1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/Support/CommandLine.h"
87 #include "llvm/Support/Debug.h"
88 #include "llvm/Support/ErrorHandling.h"
89 #include "llvm/Support/MathExtras.h"
90 #include "llvm/Support/raw_ostream.h"
91 #include "llvm/Support/SaveAndRestore.h"
95 #define DEBUG_TYPE "scalar-evolution"
97 STATISTIC(NumArrayLenItCounts,
98 "Number of trip counts computed with array length");
99 STATISTIC(NumTripCountsComputed,
100 "Number of loops with predictable loop counts");
101 STATISTIC(NumTripCountsNotComputed,
102 "Number of loops without predictable loop counts");
103 STATISTIC(NumBruteForceTripCountsComputed,
104 "Number of loops with trip counts computed by force");
106 static cl::opt<unsigned>
107 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
108 cl::desc("Maximum number of iterations SCEV will "
109 "symbolically execute a constant "
113 // FIXME: Enable this with XDEBUG when the test suite is clean.
115 VerifySCEV("verify-scev",
116 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
118 //===----------------------------------------------------------------------===//
119 // SCEV class definitions
120 //===----------------------------------------------------------------------===//
122 //===----------------------------------------------------------------------===//
123 // Implementation of the SCEV class.
126 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
127 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 (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1136 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), 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 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1272 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1273 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1275 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1276 // "S+X does not sign/unsign-overflow".
1279 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1280 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1281 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1284 // 2. Direct overflow check on the step operation's expression.
1285 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1286 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1287 const SCEV *OperandExtendedStart =
1288 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1289 (SE->*GetExtendExpr)(Step, WideTy));
1290 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1291 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1292 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1293 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1294 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1295 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1300 // 3. Loop precondition.
1301 ICmpInst::Predicate Pred;
1302 const SCEV *OverflowLimit =
1303 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1305 if (OverflowLimit &&
1306 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1312 // Get the normalized zero or sign extended expression for this AddRec's Start.
1313 template <typename ExtendOpTy>
1314 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1315 ScalarEvolution *SE) {
1316 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1318 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1320 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1322 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1323 (SE->*GetExtendExpr)(PreStart, Ty));
1326 // Try to prove away overflow by looking at "nearby" add recurrences. A
1327 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1328 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1332 // {S,+,X} == {S-T,+,X} + T
1333 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1335 // If ({S-T,+,X} + T) does not overflow ... (1)
1337 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1339 // If {S-T,+,X} does not overflow ... (2)
1341 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1342 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1344 // If (S-T)+T does not overflow ... (3)
1346 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1347 // == {Ext(S),+,Ext(X)} == LHS
1349 // Thus, if (1), (2) and (3) are true for some T, then
1350 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1352 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1353 // does not overflow" restricted to the 0th iteration. Therefore we only need
1354 // to check for (1) and (2).
1356 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1357 // is `Delta` (defined below).
1359 template <typename ExtendOpTy>
1360 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1363 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1365 // We restrict `Start` to a constant to prevent SCEV from spending too much
1366 // time here. It is correct (but more expensive) to continue with a
1367 // non-constant `Start` and do a general SCEV subtraction to compute
1368 // `PreStart` below.
1370 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1374 APInt StartAI = StartC->getValue()->getValue();
1376 for (unsigned Delta : {-2, -1, 1, 2}) {
1377 const SCEV *PreStart = getConstant(StartAI - Delta);
1379 // Give up if we don't already have the add recurrence we need because
1380 // actually constructing an add recurrence is relatively expensive.
1381 const SCEVAddRecExpr *PreAR = [&]() {
1382 FoldingSetNodeID ID;
1383 ID.AddInteger(scAddRecExpr);
1384 ID.AddPointer(PreStart);
1385 ID.AddPointer(Step);
1388 return static_cast<SCEVAddRecExpr *>(
1389 this->UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
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 // The cast wasn't folded; create an explicit cast node.
1563 // Recompute the insert position, as it may have been invalidated.
1564 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1565 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1567 UniqueSCEVs.InsertNode(S, IP);
1571 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1573 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1574 "This is not an extending conversion!");
1575 assert(isSCEVable(Ty) &&
1576 "This is not a conversion to a SCEVable type!");
1577 Ty = getEffectiveSCEVType(Ty);
1579 // Fold if the operand is constant.
1580 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1582 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1584 // sext(sext(x)) --> sext(x)
1585 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1586 return getSignExtendExpr(SS->getOperand(), Ty);
1588 // sext(zext(x)) --> zext(x)
1589 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1590 return getZeroExtendExpr(SZ->getOperand(), Ty);
1592 // Before doing any expensive analysis, check to see if we've already
1593 // computed a SCEV for this Op and Ty.
1594 FoldingSetNodeID ID;
1595 ID.AddInteger(scSignExtend);
1599 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1601 // If the input value is provably positive, build a zext instead.
1602 if (isKnownNonNegative(Op))
1603 return getZeroExtendExpr(Op, Ty);
1605 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1606 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1607 // It's possible the bits taken off by the truncate were all sign bits. If
1608 // so, we should be able to simplify this further.
1609 const SCEV *X = ST->getOperand();
1610 ConstantRange CR = getSignedRange(X);
1611 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1612 unsigned NewBits = getTypeSizeInBits(Ty);
1613 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1614 CR.sextOrTrunc(NewBits)))
1615 return getTruncateOrSignExtend(X, Ty);
1618 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1619 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1620 if (SA->getNumOperands() == 2) {
1621 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1622 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1624 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1625 const APInt &C1 = SC1->getValue()->getValue();
1626 const APInt &C2 = SC2->getValue()->getValue();
1627 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1628 C2.ugt(C1) && C2.isPowerOf2())
1629 return getAddExpr(getSignExtendExpr(SC1, Ty),
1630 getSignExtendExpr(SMul, Ty));
1635 // If the input value is a chrec scev, and we can prove that the value
1636 // did not overflow the old, smaller, value, we can sign extend all of the
1637 // operands (often constants). This allows analysis of something like
1638 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1639 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1640 if (AR->isAffine()) {
1641 const SCEV *Start = AR->getStart();
1642 const SCEV *Step = AR->getStepRecurrence(*this);
1643 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1644 const Loop *L = AR->getLoop();
1646 // If we have special knowledge that this addrec won't overflow,
1647 // we don't need to do any further analysis.
1648 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1649 return getAddRecExpr(
1650 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1651 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1653 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1654 // Note that this serves two purposes: It filters out loops that are
1655 // simply not analyzable, and it covers the case where this code is
1656 // being called from within backedge-taken count analysis, such that
1657 // attempting to ask for the backedge-taken count would likely result
1658 // in infinite recursion. In the later case, the analysis code will
1659 // cope with a conservative value, and it will take care to purge
1660 // that value once it has finished.
1661 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1662 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1663 // Manually compute the final value for AR, checking for
1666 // Check whether the backedge-taken count can be losslessly casted to
1667 // the addrec's type. The count is always unsigned.
1668 const SCEV *CastedMaxBECount =
1669 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1670 const SCEV *RecastedMaxBECount =
1671 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1672 if (MaxBECount == RecastedMaxBECount) {
1673 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1674 // Check whether Start+Step*MaxBECount has no signed overflow.
1675 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1676 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1677 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1678 const SCEV *WideMaxBECount =
1679 getZeroExtendExpr(CastedMaxBECount, WideTy);
1680 const SCEV *OperandExtendedAdd =
1681 getAddExpr(WideStart,
1682 getMulExpr(WideMaxBECount,
1683 getSignExtendExpr(Step, WideTy)));
1684 if (SAdd == OperandExtendedAdd) {
1685 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1686 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1687 // Return the expression with the addrec on the outside.
1688 return getAddRecExpr(
1689 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1690 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1692 // Similar to above, only this time treat the step value as unsigned.
1693 // This covers loops that count up with an unsigned step.
1694 OperandExtendedAdd =
1695 getAddExpr(WideStart,
1696 getMulExpr(WideMaxBECount,
1697 getZeroExtendExpr(Step, WideTy)));
1698 if (SAdd == OperandExtendedAdd) {
1699 // If AR wraps around then
1701 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1702 // => SAdd != OperandExtendedAdd
1704 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1705 // (SAdd == OperandExtendedAdd => AR is NW)
1707 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1709 // Return the expression with the addrec on the outside.
1710 return getAddRecExpr(
1711 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1712 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1716 // If the backedge is guarded by a comparison with the pre-inc value
1717 // the addrec is safe. Also, if the entry is guarded by a comparison
1718 // with the start value and the backedge is guarded by a comparison
1719 // with the post-inc value, the addrec is safe.
1720 ICmpInst::Predicate Pred;
1721 const SCEV *OverflowLimit =
1722 getSignedOverflowLimitForStep(Step, &Pred, this);
1723 if (OverflowLimit &&
1724 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1725 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1726 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1728 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1729 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1730 return getAddRecExpr(
1731 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1732 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1735 // If Start and Step are constants, check if we can apply this
1737 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1738 auto SC1 = dyn_cast<SCEVConstant>(Start);
1739 auto SC2 = dyn_cast<SCEVConstant>(Step);
1741 const APInt &C1 = SC1->getValue()->getValue();
1742 const APInt &C2 = SC2->getValue()->getValue();
1743 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1745 Start = getSignExtendExpr(Start, Ty);
1746 const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1747 AR->getNoWrapFlags());
1748 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1752 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1753 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1754 return getAddRecExpr(
1755 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1756 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1760 // The cast wasn't folded; create an explicit cast node.
1761 // Recompute the insert position, as it may have been invalidated.
1762 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1763 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1765 UniqueSCEVs.InsertNode(S, IP);
1769 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1770 /// unspecified bits out to the given type.
1772 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1774 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1775 "This is not an extending conversion!");
1776 assert(isSCEVable(Ty) &&
1777 "This is not a conversion to a SCEVable type!");
1778 Ty = getEffectiveSCEVType(Ty);
1780 // Sign-extend negative constants.
1781 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1782 if (SC->getValue()->getValue().isNegative())
1783 return getSignExtendExpr(Op, Ty);
1785 // Peel off a truncate cast.
1786 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1787 const SCEV *NewOp = T->getOperand();
1788 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1789 return getAnyExtendExpr(NewOp, Ty);
1790 return getTruncateOrNoop(NewOp, Ty);
1793 // Next try a zext cast. If the cast is folded, use it.
1794 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1795 if (!isa<SCEVZeroExtendExpr>(ZExt))
1798 // Next try a sext cast. If the cast is folded, use it.
1799 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1800 if (!isa<SCEVSignExtendExpr>(SExt))
1803 // Force the cast to be folded into the operands of an addrec.
1804 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1805 SmallVector<const SCEV *, 4> Ops;
1806 for (const SCEV *Op : AR->operands())
1807 Ops.push_back(getAnyExtendExpr(Op, Ty));
1808 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1811 // If the expression is obviously signed, use the sext cast value.
1812 if (isa<SCEVSMaxExpr>(Op))
1815 // Absent any other information, use the zext cast value.
1819 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1820 /// a list of operands to be added under the given scale, update the given
1821 /// map. This is a helper function for getAddRecExpr. As an example of
1822 /// what it does, given a sequence of operands that would form an add
1823 /// expression like this:
1825 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1827 /// where A and B are constants, update the map with these values:
1829 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1831 /// and add 13 + A*B*29 to AccumulatedConstant.
1832 /// This will allow getAddRecExpr to produce this:
1834 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1836 /// This form often exposes folding opportunities that are hidden in
1837 /// the original operand list.
1839 /// Return true iff it appears that any interesting folding opportunities
1840 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1841 /// the common case where no interesting opportunities are present, and
1842 /// is also used as a check to avoid infinite recursion.
1845 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1846 SmallVectorImpl<const SCEV *> &NewOps,
1847 APInt &AccumulatedConstant,
1848 const SCEV *const *Ops, size_t NumOperands,
1850 ScalarEvolution &SE) {
1851 bool Interesting = false;
1853 // Iterate over the add operands. They are sorted, with constants first.
1855 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1857 // Pull a buried constant out to the outside.
1858 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1860 AccumulatedConstant += Scale * C->getValue()->getValue();
1863 // Next comes everything else. We're especially interested in multiplies
1864 // here, but they're in the middle, so just visit the rest with one loop.
1865 for (; i != NumOperands; ++i) {
1866 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1867 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1869 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1870 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1871 // A multiplication of a constant with another add; recurse.
1872 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1874 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1875 Add->op_begin(), Add->getNumOperands(),
1878 // A multiplication of a constant with some other value. Update
1880 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1881 const SCEV *Key = SE.getMulExpr(MulOps);
1882 auto Pair = M.insert(std::make_pair(Key, NewScale));
1884 NewOps.push_back(Pair.first->first);
1886 Pair.first->second += NewScale;
1887 // The map already had an entry for this value, which may indicate
1888 // a folding opportunity.
1893 // An ordinary operand. Update the map.
1894 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1895 M.insert(std::make_pair(Ops[i], Scale));
1897 NewOps.push_back(Pair.first->first);
1899 Pair.first->second += Scale;
1900 // The map already had an entry for this value, which may indicate
1901 // a folding opportunity.
1911 struct APIntCompare {
1912 bool operator()(const APInt &LHS, const APInt &RHS) const {
1913 return LHS.ult(RHS);
1918 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1919 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1920 // can't-overflow flags for the operation if possible.
1921 static SCEV::NoWrapFlags
1922 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1923 const SmallVectorImpl<const SCEV *> &Ops,
1924 SCEV::NoWrapFlags OldFlags) {
1925 using namespace std::placeholders;
1928 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1930 assert(CanAnalyze && "don't call from other places!");
1932 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1933 SCEV::NoWrapFlags SignOrUnsignWrap =
1934 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1936 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1937 auto IsKnownNonNegative =
1938 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1940 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1941 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1942 return ScalarEvolution::setFlags(OldFlags,
1943 (SCEV::NoWrapFlags)SignOrUnsignMask);
1948 /// getAddExpr - Get a canonical add expression, or something simpler if
1950 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1951 SCEV::NoWrapFlags Flags) {
1952 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1953 "only nuw or nsw allowed");
1954 assert(!Ops.empty() && "Cannot get empty add!");
1955 if (Ops.size() == 1) return Ops[0];
1957 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1958 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1959 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1960 "SCEVAddExpr operand types don't match!");
1963 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1965 // Sort by complexity, this groups all similar expression types together.
1966 GroupByComplexity(Ops, &LI);
1968 // If there are any constants, fold them together.
1970 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1972 assert(Idx < Ops.size());
1973 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1974 // We found two constants, fold them together!
1975 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1976 RHSC->getValue()->getValue());
1977 if (Ops.size() == 2) return Ops[0];
1978 Ops.erase(Ops.begin()+1); // Erase the folded element
1979 LHSC = cast<SCEVConstant>(Ops[0]);
1982 // If we are left with a constant zero being added, strip it off.
1983 if (LHSC->getValue()->isZero()) {
1984 Ops.erase(Ops.begin());
1988 if (Ops.size() == 1) return Ops[0];
1991 // Okay, check to see if the same value occurs in the operand list more than
1992 // once. If so, merge them together into an multiply expression. Since we
1993 // sorted the list, these values are required to be adjacent.
1994 Type *Ty = Ops[0]->getType();
1995 bool FoundMatch = false;
1996 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1997 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1998 // Scan ahead to count how many equal operands there are.
2000 while (i+Count != e && Ops[i+Count] == Ops[i])
2002 // Merge the values into a multiply.
2003 const SCEV *Scale = getConstant(Ty, Count);
2004 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2005 if (Ops.size() == Count)
2008 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2009 --i; e -= Count - 1;
2013 return getAddExpr(Ops, Flags);
2015 // Check for truncates. If all the operands are truncated from the same
2016 // type, see if factoring out the truncate would permit the result to be
2017 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2018 // if the contents of the resulting outer trunc fold to something simple.
2019 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2020 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2021 Type *DstType = Trunc->getType();
2022 Type *SrcType = Trunc->getOperand()->getType();
2023 SmallVector<const SCEV *, 8> LargeOps;
2025 // Check all the operands to see if they can be represented in the
2026 // source type of the truncate.
2027 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2028 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2029 if (T->getOperand()->getType() != SrcType) {
2033 LargeOps.push_back(T->getOperand());
2034 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2035 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2036 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2037 SmallVector<const SCEV *, 8> LargeMulOps;
2038 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2039 if (const SCEVTruncateExpr *T =
2040 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2041 if (T->getOperand()->getType() != SrcType) {
2045 LargeMulOps.push_back(T->getOperand());
2046 } else if (const SCEVConstant *C =
2047 dyn_cast<SCEVConstant>(M->getOperand(j))) {
2048 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2055 LargeOps.push_back(getMulExpr(LargeMulOps));
2062 // Evaluate the expression in the larger type.
2063 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2064 // If it folds to something simple, use it. Otherwise, don't.
2065 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2066 return getTruncateExpr(Fold, DstType);
2070 // Skip past any other cast SCEVs.
2071 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2074 // If there are add operands they would be next.
2075 if (Idx < Ops.size()) {
2076 bool DeletedAdd = false;
2077 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2078 // If we have an add, expand the add operands onto the end of the operands
2080 Ops.erase(Ops.begin()+Idx);
2081 Ops.append(Add->op_begin(), Add->op_end());
2085 // If we deleted at least one add, we added operands to the end of the list,
2086 // and they are not necessarily sorted. Recurse to resort and resimplify
2087 // any operands we just acquired.
2089 return getAddExpr(Ops);
2092 // Skip over the add expression until we get to a multiply.
2093 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2096 // Check to see if there are any folding opportunities present with
2097 // operands multiplied by constant values.
2098 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2099 uint64_t BitWidth = getTypeSizeInBits(Ty);
2100 DenseMap<const SCEV *, APInt> M;
2101 SmallVector<const SCEV *, 8> NewOps;
2102 APInt AccumulatedConstant(BitWidth, 0);
2103 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2104 Ops.data(), Ops.size(),
2105 APInt(BitWidth, 1), *this)) {
2106 // Some interesting folding opportunity is present, so its worthwhile to
2107 // re-generate the operands list. Group the operands by constant scale,
2108 // to avoid multiplying by the same constant scale multiple times.
2109 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2110 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
2111 E = NewOps.end(); I != E; ++I)
2112 MulOpLists[M.find(*I)->second].push_back(*I);
2113 // Re-generate the operands list.
2115 if (AccumulatedConstant != 0)
2116 Ops.push_back(getConstant(AccumulatedConstant));
2117 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
2118 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
2120 Ops.push_back(getMulExpr(getConstant(I->first),
2121 getAddExpr(I->second)));
2124 if (Ops.size() == 1)
2126 return getAddExpr(Ops);
2130 // If we are adding something to a multiply expression, make sure the
2131 // something is not already an operand of the multiply. If so, merge it into
2133 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2134 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2135 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2136 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2137 if (isa<SCEVConstant>(MulOpSCEV))
2139 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2140 if (MulOpSCEV == Ops[AddOp]) {
2141 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2142 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2143 if (Mul->getNumOperands() != 2) {
2144 // If the multiply has more than two operands, we must get the
2146 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2147 Mul->op_begin()+MulOp);
2148 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2149 InnerMul = getMulExpr(MulOps);
2151 const SCEV *One = getOne(Ty);
2152 const SCEV *AddOne = getAddExpr(One, InnerMul);
2153 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2154 if (Ops.size() == 2) return OuterMul;
2156 Ops.erase(Ops.begin()+AddOp);
2157 Ops.erase(Ops.begin()+Idx-1);
2159 Ops.erase(Ops.begin()+Idx);
2160 Ops.erase(Ops.begin()+AddOp-1);
2162 Ops.push_back(OuterMul);
2163 return getAddExpr(Ops);
2166 // Check this multiply against other multiplies being added together.
2167 for (unsigned OtherMulIdx = Idx+1;
2168 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2170 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2171 // If MulOp occurs in OtherMul, we can fold the two multiplies
2173 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2174 OMulOp != e; ++OMulOp)
2175 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2176 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2177 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2178 if (Mul->getNumOperands() != 2) {
2179 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2180 Mul->op_begin()+MulOp);
2181 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2182 InnerMul1 = getMulExpr(MulOps);
2184 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2185 if (OtherMul->getNumOperands() != 2) {
2186 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2187 OtherMul->op_begin()+OMulOp);
2188 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2189 InnerMul2 = getMulExpr(MulOps);
2191 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2192 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2193 if (Ops.size() == 2) return OuterMul;
2194 Ops.erase(Ops.begin()+Idx);
2195 Ops.erase(Ops.begin()+OtherMulIdx-1);
2196 Ops.push_back(OuterMul);
2197 return getAddExpr(Ops);
2203 // If there are any add recurrences in the operands list, see if any other
2204 // added values are loop invariant. If so, we can fold them into the
2206 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2209 // Scan over all recurrences, trying to fold loop invariants into them.
2210 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2211 // Scan all of the other operands to this add and add them to the vector if
2212 // they are loop invariant w.r.t. the recurrence.
2213 SmallVector<const SCEV *, 8> LIOps;
2214 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2215 const Loop *AddRecLoop = AddRec->getLoop();
2216 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2217 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2218 LIOps.push_back(Ops[i]);
2219 Ops.erase(Ops.begin()+i);
2223 // If we found some loop invariants, fold them into the recurrence.
2224 if (!LIOps.empty()) {
2225 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2226 LIOps.push_back(AddRec->getStart());
2228 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2230 AddRecOps[0] = getAddExpr(LIOps);
2232 // Build the new addrec. Propagate the NUW and NSW flags if both the
2233 // outer add and the inner addrec are guaranteed to have no overflow.
2234 // Always propagate NW.
2235 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2236 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2238 // If all of the other operands were loop invariant, we are done.
2239 if (Ops.size() == 1) return NewRec;
2241 // Otherwise, add the folded AddRec by the non-invariant parts.
2242 for (unsigned i = 0;; ++i)
2243 if (Ops[i] == AddRec) {
2247 return getAddExpr(Ops);
2250 // Okay, if there weren't any loop invariants to be folded, check to see if
2251 // there are multiple AddRec's with the same loop induction variable being
2252 // added together. If so, we can fold them.
2253 for (unsigned OtherIdx = Idx+1;
2254 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2256 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2257 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2258 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2260 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2262 if (const SCEVAddRecExpr *OtherAddRec =
2263 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2264 if (OtherAddRec->getLoop() == AddRecLoop) {
2265 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2267 if (i >= AddRecOps.size()) {
2268 AddRecOps.append(OtherAddRec->op_begin()+i,
2269 OtherAddRec->op_end());
2272 AddRecOps[i] = getAddExpr(AddRecOps[i],
2273 OtherAddRec->getOperand(i));
2275 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2277 // Step size has changed, so we cannot guarantee no self-wraparound.
2278 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2279 return getAddExpr(Ops);
2282 // Otherwise couldn't fold anything into this recurrence. Move onto the
2286 // Okay, it looks like we really DO need an add expr. Check to see if we
2287 // already have one, otherwise create a new one.
2288 FoldingSetNodeID ID;
2289 ID.AddInteger(scAddExpr);
2290 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2291 ID.AddPointer(Ops[i]);
2294 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2296 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2297 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2298 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2300 UniqueSCEVs.InsertNode(S, IP);
2302 S->setNoWrapFlags(Flags);
2306 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2308 if (j > 1 && k / j != i) Overflow = true;
2312 /// Compute the result of "n choose k", the binomial coefficient. If an
2313 /// intermediate computation overflows, Overflow will be set and the return will
2314 /// be garbage. Overflow is not cleared on absence of overflow.
2315 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2316 // We use the multiplicative formula:
2317 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2318 // At each iteration, we take the n-th term of the numeral and divide by the
2319 // (k-n)th term of the denominator. This division will always produce an
2320 // integral result, and helps reduce the chance of overflow in the
2321 // intermediate computations. However, we can still overflow even when the
2322 // final result would fit.
2324 if (n == 0 || n == k) return 1;
2325 if (k > n) return 0;
2331 for (uint64_t i = 1; i <= k; ++i) {
2332 r = umul_ov(r, n-(i-1), Overflow);
2338 /// Determine if any of the operands in this SCEV are a constant or if
2339 /// any of the add or multiply expressions in this SCEV contain a constant.
2340 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2341 SmallVector<const SCEV *, 4> Ops;
2342 Ops.push_back(StartExpr);
2343 while (!Ops.empty()) {
2344 const SCEV *CurrentExpr = Ops.pop_back_val();
2345 if (isa<SCEVConstant>(*CurrentExpr))
2348 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2349 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2350 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2356 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2358 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2359 SCEV::NoWrapFlags Flags) {
2360 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2361 "only nuw or nsw allowed");
2362 assert(!Ops.empty() && "Cannot get empty mul!");
2363 if (Ops.size() == 1) return Ops[0];
2365 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2366 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2367 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2368 "SCEVMulExpr operand types don't match!");
2371 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2373 // Sort by complexity, this groups all similar expression types together.
2374 GroupByComplexity(Ops, &LI);
2376 // If there are any constants, fold them together.
2378 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2380 // C1*(C2+V) -> C1*C2 + C1*V
2381 if (Ops.size() == 2)
2382 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2383 // If any of Add's ops are Adds or Muls with a constant,
2384 // apply this transformation as well.
2385 if (Add->getNumOperands() == 2)
2386 if (containsConstantSomewhere(Add))
2387 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2388 getMulExpr(LHSC, Add->getOperand(1)));
2391 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2392 // We found two constants, fold them together!
2393 ConstantInt *Fold = ConstantInt::get(getContext(),
2394 LHSC->getValue()->getValue() *
2395 RHSC->getValue()->getValue());
2396 Ops[0] = getConstant(Fold);
2397 Ops.erase(Ops.begin()+1); // Erase the folded element
2398 if (Ops.size() == 1) return Ops[0];
2399 LHSC = cast<SCEVConstant>(Ops[0]);
2402 // If we are left with a constant one being multiplied, strip it off.
2403 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2404 Ops.erase(Ops.begin());
2406 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2407 // If we have a multiply of zero, it will always be zero.
2409 } else if (Ops[0]->isAllOnesValue()) {
2410 // If we have a mul by -1 of an add, try distributing the -1 among the
2412 if (Ops.size() == 2) {
2413 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2414 SmallVector<const SCEV *, 4> NewOps;
2415 bool AnyFolded = false;
2416 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2417 E = Add->op_end(); I != E; ++I) {
2418 const SCEV *Mul = getMulExpr(Ops[0], *I);
2419 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2420 NewOps.push_back(Mul);
2423 return getAddExpr(NewOps);
2425 else if (const SCEVAddRecExpr *
2426 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2427 // Negation preserves a recurrence's no self-wrap property.
2428 SmallVector<const SCEV *, 4> Operands;
2429 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2430 E = AddRec->op_end(); I != E; ++I) {
2431 Operands.push_back(getMulExpr(Ops[0], *I));
2433 return getAddRecExpr(Operands, AddRec->getLoop(),
2434 AddRec->getNoWrapFlags(SCEV::FlagNW));
2439 if (Ops.size() == 1)
2443 // Skip over the add expression until we get to a multiply.
2444 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2447 // If there are mul operands inline them all into this expression.
2448 if (Idx < Ops.size()) {
2449 bool DeletedMul = false;
2450 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2451 // If we have an mul, expand the mul operands onto the end of the operands
2453 Ops.erase(Ops.begin()+Idx);
2454 Ops.append(Mul->op_begin(), Mul->op_end());
2458 // If we deleted at least one mul, we added operands to the end of the list,
2459 // and they are not necessarily sorted. Recurse to resort and resimplify
2460 // any operands we just acquired.
2462 return getMulExpr(Ops);
2465 // If there are any add recurrences in the operands list, see if any other
2466 // added values are loop invariant. If so, we can fold them into the
2468 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2471 // Scan over all recurrences, trying to fold loop invariants into them.
2472 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2473 // Scan all of the other operands to this mul and add them to the vector if
2474 // they are loop invariant w.r.t. the recurrence.
2475 SmallVector<const SCEV *, 8> LIOps;
2476 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2477 const Loop *AddRecLoop = AddRec->getLoop();
2478 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2479 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2480 LIOps.push_back(Ops[i]);
2481 Ops.erase(Ops.begin()+i);
2485 // If we found some loop invariants, fold them into the recurrence.
2486 if (!LIOps.empty()) {
2487 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2488 SmallVector<const SCEV *, 4> NewOps;
2489 NewOps.reserve(AddRec->getNumOperands());
2490 const SCEV *Scale = getMulExpr(LIOps);
2491 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2492 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2494 // Build the new addrec. Propagate the NUW and NSW flags if both the
2495 // outer mul and the inner addrec are guaranteed to have no overflow.
2497 // No self-wrap cannot be guaranteed after changing the step size, but
2498 // will be inferred if either NUW or NSW is true.
2499 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2500 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2502 // If all of the other operands were loop invariant, we are done.
2503 if (Ops.size() == 1) return NewRec;
2505 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2506 for (unsigned i = 0;; ++i)
2507 if (Ops[i] == AddRec) {
2511 return getMulExpr(Ops);
2514 // Okay, if there weren't any loop invariants to be folded, check to see if
2515 // there are multiple AddRec's with the same loop induction variable being
2516 // multiplied together. If so, we can fold them.
2518 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2519 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2520 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2521 // ]]],+,...up to x=2n}.
2522 // Note that the arguments to choose() are always integers with values
2523 // known at compile time, never SCEV objects.
2525 // The implementation avoids pointless extra computations when the two
2526 // addrec's are of different length (mathematically, it's equivalent to
2527 // an infinite stream of zeros on the right).
2528 bool OpsModified = false;
2529 for (unsigned OtherIdx = Idx+1;
2530 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2532 const SCEVAddRecExpr *OtherAddRec =
2533 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2534 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2537 bool Overflow = false;
2538 Type *Ty = AddRec->getType();
2539 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2540 SmallVector<const SCEV*, 7> AddRecOps;
2541 for (int x = 0, xe = AddRec->getNumOperands() +
2542 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2543 const SCEV *Term = getZero(Ty);
2544 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2545 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2546 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2547 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2548 z < ze && !Overflow; ++z) {
2549 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2551 if (LargerThan64Bits)
2552 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2554 Coeff = Coeff1*Coeff2;
2555 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2556 const SCEV *Term1 = AddRec->getOperand(y-z);
2557 const SCEV *Term2 = OtherAddRec->getOperand(z);
2558 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2561 AddRecOps.push_back(Term);
2564 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2566 if (Ops.size() == 2) return NewAddRec;
2567 Ops[Idx] = NewAddRec;
2568 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2570 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2576 return getMulExpr(Ops);
2578 // Otherwise couldn't fold anything into this recurrence. Move onto the
2582 // Okay, it looks like we really DO need an mul expr. Check to see if we
2583 // already have one, otherwise create a new one.
2584 FoldingSetNodeID ID;
2585 ID.AddInteger(scMulExpr);
2586 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2587 ID.AddPointer(Ops[i]);
2590 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2592 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2593 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2594 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2596 UniqueSCEVs.InsertNode(S, IP);
2598 S->setNoWrapFlags(Flags);
2602 /// getUDivExpr - Get a canonical unsigned division expression, or something
2603 /// simpler if possible.
2604 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2606 assert(getEffectiveSCEVType(LHS->getType()) ==
2607 getEffectiveSCEVType(RHS->getType()) &&
2608 "SCEVUDivExpr operand types don't match!");
2610 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2611 if (RHSC->getValue()->equalsInt(1))
2612 return LHS; // X udiv 1 --> x
2613 // If the denominator is zero, the result of the udiv is undefined. Don't
2614 // try to analyze it, because the resolution chosen here may differ from
2615 // the resolution chosen in other parts of the compiler.
2616 if (!RHSC->getValue()->isZero()) {
2617 // Determine if the division can be folded into the operands of
2619 // TODO: Generalize this to non-constants by using known-bits information.
2620 Type *Ty = LHS->getType();
2621 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2622 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2623 // For non-power-of-two values, effectively round the value up to the
2624 // nearest power of two.
2625 if (!RHSC->getValue()->getValue().isPowerOf2())
2627 IntegerType *ExtTy =
2628 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2629 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2630 if (const SCEVConstant *Step =
2631 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2632 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2633 const APInt &StepInt = Step->getValue()->getValue();
2634 const APInt &DivInt = RHSC->getValue()->getValue();
2635 if (!StepInt.urem(DivInt) &&
2636 getZeroExtendExpr(AR, ExtTy) ==
2637 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2638 getZeroExtendExpr(Step, ExtTy),
2639 AR->getLoop(), SCEV::FlagAnyWrap)) {
2640 SmallVector<const SCEV *, 4> Operands;
2641 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2642 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2643 return getAddRecExpr(Operands, AR->getLoop(),
2646 /// Get a canonical UDivExpr for a recurrence.
2647 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2648 // We can currently only fold X%N if X is constant.
2649 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2650 if (StartC && !DivInt.urem(StepInt) &&
2651 getZeroExtendExpr(AR, ExtTy) ==
2652 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2653 getZeroExtendExpr(Step, ExtTy),
2654 AR->getLoop(), SCEV::FlagAnyWrap)) {
2655 const APInt &StartInt = StartC->getValue()->getValue();
2656 const APInt &StartRem = StartInt.urem(StepInt);
2658 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2659 AR->getLoop(), SCEV::FlagNW);
2662 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2663 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2664 SmallVector<const SCEV *, 4> Operands;
2665 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2666 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2667 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2668 // Find an operand that's safely divisible.
2669 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2670 const SCEV *Op = M->getOperand(i);
2671 const SCEV *Div = getUDivExpr(Op, RHSC);
2672 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2673 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2676 return getMulExpr(Operands);
2680 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2681 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2682 SmallVector<const SCEV *, 4> Operands;
2683 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2684 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2685 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2687 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2688 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2689 if (isa<SCEVUDivExpr>(Op) ||
2690 getMulExpr(Op, RHS) != A->getOperand(i))
2692 Operands.push_back(Op);
2694 if (Operands.size() == A->getNumOperands())
2695 return getAddExpr(Operands);
2699 // Fold if both operands are constant.
2700 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2701 Constant *LHSCV = LHSC->getValue();
2702 Constant *RHSCV = RHSC->getValue();
2703 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2709 FoldingSetNodeID ID;
2710 ID.AddInteger(scUDivExpr);
2714 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2715 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2717 UniqueSCEVs.InsertNode(S, IP);
2721 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2722 APInt A = C1->getValue()->getValue().abs();
2723 APInt B = C2->getValue()->getValue().abs();
2724 uint32_t ABW = A.getBitWidth();
2725 uint32_t BBW = B.getBitWidth();
2732 return APIntOps::GreatestCommonDivisor(A, B);
2735 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2736 /// something simpler if possible. There is no representation for an exact udiv
2737 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2738 /// We can't do this when it's not exact because the udiv may be clearing bits.
2739 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2741 // TODO: we could try to find factors in all sorts of things, but for now we
2742 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2743 // end of this file for inspiration.
2745 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2747 return getUDivExpr(LHS, RHS);
2749 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2750 // If the mulexpr multiplies by a constant, then that constant must be the
2751 // first element of the mulexpr.
2752 if (const SCEVConstant *LHSCst =
2753 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2754 if (LHSCst == RHSCst) {
2755 SmallVector<const SCEV *, 2> Operands;
2756 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2757 return getMulExpr(Operands);
2760 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2761 // that there's a factor provided by one of the other terms. We need to
2763 APInt Factor = gcd(LHSCst, RHSCst);
2764 if (!Factor.isIntN(1)) {
2765 LHSCst = cast<SCEVConstant>(
2766 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2767 RHSCst = cast<SCEVConstant>(
2768 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2769 SmallVector<const SCEV *, 2> Operands;
2770 Operands.push_back(LHSCst);
2771 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2772 LHS = getMulExpr(Operands);
2774 Mul = dyn_cast<SCEVMulExpr>(LHS);
2776 return getUDivExactExpr(LHS, RHS);
2781 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2782 if (Mul->getOperand(i) == RHS) {
2783 SmallVector<const SCEV *, 2> Operands;
2784 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2785 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2786 return getMulExpr(Operands);
2790 return getUDivExpr(LHS, RHS);
2793 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2794 /// Simplify the expression as much as possible.
2795 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2797 SCEV::NoWrapFlags Flags) {
2798 SmallVector<const SCEV *, 4> Operands;
2799 Operands.push_back(Start);
2800 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2801 if (StepChrec->getLoop() == L) {
2802 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2803 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2806 Operands.push_back(Step);
2807 return getAddRecExpr(Operands, L, Flags);
2810 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2811 /// Simplify the expression as much as possible.
2813 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2814 const Loop *L, SCEV::NoWrapFlags Flags) {
2815 if (Operands.size() == 1) return Operands[0];
2817 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2818 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2819 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2820 "SCEVAddRecExpr operand types don't match!");
2821 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2822 assert(isLoopInvariant(Operands[i], L) &&
2823 "SCEVAddRecExpr operand is not loop-invariant!");
2826 if (Operands.back()->isZero()) {
2827 Operands.pop_back();
2828 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2831 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2832 // use that information to infer NUW and NSW flags. However, computing a
2833 // BE count requires calling getAddRecExpr, so we may not yet have a
2834 // meaningful BE count at this point (and if we don't, we'd be stuck
2835 // with a SCEVCouldNotCompute as the cached BE count).
2837 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2839 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2840 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2841 const Loop *NestedLoop = NestedAR->getLoop();
2842 if (L->contains(NestedLoop)
2843 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2844 : (!NestedLoop->contains(L) &&
2845 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2846 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2847 NestedAR->op_end());
2848 Operands[0] = NestedAR->getStart();
2849 // AddRecs require their operands be loop-invariant with respect to their
2850 // loops. Don't perform this transformation if it would break this
2852 bool AllInvariant = true;
2853 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2854 if (!isLoopInvariant(Operands[i], L)) {
2855 AllInvariant = false;
2859 // Create a recurrence for the outer loop with the same step size.
2861 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2862 // inner recurrence has the same property.
2863 SCEV::NoWrapFlags OuterFlags =
2864 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2866 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2867 AllInvariant = true;
2868 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2869 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2870 AllInvariant = false;
2874 // Ok, both add recurrences are valid after the transformation.
2876 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2877 // the outer recurrence has the same property.
2878 SCEV::NoWrapFlags InnerFlags =
2879 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2880 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2883 // Reset Operands to its original state.
2884 Operands[0] = NestedAR;
2888 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2889 // already have one, otherwise create a new one.
2890 FoldingSetNodeID ID;
2891 ID.AddInteger(scAddRecExpr);
2892 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2893 ID.AddPointer(Operands[i]);
2897 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2899 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2900 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2901 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2902 O, Operands.size(), L);
2903 UniqueSCEVs.InsertNode(S, IP);
2905 S->setNoWrapFlags(Flags);
2910 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2911 const SmallVectorImpl<const SCEV *> &IndexExprs,
2913 // getSCEV(Base)->getType() has the same address space as Base->getType()
2914 // because SCEV::getType() preserves the address space.
2915 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2916 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2917 // instruction to its SCEV, because the Instruction may be guarded by control
2918 // flow and the no-overflow bits may not be valid for the expression in any
2919 // context. This can be fixed similarly to how these flags are handled for
2921 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2923 const SCEV *TotalOffset = getZero(IntPtrTy);
2924 // The address space is unimportant. The first thing we do on CurTy is getting
2925 // its element type.
2926 Type *CurTy = PointerType::getUnqual(PointeeType);
2927 for (const SCEV *IndexExpr : IndexExprs) {
2928 // Compute the (potentially symbolic) offset in bytes for this index.
2929 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2930 // For a struct, add the member offset.
2931 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2932 unsigned FieldNo = Index->getZExtValue();
2933 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2935 // Add the field offset to the running total offset.
2936 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2938 // Update CurTy to the type of the field at Index.
2939 CurTy = STy->getTypeAtIndex(Index);
2941 // Update CurTy to its element type.
2942 CurTy = cast<SequentialType>(CurTy)->getElementType();
2943 // For an array, add the element offset, explicitly scaled.
2944 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2945 // Getelementptr indices are signed.
2946 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2948 // Multiply the index by the element size to compute the element offset.
2949 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2951 // Add the element offset to the running total offset.
2952 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2956 // Add the total offset from all the GEP indices to the base.
2957 return getAddExpr(BaseExpr, TotalOffset, Wrap);
2960 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2962 SmallVector<const SCEV *, 2> Ops;
2965 return getSMaxExpr(Ops);
2969 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2970 assert(!Ops.empty() && "Cannot get empty smax!");
2971 if (Ops.size() == 1) return Ops[0];
2973 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2974 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2975 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2976 "SCEVSMaxExpr operand types don't match!");
2979 // Sort by complexity, this groups all similar expression types together.
2980 GroupByComplexity(Ops, &LI);
2982 // If there are any constants, fold them together.
2984 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2986 assert(Idx < Ops.size());
2987 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2988 // We found two constants, fold them together!
2989 ConstantInt *Fold = ConstantInt::get(getContext(),
2990 APIntOps::smax(LHSC->getValue()->getValue(),
2991 RHSC->getValue()->getValue()));
2992 Ops[0] = getConstant(Fold);
2993 Ops.erase(Ops.begin()+1); // Erase the folded element
2994 if (Ops.size() == 1) return Ops[0];
2995 LHSC = cast<SCEVConstant>(Ops[0]);
2998 // If we are left with a constant minimum-int, strip it off.
2999 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3000 Ops.erase(Ops.begin());
3002 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3003 // If we have an smax with a constant maximum-int, it will always be
3008 if (Ops.size() == 1) return Ops[0];
3011 // Find the first SMax
3012 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3015 // Check to see if one of the operands is an SMax. If so, expand its operands
3016 // onto our operand list, and recurse to simplify.
3017 if (Idx < Ops.size()) {
3018 bool DeletedSMax = false;
3019 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3020 Ops.erase(Ops.begin()+Idx);
3021 Ops.append(SMax->op_begin(), SMax->op_end());
3026 return getSMaxExpr(Ops);
3029 // Okay, check to see if the same value occurs in the operand list twice. If
3030 // so, delete one. Since we sorted the list, these values are required to
3032 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3033 // X smax Y smax Y --> X smax Y
3034 // X smax Y --> X, if X is always greater than Y
3035 if (Ops[i] == Ops[i+1] ||
3036 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3037 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3039 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3040 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3044 if (Ops.size() == 1) return Ops[0];
3046 assert(!Ops.empty() && "Reduced smax down to nothing!");
3048 // Okay, it looks like we really DO need an smax expr. Check to see if we
3049 // already have one, otherwise create a new one.
3050 FoldingSetNodeID ID;
3051 ID.AddInteger(scSMaxExpr);
3052 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3053 ID.AddPointer(Ops[i]);
3055 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3056 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3057 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3058 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3060 UniqueSCEVs.InsertNode(S, IP);
3064 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3066 SmallVector<const SCEV *, 2> Ops;
3069 return getUMaxExpr(Ops);
3073 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3074 assert(!Ops.empty() && "Cannot get empty umax!");
3075 if (Ops.size() == 1) return Ops[0];
3077 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3078 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3079 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3080 "SCEVUMaxExpr operand types don't match!");
3083 // Sort by complexity, this groups all similar expression types together.
3084 GroupByComplexity(Ops, &LI);
3086 // If there are any constants, fold them together.
3088 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3090 assert(Idx < Ops.size());
3091 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3092 // We found two constants, fold them together!
3093 ConstantInt *Fold = ConstantInt::get(getContext(),
3094 APIntOps::umax(LHSC->getValue()->getValue(),
3095 RHSC->getValue()->getValue()));
3096 Ops[0] = getConstant(Fold);
3097 Ops.erase(Ops.begin()+1); // Erase the folded element
3098 if (Ops.size() == 1) return Ops[0];
3099 LHSC = cast<SCEVConstant>(Ops[0]);
3102 // If we are left with a constant minimum-int, strip it off.
3103 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3104 Ops.erase(Ops.begin());
3106 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3107 // If we have an umax with a constant maximum-int, it will always be
3112 if (Ops.size() == 1) return Ops[0];
3115 // Find the first UMax
3116 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3119 // Check to see if one of the operands is a UMax. If so, expand its operands
3120 // onto our operand list, and recurse to simplify.
3121 if (Idx < Ops.size()) {
3122 bool DeletedUMax = false;
3123 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3124 Ops.erase(Ops.begin()+Idx);
3125 Ops.append(UMax->op_begin(), UMax->op_end());
3130 return getUMaxExpr(Ops);
3133 // Okay, check to see if the same value occurs in the operand list twice. If
3134 // so, delete one. Since we sorted the list, these values are required to
3136 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3137 // X umax Y umax Y --> X umax Y
3138 // X umax Y --> X, if X is always greater than Y
3139 if (Ops[i] == Ops[i+1] ||
3140 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3141 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3143 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3144 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3148 if (Ops.size() == 1) return Ops[0];
3150 assert(!Ops.empty() && "Reduced umax down to nothing!");
3152 // Okay, it looks like we really DO need a umax expr. Check to see if we
3153 // already have one, otherwise create a new one.
3154 FoldingSetNodeID ID;
3155 ID.AddInteger(scUMaxExpr);
3156 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3157 ID.AddPointer(Ops[i]);
3159 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3160 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3161 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3162 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3164 UniqueSCEVs.InsertNode(S, IP);
3168 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3170 // ~smax(~x, ~y) == smin(x, y).
3171 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3174 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3176 // ~umax(~x, ~y) == umin(x, y)
3177 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3180 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3181 // We can bypass creating a target-independent
3182 // constant expression and then folding it back into a ConstantInt.
3183 // This is just a compile-time optimization.
3184 return getConstant(IntTy,
3185 F.getParent()->getDataLayout().getTypeAllocSize(AllocTy));
3188 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3191 // We can bypass creating a target-independent
3192 // constant expression and then folding it back into a ConstantInt.
3193 // This is just a compile-time optimization.
3196 F.getParent()->getDataLayout().getStructLayout(STy)->getElementOffset(
3200 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3201 // Don't attempt to do anything other than create a SCEVUnknown object
3202 // here. createSCEV only calls getUnknown after checking for all other
3203 // interesting possibilities, and any other code that calls getUnknown
3204 // is doing so in order to hide a value from SCEV canonicalization.
3206 FoldingSetNodeID ID;
3207 ID.AddInteger(scUnknown);
3210 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3211 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3212 "Stale SCEVUnknown in uniquing map!");
3215 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3217 FirstUnknown = cast<SCEVUnknown>(S);
3218 UniqueSCEVs.InsertNode(S, IP);
3222 //===----------------------------------------------------------------------===//
3223 // Basic SCEV Analysis and PHI Idiom Recognition Code
3226 /// isSCEVable - Test if values of the given type are analyzable within
3227 /// the SCEV framework. This primarily includes integer types, and it
3228 /// can optionally include pointer types if the ScalarEvolution class
3229 /// has access to target-specific information.
3230 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3231 // Integers and pointers are always SCEVable.
3232 return Ty->isIntegerTy() || Ty->isPointerTy();
3235 /// getTypeSizeInBits - Return the size in bits of the specified type,
3236 /// for which isSCEVable must return true.
3237 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3238 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3239 return F.getParent()->getDataLayout().getTypeSizeInBits(Ty);
3242 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3243 /// the given type and which represents how SCEV will treat the given
3244 /// type, for which isSCEVable must return true. For pointer types,
3245 /// this is the pointer-sized integer type.
3246 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3247 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3249 if (Ty->isIntegerTy()) {
3253 // The only other support type is pointer.
3254 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3255 return F.getParent()->getDataLayout().getIntPtrType(Ty);
3258 const SCEV *ScalarEvolution::getCouldNotCompute() {
3259 return CouldNotCompute.get();
3263 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3264 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3265 // is set iff if find such SCEVUnknown.
3267 struct FindInvalidSCEVUnknown {
3269 FindInvalidSCEVUnknown() { FindOne = false; }
3270 bool follow(const SCEV *S) {
3271 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3275 if (!cast<SCEVUnknown>(S)->getValue())
3282 bool isDone() const { return FindOne; }
3286 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3287 FindInvalidSCEVUnknown F;
3288 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3294 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3295 /// expression and create a new one.
3296 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3297 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3299 const SCEV *S = getExistingSCEV(V);
3302 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3307 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3308 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3310 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3311 if (I != ValueExprMap.end()) {
3312 const SCEV *S = I->second;
3313 if (checkValidity(S))
3315 ValueExprMap.erase(I);
3320 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3322 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3323 SCEV::NoWrapFlags Flags) {
3324 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3326 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3328 Type *Ty = V->getType();
3329 Ty = getEffectiveSCEVType(Ty);
3331 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3334 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3335 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3336 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3338 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3340 Type *Ty = V->getType();
3341 Ty = getEffectiveSCEVType(Ty);
3342 const SCEV *AllOnes =
3343 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3344 return getMinusSCEV(AllOnes, V);
3347 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3348 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3349 SCEV::NoWrapFlags Flags) {
3350 // Fast path: X - X --> 0.
3352 return getZero(LHS->getType());
3354 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3355 // makes it so that we cannot make much use of NUW.
3356 auto AddFlags = SCEV::FlagAnyWrap;
3357 const bool RHSIsNotMinSigned =
3358 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3359 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3360 // Let M be the minimum representable signed value. Then (-1)*RHS
3361 // signed-wraps if and only if RHS is M. That can happen even for
3362 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3363 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3364 // (-1)*RHS, we need to prove that RHS != M.
3366 // If LHS is non-negative and we know that LHS - RHS does not
3367 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3368 // either by proving that RHS > M or that LHS >= 0.
3369 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3370 AddFlags = SCEV::FlagNSW;
3374 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3375 // RHS is NSW and LHS >= 0.
3377 // The difficulty here is that the NSW flag may have been proven
3378 // relative to a loop that is to be found in a recurrence in LHS and
3379 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3380 // larger scope than intended.
3381 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3383 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3386 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3387 /// input value to the specified type. If the type must be extended, it is zero
3390 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3391 Type *SrcTy = V->getType();
3392 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3393 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3394 "Cannot truncate or zero extend with non-integer arguments!");
3395 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3396 return V; // No conversion
3397 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3398 return getTruncateExpr(V, Ty);
3399 return getZeroExtendExpr(V, Ty);
3402 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3403 /// input value to the specified type. If the type must be extended, it is sign
3406 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3408 Type *SrcTy = V->getType();
3409 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3410 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3411 "Cannot truncate or zero extend with non-integer arguments!");
3412 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3413 return V; // No conversion
3414 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3415 return getTruncateExpr(V, Ty);
3416 return getSignExtendExpr(V, Ty);
3419 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3420 /// input value to the specified type. If the type must be extended, it is zero
3421 /// extended. The conversion must not be narrowing.
3423 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3424 Type *SrcTy = V->getType();
3425 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3426 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3427 "Cannot noop or zero extend with non-integer arguments!");
3428 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3429 "getNoopOrZeroExtend cannot truncate!");
3430 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3431 return V; // No conversion
3432 return getZeroExtendExpr(V, Ty);
3435 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3436 /// input value to the specified type. If the type must be extended, it is sign
3437 /// extended. The conversion must not be narrowing.
3439 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3440 Type *SrcTy = V->getType();
3441 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3442 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3443 "Cannot noop or sign extend with non-integer arguments!");
3444 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3445 "getNoopOrSignExtend cannot truncate!");
3446 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3447 return V; // No conversion
3448 return getSignExtendExpr(V, Ty);
3451 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3452 /// the input value to the specified type. If the type must be extended,
3453 /// it is extended with unspecified bits. The conversion must not be
3456 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3457 Type *SrcTy = V->getType();
3458 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3459 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3460 "Cannot noop or any extend with non-integer arguments!");
3461 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3462 "getNoopOrAnyExtend cannot truncate!");
3463 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3464 return V; // No conversion
3465 return getAnyExtendExpr(V, Ty);
3468 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3469 /// input value to the specified type. The conversion must not be widening.
3471 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3472 Type *SrcTy = V->getType();
3473 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3474 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3475 "Cannot truncate or noop with non-integer arguments!");
3476 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3477 "getTruncateOrNoop cannot extend!");
3478 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3479 return V; // No conversion
3480 return getTruncateExpr(V, Ty);
3483 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3484 /// the types using zero-extension, and then perform a umax operation
3486 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3488 const SCEV *PromotedLHS = LHS;
3489 const SCEV *PromotedRHS = RHS;
3491 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3492 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3494 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3496 return getUMaxExpr(PromotedLHS, PromotedRHS);
3499 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3500 /// the types using zero-extension, and then perform a umin operation
3502 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3504 const SCEV *PromotedLHS = LHS;
3505 const SCEV *PromotedRHS = RHS;
3507 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3508 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3510 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3512 return getUMinExpr(PromotedLHS, PromotedRHS);
3515 /// getPointerBase - Transitively follow the chain of pointer-type operands
3516 /// until reaching a SCEV that does not have a single pointer operand. This
3517 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3518 /// but corner cases do exist.
3519 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3520 // A pointer operand may evaluate to a nonpointer expression, such as null.
3521 if (!V->getType()->isPointerTy())
3524 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3525 return getPointerBase(Cast->getOperand());
3527 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3528 const SCEV *PtrOp = nullptr;
3529 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3531 if ((*I)->getType()->isPointerTy()) {
3532 // Cannot find the base of an expression with multiple pointer operands.
3540 return getPointerBase(PtrOp);
3545 /// PushDefUseChildren - Push users of the given Instruction
3546 /// onto the given Worklist.
3548 PushDefUseChildren(Instruction *I,
3549 SmallVectorImpl<Instruction *> &Worklist) {
3550 // Push the def-use children onto the Worklist stack.
3551 for (User *U : I->users())
3552 Worklist.push_back(cast<Instruction>(U));
3555 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3556 /// instructions that depend on the given instruction and removes them from
3557 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3560 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3561 SmallVector<Instruction *, 16> Worklist;
3562 PushDefUseChildren(PN, Worklist);
3564 SmallPtrSet<Instruction *, 8> Visited;
3566 while (!Worklist.empty()) {
3567 Instruction *I = Worklist.pop_back_val();
3568 if (!Visited.insert(I).second)
3571 ValueExprMapType::iterator It =
3572 ValueExprMap.find_as(static_cast<Value *>(I));
3573 if (It != ValueExprMap.end()) {
3574 const SCEV *Old = It->second;
3576 // Short-circuit the def-use traversal if the symbolic name
3577 // ceases to appear in expressions.
3578 if (Old != SymName && !hasOperand(Old, SymName))
3581 // SCEVUnknown for a PHI either means that it has an unrecognized
3582 // structure, it's a PHI that's in the progress of being computed
3583 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3584 // additional loop trip count information isn't going to change anything.
3585 // In the second case, createNodeForPHI will perform the necessary
3586 // updates on its own when it gets to that point. In the third, we do
3587 // want to forget the SCEVUnknown.
3588 if (!isa<PHINode>(I) ||
3589 !isa<SCEVUnknown>(Old) ||
3590 (I != PN && Old == SymName)) {
3591 forgetMemoizedResults(Old);
3592 ValueExprMap.erase(It);
3596 PushDefUseChildren(I, Worklist);
3600 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3601 /// a loop header, making it a potential recurrence, or it doesn't.
3603 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3604 if (const Loop *L = LI.getLoopFor(PN->getParent()))
3605 if (L->getHeader() == PN->getParent()) {
3606 // The loop may have multiple entrances or multiple exits; we can analyze
3607 // this phi as an addrec if it has a unique entry value and a unique
3609 Value *BEValueV = nullptr, *StartValueV = nullptr;
3610 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3611 Value *V = PN->getIncomingValue(i);
3612 if (L->contains(PN->getIncomingBlock(i))) {
3615 } else if (BEValueV != V) {
3619 } else if (!StartValueV) {
3621 } else if (StartValueV != V) {
3622 StartValueV = nullptr;
3626 if (BEValueV && StartValueV) {
3627 // While we are analyzing this PHI node, handle its value symbolically.
3628 const SCEV *SymbolicName = getUnknown(PN);
3629 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3630 "PHI node already processed?");
3631 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3633 // Using this symbolic name for the PHI, analyze the value coming around
3635 const SCEV *BEValue = getSCEV(BEValueV);
3637 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3638 // has a special value for the first iteration of the loop.
3640 // If the value coming around the backedge is an add with the symbolic
3641 // value we just inserted, then we found a simple induction variable!
3642 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3643 // If there is a single occurrence of the symbolic value, replace it
3644 // with a recurrence.
3645 unsigned FoundIndex = Add->getNumOperands();
3646 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3647 if (Add->getOperand(i) == SymbolicName)
3648 if (FoundIndex == e) {
3653 if (FoundIndex != Add->getNumOperands()) {
3654 // Create an add with everything but the specified operand.
3655 SmallVector<const SCEV *, 8> Ops;
3656 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3657 if (i != FoundIndex)
3658 Ops.push_back(Add->getOperand(i));
3659 const SCEV *Accum = getAddExpr(Ops);
3661 // This is not a valid addrec if the step amount is varying each
3662 // loop iteration, but is not itself an addrec in this loop.
3663 if (isLoopInvariant(Accum, L) ||
3664 (isa<SCEVAddRecExpr>(Accum) &&
3665 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3666 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3668 // If the increment doesn't overflow, then neither the addrec nor
3669 // the post-increment will overflow.
3670 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3671 if (OBO->getOperand(0) == PN) {
3672 if (OBO->hasNoUnsignedWrap())
3673 Flags = setFlags(Flags, SCEV::FlagNUW);
3674 if (OBO->hasNoSignedWrap())
3675 Flags = setFlags(Flags, SCEV::FlagNSW);
3677 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3678 // If the increment is an inbounds GEP, then we know the address
3679 // space cannot be wrapped around. We cannot make any guarantee
3680 // about signed or unsigned overflow because pointers are
3681 // unsigned but we may have a negative index from the base
3682 // pointer. We can guarantee that no unsigned wrap occurs if the
3683 // indices form a positive value.
3684 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3685 Flags = setFlags(Flags, SCEV::FlagNW);
3687 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3688 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3689 Flags = setFlags(Flags, SCEV::FlagNUW);
3692 // We cannot transfer nuw and nsw flags from subtraction
3693 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3697 const SCEV *StartVal = getSCEV(StartValueV);
3698 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3700 // Since the no-wrap flags are on the increment, they apply to the
3701 // post-incremented value as well.
3702 if (isLoopInvariant(Accum, L))
3703 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3706 // Okay, for the entire analysis of this edge we assumed the PHI
3707 // to be symbolic. We now need to go back and purge all of the
3708 // entries for the scalars that use the symbolic expression.
3709 ForgetSymbolicName(PN, SymbolicName);
3710 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3714 } else if (const SCEVAddRecExpr *AddRec =
3715 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3716 // Otherwise, this could be a loop like this:
3717 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3718 // In this case, j = {1,+,1} and BEValue is j.
3719 // Because the other in-value of i (0) fits the evolution of BEValue
3720 // i really is an addrec evolution.
3721 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3722 const SCEV *StartVal = getSCEV(StartValueV);
3724 // If StartVal = j.start - j.stride, we can use StartVal as the
3725 // initial step of the addrec evolution.
3726 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3727 AddRec->getOperand(1))) {
3728 // FIXME: For constant StartVal, we should be able to infer
3730 const SCEV *PHISCEV =
3731 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3734 // Okay, for the entire analysis of this edge we assumed the PHI
3735 // to be symbolic. We now need to go back and purge all of the
3736 // entries for the scalars that use the symbolic expression.
3737 ForgetSymbolicName(PN, SymbolicName);
3738 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3746 // If the PHI has a single incoming value, follow that value, unless the
3747 // PHI's incoming blocks are in a different loop, in which case doing so
3748 // risks breaking LCSSA form. Instcombine would normally zap these, but
3749 // it doesn't have DominatorTree information, so it may miss cases.
3750 if (Value *V = SimplifyInstruction(PN, F.getParent()->getDataLayout(), &TLI,
3752 if (LI.replacementPreservesLCSSAForm(PN, V))
3755 // If it's not a loop phi, we can't handle it yet.
3756 return getUnknown(PN);
3759 /// createNodeForGEP - Expand GEP instructions into add and multiply
3760 /// operations. This allows them to be analyzed by regular SCEV code.
3762 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3763 Value *Base = GEP->getOperand(0);
3764 // Don't attempt to analyze GEPs over unsized objects.
3765 if (!Base->getType()->getPointerElementType()->isSized())
3766 return getUnknown(GEP);
3768 SmallVector<const SCEV *, 4> IndexExprs;
3769 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
3770 IndexExprs.push_back(getSCEV(*Index));
3771 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
3775 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3776 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3777 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3778 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3780 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3781 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3782 return C->getValue()->getValue().countTrailingZeros();
3784 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3785 return std::min(GetMinTrailingZeros(T->getOperand()),
3786 (uint32_t)getTypeSizeInBits(T->getType()));
3788 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3789 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3790 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3791 getTypeSizeInBits(E->getType()) : OpRes;
3794 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3795 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3796 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3797 getTypeSizeInBits(E->getType()) : OpRes;
3800 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3801 // The result is the min of all operands results.
3802 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3803 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3804 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3808 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3809 // The result is the sum of all operands results.
3810 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3811 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3812 for (unsigned i = 1, e = M->getNumOperands();
3813 SumOpRes != BitWidth && i != e; ++i)
3814 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3819 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3820 // The result is the min of all operands results.
3821 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3822 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3823 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3827 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3828 // The result is the min of all operands results.
3829 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3830 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3831 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3835 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3836 // The result is the min of all operands results.
3837 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3838 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3839 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3843 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3844 // For a SCEVUnknown, ask ValueTracking.
3845 unsigned BitWidth = getTypeSizeInBits(U->getType());
3846 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3847 computeKnownBits(U->getValue(), Zeros, Ones, F.getParent()->getDataLayout(),
3848 0, &AC, nullptr, &DT);
3849 return Zeros.countTrailingOnes();
3856 /// GetRangeFromMetadata - Helper method to assign a range to V from
3857 /// metadata present in the IR.
3858 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3859 if (Instruction *I = dyn_cast<Instruction>(V)) {
3860 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3861 ConstantRange TotalRange(
3862 cast<IntegerType>(I->getType())->getBitWidth(), false);
3864 unsigned NumRanges = MD->getNumOperands() / 2;
3865 assert(NumRanges >= 1);
3867 for (unsigned i = 0; i < NumRanges; ++i) {
3868 ConstantInt *Lower =
3869 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3870 ConstantInt *Upper =
3871 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3872 ConstantRange Range(Lower->getValue(), Upper->getValue());
3873 TotalRange = TotalRange.unionWith(Range);
3883 /// getRange - Determine the range for a particular SCEV. If SignHint is
3884 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
3885 /// with a "cleaner" unsigned (resp. signed) representation.
3888 ScalarEvolution::getRange(const SCEV *S,
3889 ScalarEvolution::RangeSignHint SignHint) {
3890 DenseMap<const SCEV *, ConstantRange> &Cache =
3891 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
3894 // See if we've computed this range already.
3895 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
3896 if (I != Cache.end())
3899 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3900 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
3902 unsigned BitWidth = getTypeSizeInBits(S->getType());
3903 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3905 // If the value has known zeros, the maximum value will have those known zeros
3907 uint32_t TZ = GetMinTrailingZeros(S);
3909 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
3910 ConservativeResult =
3911 ConstantRange(APInt::getMinValue(BitWidth),
3912 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3914 ConservativeResult = ConstantRange(
3915 APInt::getSignedMinValue(BitWidth),
3916 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3919 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3920 ConstantRange X = getRange(Add->getOperand(0), SignHint);
3921 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3922 X = X.add(getRange(Add->getOperand(i), SignHint));
3923 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
3926 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3927 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
3928 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3929 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
3930 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
3933 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3934 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
3935 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3936 X = X.smax(getRange(SMax->getOperand(i), SignHint));
3937 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
3940 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3941 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
3942 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3943 X = X.umax(getRange(UMax->getOperand(i), SignHint));
3944 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
3947 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3948 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
3949 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
3950 return setRange(UDiv, SignHint,
3951 ConservativeResult.intersectWith(X.udiv(Y)));
3954 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3955 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
3956 return setRange(ZExt, SignHint,
3957 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3960 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3961 ConstantRange X = getRange(SExt->getOperand(), SignHint);
3962 return setRange(SExt, SignHint,
3963 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3966 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3967 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
3968 return setRange(Trunc, SignHint,
3969 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3972 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3973 // If there's no unsigned wrap, the value will never be less than its
3975 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3976 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3977 if (!C->getValue()->isZero())
3978 ConservativeResult =
3979 ConservativeResult.intersectWith(
3980 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3982 // If there's no signed wrap, and all the operands have the same sign or
3983 // zero, the value won't ever change sign.
3984 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3985 bool AllNonNeg = true;
3986 bool AllNonPos = true;
3987 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3988 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3989 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3992 ConservativeResult = ConservativeResult.intersectWith(
3993 ConstantRange(APInt(BitWidth, 0),
3994 APInt::getSignedMinValue(BitWidth)));
3996 ConservativeResult = ConservativeResult.intersectWith(
3997 ConstantRange(APInt::getSignedMinValue(BitWidth),
3998 APInt(BitWidth, 1)));
4001 // TODO: non-affine addrec
4002 if (AddRec->isAffine()) {
4003 Type *Ty = AddRec->getType();
4004 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4005 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4006 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4008 // Check for overflow. This must be done with ConstantRange arithmetic
4009 // because we could be called from within the ScalarEvolution overflow
4012 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4013 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4014 ConstantRange ZExtMaxBECountRange =
4015 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4017 const SCEV *Start = AddRec->getStart();
4018 const SCEV *Step = AddRec->getStepRecurrence(*this);
4019 ConstantRange StepSRange = getSignedRange(Step);
4020 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4022 ConstantRange StartURange = getUnsignedRange(Start);
4023 ConstantRange EndURange =
4024 StartURange.add(MaxBECountRange.multiply(StepSRange));
4026 // Check for unsigned overflow.
4027 ConstantRange ZExtStartURange =
4028 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4029 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4030 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4032 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4033 EndURange.getUnsignedMin());
4034 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4035 EndURange.getUnsignedMax());
4036 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4038 ConservativeResult =
4039 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4042 ConstantRange StartSRange = getSignedRange(Start);
4043 ConstantRange EndSRange =
4044 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4046 // Check for signed overflow. This must be done with ConstantRange
4047 // arithmetic because we could be called from within the ScalarEvolution
4048 // overflow checking code.
4049 ConstantRange SExtStartSRange =
4050 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4051 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4052 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4054 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4055 EndSRange.getSignedMin());
4056 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4057 EndSRange.getSignedMax());
4058 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4060 ConservativeResult =
4061 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4066 return setRange(AddRec, SignHint, ConservativeResult);
4069 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4070 // Check if the IR explicitly contains !range metadata.
4071 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4072 if (MDRange.hasValue())
4073 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4075 // Split here to avoid paying the compile-time cost of calling both
4076 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4078 const DataLayout &DL = F.getParent()->getDataLayout();
4079 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4080 // For a SCEVUnknown, ask ValueTracking.
4081 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4082 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4083 if (Ones != ~Zeros + 1)
4084 ConservativeResult =
4085 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4087 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4088 "generalize as needed!");
4089 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4091 ConservativeResult = ConservativeResult.intersectWith(
4092 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4093 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4096 return setRange(U, SignHint, ConservativeResult);
4099 return setRange(S, SignHint, ConservativeResult);
4102 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4103 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4104 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4106 // Return early if there are no flags to propagate to the SCEV.
4107 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4108 if (BinOp->hasNoUnsignedWrap())
4109 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4110 if (BinOp->hasNoSignedWrap())
4111 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4112 if (Flags == SCEV::FlagAnyWrap) {
4113 return SCEV::FlagAnyWrap;
4116 // Here we check that BinOp is in the header of the innermost loop
4117 // containing BinOp, since we only deal with instructions in the loop
4118 // header. The actual loop we need to check later will come from an add
4119 // recurrence, but getting that requires computing the SCEV of the operands,
4120 // which can be expensive. This check we can do cheaply to rule out some
4122 Loop *innermostContainingLoop = LI.getLoopFor(BinOp->getParent());
4123 if (innermostContainingLoop == nullptr ||
4124 innermostContainingLoop->getHeader() != BinOp->getParent())
4125 return SCEV::FlagAnyWrap;
4127 // Only proceed if we can prove that BinOp does not yield poison.
4128 if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
4130 // At this point we know that if V is executed, then it does not wrap
4131 // according to at least one of NSW or NUW. If V is not executed, then we do
4132 // not know if the calculation that V represents would wrap. Multiple
4133 // instructions can map to the same SCEV. If we apply NSW or NUW from V to
4134 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4135 // derived from other instructions that map to the same SCEV. We cannot make
4136 // that guarantee for cases where V is not executed. So we need to find the
4137 // loop that V is considered in relation to and prove that V is executed for
4138 // every iteration of that loop. That implies that the value that V
4139 // calculates does not wrap anywhere in the loop, so then we can apply the
4140 // flags to the SCEV.
4142 // We check isLoopInvariant to disambiguate in case we are adding two
4143 // recurrences from different loops, so that we know which loop to prove
4144 // that V is executed in.
4145 for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
4146 const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
4147 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4148 const int OtherOpIndex = 1 - OpIndex;
4149 const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
4150 if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
4151 isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
4155 return SCEV::FlagAnyWrap;
4158 /// createSCEV - We know that there is no SCEV for the specified value. Analyze
4161 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4162 if (!isSCEVable(V->getType()))
4163 return getUnknown(V);
4165 unsigned Opcode = Instruction::UserOp1;
4166 if (Instruction *I = dyn_cast<Instruction>(V)) {
4167 Opcode = I->getOpcode();
4169 // Don't attempt to analyze instructions in blocks that aren't
4170 // reachable. Such instructions don't matter, and they aren't required
4171 // to obey basic rules for definitions dominating uses which this
4172 // analysis depends on.
4173 if (!DT.isReachableFromEntry(I->getParent()))
4174 return getUnknown(V);
4175 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4176 Opcode = CE->getOpcode();
4177 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4178 return getConstant(CI);
4179 else if (isa<ConstantPointerNull>(V))
4180 return getZero(V->getType());
4181 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4182 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4184 return getUnknown(V);
4186 Operator *U = cast<Operator>(V);
4188 case Instruction::Add: {
4189 // The simple thing to do would be to just call getSCEV on both operands
4190 // and call getAddExpr with the result. However if we're looking at a
4191 // bunch of things all added together, this can be quite inefficient,
4192 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4193 // Instead, gather up all the operands and make a single getAddExpr call.
4194 // LLVM IR canonical form means we need only traverse the left operands.
4195 SmallVector<const SCEV *, 4> AddOps;
4196 for (Value *Op = U;; Op = U->getOperand(0)) {
4197 U = dyn_cast<Operator>(Op);
4198 unsigned Opcode = U ? U->getOpcode() : 0;
4199 if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
4200 assert(Op != V && "V should be an add");
4201 AddOps.push_back(getSCEV(Op));
4205 if (auto *OpSCEV = getExistingSCEV(U)) {
4206 AddOps.push_back(OpSCEV);
4210 // If a NUW or NSW flag can be applied to the SCEV for this
4211 // addition, then compute the SCEV for this addition by itself
4212 // with a separate call to getAddExpr. We need to do that
4213 // instead of pushing the operands of the addition onto AddOps,
4214 // since the flags are only known to apply to this particular
4215 // addition - they may not apply to other additions that can be
4216 // formed with operands from AddOps.
4217 const SCEV *RHS = getSCEV(U->getOperand(1));
4218 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4219 if (Flags != SCEV::FlagAnyWrap) {
4220 const SCEV *LHS = getSCEV(U->getOperand(0));
4221 if (Opcode == Instruction::Sub)
4222 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4224 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4228 if (Opcode == Instruction::Sub)
4229 AddOps.push_back(getNegativeSCEV(RHS));
4231 AddOps.push_back(RHS);
4233 return getAddExpr(AddOps);
4236 case Instruction::Mul: {
4237 SmallVector<const SCEV *, 4> MulOps;
4238 for (Value *Op = U;; Op = U->getOperand(0)) {
4239 U = dyn_cast<Operator>(Op);
4240 if (!U || U->getOpcode() != Instruction::Mul) {
4241 assert(Op != V && "V should be a mul");
4242 MulOps.push_back(getSCEV(Op));
4246 if (auto *OpSCEV = getExistingSCEV(U)) {
4247 MulOps.push_back(OpSCEV);
4251 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4252 if (Flags != SCEV::FlagAnyWrap) {
4253 MulOps.push_back(getMulExpr(getSCEV(U->getOperand(0)),
4254 getSCEV(U->getOperand(1)), Flags));
4258 MulOps.push_back(getSCEV(U->getOperand(1)));
4260 return getMulExpr(MulOps);
4262 case Instruction::UDiv:
4263 return getUDivExpr(getSCEV(U->getOperand(0)),
4264 getSCEV(U->getOperand(1)));
4265 case Instruction::Sub:
4266 return getMinusSCEV(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)),
4267 getNoWrapFlagsFromUB(U));
4268 case Instruction::And:
4269 // For an expression like x&255 that merely masks off the high bits,
4270 // use zext(trunc(x)) as the SCEV expression.
4271 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4272 if (CI->isNullValue())
4273 return getSCEV(U->getOperand(1));
4274 if (CI->isAllOnesValue())
4275 return getSCEV(U->getOperand(0));
4276 const APInt &A = CI->getValue();
4278 // Instcombine's ShrinkDemandedConstant may strip bits out of
4279 // constants, obscuring what would otherwise be a low-bits mask.
4280 // Use computeKnownBits to compute what ShrinkDemandedConstant
4281 // knew about to reconstruct a low-bits mask value.
4282 unsigned LZ = A.countLeadingZeros();
4283 unsigned TZ = A.countTrailingZeros();
4284 unsigned BitWidth = A.getBitWidth();
4285 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4286 computeKnownBits(U->getOperand(0), KnownZero, KnownOne,
4287 F.getParent()->getDataLayout(), 0, &AC, nullptr, &DT);
4289 APInt EffectiveMask =
4290 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4291 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4292 const SCEV *MulCount = getConstant(
4293 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4297 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4298 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4305 case Instruction::Or:
4306 // If the RHS of the Or is a constant, we may have something like:
4307 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4308 // optimizations will transparently handle this case.
4310 // In order for this transformation to be safe, the LHS must be of the
4311 // form X*(2^n) and the Or constant must be less than 2^n.
4312 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4313 const SCEV *LHS = getSCEV(U->getOperand(0));
4314 const APInt &CIVal = CI->getValue();
4315 if (GetMinTrailingZeros(LHS) >=
4316 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4317 // Build a plain add SCEV.
4318 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4319 // If the LHS of the add was an addrec and it has no-wrap flags,
4320 // transfer the no-wrap flags, since an or won't introduce a wrap.
4321 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4322 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4323 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4324 OldAR->getNoWrapFlags());
4330 case Instruction::Xor:
4331 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4332 // If the RHS of the xor is a signbit, then this is just an add.
4333 // Instcombine turns add of signbit into xor as a strength reduction step.
4334 if (CI->getValue().isSignBit())
4335 return getAddExpr(getSCEV(U->getOperand(0)),
4336 getSCEV(U->getOperand(1)));
4338 // If the RHS of xor is -1, then this is a not operation.
4339 if (CI->isAllOnesValue())
4340 return getNotSCEV(getSCEV(U->getOperand(0)));
4342 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4343 // This is a variant of the check for xor with -1, and it handles
4344 // the case where instcombine has trimmed non-demanded bits out
4345 // of an xor with -1.
4346 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4347 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4348 if (BO->getOpcode() == Instruction::And &&
4349 LCI->getValue() == CI->getValue())
4350 if (const SCEVZeroExtendExpr *Z =
4351 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4352 Type *UTy = U->getType();
4353 const SCEV *Z0 = Z->getOperand();
4354 Type *Z0Ty = Z0->getType();
4355 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4357 // If C is a low-bits mask, the zero extend is serving to
4358 // mask off the high bits. Complement the operand and
4359 // re-apply the zext.
4360 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4361 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4363 // If C is a single bit, it may be in the sign-bit position
4364 // before the zero-extend. In this case, represent the xor
4365 // using an add, which is equivalent, and re-apply the zext.
4366 APInt Trunc = CI->getValue().trunc(Z0TySize);
4367 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4369 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4375 case Instruction::Shl:
4376 // Turn shift left of a constant amount into a multiply.
4377 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4378 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4380 // If the shift count is not less than the bitwidth, the result of
4381 // the shift is undefined. Don't try to analyze it, because the
4382 // resolution chosen here may differ from the resolution chosen in
4383 // other parts of the compiler.
4384 if (SA->getValue().uge(BitWidth))
4387 // It is currently not resolved how to interpret NSW for left
4388 // shift by BitWidth - 1, so we avoid applying flags in that
4389 // case. Remove this check (or this comment) once the situation
4391 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
4392 // and http://reviews.llvm.org/D8890 .
4393 auto Flags = SCEV::FlagAnyWrap;
4394 if (SA->getValue().ult(BitWidth - 1)) Flags = getNoWrapFlagsFromUB(U);
4396 Constant *X = ConstantInt::get(getContext(),
4397 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4398 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X), Flags);
4402 case Instruction::LShr:
4403 // Turn logical shift right of a constant into a unsigned divide.
4404 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4405 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4407 // If the shift count is not less than the bitwidth, the result of
4408 // the shift is undefined. Don't try to analyze it, because the
4409 // resolution chosen here may differ from the resolution chosen in
4410 // other parts of the compiler.
4411 if (SA->getValue().uge(BitWidth))
4414 Constant *X = ConstantInt::get(getContext(),
4415 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4416 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4420 case Instruction::AShr:
4421 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4422 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4423 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4424 if (L->getOpcode() == Instruction::Shl &&
4425 L->getOperand(1) == U->getOperand(1)) {
4426 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4428 // If the shift count is not less than the bitwidth, the result of
4429 // the shift is undefined. Don't try to analyze it, because the
4430 // resolution chosen here may differ from the resolution chosen in
4431 // other parts of the compiler.
4432 if (CI->getValue().uge(BitWidth))
4435 uint64_t Amt = BitWidth - CI->getZExtValue();
4436 if (Amt == BitWidth)
4437 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4439 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4440 IntegerType::get(getContext(),
4446 case Instruction::Trunc:
4447 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4449 case Instruction::ZExt:
4450 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4452 case Instruction::SExt:
4453 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4455 case Instruction::BitCast:
4456 // BitCasts are no-op casts so we just eliminate the cast.
4457 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4458 return getSCEV(U->getOperand(0));
4461 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4462 // lead to pointer expressions which cannot safely be expanded to GEPs,
4463 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4464 // simplifying integer expressions.
4466 case Instruction::GetElementPtr:
4467 return createNodeForGEP(cast<GEPOperator>(U));
4469 case Instruction::PHI:
4470 return createNodeForPHI(cast<PHINode>(U));
4472 case Instruction::Select:
4473 // This could be a smax or umax that was lowered earlier.
4474 // Try to recover it.
4475 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4476 Value *LHS = ICI->getOperand(0);
4477 Value *RHS = ICI->getOperand(1);
4478 switch (ICI->getPredicate()) {
4479 case ICmpInst::ICMP_SLT:
4480 case ICmpInst::ICMP_SLE:
4481 std::swap(LHS, RHS);
4483 case ICmpInst::ICMP_SGT:
4484 case ICmpInst::ICMP_SGE:
4485 // a >s b ? a+x : b+x -> smax(a, b)+x
4486 // a >s b ? b+x : a+x -> smin(a, b)+x
4487 if (getTypeSizeInBits(LHS->getType()) <=
4488 getTypeSizeInBits(U->getType())) {
4489 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType());
4490 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType());
4491 const SCEV *LA = getSCEV(U->getOperand(1));
4492 const SCEV *RA = getSCEV(U->getOperand(2));
4493 const SCEV *LDiff = getMinusSCEV(LA, LS);
4494 const SCEV *RDiff = getMinusSCEV(RA, RS);
4496 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4497 LDiff = getMinusSCEV(LA, RS);
4498 RDiff = getMinusSCEV(RA, LS);
4500 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4503 case ICmpInst::ICMP_ULT:
4504 case ICmpInst::ICMP_ULE:
4505 std::swap(LHS, RHS);
4507 case ICmpInst::ICMP_UGT:
4508 case ICmpInst::ICMP_UGE:
4509 // a >u b ? a+x : b+x -> umax(a, b)+x
4510 // a >u b ? b+x : a+x -> umin(a, b)+x
4511 if (getTypeSizeInBits(LHS->getType()) <=
4512 getTypeSizeInBits(U->getType())) {
4513 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4514 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType());
4515 const SCEV *LA = getSCEV(U->getOperand(1));
4516 const SCEV *RA = getSCEV(U->getOperand(2));
4517 const SCEV *LDiff = getMinusSCEV(LA, LS);
4518 const SCEV *RDiff = getMinusSCEV(RA, RS);
4520 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4521 LDiff = getMinusSCEV(LA, RS);
4522 RDiff = getMinusSCEV(RA, LS);
4524 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4527 case ICmpInst::ICMP_NE:
4528 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4529 if (getTypeSizeInBits(LHS->getType()) <=
4530 getTypeSizeInBits(U->getType()) &&
4531 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4532 const SCEV *One = getOne(U->getType());
4533 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4534 const SCEV *LA = getSCEV(U->getOperand(1));
4535 const SCEV *RA = getSCEV(U->getOperand(2));
4536 const SCEV *LDiff = getMinusSCEV(LA, LS);
4537 const SCEV *RDiff = getMinusSCEV(RA, One);
4539 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4542 case ICmpInst::ICMP_EQ:
4543 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4544 if (getTypeSizeInBits(LHS->getType()) <=
4545 getTypeSizeInBits(U->getType()) &&
4546 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4547 const SCEV *One = getOne(U->getType());
4548 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4549 const SCEV *LA = getSCEV(U->getOperand(1));
4550 const SCEV *RA = getSCEV(U->getOperand(2));
4551 const SCEV *LDiff = getMinusSCEV(LA, One);
4552 const SCEV *RDiff = getMinusSCEV(RA, LS);
4554 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4562 default: // We cannot analyze this expression.
4566 return getUnknown(V);
4571 //===----------------------------------------------------------------------===//
4572 // Iteration Count Computation Code
4575 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4576 if (BasicBlock *ExitingBB = L->getExitingBlock())
4577 return getSmallConstantTripCount(L, ExitingBB);
4579 // No trip count information for multiple exits.
4583 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4584 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4585 /// constant. Will also return 0 if the maximum trip count is very large (>=
4588 /// This "trip count" assumes that control exits via ExitingBlock. More
4589 /// precisely, it is the number of times that control may reach ExitingBlock
4590 /// before taking the branch. For loops with multiple exits, it may not be the
4591 /// number times that the loop header executes because the loop may exit
4592 /// prematurely via another branch.
4593 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4594 BasicBlock *ExitingBlock) {
4595 assert(ExitingBlock && "Must pass a non-null exiting block!");
4596 assert(L->isLoopExiting(ExitingBlock) &&
4597 "Exiting block must actually branch out of the loop!");
4598 const SCEVConstant *ExitCount =
4599 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4603 ConstantInt *ExitConst = ExitCount->getValue();
4605 // Guard against huge trip counts.
4606 if (ExitConst->getValue().getActiveBits() > 32)
4609 // In case of integer overflow, this returns 0, which is correct.
4610 return ((unsigned)ExitConst->getZExtValue()) + 1;
4613 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4614 if (BasicBlock *ExitingBB = L->getExitingBlock())
4615 return getSmallConstantTripMultiple(L, ExitingBB);
4617 // No trip multiple information for multiple exits.
4621 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4622 /// trip count of this loop as a normal unsigned value, if possible. This
4623 /// means that the actual trip count is always a multiple of the returned
4624 /// value (don't forget the trip count could very well be zero as well!).
4626 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4627 /// multiple of a constant (which is also the case if the trip count is simply
4628 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4629 /// if the trip count is very large (>= 2^32).
4631 /// As explained in the comments for getSmallConstantTripCount, this assumes
4632 /// that control exits the loop via ExitingBlock.
4634 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4635 BasicBlock *ExitingBlock) {
4636 assert(ExitingBlock && "Must pass a non-null exiting block!");
4637 assert(L->isLoopExiting(ExitingBlock) &&
4638 "Exiting block must actually branch out of the loop!");
4639 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4640 if (ExitCount == getCouldNotCompute())
4643 // Get the trip count from the BE count by adding 1.
4644 const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
4645 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4646 // to factor simple cases.
4647 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4648 TCMul = Mul->getOperand(0);
4650 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4654 ConstantInt *Result = MulC->getValue();
4656 // Guard against huge trip counts (this requires checking
4657 // for zero to handle the case where the trip count == -1 and the
4659 if (!Result || Result->getValue().getActiveBits() > 32 ||
4660 Result->getValue().getActiveBits() == 0)
4663 return (unsigned)Result->getZExtValue();
4666 // getExitCount - Get the expression for the number of loop iterations for which
4667 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4668 // SCEVCouldNotCompute.
4669 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4670 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4673 /// getBackedgeTakenCount - If the specified loop has a predictable
4674 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4675 /// object. The backedge-taken count is the number of times the loop header
4676 /// will be branched to from within the loop. This is one less than the
4677 /// trip count of the loop, since it doesn't count the first iteration,
4678 /// when the header is branched to from outside the loop.
4680 /// Note that it is not valid to call this method on a loop without a
4681 /// loop-invariant backedge-taken count (see
4682 /// hasLoopInvariantBackedgeTakenCount).
4684 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4685 return getBackedgeTakenInfo(L).getExact(this);
4688 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4689 /// return the least SCEV value that is known never to be less than the
4690 /// actual backedge taken count.
4691 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4692 return getBackedgeTakenInfo(L).getMax(this);
4695 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4696 /// onto the given Worklist.
4698 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4699 BasicBlock *Header = L->getHeader();
4701 // Push all Loop-header PHIs onto the Worklist stack.
4702 for (BasicBlock::iterator I = Header->begin();
4703 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4704 Worklist.push_back(PN);
4707 const ScalarEvolution::BackedgeTakenInfo &
4708 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4709 // Initially insert an invalid entry for this loop. If the insertion
4710 // succeeds, proceed to actually compute a backedge-taken count and
4711 // update the value. The temporary CouldNotCompute value tells SCEV
4712 // code elsewhere that it shouldn't attempt to request a new
4713 // backedge-taken count, which could result in infinite recursion.
4714 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4715 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4717 return Pair.first->second;
4719 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4720 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4721 // must be cleared in this scope.
4722 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4724 if (Result.getExact(this) != getCouldNotCompute()) {
4725 assert(isLoopInvariant(Result.getExact(this), L) &&
4726 isLoopInvariant(Result.getMax(this), L) &&
4727 "Computed backedge-taken count isn't loop invariant for loop!");
4728 ++NumTripCountsComputed;
4730 else if (Result.getMax(this) == getCouldNotCompute() &&
4731 isa<PHINode>(L->getHeader()->begin())) {
4732 // Only count loops that have phi nodes as not being computable.
4733 ++NumTripCountsNotComputed;
4736 // Now that we know more about the trip count for this loop, forget any
4737 // existing SCEV values for PHI nodes in this loop since they are only
4738 // conservative estimates made without the benefit of trip count
4739 // information. This is similar to the code in forgetLoop, except that
4740 // it handles SCEVUnknown PHI nodes specially.
4741 if (Result.hasAnyInfo()) {
4742 SmallVector<Instruction *, 16> Worklist;
4743 PushLoopPHIs(L, Worklist);
4745 SmallPtrSet<Instruction *, 8> Visited;
4746 while (!Worklist.empty()) {
4747 Instruction *I = Worklist.pop_back_val();
4748 if (!Visited.insert(I).second)
4751 ValueExprMapType::iterator It =
4752 ValueExprMap.find_as(static_cast<Value *>(I));
4753 if (It != ValueExprMap.end()) {
4754 const SCEV *Old = It->second;
4756 // SCEVUnknown for a PHI either means that it has an unrecognized
4757 // structure, or it's a PHI that's in the progress of being computed
4758 // by createNodeForPHI. In the former case, additional loop trip
4759 // count information isn't going to change anything. In the later
4760 // case, createNodeForPHI will perform the necessary updates on its
4761 // own when it gets to that point.
4762 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4763 forgetMemoizedResults(Old);
4764 ValueExprMap.erase(It);
4766 if (PHINode *PN = dyn_cast<PHINode>(I))
4767 ConstantEvolutionLoopExitValue.erase(PN);
4770 PushDefUseChildren(I, Worklist);
4774 // Re-lookup the insert position, since the call to
4775 // ComputeBackedgeTakenCount above could result in a
4776 // recusive call to getBackedgeTakenInfo (on a different
4777 // loop), which would invalidate the iterator computed
4779 return BackedgeTakenCounts.find(L)->second = Result;
4782 /// forgetLoop - This method should be called by the client when it has
4783 /// changed a loop in a way that may effect ScalarEvolution's ability to
4784 /// compute a trip count, or if the loop is deleted.
4785 void ScalarEvolution::forgetLoop(const Loop *L) {
4786 // Drop any stored trip count value.
4787 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4788 BackedgeTakenCounts.find(L);
4789 if (BTCPos != BackedgeTakenCounts.end()) {
4790 BTCPos->second.clear();
4791 BackedgeTakenCounts.erase(BTCPos);
4794 // Drop information about expressions based on loop-header PHIs.
4795 SmallVector<Instruction *, 16> Worklist;
4796 PushLoopPHIs(L, Worklist);
4798 SmallPtrSet<Instruction *, 8> Visited;
4799 while (!Worklist.empty()) {
4800 Instruction *I = Worklist.pop_back_val();
4801 if (!Visited.insert(I).second)
4804 ValueExprMapType::iterator It =
4805 ValueExprMap.find_as(static_cast<Value *>(I));
4806 if (It != ValueExprMap.end()) {
4807 forgetMemoizedResults(It->second);
4808 ValueExprMap.erase(It);
4809 if (PHINode *PN = dyn_cast<PHINode>(I))
4810 ConstantEvolutionLoopExitValue.erase(PN);
4813 PushDefUseChildren(I, Worklist);
4816 // Forget all contained loops too, to avoid dangling entries in the
4817 // ValuesAtScopes map.
4818 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4822 /// forgetValue - This method should be called by the client when it has
4823 /// changed a value in a way that may effect its value, or which may
4824 /// disconnect it from a def-use chain linking it to a loop.
4825 void ScalarEvolution::forgetValue(Value *V) {
4826 Instruction *I = dyn_cast<Instruction>(V);
4829 // Drop information about expressions based on loop-header PHIs.
4830 SmallVector<Instruction *, 16> Worklist;
4831 Worklist.push_back(I);
4833 SmallPtrSet<Instruction *, 8> Visited;
4834 while (!Worklist.empty()) {
4835 I = Worklist.pop_back_val();
4836 if (!Visited.insert(I).second)
4839 ValueExprMapType::iterator It =
4840 ValueExprMap.find_as(static_cast<Value *>(I));
4841 if (It != ValueExprMap.end()) {
4842 forgetMemoizedResults(It->second);
4843 ValueExprMap.erase(It);
4844 if (PHINode *PN = dyn_cast<PHINode>(I))
4845 ConstantEvolutionLoopExitValue.erase(PN);
4848 PushDefUseChildren(I, Worklist);
4852 /// getExact - Get the exact loop backedge taken count considering all loop
4853 /// exits. A computable result can only be returned for loops with a single
4854 /// exit. Returning the minimum taken count among all exits is incorrect
4855 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
4856 /// assumes that the limit of each loop test is never skipped. This is a valid
4857 /// assumption as long as the loop exits via that test. For precise results, it
4858 /// is the caller's responsibility to specify the relevant loop exit using
4859 /// getExact(ExitingBlock, SE).
4861 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4862 // If any exits were not computable, the loop is not computable.
4863 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4865 // We need exactly one computable exit.
4866 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4867 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4869 const SCEV *BECount = nullptr;
4870 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4871 ENT != nullptr; ENT = ENT->getNextExit()) {
4873 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4876 BECount = ENT->ExactNotTaken;
4877 else if (BECount != ENT->ExactNotTaken)
4878 return SE->getCouldNotCompute();
4880 assert(BECount && "Invalid not taken count for loop exit");
4884 /// getExact - Get the exact not taken count for this loop exit.
4886 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4887 ScalarEvolution *SE) const {
4888 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4889 ENT != nullptr; ENT = ENT->getNextExit()) {
4891 if (ENT->ExitingBlock == ExitingBlock)
4892 return ENT->ExactNotTaken;
4894 return SE->getCouldNotCompute();
4897 /// getMax - Get the max backedge taken count for the loop.
4899 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4900 return Max ? Max : SE->getCouldNotCompute();
4903 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4904 ScalarEvolution *SE) const {
4905 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4908 if (!ExitNotTaken.ExitingBlock)
4911 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4912 ENT != nullptr; ENT = ENT->getNextExit()) {
4914 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4915 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4922 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4923 /// computable exit into a persistent ExitNotTakenInfo array.
4924 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4925 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4926 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4929 ExitNotTaken.setIncomplete();
4931 unsigned NumExits = ExitCounts.size();
4932 if (NumExits == 0) return;
4934 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4935 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4936 if (NumExits == 1) return;
4938 // Handle the rare case of multiple computable exits.
4939 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4941 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4942 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4943 PrevENT->setNextExit(ENT);
4944 ENT->ExitingBlock = ExitCounts[i].first;
4945 ENT->ExactNotTaken = ExitCounts[i].second;
4949 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4950 void ScalarEvolution::BackedgeTakenInfo::clear() {
4951 ExitNotTaken.ExitingBlock = nullptr;
4952 ExitNotTaken.ExactNotTaken = nullptr;
4953 delete[] ExitNotTaken.getNextExit();
4956 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4957 /// of the specified loop will execute.
4958 ScalarEvolution::BackedgeTakenInfo
4959 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4960 SmallVector<BasicBlock *, 8> ExitingBlocks;
4961 L->getExitingBlocks(ExitingBlocks);
4963 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4964 bool CouldComputeBECount = true;
4965 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4966 const SCEV *MustExitMaxBECount = nullptr;
4967 const SCEV *MayExitMaxBECount = nullptr;
4969 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4970 // and compute maxBECount.
4971 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4972 BasicBlock *ExitBB = ExitingBlocks[i];
4973 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4975 // 1. For each exit that can be computed, add an entry to ExitCounts.
4976 // CouldComputeBECount is true only if all exits can be computed.
4977 if (EL.Exact == getCouldNotCompute())
4978 // We couldn't compute an exact value for this exit, so
4979 // we won't be able to compute an exact value for the loop.
4980 CouldComputeBECount = false;
4982 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4984 // 2. Derive the loop's MaxBECount from each exit's max number of
4985 // non-exiting iterations. Partition the loop exits into two kinds:
4986 // LoopMustExits and LoopMayExits.
4988 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4989 // is a LoopMayExit. If any computable LoopMustExit is found, then
4990 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4991 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4992 // considered greater than any computable EL.Max.
4993 if (EL.Max != getCouldNotCompute() && Latch &&
4994 DT.dominates(ExitBB, Latch)) {
4995 if (!MustExitMaxBECount)
4996 MustExitMaxBECount = EL.Max;
4998 MustExitMaxBECount =
4999 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5001 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5002 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5003 MayExitMaxBECount = EL.Max;
5006 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5010 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5011 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5012 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5015 /// ComputeExitLimit - Compute the number of times the backedge of the specified
5016 /// loop will execute if it exits via the specified block.
5017 ScalarEvolution::ExitLimit
5018 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
5020 // Okay, we've chosen an exiting block. See what condition causes us to
5021 // exit at this block and remember the exit block and whether all other targets
5022 // lead to the loop header.
5023 bool MustExecuteLoopHeader = true;
5024 BasicBlock *Exit = nullptr;
5025 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5027 if (!L->contains(*SI)) {
5028 if (Exit) // Multiple exit successors.
5029 return getCouldNotCompute();
5031 } else if (*SI != L->getHeader()) {
5032 MustExecuteLoopHeader = false;
5035 // At this point, we know we have a conditional branch that determines whether
5036 // the loop is exited. However, we don't know if the branch is executed each
5037 // time through the loop. If not, then the execution count of the branch will
5038 // not be equal to the trip count of the loop.
5040 // Currently we check for this by checking to see if the Exit branch goes to
5041 // the loop header. If so, we know it will always execute the same number of
5042 // times as the loop. We also handle the case where the exit block *is* the
5043 // loop header. This is common for un-rotated loops.
5045 // If both of those tests fail, walk up the unique predecessor chain to the
5046 // header, stopping if there is an edge that doesn't exit the loop. If the
5047 // header is reached, the execution count of the branch will be equal to the
5048 // trip count of the loop.
5050 // More extensive analysis could be done to handle more cases here.
5052 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5053 // The simple checks failed, try climbing the unique predecessor chain
5054 // up to the header.
5056 for (BasicBlock *BB = ExitingBlock; BB; ) {
5057 BasicBlock *Pred = BB->getUniquePredecessor();
5059 return getCouldNotCompute();
5060 TerminatorInst *PredTerm = Pred->getTerminator();
5061 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5064 // If the predecessor has a successor that isn't BB and isn't
5065 // outside the loop, assume the worst.
5066 if (L->contains(PredSucc))
5067 return getCouldNotCompute();
5069 if (Pred == L->getHeader()) {
5076 return getCouldNotCompute();
5079 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5080 TerminatorInst *Term = ExitingBlock->getTerminator();
5081 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5082 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5083 // Proceed to the next level to examine the exit condition expression.
5084 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5085 BI->getSuccessor(1),
5086 /*ControlsExit=*/IsOnlyExit);
5089 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5090 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
5091 /*ControlsExit=*/IsOnlyExit);
5093 return getCouldNotCompute();
5096 /// ComputeExitLimitFromCond - Compute the number of times the
5097 /// backedge of the specified loop will execute if its exit condition
5098 /// were a conditional branch of ExitCond, TBB, and FBB.
5100 /// @param ControlsExit is true if ExitCond directly controls the exit
5101 /// branch. In this case, we can assume that the loop exits only if the
5102 /// condition is true and can infer that failing to meet the condition prior to
5103 /// integer wraparound results in undefined behavior.
5104 ScalarEvolution::ExitLimit
5105 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
5109 bool ControlsExit) {
5110 // Check if the controlling expression for this loop is an And or Or.
5111 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5112 if (BO->getOpcode() == Instruction::And) {
5113 // Recurse on the operands of the and.
5114 bool EitherMayExit = L->contains(TBB);
5115 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5116 ControlsExit && !EitherMayExit);
5117 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5118 ControlsExit && !EitherMayExit);
5119 const SCEV *BECount = getCouldNotCompute();
5120 const SCEV *MaxBECount = getCouldNotCompute();
5121 if (EitherMayExit) {
5122 // Both conditions must be true for the loop to continue executing.
5123 // Choose the less conservative count.
5124 if (EL0.Exact == getCouldNotCompute() ||
5125 EL1.Exact == getCouldNotCompute())
5126 BECount = getCouldNotCompute();
5128 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5129 if (EL0.Max == getCouldNotCompute())
5130 MaxBECount = EL1.Max;
5131 else if (EL1.Max == getCouldNotCompute())
5132 MaxBECount = EL0.Max;
5134 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5136 // Both conditions must be true at the same time for the loop to exit.
5137 // For now, be conservative.
5138 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5139 if (EL0.Max == EL1.Max)
5140 MaxBECount = EL0.Max;
5141 if (EL0.Exact == EL1.Exact)
5142 BECount = EL0.Exact;
5145 return ExitLimit(BECount, MaxBECount);
5147 if (BO->getOpcode() == Instruction::Or) {
5148 // Recurse on the operands of the or.
5149 bool EitherMayExit = L->contains(FBB);
5150 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5151 ControlsExit && !EitherMayExit);
5152 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5153 ControlsExit && !EitherMayExit);
5154 const SCEV *BECount = getCouldNotCompute();
5155 const SCEV *MaxBECount = getCouldNotCompute();
5156 if (EitherMayExit) {
5157 // Both conditions must be false for the loop to continue executing.
5158 // Choose the less conservative count.
5159 if (EL0.Exact == getCouldNotCompute() ||
5160 EL1.Exact == getCouldNotCompute())
5161 BECount = getCouldNotCompute();
5163 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5164 if (EL0.Max == getCouldNotCompute())
5165 MaxBECount = EL1.Max;
5166 else if (EL1.Max == getCouldNotCompute())
5167 MaxBECount = EL0.Max;
5169 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5171 // Both conditions must be false at the same time for the loop to exit.
5172 // For now, be conservative.
5173 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5174 if (EL0.Max == EL1.Max)
5175 MaxBECount = EL0.Max;
5176 if (EL0.Exact == EL1.Exact)
5177 BECount = EL0.Exact;
5180 return ExitLimit(BECount, MaxBECount);
5184 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5185 // Proceed to the next level to examine the icmp.
5186 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5187 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5189 // Check for a constant condition. These are normally stripped out by
5190 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5191 // preserve the CFG and is temporarily leaving constant conditions
5193 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5194 if (L->contains(FBB) == !CI->getZExtValue())
5195 // The backedge is always taken.
5196 return getCouldNotCompute();
5198 // The backedge is never taken.
5199 return getZero(CI->getType());
5202 // If it's not an integer or pointer comparison then compute it the hard way.
5203 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5206 /// ComputeExitLimitFromICmp - Compute the number of times the
5207 /// backedge of the specified loop will execute if its exit condition
5208 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5209 ScalarEvolution::ExitLimit
5210 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5214 bool ControlsExit) {
5216 // If the condition was exit on true, convert the condition to exit on false
5217 ICmpInst::Predicate Cond;
5218 if (!L->contains(FBB))
5219 Cond = ExitCond->getPredicate();
5221 Cond = ExitCond->getInversePredicate();
5223 // Handle common loops like: for (X = "string"; *X; ++X)
5224 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5225 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5227 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5228 if (ItCnt.hasAnyInfo())
5232 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5233 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5235 // Try to evaluate any dependencies out of the loop.
5236 LHS = getSCEVAtScope(LHS, L);
5237 RHS = getSCEVAtScope(RHS, L);
5239 // At this point, we would like to compute how many iterations of the
5240 // loop the predicate will return true for these inputs.
5241 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5242 // If there is a loop-invariant, force it into the RHS.
5243 std::swap(LHS, RHS);
5244 Cond = ICmpInst::getSwappedPredicate(Cond);
5247 // Simplify the operands before analyzing them.
5248 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5250 // If we have a comparison of a chrec against a constant, try to use value
5251 // ranges to answer this query.
5252 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5253 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5254 if (AddRec->getLoop() == L) {
5255 // Form the constant range.
5256 ConstantRange CompRange(
5257 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5259 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5260 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5264 case ICmpInst::ICMP_NE: { // while (X != Y)
5265 // Convert to: while (X-Y != 0)
5266 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5267 if (EL.hasAnyInfo()) return EL;
5270 case ICmpInst::ICMP_EQ: { // while (X == Y)
5271 // Convert to: while (X-Y == 0)
5272 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5273 if (EL.hasAnyInfo()) return EL;
5276 case ICmpInst::ICMP_SLT:
5277 case ICmpInst::ICMP_ULT: { // while (X < Y)
5278 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5279 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5280 if (EL.hasAnyInfo()) return EL;
5283 case ICmpInst::ICMP_SGT:
5284 case ICmpInst::ICMP_UGT: { // while (X > Y)
5285 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5286 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5287 if (EL.hasAnyInfo()) return EL;
5292 dbgs() << "ComputeBackedgeTakenCount ";
5293 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5294 dbgs() << "[unsigned] ";
5295 dbgs() << *LHS << " "
5296 << Instruction::getOpcodeName(Instruction::ICmp)
5297 << " " << *RHS << "\n";
5301 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5304 ScalarEvolution::ExitLimit
5305 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5307 BasicBlock *ExitingBlock,
5308 bool ControlsExit) {
5309 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5311 // Give up if the exit is the default dest of a switch.
5312 if (Switch->getDefaultDest() == ExitingBlock)
5313 return getCouldNotCompute();
5315 assert(L->contains(Switch->getDefaultDest()) &&
5316 "Default case must not exit the loop!");
5317 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5318 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5320 // while (X != Y) --> while (X-Y != 0)
5321 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5322 if (EL.hasAnyInfo())
5325 return getCouldNotCompute();
5328 static ConstantInt *
5329 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5330 ScalarEvolution &SE) {
5331 const SCEV *InVal = SE.getConstant(C);
5332 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5333 assert(isa<SCEVConstant>(Val) &&
5334 "Evaluation of SCEV at constant didn't fold correctly?");
5335 return cast<SCEVConstant>(Val)->getValue();
5338 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5339 /// 'icmp op load X, cst', try to see if we can compute the backedge
5340 /// execution count.
5341 ScalarEvolution::ExitLimit
5342 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5346 ICmpInst::Predicate predicate) {
5348 if (LI->isVolatile()) return getCouldNotCompute();
5350 // Check to see if the loaded pointer is a getelementptr of a global.
5351 // TODO: Use SCEV instead of manually grubbing with GEPs.
5352 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5353 if (!GEP) return getCouldNotCompute();
5355 // Make sure that it is really a constant global we are gepping, with an
5356 // initializer, and make sure the first IDX is really 0.
5357 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5358 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5359 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5360 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5361 return getCouldNotCompute();
5363 // Okay, we allow one non-constant index into the GEP instruction.
5364 Value *VarIdx = nullptr;
5365 std::vector<Constant*> Indexes;
5366 unsigned VarIdxNum = 0;
5367 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5368 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5369 Indexes.push_back(CI);
5370 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5371 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5372 VarIdx = GEP->getOperand(i);
5374 Indexes.push_back(nullptr);
5377 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5379 return getCouldNotCompute();
5381 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5382 // Check to see if X is a loop variant variable value now.
5383 const SCEV *Idx = getSCEV(VarIdx);
5384 Idx = getSCEVAtScope(Idx, L);
5386 // We can only recognize very limited forms of loop index expressions, in
5387 // particular, only affine AddRec's like {C1,+,C2}.
5388 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5389 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5390 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5391 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5392 return getCouldNotCompute();
5394 unsigned MaxSteps = MaxBruteForceIterations;
5395 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5396 ConstantInt *ItCst = ConstantInt::get(
5397 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5398 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5400 // Form the GEP offset.
5401 Indexes[VarIdxNum] = Val;
5403 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5405 if (!Result) break; // Cannot compute!
5407 // Evaluate the condition for this iteration.
5408 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5409 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5410 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5412 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5413 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5416 ++NumArrayLenItCounts;
5417 return getConstant(ItCst); // Found terminating iteration!
5420 return getCouldNotCompute();
5424 /// CanConstantFold - Return true if we can constant fold an instruction of the
5425 /// specified type, assuming that all operands were constants.
5426 static bool CanConstantFold(const Instruction *I) {
5427 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5428 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5432 if (const CallInst *CI = dyn_cast<CallInst>(I))
5433 if (const Function *F = CI->getCalledFunction())
5434 return canConstantFoldCallTo(F);
5438 /// Determine whether this instruction can constant evolve within this loop
5439 /// assuming its operands can all constant evolve.
5440 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5441 // An instruction outside of the loop can't be derived from a loop PHI.
5442 if (!L->contains(I)) return false;
5444 if (isa<PHINode>(I)) {
5445 // We don't currently keep track of the control flow needed to evaluate
5446 // PHIs, so we cannot handle PHIs inside of loops.
5447 return L->getHeader() == I->getParent();
5450 // If we won't be able to constant fold this expression even if the operands
5451 // are constants, bail early.
5452 return CanConstantFold(I);
5455 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5456 /// recursing through each instruction operand until reaching a loop header phi.
5458 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5459 DenseMap<Instruction *, PHINode *> &PHIMap) {
5461 // Otherwise, we can evaluate this instruction if all of its operands are
5462 // constant or derived from a PHI node themselves.
5463 PHINode *PHI = nullptr;
5464 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5465 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5467 if (isa<Constant>(*OpI)) continue;
5469 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5470 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5472 PHINode *P = dyn_cast<PHINode>(OpInst);
5474 // If this operand is already visited, reuse the prior result.
5475 // We may have P != PHI if this is the deepest point at which the
5476 // inconsistent paths meet.
5477 P = PHIMap.lookup(OpInst);
5479 // Recurse and memoize the results, whether a phi is found or not.
5480 // This recursive call invalidates pointers into PHIMap.
5481 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5485 return nullptr; // Not evolving from PHI
5486 if (PHI && PHI != P)
5487 return nullptr; // Evolving from multiple different PHIs.
5490 // This is a expression evolving from a constant PHI!
5494 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5495 /// in the loop that V is derived from. We allow arbitrary operations along the
5496 /// way, but the operands of an operation must either be constants or a value
5497 /// derived from a constant PHI. If this expression does not fit with these
5498 /// constraints, return null.
5499 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5500 Instruction *I = dyn_cast<Instruction>(V);
5501 if (!I || !canConstantEvolve(I, L)) return nullptr;
5503 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5507 // Record non-constant instructions contained by the loop.
5508 DenseMap<Instruction *, PHINode *> PHIMap;
5509 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5512 /// EvaluateExpression - Given an expression that passes the
5513 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5514 /// in the loop has the value PHIVal. If we can't fold this expression for some
5515 /// reason, return null.
5516 static Constant *EvaluateExpression(Value *V, const Loop *L,
5517 DenseMap<Instruction *, Constant *> &Vals,
5518 const DataLayout &DL,
5519 const TargetLibraryInfo *TLI) {
5520 // Convenient constant check, but redundant for recursive calls.
5521 if (Constant *C = dyn_cast<Constant>(V)) return C;
5522 Instruction *I = dyn_cast<Instruction>(V);
5523 if (!I) return nullptr;
5525 if (Constant *C = Vals.lookup(I)) return C;
5527 // An instruction inside the loop depends on a value outside the loop that we
5528 // weren't given a mapping for, or a value such as a call inside the loop.
5529 if (!canConstantEvolve(I, L)) return nullptr;
5531 // An unmapped PHI can be due to a branch or another loop inside this loop,
5532 // or due to this not being the initial iteration through a loop where we
5533 // couldn't compute the evolution of this particular PHI last time.
5534 if (isa<PHINode>(I)) return nullptr;
5536 std::vector<Constant*> Operands(I->getNumOperands());
5538 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5539 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5541 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5542 if (!Operands[i]) return nullptr;
5545 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5547 if (!C) return nullptr;
5551 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5552 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5553 Operands[1], DL, TLI);
5554 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5555 if (!LI->isVolatile())
5556 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5558 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5562 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5563 /// in the header of its containing loop, we know the loop executes a
5564 /// constant number of times, and the PHI node is just a recurrence
5565 /// involving constants, fold it.
5567 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5570 DenseMap<PHINode*, Constant*>::const_iterator I =
5571 ConstantEvolutionLoopExitValue.find(PN);
5572 if (I != ConstantEvolutionLoopExitValue.end())
5575 if (BEs.ugt(MaxBruteForceIterations))
5576 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5578 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5580 DenseMap<Instruction *, Constant *> CurrentIterVals;
5581 BasicBlock *Header = L->getHeader();
5582 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5584 // Since the loop is canonicalized, the PHI node must have two entries. One
5585 // entry must be a constant (coming in from outside of the loop), and the
5586 // second must be derived from the same PHI.
5587 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5588 PHINode *PHI = nullptr;
5589 for (BasicBlock::iterator I = Header->begin();
5590 (PHI = dyn_cast<PHINode>(I)); ++I) {
5591 Constant *StartCST =
5592 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5593 if (!StartCST) continue;
5594 CurrentIterVals[PHI] = StartCST;
5596 if (!CurrentIterVals.count(PN))
5597 return RetVal = nullptr;
5599 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5601 // Execute the loop symbolically to determine the exit value.
5602 if (BEs.getActiveBits() >= 32)
5603 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5605 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5606 unsigned IterationNum = 0;
5607 const DataLayout &DL = F.getParent()->getDataLayout();
5608 for (; ; ++IterationNum) {
5609 if (IterationNum == NumIterations)
5610 return RetVal = CurrentIterVals[PN]; // Got exit value!
5612 // Compute the value of the PHIs for the next iteration.
5613 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5614 DenseMap<Instruction *, Constant *> NextIterVals;
5616 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5618 return nullptr; // Couldn't evaluate!
5619 NextIterVals[PN] = NextPHI;
5621 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5623 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5624 // cease to be able to evaluate one of them or if they stop evolving,
5625 // because that doesn't necessarily prevent us from computing PN.
5626 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5627 for (DenseMap<Instruction *, Constant *>::const_iterator
5628 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5629 PHINode *PHI = dyn_cast<PHINode>(I->first);
5630 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5631 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5633 // We use two distinct loops because EvaluateExpression may invalidate any
5634 // iterators into CurrentIterVals.
5635 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5636 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5637 PHINode *PHI = I->first;
5638 Constant *&NextPHI = NextIterVals[PHI];
5639 if (!NextPHI) { // Not already computed.
5640 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5641 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5643 if (NextPHI != I->second)
5644 StoppedEvolving = false;
5647 // If all entries in CurrentIterVals == NextIterVals then we can stop
5648 // iterating, the loop can't continue to change.
5649 if (StoppedEvolving)
5650 return RetVal = CurrentIterVals[PN];
5652 CurrentIterVals.swap(NextIterVals);
5656 /// ComputeExitCountExhaustively - If the loop is known to execute a
5657 /// constant number of times (the condition evolves only from constants),
5658 /// try to evaluate a few iterations of the loop until we get the exit
5659 /// condition gets a value of ExitWhen (true or false). If we cannot
5660 /// evaluate the trip count of the loop, return getCouldNotCompute().
5661 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5664 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5665 if (!PN) return getCouldNotCompute();
5667 // If the loop is canonicalized, the PHI will have exactly two entries.
5668 // That's the only form we support here.
5669 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5671 DenseMap<Instruction *, Constant *> CurrentIterVals;
5672 BasicBlock *Header = L->getHeader();
5673 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5675 // One entry must be a constant (coming in from outside of the loop), and the
5676 // second must be derived from the same PHI.
5677 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5678 PHINode *PHI = nullptr;
5679 for (BasicBlock::iterator I = Header->begin();
5680 (PHI = dyn_cast<PHINode>(I)); ++I) {
5681 Constant *StartCST =
5682 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5683 if (!StartCST) continue;
5684 CurrentIterVals[PHI] = StartCST;
5686 if (!CurrentIterVals.count(PN))
5687 return getCouldNotCompute();
5689 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5690 // the loop symbolically to determine when the condition gets a value of
5692 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5693 const DataLayout &DL = F.getParent()->getDataLayout();
5694 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5695 ConstantInt *CondVal = dyn_cast_or_null<ConstantInt>(
5696 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
5698 // Couldn't symbolically evaluate.
5699 if (!CondVal) return getCouldNotCompute();
5701 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5702 ++NumBruteForceTripCountsComputed;
5703 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5706 // Update all the PHI nodes for the next iteration.
5707 DenseMap<Instruction *, Constant *> NextIterVals;
5709 // Create a list of which PHIs we need to compute. We want to do this before
5710 // calling EvaluateExpression on them because that may invalidate iterators
5711 // into CurrentIterVals.
5712 SmallVector<PHINode *, 8> PHIsToCompute;
5713 for (DenseMap<Instruction *, Constant *>::const_iterator
5714 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5715 PHINode *PHI = dyn_cast<PHINode>(I->first);
5716 if (!PHI || PHI->getParent() != Header) continue;
5717 PHIsToCompute.push_back(PHI);
5719 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5720 E = PHIsToCompute.end(); I != E; ++I) {
5722 Constant *&NextPHI = NextIterVals[PHI];
5723 if (NextPHI) continue; // Already computed!
5725 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5726 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5728 CurrentIterVals.swap(NextIterVals);
5731 // Too many iterations were needed to evaluate.
5732 return getCouldNotCompute();
5735 /// getSCEVAtScope - Return a SCEV expression for the specified value
5736 /// at the specified scope in the program. The L value specifies a loop
5737 /// nest to evaluate the expression at, where null is the top-level or a
5738 /// specified loop is immediately inside of the loop.
5740 /// This method can be used to compute the exit value for a variable defined
5741 /// in a loop by querying what the value will hold in the parent loop.
5743 /// In the case that a relevant loop exit value cannot be computed, the
5744 /// original value V is returned.
5745 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5746 // Check to see if we've folded this expression at this loop before.
5747 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5748 for (unsigned u = 0; u < Values.size(); u++) {
5749 if (Values[u].first == L)
5750 return Values[u].second ? Values[u].second : V;
5752 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5753 // Otherwise compute it.
5754 const SCEV *C = computeSCEVAtScope(V, L);
5755 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5756 for (unsigned u = Values2.size(); u > 0; u--) {
5757 if (Values2[u - 1].first == L) {
5758 Values2[u - 1].second = C;
5765 /// This builds up a Constant using the ConstantExpr interface. That way, we
5766 /// will return Constants for objects which aren't represented by a
5767 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5768 /// Returns NULL if the SCEV isn't representable as a Constant.
5769 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5770 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5771 case scCouldNotCompute:
5775 return cast<SCEVConstant>(V)->getValue();
5777 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5778 case scSignExtend: {
5779 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5780 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5781 return ConstantExpr::getSExt(CastOp, SS->getType());
5784 case scZeroExtend: {
5785 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5786 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5787 return ConstantExpr::getZExt(CastOp, SZ->getType());
5791 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5792 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5793 return ConstantExpr::getTrunc(CastOp, ST->getType());
5797 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5798 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5799 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5800 unsigned AS = PTy->getAddressSpace();
5801 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5802 C = ConstantExpr::getBitCast(C, DestPtrTy);
5804 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5805 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5806 if (!C2) return nullptr;
5809 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5810 unsigned AS = C2->getType()->getPointerAddressSpace();
5812 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5813 // The offsets have been converted to bytes. We can add bytes to an
5814 // i8* by GEP with the byte count in the first index.
5815 C = ConstantExpr::getBitCast(C, DestPtrTy);
5818 // Don't bother trying to sum two pointers. We probably can't
5819 // statically compute a load that results from it anyway.
5820 if (C2->getType()->isPointerTy())
5823 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5824 if (PTy->getElementType()->isStructTy())
5825 C2 = ConstantExpr::getIntegerCast(
5826 C2, Type::getInt32Ty(C->getContext()), true);
5827 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
5829 C = ConstantExpr::getAdd(C, C2);
5836 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5837 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5838 // Don't bother with pointers at all.
5839 if (C->getType()->isPointerTy()) return nullptr;
5840 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5841 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5842 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5843 C = ConstantExpr::getMul(C, C2);
5850 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5851 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5852 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5853 if (LHS->getType() == RHS->getType())
5854 return ConstantExpr::getUDiv(LHS, RHS);
5859 break; // TODO: smax, umax.
5864 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5865 if (isa<SCEVConstant>(V)) return V;
5867 // If this instruction is evolved from a constant-evolving PHI, compute the
5868 // exit value from the loop without using SCEVs.
5869 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5870 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5871 const Loop *LI = this->LI[I->getParent()];
5872 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5873 if (PHINode *PN = dyn_cast<PHINode>(I))
5874 if (PN->getParent() == LI->getHeader()) {
5875 // Okay, there is no closed form solution for the PHI node. Check
5876 // to see if the loop that contains it has a known backedge-taken
5877 // count. If so, we may be able to force computation of the exit
5879 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5880 if (const SCEVConstant *BTCC =
5881 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5882 // Okay, we know how many times the containing loop executes. If
5883 // this is a constant evolving PHI node, get the final value at
5884 // the specified iteration number.
5885 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5886 BTCC->getValue()->getValue(),
5888 if (RV) return getSCEV(RV);
5892 // Okay, this is an expression that we cannot symbolically evaluate
5893 // into a SCEV. Check to see if it's possible to symbolically evaluate
5894 // the arguments into constants, and if so, try to constant propagate the
5895 // result. This is particularly useful for computing loop exit values.
5896 if (CanConstantFold(I)) {
5897 SmallVector<Constant *, 4> Operands;
5898 bool MadeImprovement = false;
5899 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5900 Value *Op = I->getOperand(i);
5901 if (Constant *C = dyn_cast<Constant>(Op)) {
5902 Operands.push_back(C);
5906 // If any of the operands is non-constant and if they are
5907 // non-integer and non-pointer, don't even try to analyze them
5908 // with scev techniques.
5909 if (!isSCEVable(Op->getType()))
5912 const SCEV *OrigV = getSCEV(Op);
5913 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5914 MadeImprovement |= OrigV != OpV;
5916 Constant *C = BuildConstantFromSCEV(OpV);
5918 if (C->getType() != Op->getType())
5919 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5923 Operands.push_back(C);
5926 // Check to see if getSCEVAtScope actually made an improvement.
5927 if (MadeImprovement) {
5928 Constant *C = nullptr;
5929 const DataLayout &DL = F.getParent()->getDataLayout();
5930 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5931 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5932 Operands[1], DL, &TLI);
5933 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5934 if (!LI->isVolatile())
5935 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5937 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
5945 // This is some other type of SCEVUnknown, just return it.
5949 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5950 // Avoid performing the look-up in the common case where the specified
5951 // expression has no loop-variant portions.
5952 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5953 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5954 if (OpAtScope != Comm->getOperand(i)) {
5955 // Okay, at least one of these operands is loop variant but might be
5956 // foldable. Build a new instance of the folded commutative expression.
5957 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5958 Comm->op_begin()+i);
5959 NewOps.push_back(OpAtScope);
5961 for (++i; i != e; ++i) {
5962 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5963 NewOps.push_back(OpAtScope);
5965 if (isa<SCEVAddExpr>(Comm))
5966 return getAddExpr(NewOps);
5967 if (isa<SCEVMulExpr>(Comm))
5968 return getMulExpr(NewOps);
5969 if (isa<SCEVSMaxExpr>(Comm))
5970 return getSMaxExpr(NewOps);
5971 if (isa<SCEVUMaxExpr>(Comm))
5972 return getUMaxExpr(NewOps);
5973 llvm_unreachable("Unknown commutative SCEV type!");
5976 // If we got here, all operands are loop invariant.
5980 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5981 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5982 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5983 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5984 return Div; // must be loop invariant
5985 return getUDivExpr(LHS, RHS);
5988 // If this is a loop recurrence for a loop that does not contain L, then we
5989 // are dealing with the final value computed by the loop.
5990 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5991 // First, attempt to evaluate each operand.
5992 // Avoid performing the look-up in the common case where the specified
5993 // expression has no loop-variant portions.
5994 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5995 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5996 if (OpAtScope == AddRec->getOperand(i))
5999 // Okay, at least one of these operands is loop variant but might be
6000 // foldable. Build a new instance of the folded commutative expression.
6001 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6002 AddRec->op_begin()+i);
6003 NewOps.push_back(OpAtScope);
6004 for (++i; i != e; ++i)
6005 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6007 const SCEV *FoldedRec =
6008 getAddRecExpr(NewOps, AddRec->getLoop(),
6009 AddRec->getNoWrapFlags(SCEV::FlagNW));
6010 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6011 // The addrec may be folded to a nonrecurrence, for example, if the
6012 // induction variable is multiplied by zero after constant folding. Go
6013 // ahead and return the folded value.
6019 // If the scope is outside the addrec's loop, evaluate it by using the
6020 // loop exit value of the addrec.
6021 if (!AddRec->getLoop()->contains(L)) {
6022 // To evaluate this recurrence, we need to know how many times the AddRec
6023 // loop iterates. Compute this now.
6024 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6025 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6027 // Then, evaluate the AddRec.
6028 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6034 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6035 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6036 if (Op == Cast->getOperand())
6037 return Cast; // must be loop invariant
6038 return getZeroExtendExpr(Op, Cast->getType());
6041 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6042 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6043 if (Op == Cast->getOperand())
6044 return Cast; // must be loop invariant
6045 return getSignExtendExpr(Op, Cast->getType());
6048 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6049 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6050 if (Op == Cast->getOperand())
6051 return Cast; // must be loop invariant
6052 return getTruncateExpr(Op, Cast->getType());
6055 llvm_unreachable("Unknown SCEV type!");
6058 /// getSCEVAtScope - This is a convenience function which does
6059 /// getSCEVAtScope(getSCEV(V), L).
6060 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6061 return getSCEVAtScope(getSCEV(V), L);
6064 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6065 /// following equation:
6067 /// A * X = B (mod N)
6069 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6070 /// A and B isn't important.
6072 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6073 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6074 ScalarEvolution &SE) {
6075 uint32_t BW = A.getBitWidth();
6076 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6077 assert(A != 0 && "A must be non-zero.");
6081 // The gcd of A and N may have only one prime factor: 2. The number of
6082 // trailing zeros in A is its multiplicity
6083 uint32_t Mult2 = A.countTrailingZeros();
6086 // 2. Check if B is divisible by D.
6088 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6089 // is not less than multiplicity of this prime factor for D.
6090 if (B.countTrailingZeros() < Mult2)
6091 return SE.getCouldNotCompute();
6093 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6096 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6097 // bit width during computations.
6098 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6099 APInt Mod(BW + 1, 0);
6100 Mod.setBit(BW - Mult2); // Mod = N / D
6101 APInt I = AD.multiplicativeInverse(Mod);
6103 // 4. Compute the minimum unsigned root of the equation:
6104 // I * (B / D) mod (N / D)
6105 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6107 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6109 return SE.getConstant(Result.trunc(BW));
6112 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6113 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6114 /// might be the same) or two SCEVCouldNotCompute objects.
6116 static std::pair<const SCEV *,const SCEV *>
6117 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6118 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6119 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6120 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6121 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6123 // We currently can only solve this if the coefficients are constants.
6124 if (!LC || !MC || !NC) {
6125 const SCEV *CNC = SE.getCouldNotCompute();
6126 return std::make_pair(CNC, CNC);
6129 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6130 const APInt &L = LC->getValue()->getValue();
6131 const APInt &M = MC->getValue()->getValue();
6132 const APInt &N = NC->getValue()->getValue();
6133 APInt Two(BitWidth, 2);
6134 APInt Four(BitWidth, 4);
6137 using namespace APIntOps;
6139 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6140 // The B coefficient is M-N/2
6144 // The A coefficient is N/2
6145 APInt A(N.sdiv(Two));
6147 // Compute the B^2-4ac term.
6150 SqrtTerm -= Four * (A * C);
6152 if (SqrtTerm.isNegative()) {
6153 // The loop is provably infinite.
6154 const SCEV *CNC = SE.getCouldNotCompute();
6155 return std::make_pair(CNC, CNC);
6158 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6159 // integer value or else APInt::sqrt() will assert.
6160 APInt SqrtVal(SqrtTerm.sqrt());
6162 // Compute the two solutions for the quadratic formula.
6163 // The divisions must be performed as signed divisions.
6166 if (TwoA.isMinValue()) {
6167 const SCEV *CNC = SE.getCouldNotCompute();
6168 return std::make_pair(CNC, CNC);
6171 LLVMContext &Context = SE.getContext();
6173 ConstantInt *Solution1 =
6174 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6175 ConstantInt *Solution2 =
6176 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6178 return std::make_pair(SE.getConstant(Solution1),
6179 SE.getConstant(Solution2));
6180 } // end APIntOps namespace
6183 /// HowFarToZero - Return the number of times a backedge comparing the specified
6184 /// value to zero will execute. If not computable, return CouldNotCompute.
6186 /// This is only used for loops with a "x != y" exit test. The exit condition is
6187 /// now expressed as a single expression, V = x-y. So the exit test is
6188 /// effectively V != 0. We know and take advantage of the fact that this
6189 /// expression only being used in a comparison by zero context.
6190 ScalarEvolution::ExitLimit
6191 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6192 // If the value is a constant
6193 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6194 // If the value is already zero, the branch will execute zero times.
6195 if (C->getValue()->isZero()) return C;
6196 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6199 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6200 if (!AddRec || AddRec->getLoop() != L)
6201 return getCouldNotCompute();
6203 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6204 // the quadratic equation to solve it.
6205 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6206 std::pair<const SCEV *,const SCEV *> Roots =
6207 SolveQuadraticEquation(AddRec, *this);
6208 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6209 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6212 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6213 << " sol#2: " << *R2 << "\n";
6215 // Pick the smallest positive root value.
6216 if (ConstantInt *CB =
6217 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6220 if (!CB->getZExtValue())
6221 std::swap(R1, R2); // R1 is the minimum root now.
6223 // We can only use this value if the chrec ends up with an exact zero
6224 // value at this index. When solving for "X*X != 5", for example, we
6225 // should not accept a root of 2.
6226 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6228 return R1; // We found a quadratic root!
6231 return getCouldNotCompute();
6234 // Otherwise we can only handle this if it is affine.
6235 if (!AddRec->isAffine())
6236 return getCouldNotCompute();
6238 // If this is an affine expression, the execution count of this branch is
6239 // the minimum unsigned root of the following equation:
6241 // Start + Step*N = 0 (mod 2^BW)
6245 // Step*N = -Start (mod 2^BW)
6247 // where BW is the common bit width of Start and Step.
6249 // Get the initial value for the loop.
6250 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6251 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6253 // For now we handle only constant steps.
6255 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6256 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6257 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6258 // We have not yet seen any such cases.
6259 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6260 if (!StepC || StepC->getValue()->equalsInt(0))
6261 return getCouldNotCompute();
6263 // For positive steps (counting up until unsigned overflow):
6264 // N = -Start/Step (as unsigned)
6265 // For negative steps (counting down to zero):
6267 // First compute the unsigned distance from zero in the direction of Step.
6268 bool CountDown = StepC->getValue()->getValue().isNegative();
6269 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6271 // Handle unitary steps, which cannot wraparound.
6272 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6273 // N = Distance (as unsigned)
6274 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6275 ConstantRange CR = getUnsignedRange(Start);
6276 const SCEV *MaxBECount;
6277 if (!CountDown && CR.getUnsignedMin().isMinValue())
6278 // When counting up, the worst starting value is 1, not 0.
6279 MaxBECount = CR.getUnsignedMax().isMinValue()
6280 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6281 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6283 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6284 : -CR.getUnsignedMin());
6285 return ExitLimit(Distance, MaxBECount);
6288 // As a special case, handle the instance where Step is a positive power of
6289 // two. In this case, determining whether Step divides Distance evenly can be
6290 // done by counting and comparing the number of trailing zeros of Step and
6293 const APInt &StepV = StepC->getValue()->getValue();
6294 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6295 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6296 // case is not handled as this code is guarded by !CountDown.
6297 if (StepV.isPowerOf2() &&
6298 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
6299 // Here we've constrained the equation to be of the form
6301 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
6303 // where we're operating on a W bit wide integer domain and k is
6304 // non-negative. The smallest unsigned solution for X is the trip count.
6306 // (0) is equivalent to:
6308 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
6309 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
6310 // <=> 2^k * Distance' - X = L * 2^(W - N)
6311 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
6313 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
6316 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
6318 // E.g. say we're solving
6320 // 2 * Val = 2 * X (in i8) ... (3)
6322 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
6324 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
6325 // necessarily the smallest unsigned value of X that satisfies (3).
6326 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
6327 // is i8 1, not i8 -127
6329 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
6331 // Since SCEV does not have a URem node, we construct one using a truncate
6332 // and a zero extend.
6334 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
6335 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
6336 auto *WideTy = Distance->getType();
6338 return getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
6342 // If the condition controls loop exit (the loop exits only if the expression
6343 // is true) and the addition is no-wrap we can use unsigned divide to
6344 // compute the backedge count. In this case, the step may not divide the
6345 // distance, but we don't care because if the condition is "missed" the loop
6346 // will have undefined behavior due to wrapping.
6347 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6349 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6350 return ExitLimit(Exact, Exact);
6353 // Then, try to solve the above equation provided that Start is constant.
6354 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6355 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6356 -StartC->getValue()->getValue(),
6358 return getCouldNotCompute();
6361 /// HowFarToNonZero - Return the number of times a backedge checking the
6362 /// specified value for nonzero will execute. If not computable, return
6364 ScalarEvolution::ExitLimit
6365 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6366 // Loops that look like: while (X == 0) are very strange indeed. We don't
6367 // handle them yet except for the trivial case. This could be expanded in the
6368 // future as needed.
6370 // If the value is a constant, check to see if it is known to be non-zero
6371 // already. If so, the backedge will execute zero times.
6372 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6373 if (!C->getValue()->isNullValue())
6374 return getZero(C->getType());
6375 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6378 // We could implement others, but I really doubt anyone writes loops like
6379 // this, and if they did, they would already be constant folded.
6380 return getCouldNotCompute();
6383 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6384 /// (which may not be an immediate predecessor) which has exactly one
6385 /// successor from which BB is reachable, or null if no such block is
6388 std::pair<BasicBlock *, BasicBlock *>
6389 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6390 // If the block has a unique predecessor, then there is no path from the
6391 // predecessor to the block that does not go through the direct edge
6392 // from the predecessor to the block.
6393 if (BasicBlock *Pred = BB->getSinglePredecessor())
6394 return std::make_pair(Pred, BB);
6396 // A loop's header is defined to be a block that dominates the loop.
6397 // If the header has a unique predecessor outside the loop, it must be
6398 // a block that has exactly one successor that can reach the loop.
6399 if (Loop *L = LI.getLoopFor(BB))
6400 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6402 return std::pair<BasicBlock *, BasicBlock *>();
6405 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6406 /// testing whether two expressions are equal, however for the purposes of
6407 /// looking for a condition guarding a loop, it can be useful to be a little
6408 /// more general, since a front-end may have replicated the controlling
6411 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6412 // Quick check to see if they are the same SCEV.
6413 if (A == B) return true;
6415 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6416 // two different instructions with the same value. Check for this case.
6417 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6418 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6419 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6420 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6421 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6424 // Otherwise assume they may have a different value.
6428 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6429 /// predicate Pred. Return true iff any changes were made.
6431 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6432 const SCEV *&LHS, const SCEV *&RHS,
6434 bool Changed = false;
6436 // If we hit the max recursion limit bail out.
6440 // Canonicalize a constant to the right side.
6441 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6442 // Check for both operands constant.
6443 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6444 if (ConstantExpr::getICmp(Pred,
6446 RHSC->getValue())->isNullValue())
6447 goto trivially_false;
6449 goto trivially_true;
6451 // Otherwise swap the operands to put the constant on the right.
6452 std::swap(LHS, RHS);
6453 Pred = ICmpInst::getSwappedPredicate(Pred);
6457 // If we're comparing an addrec with a value which is loop-invariant in the
6458 // addrec's loop, put the addrec on the left. Also make a dominance check,
6459 // as both operands could be addrecs loop-invariant in each other's loop.
6460 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6461 const Loop *L = AR->getLoop();
6462 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6463 std::swap(LHS, RHS);
6464 Pred = ICmpInst::getSwappedPredicate(Pred);
6469 // If there's a constant operand, canonicalize comparisons with boundary
6470 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6471 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6472 const APInt &RA = RC->getValue()->getValue();
6474 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6475 case ICmpInst::ICMP_EQ:
6476 case ICmpInst::ICMP_NE:
6477 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6479 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6480 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6481 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6482 ME->getOperand(0)->isAllOnesValue()) {
6483 RHS = AE->getOperand(1);
6484 LHS = ME->getOperand(1);
6488 case ICmpInst::ICMP_UGE:
6489 if ((RA - 1).isMinValue()) {
6490 Pred = ICmpInst::ICMP_NE;
6491 RHS = getConstant(RA - 1);
6495 if (RA.isMaxValue()) {
6496 Pred = ICmpInst::ICMP_EQ;
6500 if (RA.isMinValue()) goto trivially_true;
6502 Pred = ICmpInst::ICMP_UGT;
6503 RHS = getConstant(RA - 1);
6506 case ICmpInst::ICMP_ULE:
6507 if ((RA + 1).isMaxValue()) {
6508 Pred = ICmpInst::ICMP_NE;
6509 RHS = getConstant(RA + 1);
6513 if (RA.isMinValue()) {
6514 Pred = ICmpInst::ICMP_EQ;
6518 if (RA.isMaxValue()) goto trivially_true;
6520 Pred = ICmpInst::ICMP_ULT;
6521 RHS = getConstant(RA + 1);
6524 case ICmpInst::ICMP_SGE:
6525 if ((RA - 1).isMinSignedValue()) {
6526 Pred = ICmpInst::ICMP_NE;
6527 RHS = getConstant(RA - 1);
6531 if (RA.isMaxSignedValue()) {
6532 Pred = ICmpInst::ICMP_EQ;
6536 if (RA.isMinSignedValue()) goto trivially_true;
6538 Pred = ICmpInst::ICMP_SGT;
6539 RHS = getConstant(RA - 1);
6542 case ICmpInst::ICMP_SLE:
6543 if ((RA + 1).isMaxSignedValue()) {
6544 Pred = ICmpInst::ICMP_NE;
6545 RHS = getConstant(RA + 1);
6549 if (RA.isMinSignedValue()) {
6550 Pred = ICmpInst::ICMP_EQ;
6554 if (RA.isMaxSignedValue()) goto trivially_true;
6556 Pred = ICmpInst::ICMP_SLT;
6557 RHS = getConstant(RA + 1);
6560 case ICmpInst::ICMP_UGT:
6561 if (RA.isMinValue()) {
6562 Pred = ICmpInst::ICMP_NE;
6566 if ((RA + 1).isMaxValue()) {
6567 Pred = ICmpInst::ICMP_EQ;
6568 RHS = getConstant(RA + 1);
6572 if (RA.isMaxValue()) goto trivially_false;
6574 case ICmpInst::ICMP_ULT:
6575 if (RA.isMaxValue()) {
6576 Pred = ICmpInst::ICMP_NE;
6580 if ((RA - 1).isMinValue()) {
6581 Pred = ICmpInst::ICMP_EQ;
6582 RHS = getConstant(RA - 1);
6586 if (RA.isMinValue()) goto trivially_false;
6588 case ICmpInst::ICMP_SGT:
6589 if (RA.isMinSignedValue()) {
6590 Pred = ICmpInst::ICMP_NE;
6594 if ((RA + 1).isMaxSignedValue()) {
6595 Pred = ICmpInst::ICMP_EQ;
6596 RHS = getConstant(RA + 1);
6600 if (RA.isMaxSignedValue()) goto trivially_false;
6602 case ICmpInst::ICMP_SLT:
6603 if (RA.isMaxSignedValue()) {
6604 Pred = ICmpInst::ICMP_NE;
6608 if ((RA - 1).isMinSignedValue()) {
6609 Pred = ICmpInst::ICMP_EQ;
6610 RHS = getConstant(RA - 1);
6614 if (RA.isMinSignedValue()) goto trivially_false;
6619 // Check for obvious equality.
6620 if (HasSameValue(LHS, RHS)) {
6621 if (ICmpInst::isTrueWhenEqual(Pred))
6622 goto trivially_true;
6623 if (ICmpInst::isFalseWhenEqual(Pred))
6624 goto trivially_false;
6627 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6628 // adding or subtracting 1 from one of the operands.
6630 case ICmpInst::ICMP_SLE:
6631 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6632 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6634 Pred = ICmpInst::ICMP_SLT;
6636 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6637 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6639 Pred = ICmpInst::ICMP_SLT;
6643 case ICmpInst::ICMP_SGE:
6644 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6645 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6647 Pred = ICmpInst::ICMP_SGT;
6649 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6650 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6652 Pred = ICmpInst::ICMP_SGT;
6656 case ICmpInst::ICMP_ULE:
6657 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6658 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6660 Pred = ICmpInst::ICMP_ULT;
6662 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6663 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6665 Pred = ICmpInst::ICMP_ULT;
6669 case ICmpInst::ICMP_UGE:
6670 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6671 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6673 Pred = ICmpInst::ICMP_UGT;
6675 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6676 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6678 Pred = ICmpInst::ICMP_UGT;
6686 // TODO: More simplifications are possible here.
6688 // Recursively simplify until we either hit a recursion limit or nothing
6691 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6697 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6698 Pred = ICmpInst::ICMP_EQ;
6703 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6704 Pred = ICmpInst::ICMP_NE;
6708 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6709 return getSignedRange(S).getSignedMax().isNegative();
6712 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6713 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6716 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6717 return !getSignedRange(S).getSignedMin().isNegative();
6720 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6721 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6724 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6725 return isKnownNegative(S) || isKnownPositive(S);
6728 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6729 const SCEV *LHS, const SCEV *RHS) {
6730 // Canonicalize the inputs first.
6731 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6733 // If LHS or RHS is an addrec, check to see if the condition is true in
6734 // every iteration of the loop.
6735 // If LHS and RHS are both addrec, both conditions must be true in
6736 // every iteration of the loop.
6737 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6738 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6739 bool LeftGuarded = false;
6740 bool RightGuarded = false;
6742 const Loop *L = LAR->getLoop();
6743 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6744 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6745 if (!RAR) return true;
6750 const Loop *L = RAR->getLoop();
6751 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6752 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6753 if (!LAR) return true;
6754 RightGuarded = true;
6757 if (LeftGuarded && RightGuarded)
6760 // Otherwise see what can be done with known constant ranges.
6761 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6764 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
6765 ICmpInst::Predicate Pred,
6767 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
6770 // Verify an invariant: inverting the predicate should turn a monotonically
6771 // increasing change to a monotonically decreasing one, and vice versa.
6772 bool IncreasingSwapped;
6773 bool ResultSwapped = isMonotonicPredicateImpl(
6774 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
6776 assert(Result == ResultSwapped && "should be able to analyze both!");
6778 assert(Increasing == !IncreasingSwapped &&
6779 "monotonicity should flip as we flip the predicate");
6785 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
6786 ICmpInst::Predicate Pred,
6789 // A zero step value for LHS means the induction variable is essentially a
6790 // loop invariant value. We don't really depend on the predicate actually
6791 // flipping from false to true (for increasing predicates, and the other way
6792 // around for decreasing predicates), all we care about is that *if* the
6793 // predicate changes then it only changes from false to true.
6795 // A zero step value in itself is not very useful, but there may be places
6796 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
6797 // as general as possible.
6801 return false; // Conservative answer
6803 case ICmpInst::ICMP_UGT:
6804 case ICmpInst::ICMP_UGE:
6805 case ICmpInst::ICMP_ULT:
6806 case ICmpInst::ICMP_ULE:
6807 if (!LHS->getNoWrapFlags(SCEV::FlagNUW))
6810 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
6813 case ICmpInst::ICMP_SGT:
6814 case ICmpInst::ICMP_SGE:
6815 case ICmpInst::ICMP_SLT:
6816 case ICmpInst::ICMP_SLE: {
6817 if (!LHS->getNoWrapFlags(SCEV::FlagNSW))
6820 const SCEV *Step = LHS->getStepRecurrence(*this);
6822 if (isKnownNonNegative(Step)) {
6823 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
6827 if (isKnownNonPositive(Step)) {
6828 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
6837 llvm_unreachable("switch has default clause!");
6840 bool ScalarEvolution::isLoopInvariantPredicate(
6841 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
6842 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
6843 const SCEV *&InvariantRHS) {
6845 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
6846 if (!isLoopInvariant(RHS, L)) {
6847 if (!isLoopInvariant(LHS, L))
6850 std::swap(LHS, RHS);
6851 Pred = ICmpInst::getSwappedPredicate(Pred);
6854 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
6855 if (!ArLHS || ArLHS->getLoop() != L)
6859 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
6862 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
6863 // true as the loop iterates, and the backedge is control dependent on
6864 // "ArLHS `Pred` RHS" == true then we can reason as follows:
6866 // * if the predicate was false in the first iteration then the predicate
6867 // is never evaluated again, since the loop exits without taking the
6869 // * if the predicate was true in the first iteration then it will
6870 // continue to be true for all future iterations since it is
6871 // monotonically increasing.
6873 // For both the above possibilities, we can replace the loop varying
6874 // predicate with its value on the first iteration of the loop (which is
6877 // A similar reasoning applies for a monotonically decreasing predicate, by
6878 // replacing true with false and false with true in the above two bullets.
6880 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
6882 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
6885 InvariantPred = Pred;
6886 InvariantLHS = ArLHS->getStart();
6892 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6893 const SCEV *LHS, const SCEV *RHS) {
6894 if (HasSameValue(LHS, RHS))
6895 return ICmpInst::isTrueWhenEqual(Pred);
6897 // This code is split out from isKnownPredicate because it is called from
6898 // within isLoopEntryGuardedByCond.
6901 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6902 case ICmpInst::ICMP_SGT:
6903 std::swap(LHS, RHS);
6904 case ICmpInst::ICMP_SLT: {
6905 ConstantRange LHSRange = getSignedRange(LHS);
6906 ConstantRange RHSRange = getSignedRange(RHS);
6907 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6909 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6913 case ICmpInst::ICMP_SGE:
6914 std::swap(LHS, RHS);
6915 case ICmpInst::ICMP_SLE: {
6916 ConstantRange LHSRange = getSignedRange(LHS);
6917 ConstantRange RHSRange = getSignedRange(RHS);
6918 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6920 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6924 case ICmpInst::ICMP_UGT:
6925 std::swap(LHS, RHS);
6926 case ICmpInst::ICMP_ULT: {
6927 ConstantRange LHSRange = getUnsignedRange(LHS);
6928 ConstantRange RHSRange = getUnsignedRange(RHS);
6929 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6931 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6935 case ICmpInst::ICMP_UGE:
6936 std::swap(LHS, RHS);
6937 case ICmpInst::ICMP_ULE: {
6938 ConstantRange LHSRange = getUnsignedRange(LHS);
6939 ConstantRange RHSRange = getUnsignedRange(RHS);
6940 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6942 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6946 case ICmpInst::ICMP_NE: {
6947 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6949 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6952 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6953 if (isKnownNonZero(Diff))
6957 case ICmpInst::ICMP_EQ:
6958 // The check at the top of the function catches the case where
6959 // the values are known to be equal.
6965 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6966 /// protected by a conditional between LHS and RHS. This is used to
6967 /// to eliminate casts.
6969 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6970 ICmpInst::Predicate Pred,
6971 const SCEV *LHS, const SCEV *RHS) {
6972 // Interpret a null as meaning no loop, where there is obviously no guard
6973 // (interprocedural conditions notwithstanding).
6974 if (!L) return true;
6976 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6978 BasicBlock *Latch = L->getLoopLatch();
6982 BranchInst *LoopContinuePredicate =
6983 dyn_cast<BranchInst>(Latch->getTerminator());
6984 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6985 isImpliedCond(Pred, LHS, RHS,
6986 LoopContinuePredicate->getCondition(),
6987 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6990 // We don't want more than one activation of the following loops on the stack
6991 // -- that can lead to O(n!) time complexity.
6992 if (WalkingBEDominatingConds)
6995 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
6997 // Check conditions due to any @llvm.assume intrinsics.
6998 for (auto &AssumeVH : AC.assumptions()) {
7001 auto *CI = cast<CallInst>(AssumeVH);
7002 if (!DT.dominates(CI, Latch->getTerminator()))
7005 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7009 // If the loop is not reachable from the entry block, we risk running into an
7010 // infinite loop as we walk up into the dom tree. These loops do not matter
7011 // anyway, so we just return a conservative answer when we see them.
7012 if (!DT.isReachableFromEntry(L->getHeader()))
7015 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7016 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7018 assert(DTN && "should reach the loop header before reaching the root!");
7020 BasicBlock *BB = DTN->getBlock();
7021 BasicBlock *PBB = BB->getSinglePredecessor();
7025 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7026 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7029 Value *Condition = ContinuePredicate->getCondition();
7031 // If we have an edge `E` within the loop body that dominates the only
7032 // latch, the condition guarding `E` also guards the backedge. This
7033 // reasoning works only for loops with a single latch.
7035 BasicBlockEdge DominatingEdge(PBB, BB);
7036 if (DominatingEdge.isSingleEdge()) {
7037 // We're constructively (and conservatively) enumerating edges within the
7038 // loop body that dominate the latch. The dominator tree better agree
7040 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7042 if (isImpliedCond(Pred, LHS, RHS, Condition,
7043 BB != ContinuePredicate->getSuccessor(0)))
7051 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7052 /// by a conditional between LHS and RHS. This is used to help avoid max
7053 /// expressions in loop trip counts, and to eliminate casts.
7055 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7056 ICmpInst::Predicate Pred,
7057 const SCEV *LHS, const SCEV *RHS) {
7058 // Interpret a null as meaning no loop, where there is obviously no guard
7059 // (interprocedural conditions notwithstanding).
7060 if (!L) return false;
7062 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7064 // Starting at the loop predecessor, climb up the predecessor chain, as long
7065 // as there are predecessors that can be found that have unique successors
7066 // leading to the original header.
7067 for (std::pair<BasicBlock *, BasicBlock *>
7068 Pair(L->getLoopPredecessor(), L->getHeader());
7070 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7072 BranchInst *LoopEntryPredicate =
7073 dyn_cast<BranchInst>(Pair.first->getTerminator());
7074 if (!LoopEntryPredicate ||
7075 LoopEntryPredicate->isUnconditional())
7078 if (isImpliedCond(Pred, LHS, RHS,
7079 LoopEntryPredicate->getCondition(),
7080 LoopEntryPredicate->getSuccessor(0) != Pair.second))
7084 // Check conditions due to any @llvm.assume intrinsics.
7085 for (auto &AssumeVH : AC.assumptions()) {
7088 auto *CI = cast<CallInst>(AssumeVH);
7089 if (!DT.dominates(CI, L->getHeader()))
7092 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7099 /// RAII wrapper to prevent recursive application of isImpliedCond.
7100 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7101 /// currently evaluating isImpliedCond.
7102 struct MarkPendingLoopPredicate {
7104 DenseSet<Value*> &LoopPreds;
7107 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7108 : Cond(C), LoopPreds(LP) {
7109 Pending = !LoopPreds.insert(Cond).second;
7111 ~MarkPendingLoopPredicate() {
7113 LoopPreds.erase(Cond);
7117 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7118 /// and RHS is true whenever the given Cond value evaluates to true.
7119 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7120 const SCEV *LHS, const SCEV *RHS,
7121 Value *FoundCondValue,
7123 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7127 // Recursively handle And and Or conditions.
7128 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7129 if (BO->getOpcode() == Instruction::And) {
7131 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7132 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7133 } else if (BO->getOpcode() == Instruction::Or) {
7135 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7136 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7140 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
7141 if (!ICI) return false;
7143 // Now that we found a conditional branch that dominates the loop or controls
7144 // the loop latch. Check to see if it is the comparison we are looking for.
7145 ICmpInst::Predicate FoundPred;
7147 FoundPred = ICI->getInversePredicate();
7149 FoundPred = ICI->getPredicate();
7151 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
7152 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
7154 // Balance the types.
7155 if (getTypeSizeInBits(LHS->getType()) <
7156 getTypeSizeInBits(FoundLHS->getType())) {
7157 if (CmpInst::isSigned(Pred)) {
7158 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
7159 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
7161 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
7162 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
7164 } else if (getTypeSizeInBits(LHS->getType()) >
7165 getTypeSizeInBits(FoundLHS->getType())) {
7166 if (CmpInst::isSigned(FoundPred)) {
7167 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
7168 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
7170 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
7171 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
7175 // Canonicalize the query to match the way instcombine will have
7176 // canonicalized the comparison.
7177 if (SimplifyICmpOperands(Pred, LHS, RHS))
7179 return CmpInst::isTrueWhenEqual(Pred);
7180 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
7181 if (FoundLHS == FoundRHS)
7182 return CmpInst::isFalseWhenEqual(FoundPred);
7184 // Check to see if we can make the LHS or RHS match.
7185 if (LHS == FoundRHS || RHS == FoundLHS) {
7186 if (isa<SCEVConstant>(RHS)) {
7187 std::swap(FoundLHS, FoundRHS);
7188 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
7190 std::swap(LHS, RHS);
7191 Pred = ICmpInst::getSwappedPredicate(Pred);
7195 // Check whether the found predicate is the same as the desired predicate.
7196 if (FoundPred == Pred)
7197 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7199 // Check whether swapping the found predicate makes it the same as the
7200 // desired predicate.
7201 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
7202 if (isa<SCEVConstant>(RHS))
7203 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
7205 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
7206 RHS, LHS, FoundLHS, FoundRHS);
7209 // Check if we can make progress by sharpening ranges.
7210 if (FoundPred == ICmpInst::ICMP_NE &&
7211 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
7213 const SCEVConstant *C = nullptr;
7214 const SCEV *V = nullptr;
7216 if (isa<SCEVConstant>(FoundLHS)) {
7217 C = cast<SCEVConstant>(FoundLHS);
7220 C = cast<SCEVConstant>(FoundRHS);
7224 // The guarding predicate tells us that C != V. If the known range
7225 // of V is [C, t), we can sharpen the range to [C + 1, t). The
7226 // range we consider has to correspond to same signedness as the
7227 // predicate we're interested in folding.
7229 APInt Min = ICmpInst::isSigned(Pred) ?
7230 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7232 if (Min == C->getValue()->getValue()) {
7233 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7234 // This is true even if (Min + 1) wraps around -- in case of
7235 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7237 APInt SharperMin = Min + 1;
7240 case ICmpInst::ICMP_SGE:
7241 case ICmpInst::ICMP_UGE:
7242 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7244 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7245 getConstant(SharperMin)))
7248 case ICmpInst::ICMP_SGT:
7249 case ICmpInst::ICMP_UGT:
7250 // We know from the range information that (V `Pred` Min ||
7251 // V == Min). We know from the guarding condition that !(V
7252 // == Min). This gives us
7254 // V `Pred` Min || V == Min && !(V == Min)
7257 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7259 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7269 // Check whether the actual condition is beyond sufficient.
7270 if (FoundPred == ICmpInst::ICMP_EQ)
7271 if (ICmpInst::isTrueWhenEqual(Pred))
7272 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7274 if (Pred == ICmpInst::ICMP_NE)
7275 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7276 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7279 // Otherwise assume the worst.
7283 /// isImpliedCondOperands - Test whether the condition described by Pred,
7284 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7285 /// and FoundRHS is true.
7286 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7287 const SCEV *LHS, const SCEV *RHS,
7288 const SCEV *FoundLHS,
7289 const SCEV *FoundRHS) {
7290 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7293 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7294 FoundLHS, FoundRHS) ||
7295 // ~x < ~y --> x > y
7296 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7297 getNotSCEV(FoundRHS),
7298 getNotSCEV(FoundLHS));
7302 /// If Expr computes ~A, return A else return nullptr
7303 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7304 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7305 if (!Add || Add->getNumOperands() != 2) return nullptr;
7307 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
7308 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
7311 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7312 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
7314 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
7315 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
7318 return AddRHS->getOperand(1);
7322 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7323 template<typename MaxExprType>
7324 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7325 const SCEV *Candidate) {
7326 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7327 if (!MaxExpr) return false;
7329 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7330 return It != MaxExpr->op_end();
7334 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7335 template<typename MaxExprType>
7336 static bool IsMinConsistingOf(ScalarEvolution &SE,
7337 const SCEV *MaybeMinExpr,
7338 const SCEV *Candidate) {
7339 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7343 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7346 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
7347 ICmpInst::Predicate Pred,
7348 const SCEV *LHS, const SCEV *RHS) {
7350 // If both sides are affine addrecs for the same loop, with equal
7351 // steps, and we know the recurrences don't wrap, then we only
7352 // need to check the predicate on the starting values.
7354 if (!ICmpInst::isRelational(Pred))
7357 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7360 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7363 if (LAR->getLoop() != RAR->getLoop())
7365 if (!LAR->isAffine() || !RAR->isAffine())
7368 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
7371 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
7372 SCEV::FlagNSW : SCEV::FlagNUW;
7373 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
7376 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
7379 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7381 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7382 ICmpInst::Predicate Pred,
7383 const SCEV *LHS, const SCEV *RHS) {
7388 case ICmpInst::ICMP_SGE:
7389 std::swap(LHS, RHS);
7391 case ICmpInst::ICMP_SLE:
7394 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7396 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7398 case ICmpInst::ICMP_UGE:
7399 std::swap(LHS, RHS);
7401 case ICmpInst::ICMP_ULE:
7404 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7406 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7409 llvm_unreachable("covered switch fell through?!");
7412 /// isImpliedCondOperandsHelper - Test whether the condition described by
7413 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7414 /// FoundLHS, and FoundRHS is true.
7416 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7417 const SCEV *LHS, const SCEV *RHS,
7418 const SCEV *FoundLHS,
7419 const SCEV *FoundRHS) {
7420 auto IsKnownPredicateFull =
7421 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7422 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7423 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
7424 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS);
7428 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7429 case ICmpInst::ICMP_EQ:
7430 case ICmpInst::ICMP_NE:
7431 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7434 case ICmpInst::ICMP_SLT:
7435 case ICmpInst::ICMP_SLE:
7436 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7437 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7440 case ICmpInst::ICMP_SGT:
7441 case ICmpInst::ICMP_SGE:
7442 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7443 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7446 case ICmpInst::ICMP_ULT:
7447 case ICmpInst::ICMP_ULE:
7448 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7449 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7452 case ICmpInst::ICMP_UGT:
7453 case ICmpInst::ICMP_UGE:
7454 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7455 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7463 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
7464 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
7465 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
7468 const SCEV *FoundLHS,
7469 const SCEV *FoundRHS) {
7470 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
7471 // The restriction on `FoundRHS` be lifted easily -- it exists only to
7472 // reduce the compile time impact of this optimization.
7475 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
7476 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
7477 !isa<SCEVConstant>(AddLHS->getOperand(0)))
7480 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
7482 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
7483 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
7484 ConstantRange FoundLHSRange =
7485 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
7487 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
7490 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
7491 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
7493 // We can also compute the range of values for `LHS` that satisfy the
7494 // consequent, "`LHS` `Pred` `RHS`":
7495 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
7496 ConstantRange SatisfyingLHSRange =
7497 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
7499 // The antecedent implies the consequent if every value of `LHS` that
7500 // satisfies the antecedent also satisfies the consequent.
7501 return SatisfyingLHSRange.contains(LHSRange);
7504 // Verify if an linear IV with positive stride can overflow when in a
7505 // less-than comparison, knowing the invariant term of the comparison, the
7506 // stride and the knowledge of NSW/NUW flags on the recurrence.
7507 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7508 bool IsSigned, bool NoWrap) {
7509 if (NoWrap) return false;
7511 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7512 const SCEV *One = getOne(Stride->getType());
7515 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7516 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7517 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7520 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7521 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7524 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7525 APInt MaxValue = APInt::getMaxValue(BitWidth);
7526 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7529 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7530 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7533 // Verify if an linear IV with negative stride can overflow when in a
7534 // greater-than comparison, knowing the invariant term of the comparison,
7535 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7536 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7537 bool IsSigned, bool NoWrap) {
7538 if (NoWrap) return false;
7540 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7541 const SCEV *One = getOne(Stride->getType());
7544 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7545 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7546 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7549 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7550 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7553 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7554 APInt MinValue = APInt::getMinValue(BitWidth);
7555 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7558 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7559 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7562 // Compute the backedge taken count knowing the interval difference, the
7563 // stride and presence of the equality in the comparison.
7564 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7566 const SCEV *One = getOne(Step->getType());
7567 Delta = Equality ? getAddExpr(Delta, Step)
7568 : getAddExpr(Delta, getMinusSCEV(Step, One));
7569 return getUDivExpr(Delta, Step);
7572 /// HowManyLessThans - Return the number of times a backedge containing the
7573 /// specified less-than comparison will execute. If not computable, return
7574 /// CouldNotCompute.
7576 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7577 /// the branch (loops exits only if condition is true). In this case, we can use
7578 /// NoWrapFlags to skip overflow checks.
7579 ScalarEvolution::ExitLimit
7580 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7581 const Loop *L, bool IsSigned,
7582 bool ControlsExit) {
7583 // We handle only IV < Invariant
7584 if (!isLoopInvariant(RHS, L))
7585 return getCouldNotCompute();
7587 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7589 // Avoid weird loops
7590 if (!IV || IV->getLoop() != L || !IV->isAffine())
7591 return getCouldNotCompute();
7593 bool NoWrap = ControlsExit &&
7594 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7596 const SCEV *Stride = IV->getStepRecurrence(*this);
7598 // Avoid negative or zero stride values
7599 if (!isKnownPositive(Stride))
7600 return getCouldNotCompute();
7602 // Avoid proven overflow cases: this will ensure that the backedge taken count
7603 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7604 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7605 // behaviors like the case of C language.
7606 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7607 return getCouldNotCompute();
7609 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7610 : ICmpInst::ICMP_ULT;
7611 const SCEV *Start = IV->getStart();
7612 const SCEV *End = RHS;
7613 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7614 const SCEV *Diff = getMinusSCEV(RHS, Start);
7615 // If we have NoWrap set, then we can assume that the increment won't
7616 // overflow, in which case if RHS - Start is a constant, we don't need to
7617 // do a max operation since we can just figure it out statically
7618 if (NoWrap && isa<SCEVConstant>(Diff)) {
7619 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7623 End = IsSigned ? getSMaxExpr(RHS, Start)
7624 : getUMaxExpr(RHS, Start);
7627 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7629 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7630 : getUnsignedRange(Start).getUnsignedMin();
7632 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7633 : getUnsignedRange(Stride).getUnsignedMin();
7635 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7636 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7637 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7639 // Although End can be a MAX expression we estimate MaxEnd considering only
7640 // the case End = RHS. This is safe because in the other case (End - Start)
7641 // is zero, leading to a zero maximum backedge taken count.
7643 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7644 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7646 const SCEV *MaxBECount;
7647 if (isa<SCEVConstant>(BECount))
7648 MaxBECount = BECount;
7650 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7651 getConstant(MinStride), false);
7653 if (isa<SCEVCouldNotCompute>(MaxBECount))
7654 MaxBECount = BECount;
7656 return ExitLimit(BECount, MaxBECount);
7659 ScalarEvolution::ExitLimit
7660 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7661 const Loop *L, bool IsSigned,
7662 bool ControlsExit) {
7663 // We handle only IV > Invariant
7664 if (!isLoopInvariant(RHS, L))
7665 return getCouldNotCompute();
7667 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7669 // Avoid weird loops
7670 if (!IV || IV->getLoop() != L || !IV->isAffine())
7671 return getCouldNotCompute();
7673 bool NoWrap = ControlsExit &&
7674 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7676 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7678 // Avoid negative or zero stride values
7679 if (!isKnownPositive(Stride))
7680 return getCouldNotCompute();
7682 // Avoid proven overflow cases: this will ensure that the backedge taken count
7683 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7684 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7685 // behaviors like the case of C language.
7686 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7687 return getCouldNotCompute();
7689 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7690 : ICmpInst::ICMP_UGT;
7692 const SCEV *Start = IV->getStart();
7693 const SCEV *End = RHS;
7694 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7695 const SCEV *Diff = getMinusSCEV(RHS, Start);
7696 // If we have NoWrap set, then we can assume that the increment won't
7697 // overflow, in which case if RHS - Start is a constant, we don't need to
7698 // do a max operation since we can just figure it out statically
7699 if (NoWrap && isa<SCEVConstant>(Diff)) {
7700 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7701 if (!D.isNegative())
7704 End = IsSigned ? getSMinExpr(RHS, Start)
7705 : getUMinExpr(RHS, Start);
7708 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7710 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7711 : getUnsignedRange(Start).getUnsignedMax();
7713 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7714 : getUnsignedRange(Stride).getUnsignedMin();
7716 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7717 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7718 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7720 // Although End can be a MIN expression we estimate MinEnd considering only
7721 // the case End = RHS. This is safe because in the other case (Start - End)
7722 // is zero, leading to a zero maximum backedge taken count.
7724 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7725 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7728 const SCEV *MaxBECount = getCouldNotCompute();
7729 if (isa<SCEVConstant>(BECount))
7730 MaxBECount = BECount;
7732 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7733 getConstant(MinStride), false);
7735 if (isa<SCEVCouldNotCompute>(MaxBECount))
7736 MaxBECount = BECount;
7738 return ExitLimit(BECount, MaxBECount);
7741 /// getNumIterationsInRange - Return the number of iterations of this loop that
7742 /// produce values in the specified constant range. Another way of looking at
7743 /// this is that it returns the first iteration number where the value is not in
7744 /// the condition, thus computing the exit count. If the iteration count can't
7745 /// be computed, an instance of SCEVCouldNotCompute is returned.
7746 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7747 ScalarEvolution &SE) const {
7748 if (Range.isFullSet()) // Infinite loop.
7749 return SE.getCouldNotCompute();
7751 // If the start is a non-zero constant, shift the range to simplify things.
7752 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7753 if (!SC->getValue()->isZero()) {
7754 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7755 Operands[0] = SE.getZero(SC->getType());
7756 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7757 getNoWrapFlags(FlagNW));
7758 if (const SCEVAddRecExpr *ShiftedAddRec =
7759 dyn_cast<SCEVAddRecExpr>(Shifted))
7760 return ShiftedAddRec->getNumIterationsInRange(
7761 Range.subtract(SC->getValue()->getValue()), SE);
7762 // This is strange and shouldn't happen.
7763 return SE.getCouldNotCompute();
7766 // The only time we can solve this is when we have all constant indices.
7767 // Otherwise, we cannot determine the overflow conditions.
7768 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7769 if (!isa<SCEVConstant>(getOperand(i)))
7770 return SE.getCouldNotCompute();
7773 // Okay at this point we know that all elements of the chrec are constants and
7774 // that the start element is zero.
7776 // First check to see if the range contains zero. If not, the first
7778 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7779 if (!Range.contains(APInt(BitWidth, 0)))
7780 return SE.getZero(getType());
7783 // If this is an affine expression then we have this situation:
7784 // Solve {0,+,A} in Range === Ax in Range
7786 // We know that zero is in the range. If A is positive then we know that
7787 // the upper value of the range must be the first possible exit value.
7788 // If A is negative then the lower of the range is the last possible loop
7789 // value. Also note that we already checked for a full range.
7790 APInt One(BitWidth,1);
7791 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7792 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7794 // The exit value should be (End+A)/A.
7795 APInt ExitVal = (End + A).udiv(A);
7796 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7798 // Evaluate at the exit value. If we really did fall out of the valid
7799 // range, then we computed our trip count, otherwise wrap around or other
7800 // things must have happened.
7801 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7802 if (Range.contains(Val->getValue()))
7803 return SE.getCouldNotCompute(); // Something strange happened
7805 // Ensure that the previous value is in the range. This is a sanity check.
7806 assert(Range.contains(
7807 EvaluateConstantChrecAtConstant(this,
7808 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7809 "Linear scev computation is off in a bad way!");
7810 return SE.getConstant(ExitValue);
7811 } else if (isQuadratic()) {
7812 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7813 // quadratic equation to solve it. To do this, we must frame our problem in
7814 // terms of figuring out when zero is crossed, instead of when
7815 // Range.getUpper() is crossed.
7816 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7817 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7818 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7819 // getNoWrapFlags(FlagNW)
7822 // Next, solve the constructed addrec
7823 std::pair<const SCEV *,const SCEV *> Roots =
7824 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7825 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7826 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7828 // Pick the smallest positive root value.
7829 if (ConstantInt *CB =
7830 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7831 R1->getValue(), R2->getValue()))) {
7832 if (!CB->getZExtValue())
7833 std::swap(R1, R2); // R1 is the minimum root now.
7835 // Make sure the root is not off by one. The returned iteration should
7836 // not be in the range, but the previous one should be. When solving
7837 // for "X*X < 5", for example, we should not return a root of 2.
7838 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7841 if (Range.contains(R1Val->getValue())) {
7842 // The next iteration must be out of the range...
7843 ConstantInt *NextVal =
7844 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7846 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7847 if (!Range.contains(R1Val->getValue()))
7848 return SE.getConstant(NextVal);
7849 return SE.getCouldNotCompute(); // Something strange happened
7852 // If R1 was not in the range, then it is a good return value. Make
7853 // sure that R1-1 WAS in the range though, just in case.
7854 ConstantInt *NextVal =
7855 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7856 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7857 if (Range.contains(R1Val->getValue()))
7859 return SE.getCouldNotCompute(); // Something strange happened
7864 return SE.getCouldNotCompute();
7870 FindUndefs() : Found(false) {}
7872 bool follow(const SCEV *S) {
7873 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7874 if (isa<UndefValue>(C->getValue()))
7876 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7877 if (isa<UndefValue>(C->getValue()))
7881 // Keep looking if we haven't found it yet.
7884 bool isDone() const {
7885 // Stop recursion if we have found an undef.
7891 // Return true when S contains at least an undef value.
7893 containsUndefs(const SCEV *S) {
7895 SCEVTraversal<FindUndefs> ST(F);
7902 // Collect all steps of SCEV expressions.
7903 struct SCEVCollectStrides {
7904 ScalarEvolution &SE;
7905 SmallVectorImpl<const SCEV *> &Strides;
7907 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7908 : SE(SE), Strides(S) {}
7910 bool follow(const SCEV *S) {
7911 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7912 Strides.push_back(AR->getStepRecurrence(SE));
7915 bool isDone() const { return false; }
7918 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7919 struct SCEVCollectTerms {
7920 SmallVectorImpl<const SCEV *> &Terms;
7922 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7925 bool follow(const SCEV *S) {
7926 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7927 if (!containsUndefs(S))
7930 // Stop recursion: once we collected a term, do not walk its operands.
7937 bool isDone() const { return false; }
7941 /// Find parametric terms in this SCEVAddRecExpr.
7942 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
7943 SmallVectorImpl<const SCEV *> &Terms) {
7944 SmallVector<const SCEV *, 4> Strides;
7945 SCEVCollectStrides StrideCollector(*this, Strides);
7946 visitAll(Expr, StrideCollector);
7949 dbgs() << "Strides:\n";
7950 for (const SCEV *S : Strides)
7951 dbgs() << *S << "\n";
7954 for (const SCEV *S : Strides) {
7955 SCEVCollectTerms TermCollector(Terms);
7956 visitAll(S, TermCollector);
7960 dbgs() << "Terms:\n";
7961 for (const SCEV *T : Terms)
7962 dbgs() << *T << "\n";
7966 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7967 SmallVectorImpl<const SCEV *> &Terms,
7968 SmallVectorImpl<const SCEV *> &Sizes) {
7969 int Last = Terms.size() - 1;
7970 const SCEV *Step = Terms[Last];
7972 // End of recursion.
7974 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7975 SmallVector<const SCEV *, 2> Qs;
7976 for (const SCEV *Op : M->operands())
7977 if (!isa<SCEVConstant>(Op))
7980 Step = SE.getMulExpr(Qs);
7983 Sizes.push_back(Step);
7987 for (const SCEV *&Term : Terms) {
7988 // Normalize the terms before the next call to findArrayDimensionsRec.
7990 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7992 // Bail out when GCD does not evenly divide one of the terms.
7999 // Remove all SCEVConstants.
8000 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
8001 return isa<SCEVConstant>(E);
8005 if (Terms.size() > 0)
8006 if (!findArrayDimensionsRec(SE, Terms, Sizes))
8009 Sizes.push_back(Step);
8014 struct FindParameter {
8015 bool FoundParameter;
8016 FindParameter() : FoundParameter(false) {}
8018 bool follow(const SCEV *S) {
8019 if (isa<SCEVUnknown>(S)) {
8020 FoundParameter = true;
8021 // Stop recursion: we found a parameter.
8027 bool isDone() const {
8028 // Stop recursion if we have found a parameter.
8029 return FoundParameter;
8034 // Returns true when S contains at least a SCEVUnknown parameter.
8036 containsParameters(const SCEV *S) {
8038 SCEVTraversal<FindParameter> ST(F);
8041 return F.FoundParameter;
8044 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
8046 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
8047 for (const SCEV *T : Terms)
8048 if (containsParameters(T))
8053 // Return the number of product terms in S.
8054 static inline int numberOfTerms(const SCEV *S) {
8055 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
8056 return Expr->getNumOperands();
8060 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
8061 if (isa<SCEVConstant>(T))
8064 if (isa<SCEVUnknown>(T))
8067 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
8068 SmallVector<const SCEV *, 2> Factors;
8069 for (const SCEV *Op : M->operands())
8070 if (!isa<SCEVConstant>(Op))
8071 Factors.push_back(Op);
8073 return SE.getMulExpr(Factors);
8079 /// Return the size of an element read or written by Inst.
8080 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
8082 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
8083 Ty = Store->getValueOperand()->getType();
8084 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
8085 Ty = Load->getType();
8089 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
8090 return getSizeOfExpr(ETy, Ty);
8093 /// Second step of delinearization: compute the array dimensions Sizes from the
8094 /// set of Terms extracted from the memory access function of this SCEVAddRec.
8095 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
8096 SmallVectorImpl<const SCEV *> &Sizes,
8097 const SCEV *ElementSize) const {
8099 if (Terms.size() < 1 || !ElementSize)
8102 // Early return when Terms do not contain parameters: we do not delinearize
8103 // non parametric SCEVs.
8104 if (!containsParameters(Terms))
8108 dbgs() << "Terms:\n";
8109 for (const SCEV *T : Terms)
8110 dbgs() << *T << "\n";
8113 // Remove duplicates.
8114 std::sort(Terms.begin(), Terms.end());
8115 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
8117 // Put larger terms first.
8118 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
8119 return numberOfTerms(LHS) > numberOfTerms(RHS);
8122 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8124 // Divide all terms by the element size.
8125 for (const SCEV *&Term : Terms) {
8127 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
8131 SmallVector<const SCEV *, 4> NewTerms;
8133 // Remove constant factors.
8134 for (const SCEV *T : Terms)
8135 if (const SCEV *NewT = removeConstantFactors(SE, T))
8136 NewTerms.push_back(NewT);
8139 dbgs() << "Terms after sorting:\n";
8140 for (const SCEV *T : NewTerms)
8141 dbgs() << *T << "\n";
8144 if (NewTerms.empty() ||
8145 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
8150 // The last element to be pushed into Sizes is the size of an element.
8151 Sizes.push_back(ElementSize);
8154 dbgs() << "Sizes:\n";
8155 for (const SCEV *S : Sizes)
8156 dbgs() << *S << "\n";
8160 /// Third step of delinearization: compute the access functions for the
8161 /// Subscripts based on the dimensions in Sizes.
8162 void ScalarEvolution::computeAccessFunctions(
8163 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
8164 SmallVectorImpl<const SCEV *> &Sizes) {
8166 // Early exit in case this SCEV is not an affine multivariate function.
8170 if (auto AR = dyn_cast<SCEVAddRecExpr>(Expr))
8171 if (!AR->isAffine())
8174 const SCEV *Res = Expr;
8175 int Last = Sizes.size() - 1;
8176 for (int i = Last; i >= 0; i--) {
8178 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
8181 dbgs() << "Res: " << *Res << "\n";
8182 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
8183 dbgs() << "Res divided by Sizes[i]:\n";
8184 dbgs() << "Quotient: " << *Q << "\n";
8185 dbgs() << "Remainder: " << *R << "\n";
8190 // Do not record the last subscript corresponding to the size of elements in
8194 // Bail out if the remainder is too complex.
8195 if (isa<SCEVAddRecExpr>(R)) {
8204 // Record the access function for the current subscript.
8205 Subscripts.push_back(R);
8208 // Also push in last position the remainder of the last division: it will be
8209 // the access function of the innermost dimension.
8210 Subscripts.push_back(Res);
8212 std::reverse(Subscripts.begin(), Subscripts.end());
8215 dbgs() << "Subscripts:\n";
8216 for (const SCEV *S : Subscripts)
8217 dbgs() << *S << "\n";
8221 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
8222 /// sizes of an array access. Returns the remainder of the delinearization that
8223 /// is the offset start of the array. The SCEV->delinearize algorithm computes
8224 /// the multiples of SCEV coefficients: that is a pattern matching of sub
8225 /// expressions in the stride and base of a SCEV corresponding to the
8226 /// computation of a GCD (greatest common divisor) of base and stride. When
8227 /// SCEV->delinearize fails, it returns the SCEV unchanged.
8229 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
8231 /// void foo(long n, long m, long o, double A[n][m][o]) {
8233 /// for (long i = 0; i < n; i++)
8234 /// for (long j = 0; j < m; j++)
8235 /// for (long k = 0; k < o; k++)
8236 /// A[i][j][k] = 1.0;
8239 /// the delinearization input is the following AddRec SCEV:
8241 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
8243 /// From this SCEV, we are able to say that the base offset of the access is %A
8244 /// because it appears as an offset that does not divide any of the strides in
8247 /// CHECK: Base offset: %A
8249 /// and then SCEV->delinearize determines the size of some of the dimensions of
8250 /// the array as these are the multiples by which the strides are happening:
8252 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
8254 /// Note that the outermost dimension remains of UnknownSize because there are
8255 /// no strides that would help identifying the size of the last dimension: when
8256 /// the array has been statically allocated, one could compute the size of that
8257 /// dimension by dividing the overall size of the array by the size of the known
8258 /// dimensions: %m * %o * 8.
8260 /// Finally delinearize provides the access functions for the array reference
8261 /// that does correspond to A[i][j][k] of the above C testcase:
8263 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
8265 /// The testcases are checking the output of a function pass:
8266 /// DelinearizationPass that walks through all loads and stores of a function
8267 /// asking for the SCEV of the memory access with respect to all enclosing
8268 /// loops, calling SCEV->delinearize on that and printing the results.
8270 void ScalarEvolution::delinearize(const SCEV *Expr,
8271 SmallVectorImpl<const SCEV *> &Subscripts,
8272 SmallVectorImpl<const SCEV *> &Sizes,
8273 const SCEV *ElementSize) {
8274 // First step: collect parametric terms.
8275 SmallVector<const SCEV *, 4> Terms;
8276 collectParametricTerms(Expr, Terms);
8281 // Second step: find subscript sizes.
8282 findArrayDimensions(Terms, Sizes, ElementSize);
8287 // Third step: compute the access functions for each subscript.
8288 computeAccessFunctions(Expr, Subscripts, Sizes);
8290 if (Subscripts.empty())
8294 dbgs() << "succeeded to delinearize " << *Expr << "\n";
8295 dbgs() << "ArrayDecl[UnknownSize]";
8296 for (const SCEV *S : Sizes)
8297 dbgs() << "[" << *S << "]";
8299 dbgs() << "\nArrayRef";
8300 for (const SCEV *S : Subscripts)
8301 dbgs() << "[" << *S << "]";
8306 //===----------------------------------------------------------------------===//
8307 // SCEVCallbackVH Class Implementation
8308 //===----------------------------------------------------------------------===//
8310 void ScalarEvolution::SCEVCallbackVH::deleted() {
8311 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8312 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
8313 SE->ConstantEvolutionLoopExitValue.erase(PN);
8314 SE->ValueExprMap.erase(getValPtr());
8315 // this now dangles!
8318 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
8319 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8321 // Forget all the expressions associated with users of the old value,
8322 // so that future queries will recompute the expressions using the new
8324 Value *Old = getValPtr();
8325 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
8326 SmallPtrSet<User *, 8> Visited;
8327 while (!Worklist.empty()) {
8328 User *U = Worklist.pop_back_val();
8329 // Deleting the Old value will cause this to dangle. Postpone
8330 // that until everything else is done.
8333 if (!Visited.insert(U).second)
8335 if (PHINode *PN = dyn_cast<PHINode>(U))
8336 SE->ConstantEvolutionLoopExitValue.erase(PN);
8337 SE->ValueExprMap.erase(U);
8338 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
8340 // Delete the Old value.
8341 if (PHINode *PN = dyn_cast<PHINode>(Old))
8342 SE->ConstantEvolutionLoopExitValue.erase(PN);
8343 SE->ValueExprMap.erase(Old);
8344 // this now dangles!
8347 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
8348 : CallbackVH(V), SE(se) {}
8350 //===----------------------------------------------------------------------===//
8351 // ScalarEvolution Class Implementation
8352 //===----------------------------------------------------------------------===//
8354 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
8355 AssumptionCache &AC, DominatorTree &DT,
8357 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
8358 CouldNotCompute(new SCEVCouldNotCompute()),
8359 WalkingBEDominatingConds(false), ValuesAtScopes(64), LoopDispositions(64),
8360 BlockDispositions(64), FirstUnknown(nullptr) {}
8362 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
8363 : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
8364 CouldNotCompute(std::move(Arg.CouldNotCompute)),
8365 ValueExprMap(std::move(Arg.ValueExprMap)),
8366 WalkingBEDominatingConds(false),
8367 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
8368 ConstantEvolutionLoopExitValue(
8369 std::move(Arg.ConstantEvolutionLoopExitValue)),
8370 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
8371 LoopDispositions(std::move(Arg.LoopDispositions)),
8372 BlockDispositions(std::move(Arg.BlockDispositions)),
8373 UnsignedRanges(std::move(Arg.UnsignedRanges)),
8374 SignedRanges(std::move(Arg.SignedRanges)),
8375 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
8376 SCEVAllocator(std::move(Arg.SCEVAllocator)),
8377 FirstUnknown(Arg.FirstUnknown) {
8378 Arg.FirstUnknown = nullptr;
8381 ScalarEvolution::~ScalarEvolution() {
8382 // Iterate through all the SCEVUnknown instances and call their
8383 // destructors, so that they release their references to their values.
8384 for (SCEVUnknown *U = FirstUnknown; U;) {
8385 SCEVUnknown *Tmp = U;
8387 Tmp->~SCEVUnknown();
8389 FirstUnknown = nullptr;
8391 ValueExprMap.clear();
8393 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
8394 // that a loop had multiple computable exits.
8395 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8396 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
8401 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
8402 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
8405 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8406 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8409 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8411 // Print all inner loops first
8412 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8413 PrintLoopInfo(OS, SE, *I);
8416 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8419 SmallVector<BasicBlock *, 8> ExitBlocks;
8420 L->getExitBlocks(ExitBlocks);
8421 if (ExitBlocks.size() != 1)
8422 OS << "<multiple exits> ";
8424 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8425 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8427 OS << "Unpredictable backedge-taken count. ";
8432 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8435 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8436 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8438 OS << "Unpredictable max backedge-taken count. ";
8444 void ScalarEvolution::print(raw_ostream &OS) const {
8445 // ScalarEvolution's implementation of the print method is to print
8446 // out SCEV values of all instructions that are interesting. Doing
8447 // this potentially causes it to create new SCEV objects though,
8448 // which technically conflicts with the const qualifier. This isn't
8449 // observable from outside the class though, so casting away the
8450 // const isn't dangerous.
8451 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8453 OS << "Classifying expressions for: ";
8454 F.printAsOperand(OS, /*PrintType=*/false);
8456 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
8457 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
8460 const SCEV *SV = SE.getSCEV(&*I);
8462 if (!isa<SCEVCouldNotCompute>(SV)) {
8464 SE.getUnsignedRange(SV).print(OS);
8466 SE.getSignedRange(SV).print(OS);
8469 const Loop *L = LI.getLoopFor((*I).getParent());
8471 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8475 if (!isa<SCEVCouldNotCompute>(AtUse)) {
8477 SE.getUnsignedRange(AtUse).print(OS);
8479 SE.getSignedRange(AtUse).print(OS);
8484 OS << "\t\t" "Exits: ";
8485 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8486 if (!SE.isLoopInvariant(ExitValue, L)) {
8487 OS << "<<Unknown>>";
8496 OS << "Determining loop execution counts for: ";
8497 F.printAsOperand(OS, /*PrintType=*/false);
8499 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
8500 PrintLoopInfo(OS, &SE, *I);
8503 ScalarEvolution::LoopDisposition
8504 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8505 auto &Values = LoopDispositions[S];
8506 for (auto &V : Values) {
8507 if (V.getPointer() == L)
8510 Values.emplace_back(L, LoopVariant);
8511 LoopDisposition D = computeLoopDisposition(S, L);
8512 auto &Values2 = LoopDispositions[S];
8513 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8514 if (V.getPointer() == L) {
8522 ScalarEvolution::LoopDisposition
8523 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8524 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8526 return LoopInvariant;
8530 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8531 case scAddRecExpr: {
8532 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8534 // If L is the addrec's loop, it's computable.
8535 if (AR->getLoop() == L)
8536 return LoopComputable;
8538 // Add recurrences are never invariant in the function-body (null loop).
8542 // This recurrence is variant w.r.t. L if L contains AR's loop.
8543 if (L->contains(AR->getLoop()))
8546 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8547 if (AR->getLoop()->contains(L))
8548 return LoopInvariant;
8550 // This recurrence is variant w.r.t. L if any of its operands
8552 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8554 if (!isLoopInvariant(*I, L))
8557 // Otherwise it's loop-invariant.
8558 return LoopInvariant;
8564 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8565 bool HasVarying = false;
8566 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8568 LoopDisposition D = getLoopDisposition(*I, L);
8569 if (D == LoopVariant)
8571 if (D == LoopComputable)
8574 return HasVarying ? LoopComputable : LoopInvariant;
8577 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8578 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8579 if (LD == LoopVariant)
8581 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8582 if (RD == LoopVariant)
8584 return (LD == LoopInvariant && RD == LoopInvariant) ?
8585 LoopInvariant : LoopComputable;
8588 // All non-instruction values are loop invariant. All instructions are loop
8589 // invariant if they are not contained in the specified loop.
8590 // Instructions are never considered invariant in the function body
8591 // (null loop) because they are defined within the "loop".
8592 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8593 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8594 return LoopInvariant;
8595 case scCouldNotCompute:
8596 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8598 llvm_unreachable("Unknown SCEV kind!");
8601 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8602 return getLoopDisposition(S, L) == LoopInvariant;
8605 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8606 return getLoopDisposition(S, L) == LoopComputable;
8609 ScalarEvolution::BlockDisposition
8610 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8611 auto &Values = BlockDispositions[S];
8612 for (auto &V : Values) {
8613 if (V.getPointer() == BB)
8616 Values.emplace_back(BB, DoesNotDominateBlock);
8617 BlockDisposition D = computeBlockDisposition(S, BB);
8618 auto &Values2 = BlockDispositions[S];
8619 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8620 if (V.getPointer() == BB) {
8628 ScalarEvolution::BlockDisposition
8629 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8630 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8632 return ProperlyDominatesBlock;
8636 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8637 case scAddRecExpr: {
8638 // This uses a "dominates" query instead of "properly dominates" query
8639 // to test for proper dominance too, because the instruction which
8640 // produces the addrec's value is a PHI, and a PHI effectively properly
8641 // dominates its entire containing block.
8642 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8643 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
8644 return DoesNotDominateBlock;
8646 // FALL THROUGH into SCEVNAryExpr handling.
8651 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8653 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8655 BlockDisposition D = getBlockDisposition(*I, BB);
8656 if (D == DoesNotDominateBlock)
8657 return DoesNotDominateBlock;
8658 if (D == DominatesBlock)
8661 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8664 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8665 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8666 BlockDisposition LD = getBlockDisposition(LHS, BB);
8667 if (LD == DoesNotDominateBlock)
8668 return DoesNotDominateBlock;
8669 BlockDisposition RD = getBlockDisposition(RHS, BB);
8670 if (RD == DoesNotDominateBlock)
8671 return DoesNotDominateBlock;
8672 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8673 ProperlyDominatesBlock : DominatesBlock;
8676 if (Instruction *I =
8677 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8678 if (I->getParent() == BB)
8679 return DominatesBlock;
8680 if (DT.properlyDominates(I->getParent(), BB))
8681 return ProperlyDominatesBlock;
8682 return DoesNotDominateBlock;
8684 return ProperlyDominatesBlock;
8685 case scCouldNotCompute:
8686 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8688 llvm_unreachable("Unknown SCEV kind!");
8691 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8692 return getBlockDisposition(S, BB) >= DominatesBlock;
8695 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8696 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8700 // Search for a SCEV expression node within an expression tree.
8701 // Implements SCEVTraversal::Visitor.
8706 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8708 bool follow(const SCEV *S) {
8709 IsFound |= (S == Node);
8712 bool isDone() const { return IsFound; }
8716 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8717 SCEVSearch Search(Op);
8718 visitAll(S, Search);
8719 return Search.IsFound;
8722 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8723 ValuesAtScopes.erase(S);
8724 LoopDispositions.erase(S);
8725 BlockDispositions.erase(S);
8726 UnsignedRanges.erase(S);
8727 SignedRanges.erase(S);
8729 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8730 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8731 BackedgeTakenInfo &BEInfo = I->second;
8732 if (BEInfo.hasOperand(S, this)) {
8734 BackedgeTakenCounts.erase(I++);
8741 typedef DenseMap<const Loop *, std::string> VerifyMap;
8743 /// replaceSubString - Replaces all occurrences of From in Str with To.
8744 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8746 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8747 Str.replace(Pos, From.size(), To.data(), To.size());
8752 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8754 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8755 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8756 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8758 std::string &S = Map[L];
8760 raw_string_ostream OS(S);
8761 SE.getBackedgeTakenCount(L)->print(OS);
8763 // false and 0 are semantically equivalent. This can happen in dead loops.
8764 replaceSubString(OS.str(), "false", "0");
8765 // Remove wrap flags, their use in SCEV is highly fragile.
8766 // FIXME: Remove this when SCEV gets smarter about them.
8767 replaceSubString(OS.str(), "<nw>", "");
8768 replaceSubString(OS.str(), "<nsw>", "");
8769 replaceSubString(OS.str(), "<nuw>", "");
8774 void ScalarEvolution::verify() const {
8775 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8777 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8778 // FIXME: It would be much better to store actual values instead of strings,
8779 // but SCEV pointers will change if we drop the caches.
8780 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8781 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
8782 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8784 // Gather stringified backedge taken counts for all loops using a fresh
8785 // ScalarEvolution object.
8786 ScalarEvolution SE2(F, TLI, AC, DT, LI);
8787 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
8788 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
8790 // Now compare whether they're the same with and without caches. This allows
8791 // verifying that no pass changed the cache.
8792 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8793 "New loops suddenly appeared!");
8795 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8796 OldE = BackedgeDumpsOld.end(),
8797 NewI = BackedgeDumpsNew.begin();
8798 OldI != OldE; ++OldI, ++NewI) {
8799 assert(OldI->first == NewI->first && "Loop order changed!");
8801 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8803 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8804 // means that a pass is buggy or SCEV has to learn a new pattern but is
8805 // usually not harmful.
8806 if (OldI->second != NewI->second &&
8807 OldI->second.find("undef") == std::string::npos &&
8808 NewI->second.find("undef") == std::string::npos &&
8809 OldI->second != "***COULDNOTCOMPUTE***" &&
8810 NewI->second != "***COULDNOTCOMPUTE***") {
8811 dbgs() << "SCEVValidator: SCEV for loop '"
8812 << OldI->first->getHeader()->getName()
8813 << "' changed from '" << OldI->second
8814 << "' to '" << NewI->second << "'!\n";
8819 // TODO: Verify more things.
8822 char ScalarEvolutionAnalysis::PassID;
8824 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
8825 AnalysisManager<Function> *AM) {
8826 return ScalarEvolution(F, AM->getResult<TargetLibraryAnalysis>(F),
8827 AM->getResult<AssumptionAnalysis>(F),
8828 AM->getResult<DominatorTreeAnalysis>(F),
8829 AM->getResult<LoopAnalysis>(F));
8833 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> *AM) {
8834 AM->getResult<ScalarEvolutionAnalysis>(F).print(OS);
8835 return PreservedAnalyses::all();
8838 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
8839 "Scalar Evolution Analysis", false, true)
8840 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
8841 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
8842 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
8843 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
8844 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
8845 "Scalar Evolution Analysis", false, true)
8846 char ScalarEvolutionWrapperPass::ID = 0;
8848 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
8849 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
8852 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
8853 SE.reset(new ScalarEvolution(
8854 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
8855 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
8856 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
8857 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
8861 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
8863 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
8867 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
8874 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
8875 AU.setPreservesAll();
8876 AU.addRequiredTransitive<AssumptionCacheTracker>();
8877 AU.addRequiredTransitive<LoopInfoWrapperPass>();
8878 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
8879 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();