N](const SCEVPredicate *I) { return I->implies(N); });
9703 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
9705 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
9706 for (auto Pred : Preds)
9707 Pred->print(OS, Depth);
9710 void SCEVUnionPredicate::add(const SCEVPredicate *N) {
9711 if (const auto *Set = dyn_cast<const SCEVUnionPredicate>(N)) {
9712 for (auto Pred : Set->Preds)
9720 const SCEV *Key = N->getExpr();
9721 assert(Key && "Only SCEVUnionPredicate doesn't have an "
9722 " associated expression!");
9724 SCEVToPreds[Key].push_back(N);