1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/IR/PatternMatch.h"
87 #include "llvm/Support/CommandLine.h"
88 #include "llvm/Support/Debug.h"
89 #include "llvm/Support/ErrorHandling.h"
90 #include "llvm/Support/MathExtras.h"
91 #include "llvm/Support/raw_ostream.h"
92 #include "llvm/Support/SaveAndRestore.h"
96 #define DEBUG_TYPE "scalar-evolution"
98 STATISTIC(NumArrayLenItCounts,
99 "Number of trip counts computed with array length");
100 STATISTIC(NumTripCountsComputed,
101 "Number of loops with predictable loop counts");
102 STATISTIC(NumTripCountsNotComputed,
103 "Number of loops without predictable loop counts");
104 STATISTIC(NumBruteForceTripCountsComputed,
105 "Number of loops with trip counts computed by force");
107 static cl::opt<unsigned>
108 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
109 cl::desc("Maximum number of iterations SCEV will "
110 "symbolically execute a constant "
114 // FIXME: Enable this with XDEBUG when the test suite is clean.
116 VerifySCEV("verify-scev",
117 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
119 //===----------------------------------------------------------------------===//
120 // SCEV class definitions
121 //===----------------------------------------------------------------------===//
123 //===----------------------------------------------------------------------===//
124 // Implementation of the SCEV class.
128 void SCEV::dump() const {
133 void SCEV::print(raw_ostream &OS) const {
134 switch (static_cast<SCEVTypes>(getSCEVType())) {
136 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
139 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
140 const SCEV *Op = Trunc->getOperand();
141 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
142 << *Trunc->getType() << ")";
146 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
147 const SCEV *Op = ZExt->getOperand();
148 OS << "(zext " << *Op->getType() << " " << *Op << " to "
149 << *ZExt->getType() << ")";
153 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
154 const SCEV *Op = SExt->getOperand();
155 OS << "(sext " << *Op->getType() << " " << *Op << " to "
156 << *SExt->getType() << ")";
160 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
161 OS << "{" << *AR->getOperand(0);
162 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
163 OS << ",+," << *AR->getOperand(i);
165 if (AR->getNoWrapFlags(FlagNUW))
167 if (AR->getNoWrapFlags(FlagNSW))
169 if (AR->getNoWrapFlags(FlagNW) &&
170 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
172 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
180 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
181 const char *OpStr = nullptr;
182 switch (NAry->getSCEVType()) {
183 case scAddExpr: OpStr = " + "; break;
184 case scMulExpr: OpStr = " * "; break;
185 case scUMaxExpr: OpStr = " umax "; break;
186 case scSMaxExpr: OpStr = " smax "; break;
189 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
192 if (std::next(I) != E)
196 switch (NAry->getSCEVType()) {
199 if (NAry->getNoWrapFlags(FlagNUW))
201 if (NAry->getNoWrapFlags(FlagNSW))
207 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
208 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
212 const SCEVUnknown *U = cast<SCEVUnknown>(this);
214 if (U->isSizeOf(AllocTy)) {
215 OS << "sizeof(" << *AllocTy << ")";
218 if (U->isAlignOf(AllocTy)) {
219 OS << "alignof(" << *AllocTy << ")";
225 if (U->isOffsetOf(CTy, FieldNo)) {
226 OS << "offsetof(" << *CTy << ", ";
227 FieldNo->printAsOperand(OS, false);
232 // Otherwise just print it normally.
233 U->getValue()->printAsOperand(OS, false);
236 case scCouldNotCompute:
237 OS << "***COULDNOTCOMPUTE***";
240 llvm_unreachable("Unknown SCEV kind!");
243 Type *SCEV::getType() const {
244 switch (static_cast<SCEVTypes>(getSCEVType())) {
246 return cast<SCEVConstant>(this)->getType();
250 return cast<SCEVCastExpr>(this)->getType();
255 return cast<SCEVNAryExpr>(this)->getType();
257 return cast<SCEVAddExpr>(this)->getType();
259 return cast<SCEVUDivExpr>(this)->getType();
261 return cast<SCEVUnknown>(this)->getType();
262 case scCouldNotCompute:
263 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
265 llvm_unreachable("Unknown SCEV kind!");
268 bool SCEV::isZero() const {
269 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
270 return SC->getValue()->isZero();
274 bool SCEV::isOne() const {
275 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
276 return SC->getValue()->isOne();
280 bool SCEV::isAllOnesValue() const {
281 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
282 return SC->getValue()->isAllOnesValue();
286 /// isNonConstantNegative - Return true if the specified scev is negated, but
288 bool SCEV::isNonConstantNegative() const {
289 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
290 if (!Mul) return false;
292 // If there is a constant factor, it will be first.
293 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
294 if (!SC) return false;
296 // Return true if the value is negative, this matches things like (-42 * V).
297 return SC->getAPInt().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->getAPInt();
537 const APInt &RA = RC->getAPInt();
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!");
621 } // end anonymous namespace
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!
669 // Returns the size of the SCEV S.
670 static inline int sizeOfSCEV(const SCEV *S) {
671 struct FindSCEVSize {
673 FindSCEVSize() : Size(0) {}
675 bool follow(const SCEV *S) {
677 // Keep looking at all operands of S.
680 bool isDone() const {
686 SCEVTraversal<FindSCEVSize> ST(F);
693 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
695 // Computes the Quotient and Remainder of the division of Numerator by
697 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
698 const SCEV *Denominator, const SCEV **Quotient,
699 const SCEV **Remainder) {
700 assert(Numerator && Denominator && "Uninitialized SCEV");
702 SCEVDivision D(SE, Numerator, Denominator);
704 // Check for the trivial case here to avoid having to check for it in the
706 if (Numerator == Denominator) {
712 if (Numerator->isZero()) {
718 // A simple case when N/1. The quotient is N.
719 if (Denominator->isOne()) {
720 *Quotient = Numerator;
725 // Split the Denominator when it is a product.
726 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
728 *Quotient = Numerator;
729 for (const SCEV *Op : T->operands()) {
730 divide(SE, *Quotient, Op, &Q, &R);
733 // Bail out when the Numerator is not divisible by one of the terms of
737 *Remainder = Numerator;
746 *Quotient = D.Quotient;
747 *Remainder = D.Remainder;
750 // Except in the trivial case described above, we do not know how to divide
751 // Expr by Denominator for the following functions with empty implementation.
752 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
753 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
754 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
755 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
756 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
757 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
758 void visitUnknown(const SCEVUnknown *Numerator) {}
759 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
761 void visitConstant(const SCEVConstant *Numerator) {
762 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
763 APInt NumeratorVal = Numerator->getAPInt();
764 APInt DenominatorVal = D->getAPInt();
765 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
766 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
768 if (NumeratorBW > DenominatorBW)
769 DenominatorVal = DenominatorVal.sext(NumeratorBW);
770 else if (NumeratorBW < DenominatorBW)
771 NumeratorVal = NumeratorVal.sext(DenominatorBW);
773 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
774 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
775 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
776 Quotient = SE.getConstant(QuotientVal);
777 Remainder = SE.getConstant(RemainderVal);
782 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
783 const SCEV *StartQ, *StartR, *StepQ, *StepR;
784 if (!Numerator->isAffine())
785 return cannotDivide(Numerator);
786 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
787 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
788 // Bail out if the types do not match.
789 Type *Ty = Denominator->getType();
790 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
791 Ty != StepQ->getType() || Ty != StepR->getType())
792 return cannotDivide(Numerator);
793 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
794 Numerator->getNoWrapFlags());
795 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
796 Numerator->getNoWrapFlags());
799 void visitAddExpr(const SCEVAddExpr *Numerator) {
800 SmallVector<const SCEV *, 2> Qs, Rs;
801 Type *Ty = Denominator->getType();
803 for (const SCEV *Op : Numerator->operands()) {
805 divide(SE, Op, Denominator, &Q, &R);
807 // Bail out if types do not match.
808 if (Ty != Q->getType() || Ty != R->getType())
809 return cannotDivide(Numerator);
815 if (Qs.size() == 1) {
821 Quotient = SE.getAddExpr(Qs);
822 Remainder = SE.getAddExpr(Rs);
825 void visitMulExpr(const SCEVMulExpr *Numerator) {
826 SmallVector<const SCEV *, 2> Qs;
827 Type *Ty = Denominator->getType();
829 bool FoundDenominatorTerm = false;
830 for (const SCEV *Op : Numerator->operands()) {
831 // Bail out if types do not match.
832 if (Ty != Op->getType())
833 return cannotDivide(Numerator);
835 if (FoundDenominatorTerm) {
840 // Check whether Denominator divides one of the product operands.
842 divide(SE, Op, Denominator, &Q, &R);
848 // Bail out if types do not match.
849 if (Ty != Q->getType())
850 return cannotDivide(Numerator);
852 FoundDenominatorTerm = true;
856 if (FoundDenominatorTerm) {
861 Quotient = SE.getMulExpr(Qs);
865 if (!isa<SCEVUnknown>(Denominator))
866 return cannotDivide(Numerator);
868 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
869 ValueToValueMap RewriteMap;
870 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
871 cast<SCEVConstant>(Zero)->getValue();
872 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
874 if (Remainder->isZero()) {
875 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
876 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
877 cast<SCEVConstant>(One)->getValue();
879 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
883 // Quotient is (Numerator - Remainder) divided by Denominator.
885 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
886 // This SCEV does not seem to simplify: fail the division here.
887 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
888 return cannotDivide(Numerator);
889 divide(SE, Diff, Denominator, &Q, &R);
891 return cannotDivide(Numerator);
896 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
897 const SCEV *Denominator)
898 : SE(S), Denominator(Denominator) {
899 Zero = SE.getZero(Denominator->getType());
900 One = SE.getOne(Denominator->getType());
902 // We generally do not know how to divide Expr by Denominator. We
903 // initialize the division to a "cannot divide" state to simplify the rest
905 cannotDivide(Numerator);
908 // Convenience function for giving up on the division. We set the quotient to
909 // be equal to zero and the remainder to be equal to the numerator.
910 void cannotDivide(const SCEV *Numerator) {
912 Remainder = Numerator;
916 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
921 //===----------------------------------------------------------------------===//
922 // Simple SCEV method implementations
923 //===----------------------------------------------------------------------===//
925 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
927 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
930 // Handle the simplest case efficiently.
932 return SE.getTruncateOrZeroExtend(It, ResultTy);
934 // We are using the following formula for BC(It, K):
936 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
938 // Suppose, W is the bitwidth of the return value. We must be prepared for
939 // overflow. Hence, we must assure that the result of our computation is
940 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
941 // safe in modular arithmetic.
943 // However, this code doesn't use exactly that formula; the formula it uses
944 // is something like the following, where T is the number of factors of 2 in
945 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
948 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
950 // This formula is trivially equivalent to the previous formula. However,
951 // this formula can be implemented much more efficiently. The trick is that
952 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
953 // arithmetic. To do exact division in modular arithmetic, all we have
954 // to do is multiply by the inverse. Therefore, this step can be done at
957 // The next issue is how to safely do the division by 2^T. The way this
958 // is done is by doing the multiplication step at a width of at least W + T
959 // bits. This way, the bottom W+T bits of the product are accurate. Then,
960 // when we perform the division by 2^T (which is equivalent to a right shift
961 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
962 // truncated out after the division by 2^T.
964 // In comparison to just directly using the first formula, this technique
965 // is much more efficient; using the first formula requires W * K bits,
966 // but this formula less than W + K bits. Also, the first formula requires
967 // a division step, whereas this formula only requires multiplies and shifts.
969 // It doesn't matter whether the subtraction step is done in the calculation
970 // width or the input iteration count's width; if the subtraction overflows,
971 // the result must be zero anyway. We prefer here to do it in the width of
972 // the induction variable because it helps a lot for certain cases; CodeGen
973 // isn't smart enough to ignore the overflow, which leads to much less
974 // efficient code if the width of the subtraction is wider than the native
977 // (It's possible to not widen at all by pulling out factors of 2 before
978 // the multiplication; for example, K=2 can be calculated as
979 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
980 // extra arithmetic, so it's not an obvious win, and it gets
981 // much more complicated for K > 3.)
983 // Protection from insane SCEVs; this bound is conservative,
984 // but it probably doesn't matter.
986 return SE.getCouldNotCompute();
988 unsigned W = SE.getTypeSizeInBits(ResultTy);
990 // Calculate K! / 2^T and T; we divide out the factors of two before
991 // multiplying for calculating K! / 2^T to avoid overflow.
992 // Other overflow doesn't matter because we only care about the bottom
993 // W bits of the result.
994 APInt OddFactorial(W, 1);
996 for (unsigned i = 3; i <= K; ++i) {
998 unsigned TwoFactors = Mult.countTrailingZeros();
1000 Mult = Mult.lshr(TwoFactors);
1001 OddFactorial *= Mult;
1004 // We need at least W + T bits for the multiplication step
1005 unsigned CalculationBits = W + T;
1007 // Calculate 2^T, at width T+W.
1008 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1010 // Calculate the multiplicative inverse of K! / 2^T;
1011 // this multiplication factor will perform the exact division by
1013 APInt Mod = APInt::getSignedMinValue(W+1);
1014 APInt MultiplyFactor = OddFactorial.zext(W+1);
1015 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1016 MultiplyFactor = MultiplyFactor.trunc(W);
1018 // Calculate the product, at width T+W
1019 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1021 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1022 for (unsigned i = 1; i != K; ++i) {
1023 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1024 Dividend = SE.getMulExpr(Dividend,
1025 SE.getTruncateOrZeroExtend(S, CalculationTy));
1029 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1031 // Truncate the result, and divide by K! / 2^T.
1033 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1034 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1037 /// evaluateAtIteration - Return the value of this chain of recurrences at
1038 /// the specified iteration number. We can evaluate this recurrence by
1039 /// multiplying each element in the chain by the binomial coefficient
1040 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1042 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1044 /// where BC(It, k) stands for binomial coefficient.
1046 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1047 ScalarEvolution &SE) const {
1048 const SCEV *Result = getStart();
1049 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1050 // The computation is correct in the face of overflow provided that the
1051 // multiplication is performed _after_ the evaluation of the binomial
1053 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1054 if (isa<SCEVCouldNotCompute>(Coeff))
1057 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1062 //===----------------------------------------------------------------------===//
1063 // SCEV Expression folder implementations
1064 //===----------------------------------------------------------------------===//
1066 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1068 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1069 "This is not a truncating conversion!");
1070 assert(isSCEVable(Ty) &&
1071 "This is not a conversion to a SCEVable type!");
1072 Ty = getEffectiveSCEVType(Ty);
1074 FoldingSetNodeID ID;
1075 ID.AddInteger(scTruncate);
1079 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1081 // Fold if the operand is constant.
1082 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1084 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1086 // trunc(trunc(x)) --> trunc(x)
1087 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1088 return getTruncateExpr(ST->getOperand(), Ty);
1090 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1091 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1092 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1094 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1095 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1096 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1098 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1099 // eliminate all the truncates, or we replace other casts with truncates.
1100 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1101 SmallVector<const SCEV *, 4> Operands;
1102 bool hasTrunc = false;
1103 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1104 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1105 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1106 hasTrunc = isa<SCEVTruncateExpr>(S);
1107 Operands.push_back(S);
1110 return getAddExpr(Operands);
1111 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1114 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1115 // eliminate all the truncates, or we replace other casts with truncates.
1116 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1117 SmallVector<const SCEV *, 4> Operands;
1118 bool hasTrunc = false;
1119 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1120 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1121 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1122 hasTrunc = isa<SCEVTruncateExpr>(S);
1123 Operands.push_back(S);
1126 return getMulExpr(Operands);
1127 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1130 // If the input value is a chrec scev, truncate the chrec's operands.
1131 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1132 SmallVector<const SCEV *, 4> Operands;
1133 for (const SCEV *Op : AddRec->operands())
1134 Operands.push_back(getTruncateExpr(Op, Ty));
1135 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1138 // The cast wasn't folded; create an explicit cast node. We can reuse
1139 // the existing insert position since if we get here, we won't have
1140 // made any changes which would invalidate it.
1141 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1143 UniqueSCEVs.InsertNode(S, IP);
1147 // Get the limit of a recurrence such that incrementing by Step cannot cause
1148 // signed overflow as long as the value of the recurrence within the
1149 // loop does not exceed this limit before incrementing.
1150 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1151 ICmpInst::Predicate *Pred,
1152 ScalarEvolution *SE) {
1153 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1154 if (SE->isKnownPositive(Step)) {
1155 *Pred = ICmpInst::ICMP_SLT;
1156 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1157 SE->getSignedRange(Step).getSignedMax());
1159 if (SE->isKnownNegative(Step)) {
1160 *Pred = ICmpInst::ICMP_SGT;
1161 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1162 SE->getSignedRange(Step).getSignedMin());
1167 // Get the limit of a recurrence such that incrementing by Step cannot cause
1168 // unsigned overflow as long as the value of the recurrence within the loop does
1169 // not exceed this limit before incrementing.
1170 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1171 ICmpInst::Predicate *Pred,
1172 ScalarEvolution *SE) {
1173 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1174 *Pred = ICmpInst::ICMP_ULT;
1176 return SE->getConstant(APInt::getMinValue(BitWidth) -
1177 SE->getUnsignedRange(Step).getUnsignedMax());
1182 struct ExtendOpTraitsBase {
1183 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1186 // Used to make code generic over signed and unsigned overflow.
1187 template <typename ExtendOp> struct ExtendOpTraits {
1190 // static const SCEV::NoWrapFlags WrapType;
1192 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1194 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1195 // ICmpInst::Predicate *Pred,
1196 // ScalarEvolution *SE);
1200 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1201 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1203 static const GetExtendExprTy GetExtendExpr;
1205 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1206 ICmpInst::Predicate *Pred,
1207 ScalarEvolution *SE) {
1208 return getSignedOverflowLimitForStep(Step, Pred, SE);
1212 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1213 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1216 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1217 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1219 static const GetExtendExprTy GetExtendExpr;
1221 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1222 ICmpInst::Predicate *Pred,
1223 ScalarEvolution *SE) {
1224 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1228 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1229 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1232 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1233 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1234 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1235 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1236 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1237 // expression "Step + sext/zext(PreIncAR)" is congruent with
1238 // "sext/zext(PostIncAR)"
1239 template <typename ExtendOpTy>
1240 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1241 ScalarEvolution *SE) {
1242 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1243 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1245 const Loop *L = AR->getLoop();
1246 const SCEV *Start = AR->getStart();
1247 const SCEV *Step = AR->getStepRecurrence(*SE);
1249 // Check for a simple looking step prior to loop entry.
1250 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1254 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1255 // subtraction is expensive. For this purpose, perform a quick and dirty
1256 // difference, by checking for Step in the operand list.
1257 SmallVector<const SCEV *, 4> DiffOps;
1258 for (const SCEV *Op : SA->operands())
1260 DiffOps.push_back(Op);
1262 if (DiffOps.size() == SA->getNumOperands())
1265 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1268 // 1. NSW/NUW flags on the step increment.
1269 auto PreStartFlags =
1270 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1271 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
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->getAPInt();
1376 for (unsigned Delta : {-2, -1, 1, 2}) {
1377 const SCEV *PreStart = getConstant(StartAI - Delta);
1379 FoldingSetNodeID ID;
1380 ID.AddInteger(scAddRecExpr);
1381 ID.AddPointer(PreStart);
1382 ID.AddPointer(Step);
1386 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1388 // Give up if we don't already have the add recurrence we need because
1389 // actually constructing an add recurrence is relatively expensive.
1390 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1391 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1392 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1393 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1394 DeltaS, &Pred, this);
1395 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1403 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1405 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1406 "This is not an extending conversion!");
1407 assert(isSCEVable(Ty) &&
1408 "This is not a conversion to a SCEVable type!");
1409 Ty = getEffectiveSCEVType(Ty);
1411 // Fold if the operand is constant.
1412 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1414 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1416 // zext(zext(x)) --> zext(x)
1417 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1418 return getZeroExtendExpr(SZ->getOperand(), Ty);
1420 // Before doing any expensive analysis, check to see if we've already
1421 // computed a SCEV for this Op and Ty.
1422 FoldingSetNodeID ID;
1423 ID.AddInteger(scZeroExtend);
1427 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1429 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1430 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1431 // It's possible the bits taken off by the truncate were all zero bits. If
1432 // so, we should be able to simplify this further.
1433 const SCEV *X = ST->getOperand();
1434 ConstantRange CR = getUnsignedRange(X);
1435 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1436 unsigned NewBits = getTypeSizeInBits(Ty);
1437 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1438 CR.zextOrTrunc(NewBits)))
1439 return getTruncateOrZeroExtend(X, Ty);
1442 // If the input value is a chrec scev, and we can prove that the value
1443 // did not overflow the old, smaller, value, we can zero extend all of the
1444 // operands (often constants). This allows analysis of something like
1445 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1446 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1447 if (AR->isAffine()) {
1448 const SCEV *Start = AR->getStart();
1449 const SCEV *Step = AR->getStepRecurrence(*this);
1450 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1451 const Loop *L = AR->getLoop();
1453 // If we have special knowledge that this addrec won't overflow,
1454 // we don't need to do any further analysis.
1455 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1456 return getAddRecExpr(
1457 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1458 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1460 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1461 // Note that this serves two purposes: It filters out loops that are
1462 // simply not analyzable, and it covers the case where this code is
1463 // being called from within backedge-taken count analysis, such that
1464 // attempting to ask for the backedge-taken count would likely result
1465 // in infinite recursion. In the later case, the analysis code will
1466 // cope with a conservative value, and it will take care to purge
1467 // that value once it has finished.
1468 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1469 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1470 // Manually compute the final value for AR, checking for
1473 // Check whether the backedge-taken count can be losslessly casted to
1474 // the addrec's type. The count is always unsigned.
1475 const SCEV *CastedMaxBECount =
1476 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1477 const SCEV *RecastedMaxBECount =
1478 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1479 if (MaxBECount == RecastedMaxBECount) {
1480 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1481 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1482 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1483 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1484 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1485 const SCEV *WideMaxBECount =
1486 getZeroExtendExpr(CastedMaxBECount, WideTy);
1487 const SCEV *OperandExtendedAdd =
1488 getAddExpr(WideStart,
1489 getMulExpr(WideMaxBECount,
1490 getZeroExtendExpr(Step, WideTy)));
1491 if (ZAdd == OperandExtendedAdd) {
1492 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1493 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1494 // Return the expression with the addrec on the outside.
1495 return getAddRecExpr(
1496 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1497 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1499 // Similar to above, only this time treat the step value as signed.
1500 // This covers loops that count down.
1501 OperandExtendedAdd =
1502 getAddExpr(WideStart,
1503 getMulExpr(WideMaxBECount,
1504 getSignExtendExpr(Step, WideTy)));
1505 if (ZAdd == OperandExtendedAdd) {
1506 // Cache knowledge of AR NW, which is propagated to this AddRec.
1507 // Negative step causes unsigned wrap, but it still can't self-wrap.
1508 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1509 // Return the expression with the addrec on the outside.
1510 return getAddRecExpr(
1511 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1512 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1516 // If the backedge is guarded by a comparison with the pre-inc value
1517 // the addrec is safe. Also, if the entry is guarded by a comparison
1518 // with the start value and the backedge is guarded by a comparison
1519 // with the post-inc value, the addrec is safe.
1520 if (isKnownPositive(Step)) {
1521 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1522 getUnsignedRange(Step).getUnsignedMax());
1523 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1524 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1525 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1526 AR->getPostIncExpr(*this), N))) {
1527 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1528 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1529 // Return the expression with the addrec on the outside.
1530 return getAddRecExpr(
1531 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1532 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1534 } else if (isKnownNegative(Step)) {
1535 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1536 getSignedRange(Step).getSignedMin());
1537 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1538 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1539 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1540 AR->getPostIncExpr(*this), N))) {
1541 // Cache knowledge of AR NW, which is propagated to this AddRec.
1542 // Negative step causes unsigned wrap, but it still can't self-wrap.
1543 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1544 // Return the expression with the addrec on the outside.
1545 return getAddRecExpr(
1546 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1547 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1552 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1553 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1554 return getAddRecExpr(
1555 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1556 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1560 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1561 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1562 if (SA->getNoWrapFlags(SCEV::FlagNUW)) {
1563 // If the addition does not unsign overflow then we can, by definition,
1564 // commute the zero extension with the addition operation.
1565 SmallVector<const SCEV *, 4> Ops;
1566 for (const auto *Op : SA->operands())
1567 Ops.push_back(getZeroExtendExpr(Op, Ty));
1568 return getAddExpr(Ops, SCEV::FlagNUW);
1572 // The cast wasn't folded; create an explicit cast node.
1573 // Recompute the insert position, as it may have been invalidated.
1574 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1575 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1577 UniqueSCEVs.InsertNode(S, IP);
1581 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1583 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1584 "This is not an extending conversion!");
1585 assert(isSCEVable(Ty) &&
1586 "This is not a conversion to a SCEVable type!");
1587 Ty = getEffectiveSCEVType(Ty);
1589 // Fold if the operand is constant.
1590 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1592 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1594 // sext(sext(x)) --> sext(x)
1595 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1596 return getSignExtendExpr(SS->getOperand(), Ty);
1598 // sext(zext(x)) --> zext(x)
1599 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1600 return getZeroExtendExpr(SZ->getOperand(), Ty);
1602 // Before doing any expensive analysis, check to see if we've already
1603 // computed a SCEV for this Op and Ty.
1604 FoldingSetNodeID ID;
1605 ID.AddInteger(scSignExtend);
1609 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1611 // If the input value is provably positive, build a zext instead.
1612 if (isKnownNonNegative(Op))
1613 return getZeroExtendExpr(Op, Ty);
1615 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1616 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1617 // It's possible the bits taken off by the truncate were all sign bits. If
1618 // so, we should be able to simplify this further.
1619 const SCEV *X = ST->getOperand();
1620 ConstantRange CR = getSignedRange(X);
1621 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1622 unsigned NewBits = getTypeSizeInBits(Ty);
1623 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1624 CR.sextOrTrunc(NewBits)))
1625 return getTruncateOrSignExtend(X, Ty);
1628 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1629 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1630 if (SA->getNumOperands() == 2) {
1631 auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1632 auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1634 if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1635 const APInt &C1 = SC1->getAPInt();
1636 const APInt &C2 = SC2->getAPInt();
1637 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1638 C2.ugt(C1) && C2.isPowerOf2())
1639 return getAddExpr(getSignExtendExpr(SC1, Ty),
1640 getSignExtendExpr(SMul, Ty));
1645 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1646 if (SA->getNoWrapFlags(SCEV::FlagNSW)) {
1647 // If the addition does not sign overflow then we can, by definition,
1648 // commute the sign extension with the addition operation.
1649 SmallVector<const SCEV *, 4> Ops;
1650 for (const auto *Op : SA->operands())
1651 Ops.push_back(getSignExtendExpr(Op, Ty));
1652 return getAddExpr(Ops, SCEV::FlagNSW);
1655 // If the input value is a chrec scev, and we can prove that the value
1656 // did not overflow the old, smaller, value, we can sign extend all of the
1657 // operands (often constants). This allows analysis of something like
1658 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1659 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1660 if (AR->isAffine()) {
1661 const SCEV *Start = AR->getStart();
1662 const SCEV *Step = AR->getStepRecurrence(*this);
1663 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1664 const Loop *L = AR->getLoop();
1666 // If we have special knowledge that this addrec won't overflow,
1667 // we don't need to do any further analysis.
1668 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1669 return getAddRecExpr(
1670 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1671 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1673 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1674 // Note that this serves two purposes: It filters out loops that are
1675 // simply not analyzable, and it covers the case where this code is
1676 // being called from within backedge-taken count analysis, such that
1677 // attempting to ask for the backedge-taken count would likely result
1678 // in infinite recursion. In the later case, the analysis code will
1679 // cope with a conservative value, and it will take care to purge
1680 // that value once it has finished.
1681 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1682 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1683 // Manually compute the final value for AR, checking for
1686 // Check whether the backedge-taken count can be losslessly casted to
1687 // the addrec's type. The count is always unsigned.
1688 const SCEV *CastedMaxBECount =
1689 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1690 const SCEV *RecastedMaxBECount =
1691 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1692 if (MaxBECount == RecastedMaxBECount) {
1693 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1694 // Check whether Start+Step*MaxBECount has no signed overflow.
1695 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1696 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1697 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1698 const SCEV *WideMaxBECount =
1699 getZeroExtendExpr(CastedMaxBECount, WideTy);
1700 const SCEV *OperandExtendedAdd =
1701 getAddExpr(WideStart,
1702 getMulExpr(WideMaxBECount,
1703 getSignExtendExpr(Step, WideTy)));
1704 if (SAdd == OperandExtendedAdd) {
1705 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1706 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1707 // Return the expression with the addrec on the outside.
1708 return getAddRecExpr(
1709 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1710 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1712 // Similar to above, only this time treat the step value as unsigned.
1713 // This covers loops that count up with an unsigned step.
1714 OperandExtendedAdd =
1715 getAddExpr(WideStart,
1716 getMulExpr(WideMaxBECount,
1717 getZeroExtendExpr(Step, WideTy)));
1718 if (SAdd == OperandExtendedAdd) {
1719 // If AR wraps around then
1721 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1722 // => SAdd != OperandExtendedAdd
1724 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1725 // (SAdd == OperandExtendedAdd => AR is NW)
1727 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1729 // Return the expression with the addrec on the outside.
1730 return getAddRecExpr(
1731 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1732 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1736 // If the backedge is guarded by a comparison with the pre-inc value
1737 // the addrec is safe. Also, if the entry is guarded by a comparison
1738 // with the start value and the backedge is guarded by a comparison
1739 // with the post-inc value, the addrec is safe.
1740 ICmpInst::Predicate Pred;
1741 const SCEV *OverflowLimit =
1742 getSignedOverflowLimitForStep(Step, &Pred, this);
1743 if (OverflowLimit &&
1744 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1745 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1746 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1748 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1749 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1750 return getAddRecExpr(
1751 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1752 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1755 // If Start and Step are constants, check if we can apply this
1757 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1758 auto *SC1 = dyn_cast<SCEVConstant>(Start);
1759 auto *SC2 = dyn_cast<SCEVConstant>(Step);
1761 const APInt &C1 = SC1->getAPInt();
1762 const APInt &C2 = SC2->getAPInt();
1763 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1765 Start = getSignExtendExpr(Start, Ty);
1766 const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1767 AR->getNoWrapFlags());
1768 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1772 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1773 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1774 return getAddRecExpr(
1775 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1776 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1780 // The cast wasn't folded; create an explicit cast node.
1781 // Recompute the insert position, as it may have been invalidated.
1782 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1783 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1785 UniqueSCEVs.InsertNode(S, IP);
1789 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1790 /// unspecified bits out to the given type.
1792 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1794 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1795 "This is not an extending conversion!");
1796 assert(isSCEVable(Ty) &&
1797 "This is not a conversion to a SCEVable type!");
1798 Ty = getEffectiveSCEVType(Ty);
1800 // Sign-extend negative constants.
1801 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1802 if (SC->getAPInt().isNegative())
1803 return getSignExtendExpr(Op, Ty);
1805 // Peel off a truncate cast.
1806 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1807 const SCEV *NewOp = T->getOperand();
1808 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1809 return getAnyExtendExpr(NewOp, Ty);
1810 return getTruncateOrNoop(NewOp, Ty);
1813 // Next try a zext cast. If the cast is folded, use it.
1814 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1815 if (!isa<SCEVZeroExtendExpr>(ZExt))
1818 // Next try a sext cast. If the cast is folded, use it.
1819 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1820 if (!isa<SCEVSignExtendExpr>(SExt))
1823 // Force the cast to be folded into the operands of an addrec.
1824 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1825 SmallVector<const SCEV *, 4> Ops;
1826 for (const SCEV *Op : AR->operands())
1827 Ops.push_back(getAnyExtendExpr(Op, Ty));
1828 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1831 // If the expression is obviously signed, use the sext cast value.
1832 if (isa<SCEVSMaxExpr>(Op))
1835 // Absent any other information, use the zext cast value.
1839 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1840 /// a list of operands to be added under the given scale, update the given
1841 /// map. This is a helper function for getAddRecExpr. As an example of
1842 /// what it does, given a sequence of operands that would form an add
1843 /// expression like this:
1845 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1847 /// where A and B are constants, update the map with these values:
1849 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1851 /// and add 13 + A*B*29 to AccumulatedConstant.
1852 /// This will allow getAddRecExpr to produce this:
1854 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1856 /// This form often exposes folding opportunities that are hidden in
1857 /// the original operand list.
1859 /// Return true iff it appears that any interesting folding opportunities
1860 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1861 /// the common case where no interesting opportunities are present, and
1862 /// is also used as a check to avoid infinite recursion.
1865 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1866 SmallVectorImpl<const SCEV *> &NewOps,
1867 APInt &AccumulatedConstant,
1868 const SCEV *const *Ops, size_t NumOperands,
1870 ScalarEvolution &SE) {
1871 bool Interesting = false;
1873 // Iterate over the add operands. They are sorted, with constants first.
1875 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1877 // Pull a buried constant out to the outside.
1878 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1880 AccumulatedConstant += Scale * C->getAPInt();
1883 // Next comes everything else. We're especially interested in multiplies
1884 // here, but they're in the middle, so just visit the rest with one loop.
1885 for (; i != NumOperands; ++i) {
1886 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1887 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1889 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
1890 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1891 // A multiplication of a constant with another add; recurse.
1892 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1894 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1895 Add->op_begin(), Add->getNumOperands(),
1898 // A multiplication of a constant with some other value. Update
1900 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1901 const SCEV *Key = SE.getMulExpr(MulOps);
1902 auto Pair = M.insert(std::make_pair(Key, NewScale));
1904 NewOps.push_back(Pair.first->first);
1906 Pair.first->second += NewScale;
1907 // The map already had an entry for this value, which may indicate
1908 // a folding opportunity.
1913 // An ordinary operand. Update the map.
1914 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1915 M.insert(std::make_pair(Ops[i], Scale));
1917 NewOps.push_back(Pair.first->first);
1919 Pair.first->second += Scale;
1920 // The map already had an entry for this value, which may indicate
1921 // a folding opportunity.
1930 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1931 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1932 // can't-overflow flags for the operation if possible.
1933 static SCEV::NoWrapFlags
1934 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1935 const SmallVectorImpl<const SCEV *> &Ops,
1936 SCEV::NoWrapFlags Flags) {
1937 using namespace std::placeholders;
1938 typedef OverflowingBinaryOperator OBO;
1941 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1943 assert(CanAnalyze && "don't call from other places!");
1945 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1946 SCEV::NoWrapFlags SignOrUnsignWrap =
1947 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1949 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1950 auto IsKnownNonNegative = [&](const SCEV *S) {
1951 return SE->isKnownNonNegative(S);
1954 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
1956 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1958 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1960 if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
1961 Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
1963 // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
1964 // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
1966 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
1967 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
1969 ConstantRange::makeNoWrapRegion(Instruction::Add, C, OBO::NoSignedWrap);
1970 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
1971 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
1973 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
1975 ConstantRange::makeNoWrapRegion(Instruction::Add, C,
1976 OBO::NoUnsignedWrap);
1977 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
1978 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
1985 /// getAddExpr - Get a canonical add expression, or something simpler if
1987 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1988 SCEV::NoWrapFlags Flags) {
1989 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1990 "only nuw or nsw allowed");
1991 assert(!Ops.empty() && "Cannot get empty add!");
1992 if (Ops.size() == 1) return Ops[0];
1994 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1995 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1996 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1997 "SCEVAddExpr operand types don't match!");
2000 // Sort by complexity, this groups all similar expression types together.
2001 GroupByComplexity(Ops, &LI);
2003 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2005 // If there are any constants, fold them together.
2007 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2009 assert(Idx < Ops.size());
2010 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2011 // We found two constants, fold them together!
2012 Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2013 if (Ops.size() == 2) return Ops[0];
2014 Ops.erase(Ops.begin()+1); // Erase the folded element
2015 LHSC = cast<SCEVConstant>(Ops[0]);
2018 // If we are left with a constant zero being added, strip it off.
2019 if (LHSC->getValue()->isZero()) {
2020 Ops.erase(Ops.begin());
2024 if (Ops.size() == 1) return Ops[0];
2027 // Okay, check to see if the same value occurs in the operand list more than
2028 // once. If so, merge them together into an multiply expression. Since we
2029 // sorted the list, these values are required to be adjacent.
2030 Type *Ty = Ops[0]->getType();
2031 bool FoundMatch = false;
2032 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2033 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2034 // Scan ahead to count how many equal operands there are.
2036 while (i+Count != e && Ops[i+Count] == Ops[i])
2038 // Merge the values into a multiply.
2039 const SCEV *Scale = getConstant(Ty, Count);
2040 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2041 if (Ops.size() == Count)
2044 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2045 --i; e -= Count - 1;
2049 return getAddExpr(Ops, Flags);
2051 // Check for truncates. If all the operands are truncated from the same
2052 // type, see if factoring out the truncate would permit the result to be
2053 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2054 // if the contents of the resulting outer trunc fold to something simple.
2055 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2056 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2057 Type *DstType = Trunc->getType();
2058 Type *SrcType = Trunc->getOperand()->getType();
2059 SmallVector<const SCEV *, 8> LargeOps;
2061 // Check all the operands to see if they can be represented in the
2062 // source type of the truncate.
2063 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2064 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2065 if (T->getOperand()->getType() != SrcType) {
2069 LargeOps.push_back(T->getOperand());
2070 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2071 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2072 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2073 SmallVector<const SCEV *, 8> LargeMulOps;
2074 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2075 if (const SCEVTruncateExpr *T =
2076 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2077 if (T->getOperand()->getType() != SrcType) {
2081 LargeMulOps.push_back(T->getOperand());
2082 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2083 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2090 LargeOps.push_back(getMulExpr(LargeMulOps));
2097 // Evaluate the expression in the larger type.
2098 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2099 // If it folds to something simple, use it. Otherwise, don't.
2100 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2101 return getTruncateExpr(Fold, DstType);
2105 // Skip past any other cast SCEVs.
2106 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2109 // If there are add operands they would be next.
2110 if (Idx < Ops.size()) {
2111 bool DeletedAdd = false;
2112 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2113 // If we have an add, expand the add operands onto the end of the operands
2115 Ops.erase(Ops.begin()+Idx);
2116 Ops.append(Add->op_begin(), Add->op_end());
2120 // If we deleted at least one add, we added operands to the end of the list,
2121 // and they are not necessarily sorted. Recurse to resort and resimplify
2122 // any operands we just acquired.
2124 return getAddExpr(Ops);
2127 // Skip over the add expression until we get to a multiply.
2128 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2131 // Check to see if there are any folding opportunities present with
2132 // operands multiplied by constant values.
2133 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2134 uint64_t BitWidth = getTypeSizeInBits(Ty);
2135 DenseMap<const SCEV *, APInt> M;
2136 SmallVector<const SCEV *, 8> NewOps;
2137 APInt AccumulatedConstant(BitWidth, 0);
2138 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2139 Ops.data(), Ops.size(),
2140 APInt(BitWidth, 1), *this)) {
2141 struct APIntCompare {
2142 bool operator()(const APInt &LHS, const APInt &RHS) const {
2143 return LHS.ult(RHS);
2147 // Some interesting folding opportunity is present, so its worthwhile to
2148 // re-generate the operands list. Group the operands by constant scale,
2149 // to avoid multiplying by the same constant scale multiple times.
2150 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2151 for (const SCEV *NewOp : NewOps)
2152 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2153 // Re-generate the operands list.
2155 if (AccumulatedConstant != 0)
2156 Ops.push_back(getConstant(AccumulatedConstant));
2157 for (auto &MulOp : MulOpLists)
2158 if (MulOp.first != 0)
2159 Ops.push_back(getMulExpr(getConstant(MulOp.first),
2160 getAddExpr(MulOp.second)));
2163 if (Ops.size() == 1)
2165 return getAddExpr(Ops);
2169 // If we are adding something to a multiply expression, make sure the
2170 // something is not already an operand of the multiply. If so, merge it into
2172 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2173 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2174 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2175 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2176 if (isa<SCEVConstant>(MulOpSCEV))
2178 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2179 if (MulOpSCEV == Ops[AddOp]) {
2180 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2181 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2182 if (Mul->getNumOperands() != 2) {
2183 // If the multiply has more than two operands, we must get the
2185 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2186 Mul->op_begin()+MulOp);
2187 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2188 InnerMul = getMulExpr(MulOps);
2190 const SCEV *One = getOne(Ty);
2191 const SCEV *AddOne = getAddExpr(One, InnerMul);
2192 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2193 if (Ops.size() == 2) return OuterMul;
2195 Ops.erase(Ops.begin()+AddOp);
2196 Ops.erase(Ops.begin()+Idx-1);
2198 Ops.erase(Ops.begin()+Idx);
2199 Ops.erase(Ops.begin()+AddOp-1);
2201 Ops.push_back(OuterMul);
2202 return getAddExpr(Ops);
2205 // Check this multiply against other multiplies being added together.
2206 for (unsigned OtherMulIdx = Idx+1;
2207 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2209 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2210 // If MulOp occurs in OtherMul, we can fold the two multiplies
2212 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2213 OMulOp != e; ++OMulOp)
2214 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2215 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2216 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2217 if (Mul->getNumOperands() != 2) {
2218 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2219 Mul->op_begin()+MulOp);
2220 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2221 InnerMul1 = getMulExpr(MulOps);
2223 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2224 if (OtherMul->getNumOperands() != 2) {
2225 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2226 OtherMul->op_begin()+OMulOp);
2227 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2228 InnerMul2 = getMulExpr(MulOps);
2230 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2231 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2232 if (Ops.size() == 2) return OuterMul;
2233 Ops.erase(Ops.begin()+Idx);
2234 Ops.erase(Ops.begin()+OtherMulIdx-1);
2235 Ops.push_back(OuterMul);
2236 return getAddExpr(Ops);
2242 // If there are any add recurrences in the operands list, see if any other
2243 // added values are loop invariant. If so, we can fold them into the
2245 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2248 // Scan over all recurrences, trying to fold loop invariants into them.
2249 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2250 // Scan all of the other operands to this add and add them to the vector if
2251 // they are loop invariant w.r.t. the recurrence.
2252 SmallVector<const SCEV *, 8> LIOps;
2253 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2254 const Loop *AddRecLoop = AddRec->getLoop();
2255 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2256 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2257 LIOps.push_back(Ops[i]);
2258 Ops.erase(Ops.begin()+i);
2262 // If we found some loop invariants, fold them into the recurrence.
2263 if (!LIOps.empty()) {
2264 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2265 LIOps.push_back(AddRec->getStart());
2267 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2269 AddRecOps[0] = getAddExpr(LIOps);
2271 // Build the new addrec. Propagate the NUW and NSW flags if both the
2272 // outer add and the inner addrec are guaranteed to have no overflow.
2273 // Always propagate NW.
2274 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2275 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2277 // If all of the other operands were loop invariant, we are done.
2278 if (Ops.size() == 1) return NewRec;
2280 // Otherwise, add the folded AddRec by the non-invariant parts.
2281 for (unsigned i = 0;; ++i)
2282 if (Ops[i] == AddRec) {
2286 return getAddExpr(Ops);
2289 // Okay, if there weren't any loop invariants to be folded, check to see if
2290 // there are multiple AddRec's with the same loop induction variable being
2291 // added together. If so, we can fold them.
2292 for (unsigned OtherIdx = Idx+1;
2293 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2295 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2296 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2297 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2299 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2301 if (const auto *OtherAddRec = dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2302 if (OtherAddRec->getLoop() == AddRecLoop) {
2303 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2305 if (i >= AddRecOps.size()) {
2306 AddRecOps.append(OtherAddRec->op_begin()+i,
2307 OtherAddRec->op_end());
2310 AddRecOps[i] = getAddExpr(AddRecOps[i],
2311 OtherAddRec->getOperand(i));
2313 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2315 // Step size has changed, so we cannot guarantee no self-wraparound.
2316 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2317 return getAddExpr(Ops);
2320 // Otherwise couldn't fold anything into this recurrence. Move onto the
2324 // Okay, it looks like we really DO need an add expr. Check to see if we
2325 // already have one, otherwise create a new one.
2326 FoldingSetNodeID ID;
2327 ID.AddInteger(scAddExpr);
2328 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2329 ID.AddPointer(Ops[i]);
2332 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2334 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2335 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2336 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2338 UniqueSCEVs.InsertNode(S, IP);
2340 S->setNoWrapFlags(Flags);
2344 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2346 if (j > 1 && k / j != i) Overflow = true;
2350 /// Compute the result of "n choose k", the binomial coefficient. If an
2351 /// intermediate computation overflows, Overflow will be set and the return will
2352 /// be garbage. Overflow is not cleared on absence of overflow.
2353 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2354 // We use the multiplicative formula:
2355 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2356 // At each iteration, we take the n-th term of the numeral and divide by the
2357 // (k-n)th term of the denominator. This division will always produce an
2358 // integral result, and helps reduce the chance of overflow in the
2359 // intermediate computations. However, we can still overflow even when the
2360 // final result would fit.
2362 if (n == 0 || n == k) return 1;
2363 if (k > n) return 0;
2369 for (uint64_t i = 1; i <= k; ++i) {
2370 r = umul_ov(r, n-(i-1), Overflow);
2376 /// Determine if any of the operands in this SCEV are a constant or if
2377 /// any of the add or multiply expressions in this SCEV contain a constant.
2378 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2379 SmallVector<const SCEV *, 4> Ops;
2380 Ops.push_back(StartExpr);
2381 while (!Ops.empty()) {
2382 const SCEV *CurrentExpr = Ops.pop_back_val();
2383 if (isa<SCEVConstant>(*CurrentExpr))
2386 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2387 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2388 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2394 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2396 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2397 SCEV::NoWrapFlags Flags) {
2398 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2399 "only nuw or nsw allowed");
2400 assert(!Ops.empty() && "Cannot get empty mul!");
2401 if (Ops.size() == 1) return Ops[0];
2403 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2404 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2405 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2406 "SCEVMulExpr operand types don't match!");
2409 // Sort by complexity, this groups all similar expression types together.
2410 GroupByComplexity(Ops, &LI);
2412 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2414 // If there are any constants, fold them together.
2416 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2418 // C1*(C2+V) -> C1*C2 + C1*V
2419 if (Ops.size() == 2)
2420 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2421 // If any of Add's ops are Adds or Muls with a constant,
2422 // apply this transformation as well.
2423 if (Add->getNumOperands() == 2)
2424 if (containsConstantSomewhere(Add))
2425 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2426 getMulExpr(LHSC, Add->getOperand(1)));
2429 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2430 // We found two constants, fold them together!
2432 ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2433 Ops[0] = getConstant(Fold);
2434 Ops.erase(Ops.begin()+1); // Erase the folded element
2435 if (Ops.size() == 1) return Ops[0];
2436 LHSC = cast<SCEVConstant>(Ops[0]);
2439 // If we are left with a constant one being multiplied, strip it off.
2440 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2441 Ops.erase(Ops.begin());
2443 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2444 // If we have a multiply of zero, it will always be zero.
2446 } else if (Ops[0]->isAllOnesValue()) {
2447 // If we have a mul by -1 of an add, try distributing the -1 among the
2449 if (Ops.size() == 2) {
2450 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2451 SmallVector<const SCEV *, 4> NewOps;
2452 bool AnyFolded = false;
2453 for (const SCEV *AddOp : Add->operands()) {
2454 const SCEV *Mul = getMulExpr(Ops[0], AddOp);
2455 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2456 NewOps.push_back(Mul);
2459 return getAddExpr(NewOps);
2460 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2461 // Negation preserves a recurrence's no self-wrap property.
2462 SmallVector<const SCEV *, 4> Operands;
2463 for (const SCEV *AddRecOp : AddRec->operands())
2464 Operands.push_back(getMulExpr(Ops[0], AddRecOp));
2466 return getAddRecExpr(Operands, AddRec->getLoop(),
2467 AddRec->getNoWrapFlags(SCEV::FlagNW));
2472 if (Ops.size() == 1)
2476 // Skip over the add expression until we get to a multiply.
2477 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2480 // If there are mul operands inline them all into this expression.
2481 if (Idx < Ops.size()) {
2482 bool DeletedMul = false;
2483 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2484 // If we have an mul, expand the mul operands onto the end of the operands
2486 Ops.erase(Ops.begin()+Idx);
2487 Ops.append(Mul->op_begin(), Mul->op_end());
2491 // If we deleted at least one mul, we added operands to the end of the list,
2492 // and they are not necessarily sorted. Recurse to resort and resimplify
2493 // any operands we just acquired.
2495 return getMulExpr(Ops);
2498 // If there are any add recurrences in the operands list, see if any other
2499 // added values are loop invariant. If so, we can fold them into the
2501 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2504 // Scan over all recurrences, trying to fold loop invariants into them.
2505 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2506 // Scan all of the other operands to this mul and add them to the vector if
2507 // they are loop invariant w.r.t. the recurrence.
2508 SmallVector<const SCEV *, 8> LIOps;
2509 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2510 const Loop *AddRecLoop = AddRec->getLoop();
2511 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2512 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2513 LIOps.push_back(Ops[i]);
2514 Ops.erase(Ops.begin()+i);
2518 // If we found some loop invariants, fold them into the recurrence.
2519 if (!LIOps.empty()) {
2520 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2521 SmallVector<const SCEV *, 4> NewOps;
2522 NewOps.reserve(AddRec->getNumOperands());
2523 const SCEV *Scale = getMulExpr(LIOps);
2524 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2525 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2527 // Build the new addrec. Propagate the NUW and NSW flags if both the
2528 // outer mul and the inner addrec are guaranteed to have no overflow.
2530 // No self-wrap cannot be guaranteed after changing the step size, but
2531 // will be inferred if either NUW or NSW is true.
2532 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2533 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2535 // If all of the other operands were loop invariant, we are done.
2536 if (Ops.size() == 1) return NewRec;
2538 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2539 for (unsigned i = 0;; ++i)
2540 if (Ops[i] == AddRec) {
2544 return getMulExpr(Ops);
2547 // Okay, if there weren't any loop invariants to be folded, check to see if
2548 // there are multiple AddRec's with the same loop induction variable being
2549 // multiplied together. If so, we can fold them.
2551 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2552 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2553 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2554 // ]]],+,...up to x=2n}.
2555 // Note that the arguments to choose() are always integers with values
2556 // known at compile time, never SCEV objects.
2558 // The implementation avoids pointless extra computations when the two
2559 // addrec's are of different length (mathematically, it's equivalent to
2560 // an infinite stream of zeros on the right).
2561 bool OpsModified = false;
2562 for (unsigned OtherIdx = Idx+1;
2563 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2565 const SCEVAddRecExpr *OtherAddRec =
2566 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2567 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2570 bool Overflow = false;
2571 Type *Ty = AddRec->getType();
2572 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2573 SmallVector<const SCEV*, 7> AddRecOps;
2574 for (int x = 0, xe = AddRec->getNumOperands() +
2575 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2576 const SCEV *Term = getZero(Ty);
2577 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2578 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2579 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2580 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2581 z < ze && !Overflow; ++z) {
2582 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2584 if (LargerThan64Bits)
2585 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2587 Coeff = Coeff1*Coeff2;
2588 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2589 const SCEV *Term1 = AddRec->getOperand(y-z);
2590 const SCEV *Term2 = OtherAddRec->getOperand(z);
2591 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2594 AddRecOps.push_back(Term);
2597 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2599 if (Ops.size() == 2) return NewAddRec;
2600 Ops[Idx] = NewAddRec;
2601 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2603 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2609 return getMulExpr(Ops);
2611 // Otherwise couldn't fold anything into this recurrence. Move onto the
2615 // Okay, it looks like we really DO need an mul expr. Check to see if we
2616 // already have one, otherwise create a new one.
2617 FoldingSetNodeID ID;
2618 ID.AddInteger(scMulExpr);
2619 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2620 ID.AddPointer(Ops[i]);
2623 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2625 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2626 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2627 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2629 UniqueSCEVs.InsertNode(S, IP);
2631 S->setNoWrapFlags(Flags);
2635 /// getUDivExpr - Get a canonical unsigned division expression, or something
2636 /// simpler if possible.
2637 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2639 assert(getEffectiveSCEVType(LHS->getType()) ==
2640 getEffectiveSCEVType(RHS->getType()) &&
2641 "SCEVUDivExpr operand types don't match!");
2643 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2644 if (RHSC->getValue()->equalsInt(1))
2645 return LHS; // X udiv 1 --> x
2646 // If the denominator is zero, the result of the udiv is undefined. Don't
2647 // try to analyze it, because the resolution chosen here may differ from
2648 // the resolution chosen in other parts of the compiler.
2649 if (!RHSC->getValue()->isZero()) {
2650 // Determine if the division can be folded into the operands of
2652 // TODO: Generalize this to non-constants by using known-bits information.
2653 Type *Ty = LHS->getType();
2654 unsigned LZ = RHSC->getAPInt().countLeadingZeros();
2655 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2656 // For non-power-of-two values, effectively round the value up to the
2657 // nearest power of two.
2658 if (!RHSC->getAPInt().isPowerOf2())
2660 IntegerType *ExtTy =
2661 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2662 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2663 if (const SCEVConstant *Step =
2664 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2665 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2666 const APInt &StepInt = Step->getAPInt();
2667 const APInt &DivInt = RHSC->getAPInt();
2668 if (!StepInt.urem(DivInt) &&
2669 getZeroExtendExpr(AR, ExtTy) ==
2670 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2671 getZeroExtendExpr(Step, ExtTy),
2672 AR->getLoop(), SCEV::FlagAnyWrap)) {
2673 SmallVector<const SCEV *, 4> Operands;
2674 for (const SCEV *Op : AR->operands())
2675 Operands.push_back(getUDivExpr(Op, RHS));
2676 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
2678 /// Get a canonical UDivExpr for a recurrence.
2679 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2680 // We can currently only fold X%N if X is constant.
2681 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2682 if (StartC && !DivInt.urem(StepInt) &&
2683 getZeroExtendExpr(AR, ExtTy) ==
2684 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2685 getZeroExtendExpr(Step, ExtTy),
2686 AR->getLoop(), SCEV::FlagAnyWrap)) {
2687 const APInt &StartInt = StartC->getAPInt();
2688 const APInt &StartRem = StartInt.urem(StepInt);
2690 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2691 AR->getLoop(), SCEV::FlagNW);
2694 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2695 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2696 SmallVector<const SCEV *, 4> Operands;
2697 for (const SCEV *Op : M->operands())
2698 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2699 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2700 // Find an operand that's safely divisible.
2701 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2702 const SCEV *Op = M->getOperand(i);
2703 const SCEV *Div = getUDivExpr(Op, RHSC);
2704 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2705 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2708 return getMulExpr(Operands);
2712 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2713 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2714 SmallVector<const SCEV *, 4> Operands;
2715 for (const SCEV *Op : A->operands())
2716 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2717 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2719 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2720 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2721 if (isa<SCEVUDivExpr>(Op) ||
2722 getMulExpr(Op, RHS) != A->getOperand(i))
2724 Operands.push_back(Op);
2726 if (Operands.size() == A->getNumOperands())
2727 return getAddExpr(Operands);
2731 // Fold if both operands are constant.
2732 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2733 Constant *LHSCV = LHSC->getValue();
2734 Constant *RHSCV = RHSC->getValue();
2735 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2741 FoldingSetNodeID ID;
2742 ID.AddInteger(scUDivExpr);
2746 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2747 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2749 UniqueSCEVs.InsertNode(S, IP);
2753 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2754 APInt A = C1->getAPInt().abs();
2755 APInt B = C2->getAPInt().abs();
2756 uint32_t ABW = A.getBitWidth();
2757 uint32_t BBW = B.getBitWidth();
2764 return APIntOps::GreatestCommonDivisor(A, B);
2767 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2768 /// something simpler if possible. There is no representation for an exact udiv
2769 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2770 /// We can't do this when it's not exact because the udiv may be clearing bits.
2771 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2773 // TODO: we could try to find factors in all sorts of things, but for now we
2774 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2775 // end of this file for inspiration.
2777 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2779 return getUDivExpr(LHS, RHS);
2781 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2782 // If the mulexpr multiplies by a constant, then that constant must be the
2783 // first element of the mulexpr.
2784 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2785 if (LHSCst == RHSCst) {
2786 SmallVector<const SCEV *, 2> Operands;
2787 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2788 return getMulExpr(Operands);
2791 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2792 // that there's a factor provided by one of the other terms. We need to
2794 APInt Factor = gcd(LHSCst, RHSCst);
2795 if (!Factor.isIntN(1)) {
2797 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
2799 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
2800 SmallVector<const SCEV *, 2> Operands;
2801 Operands.push_back(LHSCst);
2802 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2803 LHS = getMulExpr(Operands);
2805 Mul = dyn_cast<SCEVMulExpr>(LHS);
2807 return getUDivExactExpr(LHS, RHS);
2812 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2813 if (Mul->getOperand(i) == RHS) {
2814 SmallVector<const SCEV *, 2> Operands;
2815 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2816 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2817 return getMulExpr(Operands);
2821 return getUDivExpr(LHS, RHS);
2824 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2825 /// Simplify the expression as much as possible.
2826 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2828 SCEV::NoWrapFlags Flags) {
2829 SmallVector<const SCEV *, 4> Operands;
2830 Operands.push_back(Start);
2831 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2832 if (StepChrec->getLoop() == L) {
2833 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2834 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2837 Operands.push_back(Step);
2838 return getAddRecExpr(Operands, L, Flags);
2841 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2842 /// Simplify the expression as much as possible.
2844 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2845 const Loop *L, SCEV::NoWrapFlags Flags) {
2846 if (Operands.size() == 1) return Operands[0];
2848 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2849 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2850 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2851 "SCEVAddRecExpr operand types don't match!");
2852 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2853 assert(isLoopInvariant(Operands[i], L) &&
2854 "SCEVAddRecExpr operand is not loop-invariant!");
2857 if (Operands.back()->isZero()) {
2858 Operands.pop_back();
2859 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2862 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2863 // use that information to infer NUW and NSW flags. However, computing a
2864 // BE count requires calling getAddRecExpr, so we may not yet have a
2865 // meaningful BE count at this point (and if we don't, we'd be stuck
2866 // with a SCEVCouldNotCompute as the cached BE count).
2868 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2870 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2871 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2872 const Loop *NestedLoop = NestedAR->getLoop();
2873 if (L->contains(NestedLoop)
2874 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2875 : (!NestedLoop->contains(L) &&
2876 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2877 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2878 NestedAR->op_end());
2879 Operands[0] = NestedAR->getStart();
2880 // AddRecs require their operands be loop-invariant with respect to their
2881 // loops. Don't perform this transformation if it would break this
2883 bool AllInvariant = all_of(
2884 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
2887 // Create a recurrence for the outer loop with the same step size.
2889 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2890 // inner recurrence has the same property.
2891 SCEV::NoWrapFlags OuterFlags =
2892 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2894 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2895 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
2896 return isLoopInvariant(Op, NestedLoop);
2900 // Ok, both add recurrences are valid after the transformation.
2902 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2903 // the outer recurrence has the same property.
2904 SCEV::NoWrapFlags InnerFlags =
2905 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2906 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2909 // Reset Operands to its original state.
2910 Operands[0] = NestedAR;
2914 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2915 // already have one, otherwise create a new one.
2916 FoldingSetNodeID ID;
2917 ID.AddInteger(scAddRecExpr);
2918 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2919 ID.AddPointer(Operands[i]);
2923 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2925 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2926 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2927 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2928 O, Operands.size(), L);
2929 UniqueSCEVs.InsertNode(S, IP);
2931 S->setNoWrapFlags(Flags);
2936 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2937 const SmallVectorImpl<const SCEV *> &IndexExprs,
2939 // getSCEV(Base)->getType() has the same address space as Base->getType()
2940 // because SCEV::getType() preserves the address space.
2941 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2942 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2943 // instruction to its SCEV, because the Instruction may be guarded by control
2944 // flow and the no-overflow bits may not be valid for the expression in any
2945 // context. This can be fixed similarly to how these flags are handled for
2947 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2949 const SCEV *TotalOffset = getZero(IntPtrTy);
2950 // The address space is unimportant. The first thing we do on CurTy is getting
2951 // its element type.
2952 Type *CurTy = PointerType::getUnqual(PointeeType);
2953 for (const SCEV *IndexExpr : IndexExprs) {
2954 // Compute the (potentially symbolic) offset in bytes for this index.
2955 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2956 // For a struct, add the member offset.
2957 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2958 unsigned FieldNo = Index->getZExtValue();
2959 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2961 // Add the field offset to the running total offset.
2962 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2964 // Update CurTy to the type of the field at Index.
2965 CurTy = STy->getTypeAtIndex(Index);
2967 // Update CurTy to its element type.
2968 CurTy = cast<SequentialType>(CurTy)->getElementType();
2969 // For an array, add the element offset, explicitly scaled.
2970 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2971 // Getelementptr indices are signed.
2972 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2974 // Multiply the index by the element size to compute the element offset.
2975 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2977 // Add the element offset to the running total offset.
2978 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2982 // Add the total offset from all the GEP indices to the base.
2983 return getAddExpr(BaseExpr, TotalOffset, Wrap);
2986 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2988 SmallVector<const SCEV *, 2> Ops;
2991 return getSMaxExpr(Ops);
2995 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2996 assert(!Ops.empty() && "Cannot get empty smax!");
2997 if (Ops.size() == 1) return Ops[0];
2999 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3000 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3001 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3002 "SCEVSMaxExpr operand types don't match!");
3005 // Sort by complexity, this groups all similar expression types together.
3006 GroupByComplexity(Ops, &LI);
3008 // If there are any constants, fold them together.
3010 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3012 assert(Idx < Ops.size());
3013 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3014 // We found two constants, fold them together!
3015 ConstantInt *Fold = ConstantInt::get(
3016 getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
3017 Ops[0] = getConstant(Fold);
3018 Ops.erase(Ops.begin()+1); // Erase the folded element
3019 if (Ops.size() == 1) return Ops[0];
3020 LHSC = cast<SCEVConstant>(Ops[0]);
3023 // If we are left with a constant minimum-int, strip it off.
3024 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3025 Ops.erase(Ops.begin());
3027 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3028 // If we have an smax with a constant maximum-int, it will always be
3033 if (Ops.size() == 1) return Ops[0];
3036 // Find the first SMax
3037 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3040 // Check to see if one of the operands is an SMax. If so, expand its operands
3041 // onto our operand list, and recurse to simplify.
3042 if (Idx < Ops.size()) {
3043 bool DeletedSMax = false;
3044 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3045 Ops.erase(Ops.begin()+Idx);
3046 Ops.append(SMax->op_begin(), SMax->op_end());
3051 return getSMaxExpr(Ops);
3054 // Okay, check to see if the same value occurs in the operand list twice. If
3055 // so, delete one. Since we sorted the list, these values are required to
3057 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3058 // X smax Y smax Y --> X smax Y
3059 // X smax Y --> X, if X is always greater than Y
3060 if (Ops[i] == Ops[i+1] ||
3061 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3062 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3064 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3065 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3069 if (Ops.size() == 1) return Ops[0];
3071 assert(!Ops.empty() && "Reduced smax down to nothing!");
3073 // Okay, it looks like we really DO need an smax expr. Check to see if we
3074 // already have one, otherwise create a new one.
3075 FoldingSetNodeID ID;
3076 ID.AddInteger(scSMaxExpr);
3077 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3078 ID.AddPointer(Ops[i]);
3080 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3081 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3082 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3083 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3085 UniqueSCEVs.InsertNode(S, IP);
3089 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3091 SmallVector<const SCEV *, 2> Ops;
3094 return getUMaxExpr(Ops);
3098 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3099 assert(!Ops.empty() && "Cannot get empty umax!");
3100 if (Ops.size() == 1) return Ops[0];
3102 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3103 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3104 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3105 "SCEVUMaxExpr operand types don't match!");
3108 // Sort by complexity, this groups all similar expression types together.
3109 GroupByComplexity(Ops, &LI);
3111 // If there are any constants, fold them together.
3113 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3115 assert(Idx < Ops.size());
3116 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3117 // We found two constants, fold them together!
3118 ConstantInt *Fold = ConstantInt::get(
3119 getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
3120 Ops[0] = getConstant(Fold);
3121 Ops.erase(Ops.begin()+1); // Erase the folded element
3122 if (Ops.size() == 1) return Ops[0];
3123 LHSC = cast<SCEVConstant>(Ops[0]);
3126 // If we are left with a constant minimum-int, strip it off.
3127 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3128 Ops.erase(Ops.begin());
3130 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3131 // If we have an umax with a constant maximum-int, it will always be
3136 if (Ops.size() == 1) return Ops[0];
3139 // Find the first UMax
3140 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3143 // Check to see if one of the operands is a UMax. If so, expand its operands
3144 // onto our operand list, and recurse to simplify.
3145 if (Idx < Ops.size()) {
3146 bool DeletedUMax = false;
3147 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3148 Ops.erase(Ops.begin()+Idx);
3149 Ops.append(UMax->op_begin(), UMax->op_end());
3154 return getUMaxExpr(Ops);
3157 // Okay, check to see if the same value occurs in the operand list twice. If
3158 // so, delete one. Since we sorted the list, these values are required to
3160 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3161 // X umax Y umax Y --> X umax Y
3162 // X umax Y --> X, if X is always greater than Y
3163 if (Ops[i] == Ops[i+1] ||
3164 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3165 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3167 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3168 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3172 if (Ops.size() == 1) return Ops[0];
3174 assert(!Ops.empty() && "Reduced umax down to nothing!");
3176 // Okay, it looks like we really DO need a umax expr. Check to see if we
3177 // already have one, otherwise create a new one.
3178 FoldingSetNodeID ID;
3179 ID.AddInteger(scUMaxExpr);
3180 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3181 ID.AddPointer(Ops[i]);
3183 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3184 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3185 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3186 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3188 UniqueSCEVs.InsertNode(S, IP);
3192 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3194 // ~smax(~x, ~y) == smin(x, y).
3195 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3198 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3200 // ~umax(~x, ~y) == umin(x, y)
3201 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3204 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3205 // We can bypass creating a target-independent
3206 // constant expression and then folding it back into a ConstantInt.
3207 // This is just a compile-time optimization.
3208 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3211 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3214 // We can bypass creating a target-independent
3215 // constant expression and then folding it back into a ConstantInt.
3216 // This is just a compile-time optimization.
3218 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3221 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3222 // Don't attempt to do anything other than create a SCEVUnknown object
3223 // here. createSCEV only calls getUnknown after checking for all other
3224 // interesting possibilities, and any other code that calls getUnknown
3225 // is doing so in order to hide a value from SCEV canonicalization.
3227 FoldingSetNodeID ID;
3228 ID.AddInteger(scUnknown);
3231 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3232 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3233 "Stale SCEVUnknown in uniquing map!");
3236 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3238 FirstUnknown = cast<SCEVUnknown>(S);
3239 UniqueSCEVs.InsertNode(S, IP);
3243 //===----------------------------------------------------------------------===//
3244 // Basic SCEV Analysis and PHI Idiom Recognition Code
3247 /// isSCEVable - Test if values of the given type are analyzable within
3248 /// the SCEV framework. This primarily includes integer types, and it
3249 /// can optionally include pointer types if the ScalarEvolution class
3250 /// has access to target-specific information.
3251 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3252 // Integers and pointers are always SCEVable.
3253 return Ty->isIntegerTy() || Ty->isPointerTy();
3256 /// getTypeSizeInBits - Return the size in bits of the specified type,
3257 /// for which isSCEVable must return true.
3258 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3259 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3260 return getDataLayout().getTypeSizeInBits(Ty);
3263 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3264 /// the given type and which represents how SCEV will treat the given
3265 /// type, for which isSCEVable must return true. For pointer types,
3266 /// this is the pointer-sized integer type.
3267 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3268 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3270 if (Ty->isIntegerTy())
3273 // The only other support type is pointer.
3274 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3275 return getDataLayout().getIntPtrType(Ty);
3278 const SCEV *ScalarEvolution::getCouldNotCompute() {
3279 return CouldNotCompute.get();
3283 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3284 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3285 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3286 // is set iff if find such SCEVUnknown.
3288 struct FindInvalidSCEVUnknown {
3290 FindInvalidSCEVUnknown() { FindOne = false; }
3291 bool follow(const SCEV *S) {
3292 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3296 if (!cast<SCEVUnknown>(S)->getValue())
3303 bool isDone() const { return FindOne; }
3306 FindInvalidSCEVUnknown F;
3307 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3313 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3314 /// expression and create a new one.
3315 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3316 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3318 const SCEV *S = getExistingSCEV(V);
3321 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3326 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3327 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3329 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3330 if (I != ValueExprMap.end()) {
3331 const SCEV *S = I->second;
3332 if (checkValidity(S))
3334 ValueExprMap.erase(I);
3339 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3341 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3342 SCEV::NoWrapFlags Flags) {
3343 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3345 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3347 Type *Ty = V->getType();
3348 Ty = getEffectiveSCEVType(Ty);
3350 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3353 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3354 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3355 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3357 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3359 Type *Ty = V->getType();
3360 Ty = getEffectiveSCEVType(Ty);
3361 const SCEV *AllOnes =
3362 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3363 return getMinusSCEV(AllOnes, V);
3366 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3367 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3368 SCEV::NoWrapFlags Flags) {
3369 // Fast path: X - X --> 0.
3371 return getZero(LHS->getType());
3373 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3374 // makes it so that we cannot make much use of NUW.
3375 auto AddFlags = SCEV::FlagAnyWrap;
3376 const bool RHSIsNotMinSigned =
3377 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3378 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3379 // Let M be the minimum representable signed value. Then (-1)*RHS
3380 // signed-wraps if and only if RHS is M. That can happen even for
3381 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3382 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3383 // (-1)*RHS, we need to prove that RHS != M.
3385 // If LHS is non-negative and we know that LHS - RHS does not
3386 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3387 // either by proving that RHS > M or that LHS >= 0.
3388 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3389 AddFlags = SCEV::FlagNSW;
3393 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3394 // RHS is NSW and LHS >= 0.
3396 // The difficulty here is that the NSW flag may have been proven
3397 // relative to a loop that is to be found in a recurrence in LHS and
3398 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3399 // larger scope than intended.
3400 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3402 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3405 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3406 /// input value to the specified type. If the type must be extended, it is zero
3409 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3410 Type *SrcTy = V->getType();
3411 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3412 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3413 "Cannot truncate or zero extend with non-integer arguments!");
3414 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3415 return V; // No conversion
3416 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3417 return getTruncateExpr(V, Ty);
3418 return getZeroExtendExpr(V, Ty);
3421 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3422 /// input value to the specified type. If the type must be extended, it is sign
3425 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3427 Type *SrcTy = V->getType();
3428 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3429 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3430 "Cannot truncate or zero extend with non-integer arguments!");
3431 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3432 return V; // No conversion
3433 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3434 return getTruncateExpr(V, Ty);
3435 return getSignExtendExpr(V, Ty);
3438 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3439 /// input value to the specified type. If the type must be extended, it is zero
3440 /// extended. The conversion must not be narrowing.
3442 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3443 Type *SrcTy = V->getType();
3444 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3445 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3446 "Cannot noop or zero extend with non-integer arguments!");
3447 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3448 "getNoopOrZeroExtend cannot truncate!");
3449 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3450 return V; // No conversion
3451 return getZeroExtendExpr(V, Ty);
3454 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3455 /// input value to the specified type. If the type must be extended, it is sign
3456 /// extended. The conversion must not be narrowing.
3458 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3459 Type *SrcTy = V->getType();
3460 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3461 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3462 "Cannot noop or sign extend with non-integer arguments!");
3463 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3464 "getNoopOrSignExtend cannot truncate!");
3465 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3466 return V; // No conversion
3467 return getSignExtendExpr(V, Ty);
3470 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3471 /// the input value to the specified type. If the type must be extended,
3472 /// it is extended with unspecified bits. The conversion must not be
3475 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3476 Type *SrcTy = V->getType();
3477 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3478 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3479 "Cannot noop or any extend with non-integer arguments!");
3480 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3481 "getNoopOrAnyExtend cannot truncate!");
3482 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3483 return V; // No conversion
3484 return getAnyExtendExpr(V, Ty);
3487 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3488 /// input value to the specified type. The conversion must not be widening.
3490 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3491 Type *SrcTy = V->getType();
3492 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3493 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3494 "Cannot truncate or noop with non-integer arguments!");
3495 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3496 "getTruncateOrNoop cannot extend!");
3497 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3498 return V; // No conversion
3499 return getTruncateExpr(V, Ty);
3502 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3503 /// the types using zero-extension, and then perform a umax operation
3505 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3507 const SCEV *PromotedLHS = LHS;
3508 const SCEV *PromotedRHS = RHS;
3510 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3511 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3513 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3515 return getUMaxExpr(PromotedLHS, PromotedRHS);
3518 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3519 /// the types using zero-extension, and then perform a umin operation
3521 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3523 const SCEV *PromotedLHS = LHS;
3524 const SCEV *PromotedRHS = RHS;
3526 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3527 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3529 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3531 return getUMinExpr(PromotedLHS, PromotedRHS);
3534 /// getPointerBase - Transitively follow the chain of pointer-type operands
3535 /// until reaching a SCEV that does not have a single pointer operand. This
3536 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3537 /// but corner cases do exist.
3538 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3539 // A pointer operand may evaluate to a nonpointer expression, such as null.
3540 if (!V->getType()->isPointerTy())
3543 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3544 return getPointerBase(Cast->getOperand());
3545 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3546 const SCEV *PtrOp = nullptr;
3547 for (const SCEV *NAryOp : NAry->operands()) {
3548 if (NAryOp->getType()->isPointerTy()) {
3549 // Cannot find the base of an expression with multiple pointer operands.
3557 return getPointerBase(PtrOp);
3562 /// PushDefUseChildren - Push users of the given Instruction
3563 /// onto the given Worklist.
3565 PushDefUseChildren(Instruction *I,
3566 SmallVectorImpl<Instruction *> &Worklist) {
3567 // Push the def-use children onto the Worklist stack.
3568 for (User *U : I->users())
3569 Worklist.push_back(cast<Instruction>(U));
3572 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3573 /// instructions that depend on the given instruction and removes them from
3574 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3577 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3578 SmallVector<Instruction *, 16> Worklist;
3579 PushDefUseChildren(PN, Worklist);
3581 SmallPtrSet<Instruction *, 8> Visited;
3583 while (!Worklist.empty()) {
3584 Instruction *I = Worklist.pop_back_val();
3585 if (!Visited.insert(I).second)
3588 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
3589 if (It != ValueExprMap.end()) {
3590 const SCEV *Old = It->second;
3592 // Short-circuit the def-use traversal if the symbolic name
3593 // ceases to appear in expressions.
3594 if (Old != SymName && !hasOperand(Old, SymName))
3597 // SCEVUnknown for a PHI either means that it has an unrecognized
3598 // structure, it's a PHI that's in the progress of being computed
3599 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3600 // additional loop trip count information isn't going to change anything.
3601 // In the second case, createNodeForPHI will perform the necessary
3602 // updates on its own when it gets to that point. In the third, we do
3603 // want to forget the SCEVUnknown.
3604 if (!isa<PHINode>(I) ||
3605 !isa<SCEVUnknown>(Old) ||
3606 (I != PN && Old == SymName)) {
3607 forgetMemoizedResults(Old);
3608 ValueExprMap.erase(It);
3612 PushDefUseChildren(I, Worklist);
3617 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
3619 static const SCEV *rewrite(const SCEV *Scev, const Loop *L,
3620 ScalarEvolution &SE) {
3621 SCEVInitRewriter Rewriter(L, SE);
3622 const SCEV *Result = Rewriter.visit(Scev);
3623 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3626 SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
3627 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3629 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3630 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3635 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3636 // Only allow AddRecExprs for this loop.
3637 if (Expr->getLoop() == L)
3638 return Expr->getStart();
3643 bool isValid() { return Valid; }
3650 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
3652 static const SCEV *rewrite(const SCEV *Scev, const Loop *L,
3653 ScalarEvolution &SE) {
3654 SCEVShiftRewriter Rewriter(L, SE);
3655 const SCEV *Result = Rewriter.visit(Scev);
3656 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3659 SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
3660 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3662 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3663 // Only allow AddRecExprs for this loop.
3664 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3669 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3670 if (Expr->getLoop() == L && Expr->isAffine())
3671 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
3675 bool isValid() { return Valid; }
3681 } // end anonymous namespace
3683 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
3684 const Loop *L = LI.getLoopFor(PN->getParent());
3685 if (!L || L->getHeader() != PN->getParent())
3688 // The loop may have multiple entrances or multiple exits; we can analyze
3689 // this phi as an addrec if it has a unique entry value and a unique
3691 Value *BEValueV = nullptr, *StartValueV = nullptr;
3692 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3693 Value *V = PN->getIncomingValue(i);
3694 if (L->contains(PN->getIncomingBlock(i))) {
3697 } else if (BEValueV != V) {
3701 } else if (!StartValueV) {
3703 } else if (StartValueV != V) {
3704 StartValueV = nullptr;
3708 if (BEValueV && StartValueV) {
3709 // While we are analyzing this PHI node, handle its value symbolically.
3710 const SCEV *SymbolicName = getUnknown(PN);
3711 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3712 "PHI node already processed?");
3713 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3715 // Using this symbolic name for the PHI, analyze the value coming around
3717 const SCEV *BEValue = getSCEV(BEValueV);
3719 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3720 // has a special value for the first iteration of the loop.
3722 // If the value coming around the backedge is an add with the symbolic
3723 // value we just inserted, then we found a simple induction variable!
3724 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3725 // If there is a single occurrence of the symbolic value, replace it
3726 // with a recurrence.
3727 unsigned FoundIndex = Add->getNumOperands();
3728 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3729 if (Add->getOperand(i) == SymbolicName)
3730 if (FoundIndex == e) {
3735 if (FoundIndex != Add->getNumOperands()) {
3736 // Create an add with everything but the specified operand.
3737 SmallVector<const SCEV *, 8> Ops;
3738 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3739 if (i != FoundIndex)
3740 Ops.push_back(Add->getOperand(i));
3741 const SCEV *Accum = getAddExpr(Ops);
3743 // This is not a valid addrec if the step amount is varying each
3744 // loop iteration, but is not itself an addrec in this loop.
3745 if (isLoopInvariant(Accum, L) ||
3746 (isa<SCEVAddRecExpr>(Accum) &&
3747 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3748 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3750 // If the increment doesn't overflow, then neither the addrec nor
3751 // the post-increment will overflow.
3752 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3753 if (OBO->getOperand(0) == PN) {
3754 if (OBO->hasNoUnsignedWrap())
3755 Flags = setFlags(Flags, SCEV::FlagNUW);
3756 if (OBO->hasNoSignedWrap())
3757 Flags = setFlags(Flags, SCEV::FlagNSW);
3759 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3760 // If the increment is an inbounds GEP, then we know the address
3761 // space cannot be wrapped around. We cannot make any guarantee
3762 // about signed or unsigned overflow because pointers are
3763 // unsigned but we may have a negative index from the base
3764 // pointer. We can guarantee that no unsigned wrap occurs if the
3765 // indices form a positive value.
3766 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3767 Flags = setFlags(Flags, SCEV::FlagNW);
3769 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3770 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3771 Flags = setFlags(Flags, SCEV::FlagNUW);
3774 // We cannot transfer nuw and nsw flags from subtraction
3775 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3779 const SCEV *StartVal = getSCEV(StartValueV);
3780 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3782 // Since the no-wrap flags are on the increment, they apply to the
3783 // post-incremented value as well.
3784 if (isLoopInvariant(Accum, L))
3785 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
3787 // Okay, for the entire analysis of this edge we assumed the PHI
3788 // to be symbolic. We now need to go back and purge all of the
3789 // entries for the scalars that use the symbolic expression.
3790 ForgetSymbolicName(PN, SymbolicName);
3791 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3796 // Otherwise, this could be a loop like this:
3797 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3798 // In this case, j = {1,+,1} and BEValue is j.
3799 // Because the other in-value of i (0) fits the evolution of BEValue
3800 // i really is an addrec evolution.
3802 // We can generalize this saying that i is the shifted value of BEValue
3803 // by one iteration:
3804 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
3805 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
3806 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
3807 if (Shifted != getCouldNotCompute() &&
3808 Start != getCouldNotCompute()) {
3809 const SCEV *StartVal = getSCEV(StartValueV);
3810 if (Start == StartVal) {
3811 // Okay, for the entire analysis of this edge we assumed the PHI
3812 // to be symbolic. We now need to go back and purge all of the
3813 // entries for the scalars that use the symbolic expression.
3814 ForgetSymbolicName(PN, SymbolicName);
3815 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
3825 // Checks if the SCEV S is available at BB. S is considered available at BB
3826 // if S can be materialized at BB without introducing a fault.
3827 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
3829 struct CheckAvailable {
3830 bool TraversalDone = false;
3831 bool Available = true;
3833 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
3834 BasicBlock *BB = nullptr;
3837 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
3838 : L(L), BB(BB), DT(DT) {}
3840 bool setUnavailable() {
3841 TraversalDone = true;
3846 bool follow(const SCEV *S) {
3847 switch (S->getSCEVType()) {
3848 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
3849 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
3850 // These expressions are available if their operand(s) is/are.
3853 case scAddRecExpr: {
3854 // We allow add recurrences that are on the loop BB is in, or some
3855 // outer loop. This guarantees availability because the value of the
3856 // add recurrence at BB is simply the "current" value of the induction
3857 // variable. We can relax this in the future; for instance an add
3858 // recurrence on a sibling dominating loop is also available at BB.
3859 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
3860 if (L && (ARLoop == L || ARLoop->contains(L)))
3863 return setUnavailable();
3867 // For SCEVUnknown, we check for simple dominance.
3868 const auto *SU = cast<SCEVUnknown>(S);
3869 Value *V = SU->getValue();
3871 if (isa<Argument>(V))
3874 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
3877 return setUnavailable();
3881 case scCouldNotCompute:
3882 // We do not try to smart about these at all.
3883 return setUnavailable();
3885 llvm_unreachable("switch should be fully covered!");
3888 bool isDone() { return TraversalDone; }
3891 CheckAvailable CA(L, BB, DT);
3892 SCEVTraversal<CheckAvailable> ST(CA);
3895 return CA.Available;
3898 // Try to match a control flow sequence that branches out at BI and merges back
3899 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
3901 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
3902 Value *&C, Value *&LHS, Value *&RHS) {
3903 C = BI->getCondition();
3905 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
3906 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
3908 if (!LeftEdge.isSingleEdge())
3911 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
3913 Use &LeftUse = Merge->getOperandUse(0);
3914 Use &RightUse = Merge->getOperandUse(1);
3916 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
3922 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
3931 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
3932 if (PN->getNumIncomingValues() == 2) {
3933 const Loop *L = LI.getLoopFor(PN->getParent());
3935 // We don't want to break LCSSA, even in a SCEV expression tree.
3936 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
3937 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
3942 // br %cond, label %left, label %right
3948 // V = phi [ %x, %left ], [ %y, %right ]
3950 // as "select %cond, %x, %y"
3952 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
3953 assert(IDom && "At least the entry block should dominate PN");
3955 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
3956 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
3958 if (BI && BI->isConditional() &&
3959 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
3960 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
3961 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
3962 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
3968 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3969 if (const SCEV *S = createAddRecFromPHI(PN))
3972 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
3975 // If the PHI has a single incoming value, follow that value, unless the
3976 // PHI's incoming blocks are in a different loop, in which case doing so
3977 // risks breaking LCSSA form. Instcombine would normally zap these, but
3978 // it doesn't have DominatorTree information, so it may miss cases.
3979 if (Value *V = SimplifyInstruction(PN, getDataLayout(), &TLI, &DT, &AC))
3980 if (LI.replacementPreservesLCSSAForm(PN, V))
3983 // If it's not a loop phi, we can't handle it yet.
3984 return getUnknown(PN);
3987 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
3991 // Handle "constant" branch or select. This can occur for instance when a
3992 // loop pass transforms an inner loop and moves on to process the outer loop.
3993 if (auto *CI = dyn_cast<ConstantInt>(Cond))
3994 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
3996 // Try to match some simple smax or umax patterns.
3997 auto *ICI = dyn_cast<ICmpInst>(Cond);
3999 return getUnknown(I);
4001 Value *LHS = ICI->getOperand(0);
4002 Value *RHS = ICI->getOperand(1);
4004 switch (ICI->getPredicate()) {
4005 case ICmpInst::ICMP_SLT:
4006 case ICmpInst::ICMP_SLE:
4007 std::swap(LHS, RHS);
4009 case ICmpInst::ICMP_SGT:
4010 case ICmpInst::ICMP_SGE:
4011 // a >s b ? a+x : b+x -> smax(a, b)+x
4012 // a >s b ? b+x : a+x -> smin(a, b)+x
4013 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4014 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
4015 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
4016 const SCEV *LA = getSCEV(TrueVal);
4017 const SCEV *RA = getSCEV(FalseVal);
4018 const SCEV *LDiff = getMinusSCEV(LA, LS);
4019 const SCEV *RDiff = getMinusSCEV(RA, RS);
4021 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4022 LDiff = getMinusSCEV(LA, RS);
4023 RDiff = getMinusSCEV(RA, LS);
4025 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4028 case ICmpInst::ICMP_ULT:
4029 case ICmpInst::ICMP_ULE:
4030 std::swap(LHS, RHS);
4032 case ICmpInst::ICMP_UGT:
4033 case ICmpInst::ICMP_UGE:
4034 // a >u b ? a+x : b+x -> umax(a, b)+x
4035 // a >u b ? b+x : a+x -> umin(a, b)+x
4036 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4037 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4038 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
4039 const SCEV *LA = getSCEV(TrueVal);
4040 const SCEV *RA = getSCEV(FalseVal);
4041 const SCEV *LDiff = getMinusSCEV(LA, LS);
4042 const SCEV *RDiff = getMinusSCEV(RA, RS);
4044 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4045 LDiff = getMinusSCEV(LA, RS);
4046 RDiff = getMinusSCEV(RA, LS);
4048 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4051 case ICmpInst::ICMP_NE:
4052 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4053 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4054 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4055 const SCEV *One = getOne(I->getType());
4056 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4057 const SCEV *LA = getSCEV(TrueVal);
4058 const SCEV *RA = getSCEV(FalseVal);
4059 const SCEV *LDiff = getMinusSCEV(LA, LS);
4060 const SCEV *RDiff = getMinusSCEV(RA, One);
4062 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4065 case ICmpInst::ICMP_EQ:
4066 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4067 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4068 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4069 const SCEV *One = getOne(I->getType());
4070 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4071 const SCEV *LA = getSCEV(TrueVal);
4072 const SCEV *RA = getSCEV(FalseVal);
4073 const SCEV *LDiff = getMinusSCEV(LA, One);
4074 const SCEV *RDiff = getMinusSCEV(RA, LS);
4076 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4083 return getUnknown(I);
4086 /// createNodeForGEP - Expand GEP instructions into add and multiply
4087 /// operations. This allows them to be analyzed by regular SCEV code.
4089 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
4090 Value *Base = GEP->getOperand(0);
4091 // Don't attempt to analyze GEPs over unsized objects.
4092 if (!Base->getType()->getPointerElementType()->isSized())
4093 return getUnknown(GEP);
4095 SmallVector<const SCEV *, 4> IndexExprs;
4096 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4097 IndexExprs.push_back(getSCEV(*Index));
4098 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
4102 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
4103 /// guaranteed to end in (at every loop iteration). It is, at the same time,
4104 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
4105 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
4107 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4108 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4109 return C->getAPInt().countTrailingZeros();
4111 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4112 return std::min(GetMinTrailingZeros(T->getOperand()),
4113 (uint32_t)getTypeSizeInBits(T->getType()));
4115 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4116 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4117 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4118 getTypeSizeInBits(E->getType()) : OpRes;
4121 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4122 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4123 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4124 getTypeSizeInBits(E->getType()) : OpRes;
4127 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4128 // The result is the min of all operands results.
4129 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4130 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4131 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4135 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4136 // The result is the sum of all operands results.
4137 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4138 uint32_t BitWidth = getTypeSizeInBits(M->getType());
4139 for (unsigned i = 1, e = M->getNumOperands();
4140 SumOpRes != BitWidth && i != e; ++i)
4141 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4146 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4147 // The result is the min of all operands results.
4148 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4149 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4150 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4154 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4155 // The result is the min of all operands results.
4156 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4157 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4158 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4162 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4163 // The result is the min of all operands results.
4164 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4165 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4166 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4170 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4171 // For a SCEVUnknown, ask ValueTracking.
4172 unsigned BitWidth = getTypeSizeInBits(U->getType());
4173 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4174 computeKnownBits(U->getValue(), Zeros, Ones, getDataLayout(), 0, &AC,
4176 return Zeros.countTrailingOnes();
4183 /// GetRangeFromMetadata - Helper method to assign a range to V from
4184 /// metadata present in the IR.
4185 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4186 if (Instruction *I = dyn_cast<Instruction>(V))
4187 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
4188 return getConstantRangeFromMetadata(*MD);
4193 /// getRange - Determine the range for a particular SCEV. If SignHint is
4194 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4195 /// with a "cleaner" unsigned (resp. signed) representation.
4198 ScalarEvolution::getRange(const SCEV *S,
4199 ScalarEvolution::RangeSignHint SignHint) {
4200 DenseMap<const SCEV *, ConstantRange> &Cache =
4201 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4204 // See if we've computed this range already.
4205 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4206 if (I != Cache.end())
4209 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4210 return setRange(C, SignHint, ConstantRange(C->getAPInt()));
4212 unsigned BitWidth = getTypeSizeInBits(S->getType());
4213 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4215 // If the value has known zeros, the maximum value will have those known zeros
4217 uint32_t TZ = GetMinTrailingZeros(S);
4219 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4220 ConservativeResult =
4221 ConstantRange(APInt::getMinValue(BitWidth),
4222 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4224 ConservativeResult = ConstantRange(
4225 APInt::getSignedMinValue(BitWidth),
4226 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4229 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4230 ConstantRange X = getRange(Add->getOperand(0), SignHint);
4231 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4232 X = X.add(getRange(Add->getOperand(i), SignHint));
4233 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4236 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4237 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4238 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4239 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4240 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4243 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4244 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4245 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4246 X = X.smax(getRange(SMax->getOperand(i), SignHint));
4247 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4250 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4251 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4252 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4253 X = X.umax(getRange(UMax->getOperand(i), SignHint));
4254 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4257 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4258 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4259 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4260 return setRange(UDiv, SignHint,
4261 ConservativeResult.intersectWith(X.udiv(Y)));
4264 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4265 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4266 return setRange(ZExt, SignHint,
4267 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4270 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4271 ConstantRange X = getRange(SExt->getOperand(), SignHint);
4272 return setRange(SExt, SignHint,
4273 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4276 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4277 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4278 return setRange(Trunc, SignHint,
4279 ConservativeResult.intersectWith(X.truncate(BitWidth)));
4282 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4283 // If there's no unsigned wrap, the value will never be less than its
4285 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
4286 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4287 if (!C->getValue()->isZero())
4288 ConservativeResult = ConservativeResult.intersectWith(
4289 ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
4291 // If there's no signed wrap, and all the operands have the same sign or
4292 // zero, the value won't ever change sign.
4293 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
4294 bool AllNonNeg = true;
4295 bool AllNonPos = true;
4296 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4297 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4298 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4301 ConservativeResult = ConservativeResult.intersectWith(
4302 ConstantRange(APInt(BitWidth, 0),
4303 APInt::getSignedMinValue(BitWidth)));
4305 ConservativeResult = ConservativeResult.intersectWith(
4306 ConstantRange(APInt::getSignedMinValue(BitWidth),
4307 APInt(BitWidth, 1)));
4310 // TODO: non-affine addrec
4311 if (AddRec->isAffine()) {
4312 Type *Ty = AddRec->getType();
4313 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4314 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4315 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4317 // Check for overflow. This must be done with ConstantRange arithmetic
4318 // because we could be called from within the ScalarEvolution overflow
4321 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4322 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4323 ConstantRange ZExtMaxBECountRange =
4324 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4326 const SCEV *Start = AddRec->getStart();
4327 const SCEV *Step = AddRec->getStepRecurrence(*this);
4328 ConstantRange StepSRange = getSignedRange(Step);
4329 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4331 ConstantRange StartURange = getUnsignedRange(Start);
4332 ConstantRange EndURange =
4333 StartURange.add(MaxBECountRange.multiply(StepSRange));
4335 // Check for unsigned overflow.
4336 ConstantRange ZExtStartURange =
4337 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4338 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4339 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4341 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4342 EndURange.getUnsignedMin());
4343 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4344 EndURange.getUnsignedMax());
4345 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4347 ConservativeResult =
4348 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4351 ConstantRange StartSRange = getSignedRange(Start);
4352 ConstantRange EndSRange =
4353 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4355 // Check for signed overflow. This must be done with ConstantRange
4356 // arithmetic because we could be called from within the ScalarEvolution
4357 // overflow checking code.
4358 ConstantRange SExtStartSRange =
4359 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4360 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4361 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4363 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4364 EndSRange.getSignedMin());
4365 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4366 EndSRange.getSignedMax());
4367 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4369 ConservativeResult =
4370 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4375 return setRange(AddRec, SignHint, ConservativeResult);
4378 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4379 // Check if the IR explicitly contains !range metadata.
4380 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4381 if (MDRange.hasValue())
4382 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4384 // Split here to avoid paying the compile-time cost of calling both
4385 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4387 const DataLayout &DL = getDataLayout();
4388 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4389 // For a SCEVUnknown, ask ValueTracking.
4390 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4391 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4392 if (Ones != ~Zeros + 1)
4393 ConservativeResult =
4394 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4396 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4397 "generalize as needed!");
4398 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4400 ConservativeResult = ConservativeResult.intersectWith(
4401 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4402 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4405 return setRange(U, SignHint, ConservativeResult);
4408 return setRange(S, SignHint, ConservativeResult);
4411 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4412 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4413 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4415 // Return early if there are no flags to propagate to the SCEV.
4416 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4417 if (BinOp->hasNoUnsignedWrap())
4418 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4419 if (BinOp->hasNoSignedWrap())
4420 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4421 if (Flags == SCEV::FlagAnyWrap) {
4422 return SCEV::FlagAnyWrap;
4425 // Here we check that BinOp is in the header of the innermost loop
4426 // containing BinOp, since we only deal with instructions in the loop
4427 // header. The actual loop we need to check later will come from an add
4428 // recurrence, but getting that requires computing the SCEV of the operands,
4429 // which can be expensive. This check we can do cheaply to rule out some
4431 Loop *innermostContainingLoop = LI.getLoopFor(BinOp->getParent());
4432 if (innermostContainingLoop == nullptr ||
4433 innermostContainingLoop->getHeader() != BinOp->getParent())
4434 return SCEV::FlagAnyWrap;
4436 // Only proceed if we can prove that BinOp does not yield poison.
4437 if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
4439 // At this point we know that if V is executed, then it does not wrap
4440 // according to at least one of NSW or NUW. If V is not executed, then we do
4441 // not know if the calculation that V represents would wrap. Multiple
4442 // instructions can map to the same SCEV. If we apply NSW or NUW from V to
4443 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4444 // derived from other instructions that map to the same SCEV. We cannot make
4445 // that guarantee for cases where V is not executed. So we need to find the
4446 // loop that V is considered in relation to and prove that V is executed for
4447 // every iteration of that loop. That implies that the value that V
4448 // calculates does not wrap anywhere in the loop, so then we can apply the
4449 // flags to the SCEV.
4451 // We check isLoopInvariant to disambiguate in case we are adding two
4452 // recurrences from different loops, so that we know which loop to prove
4453 // that V is executed in.
4454 for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
4455 const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
4456 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4457 const int OtherOpIndex = 1 - OpIndex;
4458 const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
4459 if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
4460 isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
4464 return SCEV::FlagAnyWrap;
4467 /// createSCEV - We know that there is no SCEV for the specified value. Analyze
4470 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4471 if (!isSCEVable(V->getType()))
4472 return getUnknown(V);
4474 unsigned Opcode = Instruction::UserOp1;
4475 if (Instruction *I = dyn_cast<Instruction>(V)) {
4476 Opcode = I->getOpcode();
4478 // Don't attempt to analyze instructions in blocks that aren't
4479 // reachable. Such instructions don't matter, and they aren't required
4480 // to obey basic rules for definitions dominating uses which this
4481 // analysis depends on.
4482 if (!DT.isReachableFromEntry(I->getParent()))
4483 return getUnknown(V);
4484 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4485 Opcode = CE->getOpcode();
4486 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4487 return getConstant(CI);
4488 else if (isa<ConstantPointerNull>(V))
4489 return getZero(V->getType());
4490 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4491 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4493 return getUnknown(V);
4495 Operator *U = cast<Operator>(V);
4497 case Instruction::Add: {
4498 // The simple thing to do would be to just call getSCEV on both operands
4499 // and call getAddExpr with the result. However if we're looking at a
4500 // bunch of things all added together, this can be quite inefficient,
4501 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4502 // Instead, gather up all the operands and make a single getAddExpr call.
4503 // LLVM IR canonical form means we need only traverse the left operands.
4504 SmallVector<const SCEV *, 4> AddOps;
4505 for (Value *Op = U;; Op = U->getOperand(0)) {
4506 U = dyn_cast<Operator>(Op);
4507 unsigned Opcode = U ? U->getOpcode() : 0;
4508 if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
4509 assert(Op != V && "V should be an add");
4510 AddOps.push_back(getSCEV(Op));
4514 if (auto *OpSCEV = getExistingSCEV(U)) {
4515 AddOps.push_back(OpSCEV);
4519 // If a NUW or NSW flag can be applied to the SCEV for this
4520 // addition, then compute the SCEV for this addition by itself
4521 // with a separate call to getAddExpr. We need to do that
4522 // instead of pushing the operands of the addition onto AddOps,
4523 // since the flags are only known to apply to this particular
4524 // addition - they may not apply to other additions that can be
4525 // formed with operands from AddOps.
4526 const SCEV *RHS = getSCEV(U->getOperand(1));
4527 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4528 if (Flags != SCEV::FlagAnyWrap) {
4529 const SCEV *LHS = getSCEV(U->getOperand(0));
4530 if (Opcode == Instruction::Sub)
4531 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4533 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4537 if (Opcode == Instruction::Sub)
4538 AddOps.push_back(getNegativeSCEV(RHS));
4540 AddOps.push_back(RHS);
4542 return getAddExpr(AddOps);
4545 case Instruction::Mul: {
4546 SmallVector<const SCEV *, 4> MulOps;
4547 for (Value *Op = U;; Op = U->getOperand(0)) {
4548 U = dyn_cast<Operator>(Op);
4549 if (!U || U->getOpcode() != Instruction::Mul) {
4550 assert(Op != V && "V should be a mul");
4551 MulOps.push_back(getSCEV(Op));
4555 if (auto *OpSCEV = getExistingSCEV(U)) {
4556 MulOps.push_back(OpSCEV);
4560 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4561 if (Flags != SCEV::FlagAnyWrap) {
4562 MulOps.push_back(getMulExpr(getSCEV(U->getOperand(0)),
4563 getSCEV(U->getOperand(1)), Flags));
4567 MulOps.push_back(getSCEV(U->getOperand(1)));
4569 return getMulExpr(MulOps);
4571 case Instruction::UDiv:
4572 return getUDivExpr(getSCEV(U->getOperand(0)),
4573 getSCEV(U->getOperand(1)));
4574 case Instruction::Sub:
4575 return getMinusSCEV(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)),
4576 getNoWrapFlagsFromUB(U));
4577 case Instruction::And:
4578 // For an expression like x&255 that merely masks off the high bits,
4579 // use zext(trunc(x)) as the SCEV expression.
4580 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4581 if (CI->isNullValue())
4582 return getSCEV(U->getOperand(1));
4583 if (CI->isAllOnesValue())
4584 return getSCEV(U->getOperand(0));
4585 const APInt &A = CI->getValue();
4587 // Instcombine's ShrinkDemandedConstant may strip bits out of
4588 // constants, obscuring what would otherwise be a low-bits mask.
4589 // Use computeKnownBits to compute what ShrinkDemandedConstant
4590 // knew about to reconstruct a low-bits mask value.
4591 unsigned LZ = A.countLeadingZeros();
4592 unsigned TZ = A.countTrailingZeros();
4593 unsigned BitWidth = A.getBitWidth();
4594 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4595 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, getDataLayout(),
4596 0, &AC, nullptr, &DT);
4598 APInt EffectiveMask =
4599 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4600 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4601 const SCEV *MulCount = getConstant(
4602 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4606 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4607 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4614 case Instruction::Or:
4615 // If the RHS of the Or is a constant, we may have something like:
4616 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4617 // optimizations will transparently handle this case.
4619 // In order for this transformation to be safe, the LHS must be of the
4620 // form X*(2^n) and the Or constant must be less than 2^n.
4621 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4622 const SCEV *LHS = getSCEV(U->getOperand(0));
4623 const APInt &CIVal = CI->getValue();
4624 if (GetMinTrailingZeros(LHS) >=
4625 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4626 // Build a plain add SCEV.
4627 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4628 // If the LHS of the add was an addrec and it has no-wrap flags,
4629 // transfer the no-wrap flags, since an or won't introduce a wrap.
4630 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4631 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4632 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4633 OldAR->getNoWrapFlags());
4639 case Instruction::Xor:
4640 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4641 // If the RHS of the xor is a signbit, then this is just an add.
4642 // Instcombine turns add of signbit into xor as a strength reduction step.
4643 if (CI->getValue().isSignBit())
4644 return getAddExpr(getSCEV(U->getOperand(0)),
4645 getSCEV(U->getOperand(1)));
4647 // If the RHS of xor is -1, then this is a not operation.
4648 if (CI->isAllOnesValue())
4649 return getNotSCEV(getSCEV(U->getOperand(0)));
4651 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4652 // This is a variant of the check for xor with -1, and it handles
4653 // the case where instcombine has trimmed non-demanded bits out
4654 // of an xor with -1.
4655 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4656 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4657 if (BO->getOpcode() == Instruction::And &&
4658 LCI->getValue() == CI->getValue())
4659 if (const SCEVZeroExtendExpr *Z =
4660 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4661 Type *UTy = U->getType();
4662 const SCEV *Z0 = Z->getOperand();
4663 Type *Z0Ty = Z0->getType();
4664 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4666 // If C is a low-bits mask, the zero extend is serving to
4667 // mask off the high bits. Complement the operand and
4668 // re-apply the zext.
4669 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4670 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4672 // If C is a single bit, it may be in the sign-bit position
4673 // before the zero-extend. In this case, represent the xor
4674 // using an add, which is equivalent, and re-apply the zext.
4675 APInt Trunc = CI->getValue().trunc(Z0TySize);
4676 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4678 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4684 case Instruction::Shl:
4685 // Turn shift left of a constant amount into a multiply.
4686 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4687 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4689 // If the shift count is not less than the bitwidth, the result of
4690 // the shift is undefined. Don't try to analyze it, because the
4691 // resolution chosen here may differ from the resolution chosen in
4692 // other parts of the compiler.
4693 if (SA->getValue().uge(BitWidth))
4696 // It is currently not resolved how to interpret NSW for left
4697 // shift by BitWidth - 1, so we avoid applying flags in that
4698 // case. Remove this check (or this comment) once the situation
4700 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
4701 // and http://reviews.llvm.org/D8890 .
4702 auto Flags = SCEV::FlagAnyWrap;
4703 if (SA->getValue().ult(BitWidth - 1)) Flags = getNoWrapFlagsFromUB(U);
4705 Constant *X = ConstantInt::get(getContext(),
4706 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4707 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X), Flags);
4711 case Instruction::LShr:
4712 // Turn logical shift right of a constant into a unsigned divide.
4713 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4714 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4716 // If the shift count is not less than the bitwidth, the result of
4717 // the shift is undefined. Don't try to analyze it, because the
4718 // resolution chosen here may differ from the resolution chosen in
4719 // other parts of the compiler.
4720 if (SA->getValue().uge(BitWidth))
4723 Constant *X = ConstantInt::get(getContext(),
4724 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4725 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4729 case Instruction::AShr:
4730 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4731 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4732 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4733 if (L->getOpcode() == Instruction::Shl &&
4734 L->getOperand(1) == U->getOperand(1)) {
4735 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4737 // If the shift count is not less than the bitwidth, the result of
4738 // the shift is undefined. Don't try to analyze it, because the
4739 // resolution chosen here may differ from the resolution chosen in
4740 // other parts of the compiler.
4741 if (CI->getValue().uge(BitWidth))
4744 uint64_t Amt = BitWidth - CI->getZExtValue();
4745 if (Amt == BitWidth)
4746 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4748 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4749 IntegerType::get(getContext(),
4755 case Instruction::Trunc:
4756 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4758 case Instruction::ZExt:
4759 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4761 case Instruction::SExt:
4762 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4764 case Instruction::BitCast:
4765 // BitCasts are no-op casts so we just eliminate the cast.
4766 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4767 return getSCEV(U->getOperand(0));
4770 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4771 // lead to pointer expressions which cannot safely be expanded to GEPs,
4772 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4773 // simplifying integer expressions.
4775 case Instruction::GetElementPtr:
4776 return createNodeForGEP(cast<GEPOperator>(U));
4778 case Instruction::PHI:
4779 return createNodeForPHI(cast<PHINode>(U));
4781 case Instruction::Select:
4782 // U can also be a select constant expr, which let fall through. Since
4783 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
4784 // constant expressions cannot have instructions as operands, we'd have
4785 // returned getUnknown for a select constant expressions anyway.
4786 if (isa<Instruction>(U))
4787 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
4788 U->getOperand(1), U->getOperand(2));
4790 default: // We cannot analyze this expression.
4794 return getUnknown(V);
4799 //===----------------------------------------------------------------------===//
4800 // Iteration Count Computation Code
4803 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4804 if (BasicBlock *ExitingBB = L->getExitingBlock())
4805 return getSmallConstantTripCount(L, ExitingBB);
4807 // No trip count information for multiple exits.
4811 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4812 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4813 /// constant. Will also return 0 if the maximum trip count is very large (>=
4816 /// This "trip count" assumes that control exits via ExitingBlock. More
4817 /// precisely, it is the number of times that control may reach ExitingBlock
4818 /// before taking the branch. For loops with multiple exits, it may not be the
4819 /// number times that the loop header executes because the loop may exit
4820 /// prematurely via another branch.
4821 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4822 BasicBlock *ExitingBlock) {
4823 assert(ExitingBlock && "Must pass a non-null exiting block!");
4824 assert(L->isLoopExiting(ExitingBlock) &&
4825 "Exiting block must actually branch out of the loop!");
4826 const SCEVConstant *ExitCount =
4827 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4831 ConstantInt *ExitConst = ExitCount->getValue();
4833 // Guard against huge trip counts.
4834 if (ExitConst->getValue().getActiveBits() > 32)
4837 // In case of integer overflow, this returns 0, which is correct.
4838 return ((unsigned)ExitConst->getZExtValue()) + 1;
4841 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4842 if (BasicBlock *ExitingBB = L->getExitingBlock())
4843 return getSmallConstantTripMultiple(L, ExitingBB);
4845 // No trip multiple information for multiple exits.
4849 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4850 /// trip count of this loop as a normal unsigned value, if possible. This
4851 /// means that the actual trip count is always a multiple of the returned
4852 /// value (don't forget the trip count could very well be zero as well!).
4854 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4855 /// multiple of a constant (which is also the case if the trip count is simply
4856 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4857 /// if the trip count is very large (>= 2^32).
4859 /// As explained in the comments for getSmallConstantTripCount, this assumes
4860 /// that control exits the loop via ExitingBlock.
4862 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4863 BasicBlock *ExitingBlock) {
4864 assert(ExitingBlock && "Must pass a non-null exiting block!");
4865 assert(L->isLoopExiting(ExitingBlock) &&
4866 "Exiting block must actually branch out of the loop!");
4867 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4868 if (ExitCount == getCouldNotCompute())
4871 // Get the trip count from the BE count by adding 1.
4872 const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
4873 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4874 // to factor simple cases.
4875 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4876 TCMul = Mul->getOperand(0);
4878 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4882 ConstantInt *Result = MulC->getValue();
4884 // Guard against huge trip counts (this requires checking
4885 // for zero to handle the case where the trip count == -1 and the
4887 if (!Result || Result->getValue().getActiveBits() > 32 ||
4888 Result->getValue().getActiveBits() == 0)
4891 return (unsigned)Result->getZExtValue();
4894 // getExitCount - Get the expression for the number of loop iterations for which
4895 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4896 // SCEVCouldNotCompute.
4897 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4898 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4901 /// getBackedgeTakenCount - If the specified loop has a predictable
4902 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4903 /// object. The backedge-taken count is the number of times the loop header
4904 /// will be branched to from within the loop. This is one less than the
4905 /// trip count of the loop, since it doesn't count the first iteration,
4906 /// when the header is branched to from outside the loop.
4908 /// Note that it is not valid to call this method on a loop without a
4909 /// loop-invariant backedge-taken count (see
4910 /// hasLoopInvariantBackedgeTakenCount).
4912 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4913 return getBackedgeTakenInfo(L).getExact(this);
4916 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4917 /// return the least SCEV value that is known never to be less than the
4918 /// actual backedge taken count.
4919 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4920 return getBackedgeTakenInfo(L).getMax(this);
4923 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4924 /// onto the given Worklist.
4926 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4927 BasicBlock *Header = L->getHeader();
4929 // Push all Loop-header PHIs onto the Worklist stack.
4930 for (BasicBlock::iterator I = Header->begin();
4931 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4932 Worklist.push_back(PN);
4935 const ScalarEvolution::BackedgeTakenInfo &
4936 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4937 // Initially insert an invalid entry for this loop. If the insertion
4938 // succeeds, proceed to actually compute a backedge-taken count and
4939 // update the value. The temporary CouldNotCompute value tells SCEV
4940 // code elsewhere that it shouldn't attempt to request a new
4941 // backedge-taken count, which could result in infinite recursion.
4942 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4943 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4945 return Pair.first->second;
4947 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
4948 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4949 // must be cleared in this scope.
4950 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
4952 if (Result.getExact(this) != getCouldNotCompute()) {
4953 assert(isLoopInvariant(Result.getExact(this), L) &&
4954 isLoopInvariant(Result.getMax(this), L) &&
4955 "Computed backedge-taken count isn't loop invariant for loop!");
4956 ++NumTripCountsComputed;
4958 else if (Result.getMax(this) == getCouldNotCompute() &&
4959 isa<PHINode>(L->getHeader()->begin())) {
4960 // Only count loops that have phi nodes as not being computable.
4961 ++NumTripCountsNotComputed;
4964 // Now that we know more about the trip count for this loop, forget any
4965 // existing SCEV values for PHI nodes in this loop since they are only
4966 // conservative estimates made without the benefit of trip count
4967 // information. This is similar to the code in forgetLoop, except that
4968 // it handles SCEVUnknown PHI nodes specially.
4969 if (Result.hasAnyInfo()) {
4970 SmallVector<Instruction *, 16> Worklist;
4971 PushLoopPHIs(L, Worklist);
4973 SmallPtrSet<Instruction *, 8> Visited;
4974 while (!Worklist.empty()) {
4975 Instruction *I = Worklist.pop_back_val();
4976 if (!Visited.insert(I).second)
4979 ValueExprMapType::iterator It =
4980 ValueExprMap.find_as(static_cast<Value *>(I));
4981 if (It != ValueExprMap.end()) {
4982 const SCEV *Old = It->second;
4984 // SCEVUnknown for a PHI either means that it has an unrecognized
4985 // structure, or it's a PHI that's in the progress of being computed
4986 // by createNodeForPHI. In the former case, additional loop trip
4987 // count information isn't going to change anything. In the later
4988 // case, createNodeForPHI will perform the necessary updates on its
4989 // own when it gets to that point.
4990 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4991 forgetMemoizedResults(Old);
4992 ValueExprMap.erase(It);
4994 if (PHINode *PN = dyn_cast<PHINode>(I))
4995 ConstantEvolutionLoopExitValue.erase(PN);
4998 PushDefUseChildren(I, Worklist);
5002 // Re-lookup the insert position, since the call to
5003 // computeBackedgeTakenCount above could result in a
5004 // recusive call to getBackedgeTakenInfo (on a different
5005 // loop), which would invalidate the iterator computed
5007 return BackedgeTakenCounts.find(L)->second = Result;
5010 /// forgetLoop - This method should be called by the client when it has
5011 /// changed a loop in a way that may effect ScalarEvolution's ability to
5012 /// compute a trip count, or if the loop is deleted.
5013 void ScalarEvolution::forgetLoop(const Loop *L) {
5014 // Drop any stored trip count value.
5015 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
5016 BackedgeTakenCounts.find(L);
5017 if (BTCPos != BackedgeTakenCounts.end()) {
5018 BTCPos->second.clear();
5019 BackedgeTakenCounts.erase(BTCPos);
5022 // Drop information about expressions based on loop-header PHIs.
5023 SmallVector<Instruction *, 16> Worklist;
5024 PushLoopPHIs(L, Worklist);
5026 SmallPtrSet<Instruction *, 8> Visited;
5027 while (!Worklist.empty()) {
5028 Instruction *I = Worklist.pop_back_val();
5029 if (!Visited.insert(I).second)
5032 ValueExprMapType::iterator It =
5033 ValueExprMap.find_as(static_cast<Value *>(I));
5034 if (It != ValueExprMap.end()) {
5035 forgetMemoizedResults(It->second);
5036 ValueExprMap.erase(It);
5037 if (PHINode *PN = dyn_cast<PHINode>(I))
5038 ConstantEvolutionLoopExitValue.erase(PN);
5041 PushDefUseChildren(I, Worklist);
5044 // Forget all contained loops too, to avoid dangling entries in the
5045 // ValuesAtScopes map.
5046 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5050 /// forgetValue - This method should be called by the client when it has
5051 /// changed a value in a way that may effect its value, or which may
5052 /// disconnect it from a def-use chain linking it to a loop.
5053 void ScalarEvolution::forgetValue(Value *V) {
5054 Instruction *I = dyn_cast<Instruction>(V);
5057 // Drop information about expressions based on loop-header PHIs.
5058 SmallVector<Instruction *, 16> Worklist;
5059 Worklist.push_back(I);
5061 SmallPtrSet<Instruction *, 8> Visited;
5062 while (!Worklist.empty()) {
5063 I = Worklist.pop_back_val();
5064 if (!Visited.insert(I).second)
5067 ValueExprMapType::iterator It =
5068 ValueExprMap.find_as(static_cast<Value *>(I));
5069 if (It != ValueExprMap.end()) {
5070 forgetMemoizedResults(It->second);
5071 ValueExprMap.erase(It);
5072 if (PHINode *PN = dyn_cast<PHINode>(I))
5073 ConstantEvolutionLoopExitValue.erase(PN);
5076 PushDefUseChildren(I, Worklist);
5080 /// getExact - Get the exact loop backedge taken count considering all loop
5081 /// exits. A computable result can only be returned for loops with a single
5082 /// exit. Returning the minimum taken count among all exits is incorrect
5083 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
5084 /// assumes that the limit of each loop test is never skipped. This is a valid
5085 /// assumption as long as the loop exits via that test. For precise results, it
5086 /// is the caller's responsibility to specify the relevant loop exit using
5087 /// getExact(ExitingBlock, SE).
5089 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
5090 // If any exits were not computable, the loop is not computable.
5091 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
5093 // We need exactly one computable exit.
5094 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
5095 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
5097 const SCEV *BECount = nullptr;
5098 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5099 ENT != nullptr; ENT = ENT->getNextExit()) {
5101 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5104 BECount = ENT->ExactNotTaken;
5105 else if (BECount != ENT->ExactNotTaken)
5106 return SE->getCouldNotCompute();
5108 assert(BECount && "Invalid not taken count for loop exit");
5112 /// getExact - Get the exact not taken count for this loop exit.
5114 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5115 ScalarEvolution *SE) const {
5116 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5117 ENT != nullptr; ENT = ENT->getNextExit()) {
5119 if (ENT->ExitingBlock == ExitingBlock)
5120 return ENT->ExactNotTaken;
5122 return SE->getCouldNotCompute();
5125 /// getMax - Get the max backedge taken count for the loop.
5127 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5128 return Max ? Max : SE->getCouldNotCompute();
5131 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5132 ScalarEvolution *SE) const {
5133 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
5136 if (!ExitNotTaken.ExitingBlock)
5139 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5140 ENT != nullptr; ENT = ENT->getNextExit()) {
5142 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
5143 && SE->hasOperand(ENT->ExactNotTaken, S)) {
5150 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5151 /// computable exit into a persistent ExitNotTakenInfo array.
5152 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5153 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
5154 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
5157 ExitNotTaken.setIncomplete();
5159 unsigned NumExits = ExitCounts.size();
5160 if (NumExits == 0) return;
5162 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
5163 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
5164 if (NumExits == 1) return;
5166 // Handle the rare case of multiple computable exits.
5167 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
5169 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
5170 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
5171 PrevENT->setNextExit(ENT);
5172 ENT->ExitingBlock = ExitCounts[i].first;
5173 ENT->ExactNotTaken = ExitCounts[i].second;
5177 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
5178 void ScalarEvolution::BackedgeTakenInfo::clear() {
5179 ExitNotTaken.ExitingBlock = nullptr;
5180 ExitNotTaken.ExactNotTaken = nullptr;
5181 delete[] ExitNotTaken.getNextExit();
5184 /// computeBackedgeTakenCount - Compute the number of times the backedge
5185 /// of the specified loop will execute.
5186 ScalarEvolution::BackedgeTakenInfo
5187 ScalarEvolution::computeBackedgeTakenCount(const Loop *L) {
5188 SmallVector<BasicBlock *, 8> ExitingBlocks;
5189 L->getExitingBlocks(ExitingBlocks);
5191 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
5192 bool CouldComputeBECount = true;
5193 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5194 const SCEV *MustExitMaxBECount = nullptr;
5195 const SCEV *MayExitMaxBECount = nullptr;
5197 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5198 // and compute maxBECount.
5199 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5200 BasicBlock *ExitBB = ExitingBlocks[i];
5201 ExitLimit EL = computeExitLimit(L, ExitBB);
5203 // 1. For each exit that can be computed, add an entry to ExitCounts.
5204 // CouldComputeBECount is true only if all exits can be computed.
5205 if (EL.Exact == getCouldNotCompute())
5206 // We couldn't compute an exact value for this exit, so
5207 // we won't be able to compute an exact value for the loop.
5208 CouldComputeBECount = false;
5210 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
5212 // 2. Derive the loop's MaxBECount from each exit's max number of
5213 // non-exiting iterations. Partition the loop exits into two kinds:
5214 // LoopMustExits and LoopMayExits.
5216 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5217 // is a LoopMayExit. If any computable LoopMustExit is found, then
5218 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
5219 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
5220 // considered greater than any computable EL.Max.
5221 if (EL.Max != getCouldNotCompute() && Latch &&
5222 DT.dominates(ExitBB, Latch)) {
5223 if (!MustExitMaxBECount)
5224 MustExitMaxBECount = EL.Max;
5226 MustExitMaxBECount =
5227 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5229 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5230 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5231 MayExitMaxBECount = EL.Max;
5234 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5238 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5239 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5240 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5243 ScalarEvolution::ExitLimit
5244 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
5246 // Okay, we've chosen an exiting block. See what condition causes us to exit
5247 // at this block and remember the exit block and whether all other targets
5248 // lead to the loop header.
5249 bool MustExecuteLoopHeader = true;
5250 BasicBlock *Exit = nullptr;
5251 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5253 if (!L->contains(*SI)) {
5254 if (Exit) // Multiple exit successors.
5255 return getCouldNotCompute();
5257 } else if (*SI != L->getHeader()) {
5258 MustExecuteLoopHeader = false;
5261 // At this point, we know we have a conditional branch that determines whether
5262 // the loop is exited. However, we don't know if the branch is executed each
5263 // time through the loop. If not, then the execution count of the branch will
5264 // not be equal to the trip count of the loop.
5266 // Currently we check for this by checking to see if the Exit branch goes to
5267 // the loop header. If so, we know it will always execute the same number of
5268 // times as the loop. We also handle the case where the exit block *is* the
5269 // loop header. This is common for un-rotated loops.
5271 // If both of those tests fail, walk up the unique predecessor chain to the
5272 // header, stopping if there is an edge that doesn't exit the loop. If the
5273 // header is reached, the execution count of the branch will be equal to the
5274 // trip count of the loop.
5276 // More extensive analysis could be done to handle more cases here.
5278 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5279 // The simple checks failed, try climbing the unique predecessor chain
5280 // up to the header.
5282 for (BasicBlock *BB = ExitingBlock; BB; ) {
5283 BasicBlock *Pred = BB->getUniquePredecessor();
5285 return getCouldNotCompute();
5286 TerminatorInst *PredTerm = Pred->getTerminator();
5287 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5290 // If the predecessor has a successor that isn't BB and isn't
5291 // outside the loop, assume the worst.
5292 if (L->contains(PredSucc))
5293 return getCouldNotCompute();
5295 if (Pred == L->getHeader()) {
5302 return getCouldNotCompute();
5305 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5306 TerminatorInst *Term = ExitingBlock->getTerminator();
5307 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5308 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5309 // Proceed to the next level to examine the exit condition expression.
5310 return computeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5311 BI->getSuccessor(1),
5312 /*ControlsExit=*/IsOnlyExit);
5315 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5316 return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
5317 /*ControlsExit=*/IsOnlyExit);
5319 return getCouldNotCompute();
5322 /// computeExitLimitFromCond - Compute the number of times the
5323 /// backedge of the specified loop will execute if its exit condition
5324 /// were a conditional branch of ExitCond, TBB, and FBB.
5326 /// @param ControlsExit is true if ExitCond directly controls the exit
5327 /// branch. In this case, we can assume that the loop exits only if the
5328 /// condition is true and can infer that failing to meet the condition prior to
5329 /// integer wraparound results in undefined behavior.
5330 ScalarEvolution::ExitLimit
5331 ScalarEvolution::computeExitLimitFromCond(const Loop *L,
5335 bool ControlsExit) {
5336 // Check if the controlling expression for this loop is an And or Or.
5337 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5338 if (BO->getOpcode() == Instruction::And) {
5339 // Recurse on the operands of the and.
5340 bool EitherMayExit = L->contains(TBB);
5341 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5342 ControlsExit && !EitherMayExit);
5343 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5344 ControlsExit && !EitherMayExit);
5345 const SCEV *BECount = getCouldNotCompute();
5346 const SCEV *MaxBECount = getCouldNotCompute();
5347 if (EitherMayExit) {
5348 // Both conditions must be true for the loop to continue executing.
5349 // Choose the less conservative count.
5350 if (EL0.Exact == getCouldNotCompute() ||
5351 EL1.Exact == getCouldNotCompute())
5352 BECount = getCouldNotCompute();
5354 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5355 if (EL0.Max == getCouldNotCompute())
5356 MaxBECount = EL1.Max;
5357 else if (EL1.Max == getCouldNotCompute())
5358 MaxBECount = EL0.Max;
5360 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5362 // Both conditions must be true at the same time for the loop to exit.
5363 // For now, be conservative.
5364 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5365 if (EL0.Max == EL1.Max)
5366 MaxBECount = EL0.Max;
5367 if (EL0.Exact == EL1.Exact)
5368 BECount = EL0.Exact;
5371 return ExitLimit(BECount, MaxBECount);
5373 if (BO->getOpcode() == Instruction::Or) {
5374 // Recurse on the operands of the or.
5375 bool EitherMayExit = L->contains(FBB);
5376 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5377 ControlsExit && !EitherMayExit);
5378 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5379 ControlsExit && !EitherMayExit);
5380 const SCEV *BECount = getCouldNotCompute();
5381 const SCEV *MaxBECount = getCouldNotCompute();
5382 if (EitherMayExit) {
5383 // Both conditions must be false for the loop to continue executing.
5384 // Choose the less conservative count.
5385 if (EL0.Exact == getCouldNotCompute() ||
5386 EL1.Exact == getCouldNotCompute())
5387 BECount = getCouldNotCompute();
5389 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5390 if (EL0.Max == getCouldNotCompute())
5391 MaxBECount = EL1.Max;
5392 else if (EL1.Max == getCouldNotCompute())
5393 MaxBECount = EL0.Max;
5395 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5397 // Both conditions must be false at the same time for the loop to exit.
5398 // For now, be conservative.
5399 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5400 if (EL0.Max == EL1.Max)
5401 MaxBECount = EL0.Max;
5402 if (EL0.Exact == EL1.Exact)
5403 BECount = EL0.Exact;
5406 return ExitLimit(BECount, MaxBECount);
5410 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5411 // Proceed to the next level to examine the icmp.
5412 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5413 return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5415 // Check for a constant condition. These are normally stripped out by
5416 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5417 // preserve the CFG and is temporarily leaving constant conditions
5419 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5420 if (L->contains(FBB) == !CI->getZExtValue())
5421 // The backedge is always taken.
5422 return getCouldNotCompute();
5424 // The backedge is never taken.
5425 return getZero(CI->getType());
5428 // If it's not an integer or pointer comparison then compute it the hard way.
5429 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5432 ScalarEvolution::ExitLimit
5433 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
5437 bool ControlsExit) {
5439 // If the condition was exit on true, convert the condition to exit on false
5440 ICmpInst::Predicate Cond;
5441 if (!L->contains(FBB))
5442 Cond = ExitCond->getPredicate();
5444 Cond = ExitCond->getInversePredicate();
5446 // Handle common loops like: for (X = "string"; *X; ++X)
5447 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5448 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5450 computeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5451 if (ItCnt.hasAnyInfo())
5455 ExitLimit ShiftEL = computeShiftCompareExitLimit(
5456 ExitCond->getOperand(0), ExitCond->getOperand(1), L, Cond);
5457 if (ShiftEL.hasAnyInfo())
5460 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5461 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5463 // Try to evaluate any dependencies out of the loop.
5464 LHS = getSCEVAtScope(LHS, L);
5465 RHS = getSCEVAtScope(RHS, L);
5467 // At this point, we would like to compute how many iterations of the
5468 // loop the predicate will return true for these inputs.
5469 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5470 // If there is a loop-invariant, force it into the RHS.
5471 std::swap(LHS, RHS);
5472 Cond = ICmpInst::getSwappedPredicate(Cond);
5475 // Simplify the operands before analyzing them.
5476 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5478 // If we have a comparison of a chrec against a constant, try to use value
5479 // ranges to answer this query.
5480 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5481 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5482 if (AddRec->getLoop() == L) {
5483 // Form the constant range.
5484 ConstantRange CompRange(
5485 ICmpInst::makeConstantRange(Cond, RHSC->getAPInt()));
5487 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5488 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5492 case ICmpInst::ICMP_NE: { // while (X != Y)
5493 // Convert to: while (X-Y != 0)
5494 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5495 if (EL.hasAnyInfo()) return EL;
5498 case ICmpInst::ICMP_EQ: { // while (X == Y)
5499 // Convert to: while (X-Y == 0)
5500 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5501 if (EL.hasAnyInfo()) return EL;
5504 case ICmpInst::ICMP_SLT:
5505 case ICmpInst::ICMP_ULT: { // while (X < Y)
5506 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5507 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5508 if (EL.hasAnyInfo()) return EL;
5511 case ICmpInst::ICMP_SGT:
5512 case ICmpInst::ICMP_UGT: { // while (X > Y)
5513 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5514 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5515 if (EL.hasAnyInfo()) return EL;
5521 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5524 ScalarEvolution::ExitLimit
5525 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
5527 BasicBlock *ExitingBlock,
5528 bool ControlsExit) {
5529 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5531 // Give up if the exit is the default dest of a switch.
5532 if (Switch->getDefaultDest() == ExitingBlock)
5533 return getCouldNotCompute();
5535 assert(L->contains(Switch->getDefaultDest()) &&
5536 "Default case must not exit the loop!");
5537 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5538 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5540 // while (X != Y) --> while (X-Y != 0)
5541 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5542 if (EL.hasAnyInfo())
5545 return getCouldNotCompute();
5548 static ConstantInt *
5549 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5550 ScalarEvolution &SE) {
5551 const SCEV *InVal = SE.getConstant(C);
5552 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5553 assert(isa<SCEVConstant>(Val) &&
5554 "Evaluation of SCEV at constant didn't fold correctly?");
5555 return cast<SCEVConstant>(Val)->getValue();
5558 /// computeLoadConstantCompareExitLimit - Given an exit condition of
5559 /// 'icmp op load X, cst', try to see if we can compute the backedge
5560 /// execution count.
5561 ScalarEvolution::ExitLimit
5562 ScalarEvolution::computeLoadConstantCompareExitLimit(
5566 ICmpInst::Predicate predicate) {
5568 if (LI->isVolatile()) return getCouldNotCompute();
5570 // Check to see if the loaded pointer is a getelementptr of a global.
5571 // TODO: Use SCEV instead of manually grubbing with GEPs.
5572 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5573 if (!GEP) return getCouldNotCompute();
5575 // Make sure that it is really a constant global we are gepping, with an
5576 // initializer, and make sure the first IDX is really 0.
5577 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5578 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5579 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5580 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5581 return getCouldNotCompute();
5583 // Okay, we allow one non-constant index into the GEP instruction.
5584 Value *VarIdx = nullptr;
5585 std::vector<Constant*> Indexes;
5586 unsigned VarIdxNum = 0;
5587 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5588 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5589 Indexes.push_back(CI);
5590 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5591 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5592 VarIdx = GEP->getOperand(i);
5594 Indexes.push_back(nullptr);
5597 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5599 return getCouldNotCompute();
5601 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5602 // Check to see if X is a loop variant variable value now.
5603 const SCEV *Idx = getSCEV(VarIdx);
5604 Idx = getSCEVAtScope(Idx, L);
5606 // We can only recognize very limited forms of loop index expressions, in
5607 // particular, only affine AddRec's like {C1,+,C2}.
5608 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5609 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5610 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5611 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5612 return getCouldNotCompute();
5614 unsigned MaxSteps = MaxBruteForceIterations;
5615 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5616 ConstantInt *ItCst = ConstantInt::get(
5617 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5618 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5620 // Form the GEP offset.
5621 Indexes[VarIdxNum] = Val;
5623 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5625 if (!Result) break; // Cannot compute!
5627 // Evaluate the condition for this iteration.
5628 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5629 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5630 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5631 ++NumArrayLenItCounts;
5632 return getConstant(ItCst); // Found terminating iteration!
5635 return getCouldNotCompute();
5638 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
5639 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
5640 ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
5642 return getCouldNotCompute();
5644 const BasicBlock *Latch = L->getLoopLatch();
5646 return getCouldNotCompute();
5648 const BasicBlock *Predecessor = L->getLoopPredecessor();
5650 return getCouldNotCompute();
5652 // Return true if V is of the form "LHS `shift_op` <positive constant>".
5653 // Return LHS in OutLHS and shift_opt in OutOpCode.
5654 auto MatchPositiveShift =
5655 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
5657 using namespace PatternMatch;
5659 ConstantInt *ShiftAmt;
5660 if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
5661 OutOpCode = Instruction::LShr;
5662 else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
5663 OutOpCode = Instruction::AShr;
5664 else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
5665 OutOpCode = Instruction::Shl;
5669 return ShiftAmt->getValue().isStrictlyPositive();
5672 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
5675 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
5676 // %iv.shifted = lshr i32 %iv, <positive constant>
5678 // Return true on a succesful match. Return the corresponding PHI node (%iv
5679 // above) in PNOut and the opcode of the shift operation in OpCodeOut.
5680 auto MatchShiftRecurrence =
5681 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
5682 Optional<Instruction::BinaryOps> PostShiftOpCode;
5685 Instruction::BinaryOps OpC;
5688 // If we encounter a shift instruction, "peel off" the shift operation,
5689 // and remember that we did so. Later when we inspect %iv's backedge
5690 // value, we will make sure that the backedge value uses the same
5693 // Note: the peeled shift operation does not have to be the same
5694 // instruction as the one feeding into the PHI's backedge value. We only
5695 // really care about it being the same *kind* of shift instruction --
5696 // that's all that is required for our later inferences to hold.
5697 if (MatchPositiveShift(LHS, V, OpC)) {
5698 PostShiftOpCode = OpC;
5703 PNOut = dyn_cast<PHINode>(LHS);
5704 if (!PNOut || PNOut->getParent() != L->getHeader())
5707 Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
5711 // The backedge value for the PHI node must be a shift by a positive
5713 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
5715 // of the PHI node itself
5718 // and the kind of shift should be match the kind of shift we peeled
5720 (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
5724 Instruction::BinaryOps OpCode;
5725 if (!MatchShiftRecurrence(LHS, PN, OpCode))
5726 return getCouldNotCompute();
5728 const DataLayout &DL = getDataLayout();
5730 // The key rationale for this optimization is that for some kinds of shift
5731 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
5732 // within a finite number of iterations. If the condition guarding the
5733 // backedge (in the sense that the backedge is taken if the condition is true)
5734 // is false for the value the shift recurrence stabilizes to, then we know
5735 // that the backedge is taken only a finite number of times.
5737 ConstantInt *StableValue = nullptr;
5740 llvm_unreachable("Impossible case!");
5742 case Instruction::AShr: {
5743 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
5744 // bitwidth(K) iterations.
5745 Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
5746 bool KnownZero, KnownOne;
5747 ComputeSignBit(FirstValue, KnownZero, KnownOne, DL, 0, nullptr,
5748 Predecessor->getTerminator(), &DT);
5749 auto *Ty = cast<IntegerType>(RHS->getType());
5751 StableValue = ConstantInt::get(Ty, 0);
5753 StableValue = ConstantInt::get(Ty, -1, true);
5755 return getCouldNotCompute();
5759 case Instruction::LShr:
5760 case Instruction::Shl:
5761 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
5762 // stabilize to 0 in at most bitwidth(K) iterations.
5763 StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
5768 ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
5769 assert(Result->getType()->isIntegerTy(1) &&
5770 "Otherwise cannot be an operand to a branch instruction");
5772 if (Result->isZeroValue()) {
5773 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
5774 const SCEV *UpperBound =
5775 getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
5776 return ExitLimit(getCouldNotCompute(), UpperBound);
5779 return getCouldNotCompute();
5782 /// CanConstantFold - Return true if we can constant fold an instruction of the
5783 /// specified type, assuming that all operands were constants.
5784 static bool CanConstantFold(const Instruction *I) {
5785 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5786 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5790 if (const CallInst *CI = dyn_cast<CallInst>(I))
5791 if (const Function *F = CI->getCalledFunction())
5792 return canConstantFoldCallTo(F);
5796 /// Determine whether this instruction can constant evolve within this loop
5797 /// assuming its operands can all constant evolve.
5798 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5799 // An instruction outside of the loop can't be derived from a loop PHI.
5800 if (!L->contains(I)) return false;
5802 if (isa<PHINode>(I)) {
5803 // We don't currently keep track of the control flow needed to evaluate
5804 // PHIs, so we cannot handle PHIs inside of loops.
5805 return L->getHeader() == I->getParent();
5808 // If we won't be able to constant fold this expression even if the operands
5809 // are constants, bail early.
5810 return CanConstantFold(I);
5813 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5814 /// recursing through each instruction operand until reaching a loop header phi.
5816 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5817 DenseMap<Instruction *, PHINode *> &PHIMap) {
5819 // Otherwise, we can evaluate this instruction if all of its operands are
5820 // constant or derived from a PHI node themselves.
5821 PHINode *PHI = nullptr;
5822 for (Value *Op : UseInst->operands()) {
5823 if (isa<Constant>(Op)) continue;
5825 Instruction *OpInst = dyn_cast<Instruction>(Op);
5826 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5828 PHINode *P = dyn_cast<PHINode>(OpInst);
5830 // If this operand is already visited, reuse the prior result.
5831 // We may have P != PHI if this is the deepest point at which the
5832 // inconsistent paths meet.
5833 P = PHIMap.lookup(OpInst);
5835 // Recurse and memoize the results, whether a phi is found or not.
5836 // This recursive call invalidates pointers into PHIMap.
5837 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5841 return nullptr; // Not evolving from PHI
5842 if (PHI && PHI != P)
5843 return nullptr; // Evolving from multiple different PHIs.
5846 // This is a expression evolving from a constant PHI!
5850 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5851 /// in the loop that V is derived from. We allow arbitrary operations along the
5852 /// way, but the operands of an operation must either be constants or a value
5853 /// derived from a constant PHI. If this expression does not fit with these
5854 /// constraints, return null.
5855 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5856 Instruction *I = dyn_cast<Instruction>(V);
5857 if (!I || !canConstantEvolve(I, L)) return nullptr;
5859 if (PHINode *PN = dyn_cast<PHINode>(I))
5862 // Record non-constant instructions contained by the loop.
5863 DenseMap<Instruction *, PHINode *> PHIMap;
5864 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5867 /// EvaluateExpression - Given an expression that passes the
5868 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5869 /// in the loop has the value PHIVal. If we can't fold this expression for some
5870 /// reason, return null.
5871 static Constant *EvaluateExpression(Value *V, const Loop *L,
5872 DenseMap<Instruction *, Constant *> &Vals,
5873 const DataLayout &DL,
5874 const TargetLibraryInfo *TLI) {
5875 // Convenient constant check, but redundant for recursive calls.
5876 if (Constant *C = dyn_cast<Constant>(V)) return C;
5877 Instruction *I = dyn_cast<Instruction>(V);
5878 if (!I) return nullptr;
5880 if (Constant *C = Vals.lookup(I)) return C;
5882 // An instruction inside the loop depends on a value outside the loop that we
5883 // weren't given a mapping for, or a value such as a call inside the loop.
5884 if (!canConstantEvolve(I, L)) return nullptr;
5886 // An unmapped PHI can be due to a branch or another loop inside this loop,
5887 // or due to this not being the initial iteration through a loop where we
5888 // couldn't compute the evolution of this particular PHI last time.
5889 if (isa<PHINode>(I)) return nullptr;
5891 std::vector<Constant*> Operands(I->getNumOperands());
5893 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5894 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5896 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5897 if (!Operands[i]) return nullptr;
5900 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5902 if (!C) return nullptr;
5906 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5907 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5908 Operands[1], DL, TLI);
5909 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5910 if (!LI->isVolatile())
5911 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5913 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5918 // If every incoming value to PN except the one for BB is a specific Constant,
5919 // return that, else return nullptr.
5920 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
5921 Constant *IncomingVal = nullptr;
5923 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
5924 if (PN->getIncomingBlock(i) == BB)
5927 auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
5931 if (IncomingVal != CurrentVal) {
5934 IncomingVal = CurrentVal;
5941 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5942 /// in the header of its containing loop, we know the loop executes a
5943 /// constant number of times, and the PHI node is just a recurrence
5944 /// involving constants, fold it.
5946 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5949 auto I = ConstantEvolutionLoopExitValue.find(PN);
5950 if (I != ConstantEvolutionLoopExitValue.end())
5953 if (BEs.ugt(MaxBruteForceIterations))
5954 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5956 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5958 DenseMap<Instruction *, Constant *> CurrentIterVals;
5959 BasicBlock *Header = L->getHeader();
5960 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5962 BasicBlock *Latch = L->getLoopLatch();
5966 for (auto &I : *Header) {
5967 PHINode *PHI = dyn_cast<PHINode>(&I);
5969 auto *StartCST = getOtherIncomingValue(PHI, Latch);
5970 if (!StartCST) continue;
5971 CurrentIterVals[PHI] = StartCST;
5973 if (!CurrentIterVals.count(PN))
5974 return RetVal = nullptr;
5976 Value *BEValue = PN->getIncomingValueForBlock(Latch);
5978 // Execute the loop symbolically to determine the exit value.
5979 if (BEs.getActiveBits() >= 32)
5980 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5982 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5983 unsigned IterationNum = 0;
5984 const DataLayout &DL = getDataLayout();
5985 for (; ; ++IterationNum) {
5986 if (IterationNum == NumIterations)
5987 return RetVal = CurrentIterVals[PN]; // Got exit value!
5989 // Compute the value of the PHIs for the next iteration.
5990 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5991 DenseMap<Instruction *, Constant *> NextIterVals;
5993 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5995 return nullptr; // Couldn't evaluate!
5996 NextIterVals[PN] = NextPHI;
5998 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
6000 // Also evaluate the other PHI nodes. However, we don't get to stop if we
6001 // cease to be able to evaluate one of them or if they stop evolving,
6002 // because that doesn't necessarily prevent us from computing PN.
6003 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
6004 for (const auto &I : CurrentIterVals) {
6005 PHINode *PHI = dyn_cast<PHINode>(I.first);
6006 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
6007 PHIsToCompute.emplace_back(PHI, I.second);
6009 // We use two distinct loops because EvaluateExpression may invalidate any
6010 // iterators into CurrentIterVals.
6011 for (const auto &I : PHIsToCompute) {
6012 PHINode *PHI = I.first;
6013 Constant *&NextPHI = NextIterVals[PHI];
6014 if (!NextPHI) { // Not already computed.
6015 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6016 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6018 if (NextPHI != I.second)
6019 StoppedEvolving = false;
6022 // If all entries in CurrentIterVals == NextIterVals then we can stop
6023 // iterating, the loop can't continue to change.
6024 if (StoppedEvolving)
6025 return RetVal = CurrentIterVals[PN];
6027 CurrentIterVals.swap(NextIterVals);
6031 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
6034 PHINode *PN = getConstantEvolvingPHI(Cond, L);
6035 if (!PN) return getCouldNotCompute();
6037 // If the loop is canonicalized, the PHI will have exactly two entries.
6038 // That's the only form we support here.
6039 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
6041 DenseMap<Instruction *, Constant *> CurrentIterVals;
6042 BasicBlock *Header = L->getHeader();
6043 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6045 BasicBlock *Latch = L->getLoopLatch();
6046 assert(Latch && "Should follow from NumIncomingValues == 2!");
6048 for (auto &I : *Header) {
6049 PHINode *PHI = dyn_cast<PHINode>(&I);
6052 auto *StartCST = getOtherIncomingValue(PHI, Latch);
6053 if (!StartCST) continue;
6054 CurrentIterVals[PHI] = StartCST;
6056 if (!CurrentIterVals.count(PN))
6057 return getCouldNotCompute();
6059 // Okay, we find a PHI node that defines the trip count of this loop. Execute
6060 // the loop symbolically to determine when the condition gets a value of
6062 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
6063 const DataLayout &DL = getDataLayout();
6064 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
6065 auto *CondVal = dyn_cast_or_null<ConstantInt>(
6066 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
6068 // Couldn't symbolically evaluate.
6069 if (!CondVal) return getCouldNotCompute();
6071 if (CondVal->getValue() == uint64_t(ExitWhen)) {
6072 ++NumBruteForceTripCountsComputed;
6073 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
6076 // Update all the PHI nodes for the next iteration.
6077 DenseMap<Instruction *, Constant *> NextIterVals;
6079 // Create a list of which PHIs we need to compute. We want to do this before
6080 // calling EvaluateExpression on them because that may invalidate iterators
6081 // into CurrentIterVals.
6082 SmallVector<PHINode *, 8> PHIsToCompute;
6083 for (const auto &I : CurrentIterVals) {
6084 PHINode *PHI = dyn_cast<PHINode>(I.first);
6085 if (!PHI || PHI->getParent() != Header) continue;
6086 PHIsToCompute.push_back(PHI);
6088 for (PHINode *PHI : PHIsToCompute) {
6089 Constant *&NextPHI = NextIterVals[PHI];
6090 if (NextPHI) continue; // Already computed!
6092 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6093 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6095 CurrentIterVals.swap(NextIterVals);
6098 // Too many iterations were needed to evaluate.
6099 return getCouldNotCompute();
6102 /// getSCEVAtScope - Return a SCEV expression for the specified value
6103 /// at the specified scope in the program. The L value specifies a loop
6104 /// nest to evaluate the expression at, where null is the top-level or a
6105 /// specified loop is immediately inside of the loop.
6107 /// This method can be used to compute the exit value for a variable defined
6108 /// in a loop by querying what the value will hold in the parent loop.
6110 /// In the case that a relevant loop exit value cannot be computed, the
6111 /// original value V is returned.
6112 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
6113 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
6115 // Check to see if we've folded this expression at this loop before.
6116 for (auto &LS : Values)
6118 return LS.second ? LS.second : V;
6120 Values.emplace_back(L, nullptr);
6122 // Otherwise compute it.
6123 const SCEV *C = computeSCEVAtScope(V, L);
6124 for (auto &LS : reverse(ValuesAtScopes[V]))
6125 if (LS.first == L) {
6132 /// This builds up a Constant using the ConstantExpr interface. That way, we
6133 /// will return Constants for objects which aren't represented by a
6134 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
6135 /// Returns NULL if the SCEV isn't representable as a Constant.
6136 static Constant *BuildConstantFromSCEV(const SCEV *V) {
6137 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
6138 case scCouldNotCompute:
6142 return cast<SCEVConstant>(V)->getValue();
6144 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
6145 case scSignExtend: {
6146 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
6147 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
6148 return ConstantExpr::getSExt(CastOp, SS->getType());
6151 case scZeroExtend: {
6152 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
6153 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
6154 return ConstantExpr::getZExt(CastOp, SZ->getType());
6158 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
6159 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
6160 return ConstantExpr::getTrunc(CastOp, ST->getType());
6164 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
6165 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
6166 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6167 unsigned AS = PTy->getAddressSpace();
6168 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6169 C = ConstantExpr::getBitCast(C, DestPtrTy);
6171 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
6172 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
6173 if (!C2) return nullptr;
6176 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
6177 unsigned AS = C2->getType()->getPointerAddressSpace();
6179 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6180 // The offsets have been converted to bytes. We can add bytes to an
6181 // i8* by GEP with the byte count in the first index.
6182 C = ConstantExpr::getBitCast(C, DestPtrTy);
6185 // Don't bother trying to sum two pointers. We probably can't
6186 // statically compute a load that results from it anyway.
6187 if (C2->getType()->isPointerTy())
6190 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6191 if (PTy->getElementType()->isStructTy())
6192 C2 = ConstantExpr::getIntegerCast(
6193 C2, Type::getInt32Ty(C->getContext()), true);
6194 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
6196 C = ConstantExpr::getAdd(C, C2);
6203 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
6204 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
6205 // Don't bother with pointers at all.
6206 if (C->getType()->isPointerTy()) return nullptr;
6207 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
6208 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
6209 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
6210 C = ConstantExpr::getMul(C, C2);
6217 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6218 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6219 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6220 if (LHS->getType() == RHS->getType())
6221 return ConstantExpr::getUDiv(LHS, RHS);
6226 break; // TODO: smax, umax.
6231 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6232 if (isa<SCEVConstant>(V)) return V;
6234 // If this instruction is evolved from a constant-evolving PHI, compute the
6235 // exit value from the loop without using SCEVs.
6236 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6237 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6238 const Loop *LI = this->LI[I->getParent()];
6239 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
6240 if (PHINode *PN = dyn_cast<PHINode>(I))
6241 if (PN->getParent() == LI->getHeader()) {
6242 // Okay, there is no closed form solution for the PHI node. Check
6243 // to see if the loop that contains it has a known backedge-taken
6244 // count. If so, we may be able to force computation of the exit
6246 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6247 if (const SCEVConstant *BTCC =
6248 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6249 // Okay, we know how many times the containing loop executes. If
6250 // this is a constant evolving PHI node, get the final value at
6251 // the specified iteration number.
6253 getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
6254 if (RV) return getSCEV(RV);
6258 // Okay, this is an expression that we cannot symbolically evaluate
6259 // into a SCEV. Check to see if it's possible to symbolically evaluate
6260 // the arguments into constants, and if so, try to constant propagate the
6261 // result. This is particularly useful for computing loop exit values.
6262 if (CanConstantFold(I)) {
6263 SmallVector<Constant *, 4> Operands;
6264 bool MadeImprovement = false;
6265 for (Value *Op : I->operands()) {
6266 if (Constant *C = dyn_cast<Constant>(Op)) {
6267 Operands.push_back(C);
6271 // If any of the operands is non-constant and if they are
6272 // non-integer and non-pointer, don't even try to analyze them
6273 // with scev techniques.
6274 if (!isSCEVable(Op->getType()))
6277 const SCEV *OrigV = getSCEV(Op);
6278 const SCEV *OpV = getSCEVAtScope(OrigV, L);
6279 MadeImprovement |= OrigV != OpV;
6281 Constant *C = BuildConstantFromSCEV(OpV);
6283 if (C->getType() != Op->getType())
6284 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6288 Operands.push_back(C);
6291 // Check to see if getSCEVAtScope actually made an improvement.
6292 if (MadeImprovement) {
6293 Constant *C = nullptr;
6294 const DataLayout &DL = getDataLayout();
6295 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6296 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6297 Operands[1], DL, &TLI);
6298 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6299 if (!LI->isVolatile())
6300 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
6302 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
6310 // This is some other type of SCEVUnknown, just return it.
6314 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6315 // Avoid performing the look-up in the common case where the specified
6316 // expression has no loop-variant portions.
6317 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6318 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6319 if (OpAtScope != Comm->getOperand(i)) {
6320 // Okay, at least one of these operands is loop variant but might be
6321 // foldable. Build a new instance of the folded commutative expression.
6322 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6323 Comm->op_begin()+i);
6324 NewOps.push_back(OpAtScope);
6326 for (++i; i != e; ++i) {
6327 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6328 NewOps.push_back(OpAtScope);
6330 if (isa<SCEVAddExpr>(Comm))
6331 return getAddExpr(NewOps);
6332 if (isa<SCEVMulExpr>(Comm))
6333 return getMulExpr(NewOps);
6334 if (isa<SCEVSMaxExpr>(Comm))
6335 return getSMaxExpr(NewOps);
6336 if (isa<SCEVUMaxExpr>(Comm))
6337 return getUMaxExpr(NewOps);
6338 llvm_unreachable("Unknown commutative SCEV type!");
6341 // If we got here, all operands are loop invariant.
6345 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6346 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6347 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6348 if (LHS == Div->getLHS() && RHS == Div->getRHS())
6349 return Div; // must be loop invariant
6350 return getUDivExpr(LHS, RHS);
6353 // If this is a loop recurrence for a loop that does not contain L, then we
6354 // are dealing with the final value computed by the loop.
6355 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6356 // First, attempt to evaluate each operand.
6357 // Avoid performing the look-up in the common case where the specified
6358 // expression has no loop-variant portions.
6359 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6360 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6361 if (OpAtScope == AddRec->getOperand(i))
6364 // Okay, at least one of these operands is loop variant but might be
6365 // foldable. Build a new instance of the folded commutative expression.
6366 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6367 AddRec->op_begin()+i);
6368 NewOps.push_back(OpAtScope);
6369 for (++i; i != e; ++i)
6370 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6372 const SCEV *FoldedRec =
6373 getAddRecExpr(NewOps, AddRec->getLoop(),
6374 AddRec->getNoWrapFlags(SCEV::FlagNW));
6375 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6376 // The addrec may be folded to a nonrecurrence, for example, if the
6377 // induction variable is multiplied by zero after constant folding. Go
6378 // ahead and return the folded value.
6384 // If the scope is outside the addrec's loop, evaluate it by using the
6385 // loop exit value of the addrec.
6386 if (!AddRec->getLoop()->contains(L)) {
6387 // To evaluate this recurrence, we need to know how many times the AddRec
6388 // loop iterates. Compute this now.
6389 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6390 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6392 // Then, evaluate the AddRec.
6393 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6399 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6400 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6401 if (Op == Cast->getOperand())
6402 return Cast; // must be loop invariant
6403 return getZeroExtendExpr(Op, Cast->getType());
6406 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6407 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6408 if (Op == Cast->getOperand())
6409 return Cast; // must be loop invariant
6410 return getSignExtendExpr(Op, Cast->getType());
6413 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6414 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6415 if (Op == Cast->getOperand())
6416 return Cast; // must be loop invariant
6417 return getTruncateExpr(Op, Cast->getType());
6420 llvm_unreachable("Unknown SCEV type!");
6423 /// getSCEVAtScope - This is a convenience function which does
6424 /// getSCEVAtScope(getSCEV(V), L).
6425 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6426 return getSCEVAtScope(getSCEV(V), L);
6429 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6430 /// following equation:
6432 /// A * X = B (mod N)
6434 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6435 /// A and B isn't important.
6437 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6438 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6439 ScalarEvolution &SE) {
6440 uint32_t BW = A.getBitWidth();
6441 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6442 assert(A != 0 && "A must be non-zero.");
6446 // The gcd of A and N may have only one prime factor: 2. The number of
6447 // trailing zeros in A is its multiplicity
6448 uint32_t Mult2 = A.countTrailingZeros();
6451 // 2. Check if B is divisible by D.
6453 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6454 // is not less than multiplicity of this prime factor for D.
6455 if (B.countTrailingZeros() < Mult2)
6456 return SE.getCouldNotCompute();
6458 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6461 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6462 // bit width during computations.
6463 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6464 APInt Mod(BW + 1, 0);
6465 Mod.setBit(BW - Mult2); // Mod = N / D
6466 APInt I = AD.multiplicativeInverse(Mod);
6468 // 4. Compute the minimum unsigned root of the equation:
6469 // I * (B / D) mod (N / D)
6470 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6472 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6474 return SE.getConstant(Result.trunc(BW));
6477 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6478 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6479 /// might be the same) or two SCEVCouldNotCompute objects.
6481 static std::pair<const SCEV *,const SCEV *>
6482 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6483 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6484 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6485 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6486 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6488 // We currently can only solve this if the coefficients are constants.
6489 if (!LC || !MC || !NC) {
6490 const SCEV *CNC = SE.getCouldNotCompute();
6491 return std::make_pair(CNC, CNC);
6494 uint32_t BitWidth = LC->getAPInt().getBitWidth();
6495 const APInt &L = LC->getAPInt();
6496 const APInt &M = MC->getAPInt();
6497 const APInt &N = NC->getAPInt();
6498 APInt Two(BitWidth, 2);
6499 APInt Four(BitWidth, 4);
6502 using namespace APIntOps;
6504 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6505 // The B coefficient is M-N/2
6509 // The A coefficient is N/2
6510 APInt A(N.sdiv(Two));
6512 // Compute the B^2-4ac term.
6515 SqrtTerm -= Four * (A * C);
6517 if (SqrtTerm.isNegative()) {
6518 // The loop is provably infinite.
6519 const SCEV *CNC = SE.getCouldNotCompute();
6520 return std::make_pair(CNC, CNC);
6523 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6524 // integer value or else APInt::sqrt() will assert.
6525 APInt SqrtVal(SqrtTerm.sqrt());
6527 // Compute the two solutions for the quadratic formula.
6528 // The divisions must be performed as signed divisions.
6531 if (TwoA.isMinValue()) {
6532 const SCEV *CNC = SE.getCouldNotCompute();
6533 return std::make_pair(CNC, CNC);
6536 LLVMContext &Context = SE.getContext();
6538 ConstantInt *Solution1 =
6539 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6540 ConstantInt *Solution2 =
6541 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6543 return std::make_pair(SE.getConstant(Solution1),
6544 SE.getConstant(Solution2));
6545 } // end APIntOps namespace
6548 /// HowFarToZero - Return the number of times a backedge comparing the specified
6549 /// value to zero will execute. If not computable, return CouldNotCompute.
6551 /// This is only used for loops with a "x != y" exit test. The exit condition is
6552 /// now expressed as a single expression, V = x-y. So the exit test is
6553 /// effectively V != 0. We know and take advantage of the fact that this
6554 /// expression only being used in a comparison by zero context.
6555 ScalarEvolution::ExitLimit
6556 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6557 // If the value is a constant
6558 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6559 // If the value is already zero, the branch will execute zero times.
6560 if (C->getValue()->isZero()) return C;
6561 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6564 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6565 if (!AddRec || AddRec->getLoop() != L)
6566 return getCouldNotCompute();
6568 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6569 // the quadratic equation to solve it.
6570 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6571 std::pair<const SCEV *,const SCEV *> Roots =
6572 SolveQuadraticEquation(AddRec, *this);
6573 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6574 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6576 // Pick the smallest positive root value.
6577 if (ConstantInt *CB =
6578 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6581 if (!CB->getZExtValue())
6582 std::swap(R1, R2); // R1 is the minimum root now.
6584 // We can only use this value if the chrec ends up with an exact zero
6585 // value at this index. When solving for "X*X != 5", for example, we
6586 // should not accept a root of 2.
6587 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6589 return R1; // We found a quadratic root!
6592 return getCouldNotCompute();
6595 // Otherwise we can only handle this if it is affine.
6596 if (!AddRec->isAffine())
6597 return getCouldNotCompute();
6599 // If this is an affine expression, the execution count of this branch is
6600 // the minimum unsigned root of the following equation:
6602 // Start + Step*N = 0 (mod 2^BW)
6606 // Step*N = -Start (mod 2^BW)
6608 // where BW is the common bit width of Start and Step.
6610 // Get the initial value for the loop.
6611 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6612 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6614 // For now we handle only constant steps.
6616 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6617 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6618 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6619 // We have not yet seen any such cases.
6620 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6621 if (!StepC || StepC->getValue()->equalsInt(0))
6622 return getCouldNotCompute();
6624 // For positive steps (counting up until unsigned overflow):
6625 // N = -Start/Step (as unsigned)
6626 // For negative steps (counting down to zero):
6628 // First compute the unsigned distance from zero in the direction of Step.
6629 bool CountDown = StepC->getAPInt().isNegative();
6630 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6632 // Handle unitary steps, which cannot wraparound.
6633 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6634 // N = Distance (as unsigned)
6635 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6636 ConstantRange CR = getUnsignedRange(Start);
6637 const SCEV *MaxBECount;
6638 if (!CountDown && CR.getUnsignedMin().isMinValue())
6639 // When counting up, the worst starting value is 1, not 0.
6640 MaxBECount = CR.getUnsignedMax().isMinValue()
6641 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6642 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6644 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6645 : -CR.getUnsignedMin());
6646 return ExitLimit(Distance, MaxBECount);
6649 // As a special case, handle the instance where Step is a positive power of
6650 // two. In this case, determining whether Step divides Distance evenly can be
6651 // done by counting and comparing the number of trailing zeros of Step and
6654 const APInt &StepV = StepC->getAPInt();
6655 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6656 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6657 // case is not handled as this code is guarded by !CountDown.
6658 if (StepV.isPowerOf2() &&
6659 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
6660 // Here we've constrained the equation to be of the form
6662 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
6664 // where we're operating on a W bit wide integer domain and k is
6665 // non-negative. The smallest unsigned solution for X is the trip count.
6667 // (0) is equivalent to:
6669 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
6670 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
6671 // <=> 2^k * Distance' - X = L * 2^(W - N)
6672 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
6674 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
6677 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
6679 // E.g. say we're solving
6681 // 2 * Val = 2 * X (in i8) ... (3)
6683 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
6685 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
6686 // necessarily the smallest unsigned value of X that satisfies (3).
6687 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
6688 // is i8 1, not i8 -127
6690 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
6692 // Since SCEV does not have a URem node, we construct one using a truncate
6693 // and a zero extend.
6695 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
6696 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
6697 auto *WideTy = Distance->getType();
6699 return getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
6703 // If the condition controls loop exit (the loop exits only if the expression
6704 // is true) and the addition is no-wrap we can use unsigned divide to
6705 // compute the backedge count. In this case, the step may not divide the
6706 // distance, but we don't care because if the condition is "missed" the loop
6707 // will have undefined behavior due to wrapping.
6708 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6710 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6711 return ExitLimit(Exact, Exact);
6714 // Then, try to solve the above equation provided that Start is constant.
6715 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6716 return SolveLinEquationWithOverflow(StepC->getAPInt(), -StartC->getAPInt(),
6718 return getCouldNotCompute();
6721 /// HowFarToNonZero - Return the number of times a backedge checking the
6722 /// specified value for nonzero will execute. If not computable, return
6724 ScalarEvolution::ExitLimit
6725 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6726 // Loops that look like: while (X == 0) are very strange indeed. We don't
6727 // handle them yet except for the trivial case. This could be expanded in the
6728 // future as needed.
6730 // If the value is a constant, check to see if it is known to be non-zero
6731 // already. If so, the backedge will execute zero times.
6732 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6733 if (!C->getValue()->isNullValue())
6734 return getZero(C->getType());
6735 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6738 // We could implement others, but I really doubt anyone writes loops like
6739 // this, and if they did, they would already be constant folded.
6740 return getCouldNotCompute();
6743 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6744 /// (which may not be an immediate predecessor) which has exactly one
6745 /// successor from which BB is reachable, or null if no such block is
6748 std::pair<BasicBlock *, BasicBlock *>
6749 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6750 // If the block has a unique predecessor, then there is no path from the
6751 // predecessor to the block that does not go through the direct edge
6752 // from the predecessor to the block.
6753 if (BasicBlock *Pred = BB->getSinglePredecessor())
6754 return std::make_pair(Pred, BB);
6756 // A loop's header is defined to be a block that dominates the loop.
6757 // If the header has a unique predecessor outside the loop, it must be
6758 // a block that has exactly one successor that can reach the loop.
6759 if (Loop *L = LI.getLoopFor(BB))
6760 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6762 return std::pair<BasicBlock *, BasicBlock *>();
6765 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6766 /// testing whether two expressions are equal, however for the purposes of
6767 /// looking for a condition guarding a loop, it can be useful to be a little
6768 /// more general, since a front-end may have replicated the controlling
6771 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6772 // Quick check to see if they are the same SCEV.
6773 if (A == B) return true;
6775 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
6776 // Not all instructions that are "identical" compute the same value. For
6777 // instance, two distinct alloca instructions allocating the same type are
6778 // identical and do not read memory; but compute distinct values.
6779 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
6782 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6783 // two different instructions with the same value. Check for this case.
6784 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6785 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6786 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6787 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6788 if (ComputesEqualValues(AI, BI))
6791 // Otherwise assume they may have a different value.
6795 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6796 /// predicate Pred. Return true iff any changes were made.
6798 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6799 const SCEV *&LHS, const SCEV *&RHS,
6801 bool Changed = false;
6803 // If we hit the max recursion limit bail out.
6807 // Canonicalize a constant to the right side.
6808 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6809 // Check for both operands constant.
6810 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6811 if (ConstantExpr::getICmp(Pred,
6813 RHSC->getValue())->isNullValue())
6814 goto trivially_false;
6816 goto trivially_true;
6818 // Otherwise swap the operands to put the constant on the right.
6819 std::swap(LHS, RHS);
6820 Pred = ICmpInst::getSwappedPredicate(Pred);
6824 // If we're comparing an addrec with a value which is loop-invariant in the
6825 // addrec's loop, put the addrec on the left. Also make a dominance check,
6826 // as both operands could be addrecs loop-invariant in each other's loop.
6827 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6828 const Loop *L = AR->getLoop();
6829 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6830 std::swap(LHS, RHS);
6831 Pred = ICmpInst::getSwappedPredicate(Pred);
6836 // If there's a constant operand, canonicalize comparisons with boundary
6837 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6838 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6839 const APInt &RA = RC->getAPInt();
6841 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6842 case ICmpInst::ICMP_EQ:
6843 case ICmpInst::ICMP_NE:
6844 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6846 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6847 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6848 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6849 ME->getOperand(0)->isAllOnesValue()) {
6850 RHS = AE->getOperand(1);
6851 LHS = ME->getOperand(1);
6855 case ICmpInst::ICMP_UGE:
6856 if ((RA - 1).isMinValue()) {
6857 Pred = ICmpInst::ICMP_NE;
6858 RHS = getConstant(RA - 1);
6862 if (RA.isMaxValue()) {
6863 Pred = ICmpInst::ICMP_EQ;
6867 if (RA.isMinValue()) goto trivially_true;
6869 Pred = ICmpInst::ICMP_UGT;
6870 RHS = getConstant(RA - 1);
6873 case ICmpInst::ICMP_ULE:
6874 if ((RA + 1).isMaxValue()) {
6875 Pred = ICmpInst::ICMP_NE;
6876 RHS = getConstant(RA + 1);
6880 if (RA.isMinValue()) {
6881 Pred = ICmpInst::ICMP_EQ;
6885 if (RA.isMaxValue()) goto trivially_true;
6887 Pred = ICmpInst::ICMP_ULT;
6888 RHS = getConstant(RA + 1);
6891 case ICmpInst::ICMP_SGE:
6892 if ((RA - 1).isMinSignedValue()) {
6893 Pred = ICmpInst::ICMP_NE;
6894 RHS = getConstant(RA - 1);
6898 if (RA.isMaxSignedValue()) {
6899 Pred = ICmpInst::ICMP_EQ;
6903 if (RA.isMinSignedValue()) goto trivially_true;
6905 Pred = ICmpInst::ICMP_SGT;
6906 RHS = getConstant(RA - 1);
6909 case ICmpInst::ICMP_SLE:
6910 if ((RA + 1).isMaxSignedValue()) {
6911 Pred = ICmpInst::ICMP_NE;
6912 RHS = getConstant(RA + 1);
6916 if (RA.isMinSignedValue()) {
6917 Pred = ICmpInst::ICMP_EQ;
6921 if (RA.isMaxSignedValue()) goto trivially_true;
6923 Pred = ICmpInst::ICMP_SLT;
6924 RHS = getConstant(RA + 1);
6927 case ICmpInst::ICMP_UGT:
6928 if (RA.isMinValue()) {
6929 Pred = ICmpInst::ICMP_NE;
6933 if ((RA + 1).isMaxValue()) {
6934 Pred = ICmpInst::ICMP_EQ;
6935 RHS = getConstant(RA + 1);
6939 if (RA.isMaxValue()) goto trivially_false;
6941 case ICmpInst::ICMP_ULT:
6942 if (RA.isMaxValue()) {
6943 Pred = ICmpInst::ICMP_NE;
6947 if ((RA - 1).isMinValue()) {
6948 Pred = ICmpInst::ICMP_EQ;
6949 RHS = getConstant(RA - 1);
6953 if (RA.isMinValue()) goto trivially_false;
6955 case ICmpInst::ICMP_SGT:
6956 if (RA.isMinSignedValue()) {
6957 Pred = ICmpInst::ICMP_NE;
6961 if ((RA + 1).isMaxSignedValue()) {
6962 Pred = ICmpInst::ICMP_EQ;
6963 RHS = getConstant(RA + 1);
6967 if (RA.isMaxSignedValue()) goto trivially_false;
6969 case ICmpInst::ICMP_SLT:
6970 if (RA.isMaxSignedValue()) {
6971 Pred = ICmpInst::ICMP_NE;
6975 if ((RA - 1).isMinSignedValue()) {
6976 Pred = ICmpInst::ICMP_EQ;
6977 RHS = getConstant(RA - 1);
6981 if (RA.isMinSignedValue()) goto trivially_false;
6986 // Check for obvious equality.
6987 if (HasSameValue(LHS, RHS)) {
6988 if (ICmpInst::isTrueWhenEqual(Pred))
6989 goto trivially_true;
6990 if (ICmpInst::isFalseWhenEqual(Pred))
6991 goto trivially_false;
6994 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6995 // adding or subtracting 1 from one of the operands.
6997 case ICmpInst::ICMP_SLE:
6998 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6999 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7001 Pred = ICmpInst::ICMP_SLT;
7003 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
7004 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
7006 Pred = ICmpInst::ICMP_SLT;
7010 case ICmpInst::ICMP_SGE:
7011 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
7012 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
7014 Pred = ICmpInst::ICMP_SGT;
7016 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
7017 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7019 Pred = ICmpInst::ICMP_SGT;
7023 case ICmpInst::ICMP_ULE:
7024 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
7025 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7027 Pred = ICmpInst::ICMP_ULT;
7029 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
7030 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
7031 Pred = ICmpInst::ICMP_ULT;
7035 case ICmpInst::ICMP_UGE:
7036 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
7037 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
7038 Pred = ICmpInst::ICMP_UGT;
7040 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
7041 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7043 Pred = ICmpInst::ICMP_UGT;
7051 // TODO: More simplifications are possible here.
7053 // Recursively simplify until we either hit a recursion limit or nothing
7056 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
7062 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7063 Pred = ICmpInst::ICMP_EQ;
7068 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7069 Pred = ICmpInst::ICMP_NE;
7073 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
7074 return getSignedRange(S).getSignedMax().isNegative();
7077 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
7078 return getSignedRange(S).getSignedMin().isStrictlyPositive();
7081 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
7082 return !getSignedRange(S).getSignedMin().isNegative();
7085 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
7086 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
7089 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
7090 return isKnownNegative(S) || isKnownPositive(S);
7093 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
7094 const SCEV *LHS, const SCEV *RHS) {
7095 // Canonicalize the inputs first.
7096 (void)SimplifyICmpOperands(Pred, LHS, RHS);
7098 // If LHS or RHS is an addrec, check to see if the condition is true in
7099 // every iteration of the loop.
7100 // If LHS and RHS are both addrec, both conditions must be true in
7101 // every iteration of the loop.
7102 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7103 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7104 bool LeftGuarded = false;
7105 bool RightGuarded = false;
7107 const Loop *L = LAR->getLoop();
7108 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
7109 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
7110 if (!RAR) return true;
7115 const Loop *L = RAR->getLoop();
7116 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
7117 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
7118 if (!LAR) return true;
7119 RightGuarded = true;
7122 if (LeftGuarded && RightGuarded)
7125 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
7128 // Otherwise see what can be done with known constant ranges.
7129 return isKnownPredicateWithRanges(Pred, LHS, RHS);
7132 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
7133 ICmpInst::Predicate Pred,
7135 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
7138 // Verify an invariant: inverting the predicate should turn a monotonically
7139 // increasing change to a monotonically decreasing one, and vice versa.
7140 bool IncreasingSwapped;
7141 bool ResultSwapped = isMonotonicPredicateImpl(
7142 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
7144 assert(Result == ResultSwapped && "should be able to analyze both!");
7146 assert(Increasing == !IncreasingSwapped &&
7147 "monotonicity should flip as we flip the predicate");
7153 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
7154 ICmpInst::Predicate Pred,
7157 // A zero step value for LHS means the induction variable is essentially a
7158 // loop invariant value. We don't really depend on the predicate actually
7159 // flipping from false to true (for increasing predicates, and the other way
7160 // around for decreasing predicates), all we care about is that *if* the
7161 // predicate changes then it only changes from false to true.
7163 // A zero step value in itself is not very useful, but there may be places
7164 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
7165 // as general as possible.
7169 return false; // Conservative answer
7171 case ICmpInst::ICMP_UGT:
7172 case ICmpInst::ICMP_UGE:
7173 case ICmpInst::ICMP_ULT:
7174 case ICmpInst::ICMP_ULE:
7175 if (!LHS->getNoWrapFlags(SCEV::FlagNUW))
7178 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
7181 case ICmpInst::ICMP_SGT:
7182 case ICmpInst::ICMP_SGE:
7183 case ICmpInst::ICMP_SLT:
7184 case ICmpInst::ICMP_SLE: {
7185 if (!LHS->getNoWrapFlags(SCEV::FlagNSW))
7188 const SCEV *Step = LHS->getStepRecurrence(*this);
7190 if (isKnownNonNegative(Step)) {
7191 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
7195 if (isKnownNonPositive(Step)) {
7196 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7205 llvm_unreachable("switch has default clause!");
7208 bool ScalarEvolution::isLoopInvariantPredicate(
7209 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7210 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7211 const SCEV *&InvariantRHS) {
7213 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7214 if (!isLoopInvariant(RHS, L)) {
7215 if (!isLoopInvariant(LHS, L))
7218 std::swap(LHS, RHS);
7219 Pred = ICmpInst::getSwappedPredicate(Pred);
7222 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7223 if (!ArLHS || ArLHS->getLoop() != L)
7227 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7230 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7231 // true as the loop iterates, and the backedge is control dependent on
7232 // "ArLHS `Pred` RHS" == true then we can reason as follows:
7234 // * if the predicate was false in the first iteration then the predicate
7235 // is never evaluated again, since the loop exits without taking the
7237 // * if the predicate was true in the first iteration then it will
7238 // continue to be true for all future iterations since it is
7239 // monotonically increasing.
7241 // For both the above possibilities, we can replace the loop varying
7242 // predicate with its value on the first iteration of the loop (which is
7245 // A similar reasoning applies for a monotonically decreasing predicate, by
7246 // replacing true with false and false with true in the above two bullets.
7248 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7250 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7253 InvariantPred = Pred;
7254 InvariantLHS = ArLHS->getStart();
7260 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
7261 const SCEV *LHS, const SCEV *RHS) {
7262 if (HasSameValue(LHS, RHS))
7263 return ICmpInst::isTrueWhenEqual(Pred);
7265 // This code is split out from isKnownPredicate because it is called from
7266 // within isLoopEntryGuardedByCond.
7269 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7270 case ICmpInst::ICMP_SGT:
7271 std::swap(LHS, RHS);
7272 case ICmpInst::ICMP_SLT: {
7273 ConstantRange LHSRange = getSignedRange(LHS);
7274 ConstantRange RHSRange = getSignedRange(RHS);
7275 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
7277 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
7281 case ICmpInst::ICMP_SGE:
7282 std::swap(LHS, RHS);
7283 case ICmpInst::ICMP_SLE: {
7284 ConstantRange LHSRange = getSignedRange(LHS);
7285 ConstantRange RHSRange = getSignedRange(RHS);
7286 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
7288 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
7292 case ICmpInst::ICMP_UGT:
7293 std::swap(LHS, RHS);
7294 case ICmpInst::ICMP_ULT: {
7295 ConstantRange LHSRange = getUnsignedRange(LHS);
7296 ConstantRange RHSRange = getUnsignedRange(RHS);
7297 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
7299 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
7303 case ICmpInst::ICMP_UGE:
7304 std::swap(LHS, RHS);
7305 case ICmpInst::ICMP_ULE: {
7306 ConstantRange LHSRange = getUnsignedRange(LHS);
7307 ConstantRange RHSRange = getUnsignedRange(RHS);
7308 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
7310 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
7314 case ICmpInst::ICMP_NE: {
7315 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
7317 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
7320 const SCEV *Diff = getMinusSCEV(LHS, RHS);
7321 if (isKnownNonZero(Diff))
7325 case ICmpInst::ICMP_EQ:
7326 // The check at the top of the function catches the case where
7327 // the values are known to be equal.
7333 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
7337 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
7338 // Return Y via OutY.
7339 auto MatchBinaryAddToConst =
7340 [this](const SCEV *Result, const SCEV *X, APInt &OutY,
7341 SCEV::NoWrapFlags ExpectedFlags) {
7342 const SCEV *NonConstOp, *ConstOp;
7343 SCEV::NoWrapFlags FlagsPresent;
7345 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
7346 !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
7349 OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
7350 return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
7359 case ICmpInst::ICMP_SGE:
7360 std::swap(LHS, RHS);
7361 case ICmpInst::ICMP_SLE:
7362 // X s<= (X + C)<nsw> if C >= 0
7363 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
7366 // (X + C)<nsw> s<= X if C <= 0
7367 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
7368 !C.isStrictlyPositive())
7372 case ICmpInst::ICMP_SGT:
7373 std::swap(LHS, RHS);
7374 case ICmpInst::ICMP_SLT:
7375 // X s< (X + C)<nsw> if C > 0
7376 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
7377 C.isStrictlyPositive())
7380 // (X + C)<nsw> s< X if C < 0
7381 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
7389 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7392 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
7395 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7396 // the stack can result in exponential time complexity.
7397 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7399 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7401 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7402 // isKnownPredicate. isKnownPredicate is more powerful, but also more
7403 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7404 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
7405 // use isKnownPredicate later if needed.
7406 return isKnownNonNegative(RHS) &&
7407 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7408 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
7411 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7412 /// protected by a conditional between LHS and RHS. This is used to
7413 /// to eliminate casts.
7415 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7416 ICmpInst::Predicate Pred,
7417 const SCEV *LHS, const SCEV *RHS) {
7418 // Interpret a null as meaning no loop, where there is obviously no guard
7419 // (interprocedural conditions notwithstanding).
7420 if (!L) return true;
7422 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7424 BasicBlock *Latch = L->getLoopLatch();
7428 BranchInst *LoopContinuePredicate =
7429 dyn_cast<BranchInst>(Latch->getTerminator());
7430 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7431 isImpliedCond(Pred, LHS, RHS,
7432 LoopContinuePredicate->getCondition(),
7433 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7436 // We don't want more than one activation of the following loops on the stack
7437 // -- that can lead to O(n!) time complexity.
7438 if (WalkingBEDominatingConds)
7441 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7443 // See if we can exploit a trip count to prove the predicate.
7444 const auto &BETakenInfo = getBackedgeTakenInfo(L);
7445 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7446 if (LatchBECount != getCouldNotCompute()) {
7447 // We know that Latch branches back to the loop header exactly
7448 // LatchBECount times. This means the backdege condition at Latch is
7449 // equivalent to "{0,+,1} u< LatchBECount".
7450 Type *Ty = LatchBECount->getType();
7451 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7452 const SCEV *LoopCounter =
7453 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7454 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7459 // Check conditions due to any @llvm.assume intrinsics.
7460 for (auto &AssumeVH : AC.assumptions()) {
7463 auto *CI = cast<CallInst>(AssumeVH);
7464 if (!DT.dominates(CI, Latch->getTerminator()))
7467 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7471 // If the loop is not reachable from the entry block, we risk running into an
7472 // infinite loop as we walk up into the dom tree. These loops do not matter
7473 // anyway, so we just return a conservative answer when we see them.
7474 if (!DT.isReachableFromEntry(L->getHeader()))
7477 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7478 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7480 assert(DTN && "should reach the loop header before reaching the root!");
7482 BasicBlock *BB = DTN->getBlock();
7483 BasicBlock *PBB = BB->getSinglePredecessor();
7487 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7488 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7491 Value *Condition = ContinuePredicate->getCondition();
7493 // If we have an edge `E` within the loop body that dominates the only
7494 // latch, the condition guarding `E` also guards the backedge. This
7495 // reasoning works only for loops with a single latch.
7497 BasicBlockEdge DominatingEdge(PBB, BB);
7498 if (DominatingEdge.isSingleEdge()) {
7499 // We're constructively (and conservatively) enumerating edges within the
7500 // loop body that dominate the latch. The dominator tree better agree
7502 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7504 if (isImpliedCond(Pred, LHS, RHS, Condition,
7505 BB != ContinuePredicate->getSuccessor(0)))
7513 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7514 /// by a conditional between LHS and RHS. This is used to help avoid max
7515 /// expressions in loop trip counts, and to eliminate casts.
7517 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7518 ICmpInst::Predicate Pred,
7519 const SCEV *LHS, const SCEV *RHS) {
7520 // Interpret a null as meaning no loop, where there is obviously no guard
7521 // (interprocedural conditions notwithstanding).
7522 if (!L) return false;
7524 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7526 // Starting at the loop predecessor, climb up the predecessor chain, as long
7527 // as there are predecessors that can be found that have unique successors
7528 // leading to the original header.
7529 for (std::pair<BasicBlock *, BasicBlock *>
7530 Pair(L->getLoopPredecessor(), L->getHeader());
7532 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7534 BranchInst *LoopEntryPredicate =
7535 dyn_cast<BranchInst>(Pair.first->getTerminator());
7536 if (!LoopEntryPredicate ||
7537 LoopEntryPredicate->isUnconditional())
7540 if (isImpliedCond(Pred, LHS, RHS,
7541 LoopEntryPredicate->getCondition(),
7542 LoopEntryPredicate->getSuccessor(0) != Pair.second))
7546 // Check conditions due to any @llvm.assume intrinsics.
7547 for (auto &AssumeVH : AC.assumptions()) {
7550 auto *CI = cast<CallInst>(AssumeVH);
7551 if (!DT.dominates(CI, L->getHeader()))
7554 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7562 /// RAII wrapper to prevent recursive application of isImpliedCond.
7563 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7564 /// currently evaluating isImpliedCond.
7565 struct MarkPendingLoopPredicate {
7567 DenseSet<Value*> &LoopPreds;
7570 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7571 : Cond(C), LoopPreds(LP) {
7572 Pending = !LoopPreds.insert(Cond).second;
7574 ~MarkPendingLoopPredicate() {
7576 LoopPreds.erase(Cond);
7579 } // end anonymous namespace
7581 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7582 /// and RHS is true whenever the given Cond value evaluates to true.
7583 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7584 const SCEV *LHS, const SCEV *RHS,
7585 Value *FoundCondValue,
7587 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7591 // Recursively handle And and Or conditions.
7592 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7593 if (BO->getOpcode() == Instruction::And) {
7595 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7596 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7597 } else if (BO->getOpcode() == Instruction::Or) {
7599 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7600 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7604 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
7605 if (!ICI) return false;
7607 // Now that we found a conditional branch that dominates the loop or controls
7608 // the loop latch. Check to see if it is the comparison we are looking for.
7609 ICmpInst::Predicate FoundPred;
7611 FoundPred = ICI->getInversePredicate();
7613 FoundPred = ICI->getPredicate();
7615 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
7616 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
7618 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
7621 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
7623 ICmpInst::Predicate FoundPred,
7624 const SCEV *FoundLHS,
7625 const SCEV *FoundRHS) {
7626 // Balance the types.
7627 if (getTypeSizeInBits(LHS->getType()) <
7628 getTypeSizeInBits(FoundLHS->getType())) {
7629 if (CmpInst::isSigned(Pred)) {
7630 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
7631 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
7633 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
7634 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
7636 } else if (getTypeSizeInBits(LHS->getType()) >
7637 getTypeSizeInBits(FoundLHS->getType())) {
7638 if (CmpInst::isSigned(FoundPred)) {
7639 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
7640 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
7642 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
7643 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
7647 // Canonicalize the query to match the way instcombine will have
7648 // canonicalized the comparison.
7649 if (SimplifyICmpOperands(Pred, LHS, RHS))
7651 return CmpInst::isTrueWhenEqual(Pred);
7652 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
7653 if (FoundLHS == FoundRHS)
7654 return CmpInst::isFalseWhenEqual(FoundPred);
7656 // Check to see if we can make the LHS or RHS match.
7657 if (LHS == FoundRHS || RHS == FoundLHS) {
7658 if (isa<SCEVConstant>(RHS)) {
7659 std::swap(FoundLHS, FoundRHS);
7660 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
7662 std::swap(LHS, RHS);
7663 Pred = ICmpInst::getSwappedPredicate(Pred);
7667 // Check whether the found predicate is the same as the desired predicate.
7668 if (FoundPred == Pred)
7669 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7671 // Check whether swapping the found predicate makes it the same as the
7672 // desired predicate.
7673 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
7674 if (isa<SCEVConstant>(RHS))
7675 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
7677 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
7678 RHS, LHS, FoundLHS, FoundRHS);
7681 // Unsigned comparison is the same as signed comparison when both the operands
7682 // are non-negative.
7683 if (CmpInst::isUnsigned(FoundPred) &&
7684 CmpInst::getSignedPredicate(FoundPred) == Pred &&
7685 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
7686 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7688 // Check if we can make progress by sharpening ranges.
7689 if (FoundPred == ICmpInst::ICMP_NE &&
7690 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
7692 const SCEVConstant *C = nullptr;
7693 const SCEV *V = nullptr;
7695 if (isa<SCEVConstant>(FoundLHS)) {
7696 C = cast<SCEVConstant>(FoundLHS);
7699 C = cast<SCEVConstant>(FoundRHS);
7703 // The guarding predicate tells us that C != V. If the known range
7704 // of V is [C, t), we can sharpen the range to [C + 1, t). The
7705 // range we consider has to correspond to same signedness as the
7706 // predicate we're interested in folding.
7708 APInt Min = ICmpInst::isSigned(Pred) ?
7709 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7711 if (Min == C->getAPInt()) {
7712 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7713 // This is true even if (Min + 1) wraps around -- in case of
7714 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7716 APInt SharperMin = Min + 1;
7719 case ICmpInst::ICMP_SGE:
7720 case ICmpInst::ICMP_UGE:
7721 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7723 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7724 getConstant(SharperMin)))
7727 case ICmpInst::ICMP_SGT:
7728 case ICmpInst::ICMP_UGT:
7729 // We know from the range information that (V `Pred` Min ||
7730 // V == Min). We know from the guarding condition that !(V
7731 // == Min). This gives us
7733 // V `Pred` Min || V == Min && !(V == Min)
7736 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7738 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7748 // Check whether the actual condition is beyond sufficient.
7749 if (FoundPred == ICmpInst::ICMP_EQ)
7750 if (ICmpInst::isTrueWhenEqual(Pred))
7751 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7753 if (Pred == ICmpInst::ICMP_NE)
7754 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7755 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7758 // Otherwise assume the worst.
7762 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
7763 const SCEV *&L, const SCEV *&R,
7764 SCEV::NoWrapFlags &Flags) {
7765 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
7766 if (!AE || AE->getNumOperands() != 2)
7769 L = AE->getOperand(0);
7770 R = AE->getOperand(1);
7771 Flags = AE->getNoWrapFlags();
7775 bool ScalarEvolution::computeConstantDifference(const SCEV *Less,
7778 // We avoid subtracting expressions here because this function is usually
7779 // fairly deep in the call stack (i.e. is called many times).
7781 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
7782 const auto *LAR = cast<SCEVAddRecExpr>(Less);
7783 const auto *MAR = cast<SCEVAddRecExpr>(More);
7785 if (LAR->getLoop() != MAR->getLoop())
7788 // We look at affine expressions only; not for correctness but to keep
7789 // getStepRecurrence cheap.
7790 if (!LAR->isAffine() || !MAR->isAffine())
7793 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
7796 Less = LAR->getStart();
7797 More = MAR->getStart();
7802 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
7803 const auto &M = cast<SCEVConstant>(More)->getAPInt();
7804 const auto &L = cast<SCEVConstant>(Less)->getAPInt();
7810 SCEV::NoWrapFlags Flags;
7811 if (splitBinaryAdd(Less, L, R, Flags))
7812 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7814 C = -(LC->getAPInt());
7818 if (splitBinaryAdd(More, L, R, Flags))
7819 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7828 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
7829 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
7830 const SCEV *FoundLHS, const SCEV *FoundRHS) {
7831 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
7834 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7838 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
7839 if (!AddRecFoundLHS)
7842 // We'd like to let SCEV reason about control dependencies, so we constrain
7843 // both the inequalities to be about add recurrences on the same loop. This
7844 // way we can use isLoopEntryGuardedByCond later.
7846 const Loop *L = AddRecFoundLHS->getLoop();
7847 if (L != AddRecLHS->getLoop())
7850 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
7852 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
7855 // Informal proof for (2), assuming (1) [*]:
7857 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
7861 // FoundLHS s< FoundRHS s< INT_MIN - C
7862 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
7863 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
7864 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
7865 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
7866 // <=> FoundLHS + C s< FoundRHS + C
7868 // [*]: (1) can be proved by ruling out overflow.
7870 // [**]: This can be proved by analyzing all the four possibilities:
7871 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
7872 // (A s>= 0, B s>= 0).
7875 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
7876 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
7877 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
7878 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
7879 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
7883 if (!computeConstantDifference(FoundLHS, LHS, LDiff) ||
7884 !computeConstantDifference(FoundRHS, RHS, RDiff) ||
7891 APInt FoundRHSLimit;
7893 if (Pred == CmpInst::ICMP_ULT) {
7894 FoundRHSLimit = -RDiff;
7896 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
7897 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - RDiff;
7900 // Try to prove (1) or (2), as needed.
7901 return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
7902 getConstant(FoundRHSLimit));
7905 /// isImpliedCondOperands - Test whether the condition described by Pred,
7906 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7907 /// and FoundRHS is true.
7908 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7909 const SCEV *LHS, const SCEV *RHS,
7910 const SCEV *FoundLHS,
7911 const SCEV *FoundRHS) {
7912 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7915 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
7918 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7919 FoundLHS, FoundRHS) ||
7920 // ~x < ~y --> x > y
7921 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7922 getNotSCEV(FoundRHS),
7923 getNotSCEV(FoundLHS));
7927 /// If Expr computes ~A, return A else return nullptr
7928 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7929 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7930 if (!Add || Add->getNumOperands() != 2 ||
7931 !Add->getOperand(0)->isAllOnesValue())
7934 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7935 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
7936 !AddRHS->getOperand(0)->isAllOnesValue())
7939 return AddRHS->getOperand(1);
7943 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7944 template<typename MaxExprType>
7945 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7946 const SCEV *Candidate) {
7947 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7948 if (!MaxExpr) return false;
7950 return find(MaxExpr->operands(), Candidate) != MaxExpr->op_end();
7954 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7955 template<typename MaxExprType>
7956 static bool IsMinConsistingOf(ScalarEvolution &SE,
7957 const SCEV *MaybeMinExpr,
7958 const SCEV *Candidate) {
7959 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7963 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7966 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
7967 ICmpInst::Predicate Pred,
7968 const SCEV *LHS, const SCEV *RHS) {
7970 // If both sides are affine addrecs for the same loop, with equal
7971 // steps, and we know the recurrences don't wrap, then we only
7972 // need to check the predicate on the starting values.
7974 if (!ICmpInst::isRelational(Pred))
7977 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7980 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7983 if (LAR->getLoop() != RAR->getLoop())
7985 if (!LAR->isAffine() || !RAR->isAffine())
7988 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
7991 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
7992 SCEV::FlagNSW : SCEV::FlagNUW;
7993 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
7996 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
7999 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
8001 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
8002 ICmpInst::Predicate Pred,
8003 const SCEV *LHS, const SCEV *RHS) {
8008 case ICmpInst::ICMP_SGE:
8009 std::swap(LHS, RHS);
8011 case ICmpInst::ICMP_SLE:
8014 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
8016 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
8018 case ICmpInst::ICMP_UGE:
8019 std::swap(LHS, RHS);
8021 case ICmpInst::ICMP_ULE:
8024 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
8026 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
8029 llvm_unreachable("covered switch fell through?!");
8032 /// isImpliedCondOperandsHelper - Test whether the condition described by
8033 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
8034 /// FoundLHS, and FoundRHS is true.
8036 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
8037 const SCEV *LHS, const SCEV *RHS,
8038 const SCEV *FoundLHS,
8039 const SCEV *FoundRHS) {
8040 auto IsKnownPredicateFull =
8041 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
8042 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
8043 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
8044 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
8045 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
8049 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
8050 case ICmpInst::ICMP_EQ:
8051 case ICmpInst::ICMP_NE:
8052 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
8055 case ICmpInst::ICMP_SLT:
8056 case ICmpInst::ICMP_SLE:
8057 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
8058 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
8061 case ICmpInst::ICMP_SGT:
8062 case ICmpInst::ICMP_SGE:
8063 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
8064 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
8067 case ICmpInst::ICMP_ULT:
8068 case ICmpInst::ICMP_ULE:
8069 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
8070 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
8073 case ICmpInst::ICMP_UGT:
8074 case ICmpInst::ICMP_UGE:
8075 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
8076 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
8084 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
8085 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
8086 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
8089 const SCEV *FoundLHS,
8090 const SCEV *FoundRHS) {
8091 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
8092 // The restriction on `FoundRHS` be lifted easily -- it exists only to
8093 // reduce the compile time impact of this optimization.
8096 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
8097 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
8098 !isa<SCEVConstant>(AddLHS->getOperand(0)))
8101 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
8103 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
8104 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
8105 ConstantRange FoundLHSRange =
8106 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
8108 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
8110 APInt Addend = cast<SCEVConstant>(AddLHS->getOperand(0))->getAPInt();
8111 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
8113 // We can also compute the range of values for `LHS` that satisfy the
8114 // consequent, "`LHS` `Pred` `RHS`":
8115 APInt ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
8116 ConstantRange SatisfyingLHSRange =
8117 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
8119 // The antecedent implies the consequent if every value of `LHS` that
8120 // satisfies the antecedent also satisfies the consequent.
8121 return SatisfyingLHSRange.contains(LHSRange);
8124 // Verify if an linear IV with positive stride can overflow when in a
8125 // less-than comparison, knowing the invariant term of the comparison, the
8126 // stride and the knowledge of NSW/NUW flags on the recurrence.
8127 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
8128 bool IsSigned, bool NoWrap) {
8129 if (NoWrap) return false;
8131 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8132 const SCEV *One = getOne(Stride->getType());
8135 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
8136 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
8137 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8140 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
8141 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
8144 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
8145 APInt MaxValue = APInt::getMaxValue(BitWidth);
8146 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8149 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
8150 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
8153 // Verify if an linear IV with negative stride can overflow when in a
8154 // greater-than comparison, knowing the invariant term of the comparison,
8155 // the stride and the knowledge of NSW/NUW flags on the recurrence.
8156 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
8157 bool IsSigned, bool NoWrap) {
8158 if (NoWrap) return false;
8160 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8161 const SCEV *One = getOne(Stride->getType());
8164 APInt MinRHS = getSignedRange(RHS).getSignedMin();
8165 APInt MinValue = APInt::getSignedMinValue(BitWidth);
8166 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8169 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
8170 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
8173 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
8174 APInt MinValue = APInt::getMinValue(BitWidth);
8175 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8178 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
8179 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
8182 // Compute the backedge taken count knowing the interval difference, the
8183 // stride and presence of the equality in the comparison.
8184 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
8186 const SCEV *One = getOne(Step->getType());
8187 Delta = Equality ? getAddExpr(Delta, Step)
8188 : getAddExpr(Delta, getMinusSCEV(Step, One));
8189 return getUDivExpr(Delta, Step);
8192 /// HowManyLessThans - Return the number of times a backedge containing the
8193 /// specified less-than comparison will execute. If not computable, return
8194 /// CouldNotCompute.
8196 /// @param ControlsExit is true when the LHS < RHS condition directly controls
8197 /// the branch (loops exits only if condition is true). In this case, we can use
8198 /// NoWrapFlags to skip overflow checks.
8199 ScalarEvolution::ExitLimit
8200 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
8201 const Loop *L, bool IsSigned,
8202 bool ControlsExit) {
8203 // We handle only IV < Invariant
8204 if (!isLoopInvariant(RHS, L))
8205 return getCouldNotCompute();
8207 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8209 // Avoid weird loops
8210 if (!IV || IV->getLoop() != L || !IV->isAffine())
8211 return getCouldNotCompute();
8213 bool NoWrap = ControlsExit &&
8214 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8216 const SCEV *Stride = IV->getStepRecurrence(*this);
8218 // Avoid negative or zero stride values
8219 if (!isKnownPositive(Stride))
8220 return getCouldNotCompute();
8222 // Avoid proven overflow cases: this will ensure that the backedge taken count
8223 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8224 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8225 // behaviors like the case of C language.
8226 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
8227 return getCouldNotCompute();
8229 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
8230 : ICmpInst::ICMP_ULT;
8231 const SCEV *Start = IV->getStart();
8232 const SCEV *End = RHS;
8233 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
8234 const SCEV *Diff = getMinusSCEV(RHS, Start);
8235 // If we have NoWrap set, then we can assume that the increment won't
8236 // overflow, in which case if RHS - Start is a constant, we don't need to
8237 // do a max operation since we can just figure it out statically
8238 if (NoWrap && isa<SCEVConstant>(Diff)) {
8239 APInt D = dyn_cast<const SCEVConstant>(Diff)->getAPInt();
8243 End = IsSigned ? getSMaxExpr(RHS, Start)
8244 : getUMaxExpr(RHS, Start);
8247 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
8249 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
8250 : getUnsignedRange(Start).getUnsignedMin();
8252 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8253 : getUnsignedRange(Stride).getUnsignedMin();
8255 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8256 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
8257 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
8259 // Although End can be a MAX expression we estimate MaxEnd considering only
8260 // the case End = RHS. This is safe because in the other case (End - Start)
8261 // is zero, leading to a zero maximum backedge taken count.
8263 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8264 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8266 const SCEV *MaxBECount;
8267 if (isa<SCEVConstant>(BECount))
8268 MaxBECount = BECount;
8270 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8271 getConstant(MinStride), false);
8273 if (isa<SCEVCouldNotCompute>(MaxBECount))
8274 MaxBECount = BECount;
8276 return ExitLimit(BECount, MaxBECount);
8279 ScalarEvolution::ExitLimit
8280 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8281 const Loop *L, bool IsSigned,
8282 bool ControlsExit) {
8283 // We handle only IV > Invariant
8284 if (!isLoopInvariant(RHS, L))
8285 return getCouldNotCompute();
8287 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8289 // Avoid weird loops
8290 if (!IV || IV->getLoop() != L || !IV->isAffine())
8291 return getCouldNotCompute();
8293 bool NoWrap = ControlsExit &&
8294 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8296 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8298 // Avoid negative or zero stride values
8299 if (!isKnownPositive(Stride))
8300 return getCouldNotCompute();
8302 // Avoid proven overflow cases: this will ensure that the backedge taken count
8303 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8304 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8305 // behaviors like the case of C language.
8306 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8307 return getCouldNotCompute();
8309 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8310 : ICmpInst::ICMP_UGT;
8312 const SCEV *Start = IV->getStart();
8313 const SCEV *End = RHS;
8314 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
8315 const SCEV *Diff = getMinusSCEV(RHS, Start);
8316 // If we have NoWrap set, then we can assume that the increment won't
8317 // overflow, in which case if RHS - Start is a constant, we don't need to
8318 // do a max operation since we can just figure it out statically
8319 if (NoWrap && isa<SCEVConstant>(Diff)) {
8320 APInt D = dyn_cast<const SCEVConstant>(Diff)->getAPInt();
8321 if (!D.isNegative())
8324 End = IsSigned ? getSMinExpr(RHS, Start)
8325 : getUMinExpr(RHS, Start);
8328 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8330 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8331 : getUnsignedRange(Start).getUnsignedMax();
8333 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8334 : getUnsignedRange(Stride).getUnsignedMin();
8336 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8337 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8338 : APInt::getMinValue(BitWidth) + (MinStride - 1);
8340 // Although End can be a MIN expression we estimate MinEnd considering only
8341 // the case End = RHS. This is safe because in the other case (Start - End)
8342 // is zero, leading to a zero maximum backedge taken count.
8344 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8345 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8348 const SCEV *MaxBECount = getCouldNotCompute();
8349 if (isa<SCEVConstant>(BECount))
8350 MaxBECount = BECount;
8352 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8353 getConstant(MinStride), false);
8355 if (isa<SCEVCouldNotCompute>(MaxBECount))
8356 MaxBECount = BECount;
8358 return ExitLimit(BECount, MaxBECount);
8361 /// getNumIterationsInRange - Return the number of iterations of this loop that
8362 /// produce values in the specified constant range. Another way of looking at
8363 /// this is that it returns the first iteration number where the value is not in
8364 /// the condition, thus computing the exit count. If the iteration count can't
8365 /// be computed, an instance of SCEVCouldNotCompute is returned.
8366 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
8367 ScalarEvolution &SE) const {
8368 if (Range.isFullSet()) // Infinite loop.
8369 return SE.getCouldNotCompute();
8371 // If the start is a non-zero constant, shift the range to simplify things.
8372 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8373 if (!SC->getValue()->isZero()) {
8374 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8375 Operands[0] = SE.getZero(SC->getType());
8376 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8377 getNoWrapFlags(FlagNW));
8378 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
8379 return ShiftedAddRec->getNumIterationsInRange(
8380 Range.subtract(SC->getAPInt()), SE);
8381 // This is strange and shouldn't happen.
8382 return SE.getCouldNotCompute();
8385 // The only time we can solve this is when we have all constant indices.
8386 // Otherwise, we cannot determine the overflow conditions.
8387 if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
8388 return SE.getCouldNotCompute();
8390 // Okay at this point we know that all elements of the chrec are constants and
8391 // that the start element is zero.
8393 // First check to see if the range contains zero. If not, the first
8395 unsigned BitWidth = SE.getTypeSizeInBits(getType());
8396 if (!Range.contains(APInt(BitWidth, 0)))
8397 return SE.getZero(getType());
8400 // If this is an affine expression then we have this situation:
8401 // Solve {0,+,A} in Range === Ax in Range
8403 // We know that zero is in the range. If A is positive then we know that
8404 // the upper value of the range must be the first possible exit value.
8405 // If A is negative then the lower of the range is the last possible loop
8406 // value. Also note that we already checked for a full range.
8407 APInt One(BitWidth,1);
8408 APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
8409 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8411 // The exit value should be (End+A)/A.
8412 APInt ExitVal = (End + A).udiv(A);
8413 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8415 // Evaluate at the exit value. If we really did fall out of the valid
8416 // range, then we computed our trip count, otherwise wrap around or other
8417 // things must have happened.
8418 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8419 if (Range.contains(Val->getValue()))
8420 return SE.getCouldNotCompute(); // Something strange happened
8422 // Ensure that the previous value is in the range. This is a sanity check.
8423 assert(Range.contains(
8424 EvaluateConstantChrecAtConstant(this,
8425 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8426 "Linear scev computation is off in a bad way!");
8427 return SE.getConstant(ExitValue);
8428 } else if (isQuadratic()) {
8429 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8430 // quadratic equation to solve it. To do this, we must frame our problem in
8431 // terms of figuring out when zero is crossed, instead of when
8432 // Range.getUpper() is crossed.
8433 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8434 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8435 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
8436 // getNoWrapFlags(FlagNW)
8439 // Next, solve the constructed addrec
8440 auto Roots = SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
8441 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
8442 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
8444 // Pick the smallest positive root value.
8445 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
8446 ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
8447 if (!CB->getZExtValue())
8448 std::swap(R1, R2); // R1 is the minimum root now.
8450 // Make sure the root is not off by one. The returned iteration should
8451 // not be in the range, but the previous one should be. When solving
8452 // for "X*X < 5", for example, we should not return a root of 2.
8453 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
8456 if (Range.contains(R1Val->getValue())) {
8457 // The next iteration must be out of the range...
8458 ConstantInt *NextVal =
8459 ConstantInt::get(SE.getContext(), R1->getAPInt() + 1);
8461 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8462 if (!Range.contains(R1Val->getValue()))
8463 return SE.getConstant(NextVal);
8464 return SE.getCouldNotCompute(); // Something strange happened
8467 // If R1 was not in the range, then it is a good return value. Make
8468 // sure that R1-1 WAS in the range though, just in case.
8469 ConstantInt *NextVal =
8470 ConstantInt::get(SE.getContext(), R1->getAPInt() - 1);
8471 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8472 if (Range.contains(R1Val->getValue()))
8474 return SE.getCouldNotCompute(); // Something strange happened
8479 return SE.getCouldNotCompute();
8485 FindUndefs() : Found(false) {}
8487 bool follow(const SCEV *S) {
8488 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
8489 if (isa<UndefValue>(C->getValue()))
8491 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
8492 if (isa<UndefValue>(C->getValue()))
8496 // Keep looking if we haven't found it yet.
8499 bool isDone() const {
8500 // Stop recursion if we have found an undef.
8506 // Return true when S contains at least an undef value.
8508 containsUndefs(const SCEV *S) {
8510 SCEVTraversal<FindUndefs> ST(F);
8517 // Collect all steps of SCEV expressions.
8518 struct SCEVCollectStrides {
8519 ScalarEvolution &SE;
8520 SmallVectorImpl<const SCEV *> &Strides;
8522 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
8523 : SE(SE), Strides(S) {}
8525 bool follow(const SCEV *S) {
8526 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
8527 Strides.push_back(AR->getStepRecurrence(SE));
8530 bool isDone() const { return false; }
8533 // Collect all SCEVUnknown and SCEVMulExpr expressions.
8534 struct SCEVCollectTerms {
8535 SmallVectorImpl<const SCEV *> &Terms;
8537 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
8540 bool follow(const SCEV *S) {
8541 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
8542 if (!containsUndefs(S))
8545 // Stop recursion: once we collected a term, do not walk its operands.
8552 bool isDone() const { return false; }
8555 // Check if a SCEV contains an AddRecExpr.
8556 struct SCEVHasAddRec {
8557 bool &ContainsAddRec;
8559 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
8560 ContainsAddRec = false;
8563 bool follow(const SCEV *S) {
8564 if (isa<SCEVAddRecExpr>(S)) {
8565 ContainsAddRec = true;
8567 // Stop recursion: once we collected a term, do not walk its operands.
8574 bool isDone() const { return false; }
8577 // Find factors that are multiplied with an expression that (possibly as a
8578 // subexpression) contains an AddRecExpr. In the expression:
8580 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
8582 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
8583 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
8584 // parameters as they form a product with an induction variable.
8586 // This collector expects all array size parameters to be in the same MulExpr.
8587 // It might be necessary to later add support for collecting parameters that are
8588 // spread over different nested MulExpr.
8589 struct SCEVCollectAddRecMultiplies {
8590 SmallVectorImpl<const SCEV *> &Terms;
8591 ScalarEvolution &SE;
8593 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
8594 : Terms(T), SE(SE) {}
8596 bool follow(const SCEV *S) {
8597 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
8598 bool HasAddRec = false;
8599 SmallVector<const SCEV *, 0> Operands;
8600 for (auto Op : Mul->operands()) {
8601 if (isa<SCEVUnknown>(Op)) {
8602 Operands.push_back(Op);
8604 bool ContainsAddRec;
8605 SCEVHasAddRec ContiansAddRec(ContainsAddRec);
8606 visitAll(Op, ContiansAddRec);
8607 HasAddRec |= ContainsAddRec;
8610 if (Operands.size() == 0)
8616 Terms.push_back(SE.getMulExpr(Operands));
8617 // Stop recursion: once we collected a term, do not walk its operands.
8624 bool isDone() const { return false; }
8628 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
8630 /// 1) The strides of AddRec expressions.
8631 /// 2) Unknowns that are multiplied with AddRec expressions.
8632 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
8633 SmallVectorImpl<const SCEV *> &Terms) {
8634 SmallVector<const SCEV *, 4> Strides;
8635 SCEVCollectStrides StrideCollector(*this, Strides);
8636 visitAll(Expr, StrideCollector);
8639 dbgs() << "Strides:\n";
8640 for (const SCEV *S : Strides)
8641 dbgs() << *S << "\n";
8644 for (const SCEV *S : Strides) {
8645 SCEVCollectTerms TermCollector(Terms);
8646 visitAll(S, TermCollector);
8650 dbgs() << "Terms:\n";
8651 for (const SCEV *T : Terms)
8652 dbgs() << *T << "\n";
8655 SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
8656 visitAll(Expr, MulCollector);
8659 static bool findArrayDimensionsRec(ScalarEvolution &SE,
8660 SmallVectorImpl<const SCEV *> &Terms,
8661 SmallVectorImpl<const SCEV *> &Sizes) {
8662 int Last = Terms.size() - 1;
8663 const SCEV *Step = Terms[Last];
8665 // End of recursion.
8667 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
8668 SmallVector<const SCEV *, 2> Qs;
8669 for (const SCEV *Op : M->operands())
8670 if (!isa<SCEVConstant>(Op))
8673 Step = SE.getMulExpr(Qs);
8676 Sizes.push_back(Step);
8680 for (const SCEV *&Term : Terms) {
8681 // Normalize the terms before the next call to findArrayDimensionsRec.
8683 SCEVDivision::divide(SE, Term, Step, &Q, &R);
8685 // Bail out when GCD does not evenly divide one of the terms.
8692 // Remove all SCEVConstants.
8693 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
8694 return isa<SCEVConstant>(E);
8698 if (Terms.size() > 0)
8699 if (!findArrayDimensionsRec(SE, Terms, Sizes))
8702 Sizes.push_back(Step);
8706 // Returns true when S contains at least a SCEVUnknown parameter.
8708 containsParameters(const SCEV *S) {
8709 struct FindParameter {
8710 bool FoundParameter;
8711 FindParameter() : FoundParameter(false) {}
8713 bool follow(const SCEV *S) {
8714 if (isa<SCEVUnknown>(S)) {
8715 FoundParameter = true;
8716 // Stop recursion: we found a parameter.
8722 bool isDone() const {
8723 // Stop recursion if we have found a parameter.
8724 return FoundParameter;
8729 SCEVTraversal<FindParameter> ST(F);
8732 return F.FoundParameter;
8735 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
8737 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
8738 for (const SCEV *T : Terms)
8739 if (containsParameters(T))
8744 // Return the number of product terms in S.
8745 static inline int numberOfTerms(const SCEV *S) {
8746 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
8747 return Expr->getNumOperands();
8751 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
8752 if (isa<SCEVConstant>(T))
8755 if (isa<SCEVUnknown>(T))
8758 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
8759 SmallVector<const SCEV *, 2> Factors;
8760 for (const SCEV *Op : M->operands())
8761 if (!isa<SCEVConstant>(Op))
8762 Factors.push_back(Op);
8764 return SE.getMulExpr(Factors);
8770 /// Return the size of an element read or written by Inst.
8771 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
8773 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
8774 Ty = Store->getValueOperand()->getType();
8775 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
8776 Ty = Load->getType();
8780 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
8781 return getSizeOfExpr(ETy, Ty);
8784 /// Second step of delinearization: compute the array dimensions Sizes from the
8785 /// set of Terms extracted from the memory access function of this SCEVAddRec.
8786 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
8787 SmallVectorImpl<const SCEV *> &Sizes,
8788 const SCEV *ElementSize) const {
8790 if (Terms.size() < 1 || !ElementSize)
8793 // Early return when Terms do not contain parameters: we do not delinearize
8794 // non parametric SCEVs.
8795 if (!containsParameters(Terms))
8799 dbgs() << "Terms:\n";
8800 for (const SCEV *T : Terms)
8801 dbgs() << *T << "\n";
8804 // Remove duplicates.
8805 std::sort(Terms.begin(), Terms.end());
8806 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
8808 // Put larger terms first.
8809 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
8810 return numberOfTerms(LHS) > numberOfTerms(RHS);
8813 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8815 // Try to divide all terms by the element size. If term is not divisible by
8816 // element size, proceed with the original term.
8817 for (const SCEV *&Term : Terms) {
8819 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
8824 SmallVector<const SCEV *, 4> NewTerms;
8826 // Remove constant factors.
8827 for (const SCEV *T : Terms)
8828 if (const SCEV *NewT = removeConstantFactors(SE, T))
8829 NewTerms.push_back(NewT);
8832 dbgs() << "Terms after sorting:\n";
8833 for (const SCEV *T : NewTerms)
8834 dbgs() << *T << "\n";
8837 if (NewTerms.empty() ||
8838 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
8843 // The last element to be pushed into Sizes is the size of an element.
8844 Sizes.push_back(ElementSize);
8847 dbgs() << "Sizes:\n";
8848 for (const SCEV *S : Sizes)
8849 dbgs() << *S << "\n";
8853 /// Third step of delinearization: compute the access functions for the
8854 /// Subscripts based on the dimensions in Sizes.
8855 void ScalarEvolution::computeAccessFunctions(
8856 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
8857 SmallVectorImpl<const SCEV *> &Sizes) {
8859 // Early exit in case this SCEV is not an affine multivariate function.
8863 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
8864 if (!AR->isAffine())
8867 const SCEV *Res = Expr;
8868 int Last = Sizes.size() - 1;
8869 for (int i = Last; i >= 0; i--) {
8871 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
8874 dbgs() << "Res: " << *Res << "\n";
8875 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
8876 dbgs() << "Res divided by Sizes[i]:\n";
8877 dbgs() << "Quotient: " << *Q << "\n";
8878 dbgs() << "Remainder: " << *R << "\n";
8883 // Do not record the last subscript corresponding to the size of elements in
8887 // Bail out if the remainder is too complex.
8888 if (isa<SCEVAddRecExpr>(R)) {
8897 // Record the access function for the current subscript.
8898 Subscripts.push_back(R);
8901 // Also push in last position the remainder of the last division: it will be
8902 // the access function of the innermost dimension.
8903 Subscripts.push_back(Res);
8905 std::reverse(Subscripts.begin(), Subscripts.end());
8908 dbgs() << "Subscripts:\n";
8909 for (const SCEV *S : Subscripts)
8910 dbgs() << *S << "\n";
8914 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
8915 /// sizes of an array access. Returns the remainder of the delinearization that
8916 /// is the offset start of the array. The SCEV->delinearize algorithm computes
8917 /// the multiples of SCEV coefficients: that is a pattern matching of sub
8918 /// expressions in the stride and base of a SCEV corresponding to the
8919 /// computation of a GCD (greatest common divisor) of base and stride. When
8920 /// SCEV->delinearize fails, it returns the SCEV unchanged.
8922 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
8924 /// void foo(long n, long m, long o, double A[n][m][o]) {
8926 /// for (long i = 0; i < n; i++)
8927 /// for (long j = 0; j < m; j++)
8928 /// for (long k = 0; k < o; k++)
8929 /// A[i][j][k] = 1.0;
8932 /// the delinearization input is the following AddRec SCEV:
8934 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
8936 /// From this SCEV, we are able to say that the base offset of the access is %A
8937 /// because it appears as an offset that does not divide any of the strides in
8940 /// CHECK: Base offset: %A
8942 /// and then SCEV->delinearize determines the size of some of the dimensions of
8943 /// the array as these are the multiples by which the strides are happening:
8945 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
8947 /// Note that the outermost dimension remains of UnknownSize because there are
8948 /// no strides that would help identifying the size of the last dimension: when
8949 /// the array has been statically allocated, one could compute the size of that
8950 /// dimension by dividing the overall size of the array by the size of the known
8951 /// dimensions: %m * %o * 8.
8953 /// Finally delinearize provides the access functions for the array reference
8954 /// that does correspond to A[i][j][k] of the above C testcase:
8956 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
8958 /// The testcases are checking the output of a function pass:
8959 /// DelinearizationPass that walks through all loads and stores of a function
8960 /// asking for the SCEV of the memory access with respect to all enclosing
8961 /// loops, calling SCEV->delinearize on that and printing the results.
8963 void ScalarEvolution::delinearize(const SCEV *Expr,
8964 SmallVectorImpl<const SCEV *> &Subscripts,
8965 SmallVectorImpl<const SCEV *> &Sizes,
8966 const SCEV *ElementSize) {
8967 // First step: collect parametric terms.
8968 SmallVector<const SCEV *, 4> Terms;
8969 collectParametricTerms(Expr, Terms);
8974 // Second step: find subscript sizes.
8975 findArrayDimensions(Terms, Sizes, ElementSize);
8980 // Third step: compute the access functions for each subscript.
8981 computeAccessFunctions(Expr, Subscripts, Sizes);
8983 if (Subscripts.empty())
8987 dbgs() << "succeeded to delinearize " << *Expr << "\n";
8988 dbgs() << "ArrayDecl[UnknownSize]";
8989 for (const SCEV *S : Sizes)
8990 dbgs() << "[" << *S << "]";
8992 dbgs() << "\nArrayRef";
8993 for (const SCEV *S : Subscripts)
8994 dbgs() << "[" << *S << "]";
8999 //===----------------------------------------------------------------------===//
9000 // SCEVCallbackVH Class Implementation
9001 //===----------------------------------------------------------------------===//
9003 void ScalarEvolution::SCEVCallbackVH::deleted() {
9004 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9005 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
9006 SE->ConstantEvolutionLoopExitValue.erase(PN);
9007 SE->ValueExprMap.erase(getValPtr());
9008 // this now dangles!
9011 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
9012 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9014 // Forget all the expressions associated with users of the old value,
9015 // so that future queries will recompute the expressions using the new
9017 Value *Old = getValPtr();
9018 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
9019 SmallPtrSet<User *, 8> Visited;
9020 while (!Worklist.empty()) {
9021 User *U = Worklist.pop_back_val();
9022 // Deleting the Old value will cause this to dangle. Postpone
9023 // that until everything else is done.
9026 if (!Visited.insert(U).second)
9028 if (PHINode *PN = dyn_cast<PHINode>(U))
9029 SE->ConstantEvolutionLoopExitValue.erase(PN);
9030 SE->ValueExprMap.erase(U);
9031 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
9033 // Delete the Old value.
9034 if (PHINode *PN = dyn_cast<PHINode>(Old))
9035 SE->ConstantEvolutionLoopExitValue.erase(PN);
9036 SE->ValueExprMap.erase(Old);
9037 // this now dangles!
9040 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
9041 : CallbackVH(V), SE(se) {}
9043 //===----------------------------------------------------------------------===//
9044 // ScalarEvolution Class Implementation
9045 //===----------------------------------------------------------------------===//
9047 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
9048 AssumptionCache &AC, DominatorTree &DT,
9050 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
9051 CouldNotCompute(new SCEVCouldNotCompute()),
9052 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9053 ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
9054 FirstUnknown(nullptr) {}
9056 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
9057 : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
9058 CouldNotCompute(std::move(Arg.CouldNotCompute)),
9059 ValueExprMap(std::move(Arg.ValueExprMap)),
9060 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9061 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
9062 ConstantEvolutionLoopExitValue(
9063 std::move(Arg.ConstantEvolutionLoopExitValue)),
9064 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
9065 LoopDispositions(std::move(Arg.LoopDispositions)),
9066 BlockDispositions(std::move(Arg.BlockDispositions)),
9067 UnsignedRanges(std::move(Arg.UnsignedRanges)),
9068 SignedRanges(std::move(Arg.SignedRanges)),
9069 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
9070 UniquePreds(std::move(Arg.UniquePreds)),
9071 SCEVAllocator(std::move(Arg.SCEVAllocator)),
9072 FirstUnknown(Arg.FirstUnknown) {
9073 Arg.FirstUnknown = nullptr;
9076 ScalarEvolution::~ScalarEvolution() {
9077 // Iterate through all the SCEVUnknown instances and call their
9078 // destructors, so that they release their references to their values.
9079 for (SCEVUnknown *U = FirstUnknown; U;) {
9080 SCEVUnknown *Tmp = U;
9082 Tmp->~SCEVUnknown();
9084 FirstUnknown = nullptr;
9086 ValueExprMap.clear();
9088 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
9089 // that a loop had multiple computable exits.
9090 for (auto &BTCI : BackedgeTakenCounts)
9091 BTCI.second.clear();
9093 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
9094 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
9095 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
9098 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
9099 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
9102 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
9104 // Print all inner loops first
9105 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
9106 PrintLoopInfo(OS, SE, *I);
9109 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9112 SmallVector<BasicBlock *, 8> ExitBlocks;
9113 L->getExitBlocks(ExitBlocks);
9114 if (ExitBlocks.size() != 1)
9115 OS << "<multiple exits> ";
9117 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
9118 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
9120 OS << "Unpredictable backedge-taken count. ";
9125 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9128 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
9129 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
9131 OS << "Unpredictable max backedge-taken count. ";
9137 void ScalarEvolution::print(raw_ostream &OS) const {
9138 // ScalarEvolution's implementation of the print method is to print
9139 // out SCEV values of all instructions that are interesting. Doing
9140 // this potentially causes it to create new SCEV objects though,
9141 // which technically conflicts with the const qualifier. This isn't
9142 // observable from outside the class though, so casting away the
9143 // const isn't dangerous.
9144 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9146 OS << "Classifying expressions for: ";
9147 F.printAsOperand(OS, /*PrintType=*/false);
9149 for (Instruction &I : instructions(F))
9150 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
9153 const SCEV *SV = SE.getSCEV(&I);
9155 if (!isa<SCEVCouldNotCompute>(SV)) {
9157 SE.getUnsignedRange(SV).print(OS);
9159 SE.getSignedRange(SV).print(OS);
9162 const Loop *L = LI.getLoopFor(I.getParent());
9164 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
9168 if (!isa<SCEVCouldNotCompute>(AtUse)) {
9170 SE.getUnsignedRange(AtUse).print(OS);
9172 SE.getSignedRange(AtUse).print(OS);
9177 OS << "\t\t" "Exits: ";
9178 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
9179 if (!SE.isLoopInvariant(ExitValue, L)) {
9180 OS << "<<Unknown>>";
9189 OS << "Determining loop execution counts for: ";
9190 F.printAsOperand(OS, /*PrintType=*/false);
9192 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
9193 PrintLoopInfo(OS, &SE, *I);
9196 ScalarEvolution::LoopDisposition
9197 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
9198 auto &Values = LoopDispositions[S];
9199 for (auto &V : Values) {
9200 if (V.getPointer() == L)
9203 Values.emplace_back(L, LoopVariant);
9204 LoopDisposition D = computeLoopDisposition(S, L);
9205 auto &Values2 = LoopDispositions[S];
9206 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9207 if (V.getPointer() == L) {
9215 ScalarEvolution::LoopDisposition
9216 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
9217 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9219 return LoopInvariant;
9223 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
9224 case scAddRecExpr: {
9225 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9227 // If L is the addrec's loop, it's computable.
9228 if (AR->getLoop() == L)
9229 return LoopComputable;
9231 // Add recurrences are never invariant in the function-body (null loop).
9235 // This recurrence is variant w.r.t. L if L contains AR's loop.
9236 if (L->contains(AR->getLoop()))
9239 // This recurrence is invariant w.r.t. L if AR's loop contains L.
9240 if (AR->getLoop()->contains(L))
9241 return LoopInvariant;
9243 // This recurrence is variant w.r.t. L if any of its operands
9245 for (auto *Op : AR->operands())
9246 if (!isLoopInvariant(Op, L))
9249 // Otherwise it's loop-invariant.
9250 return LoopInvariant;
9256 bool HasVarying = false;
9257 for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
9258 LoopDisposition D = getLoopDisposition(Op, L);
9259 if (D == LoopVariant)
9261 if (D == LoopComputable)
9264 return HasVarying ? LoopComputable : LoopInvariant;
9267 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9268 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
9269 if (LD == LoopVariant)
9271 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
9272 if (RD == LoopVariant)
9274 return (LD == LoopInvariant && RD == LoopInvariant) ?
9275 LoopInvariant : LoopComputable;
9278 // All non-instruction values are loop invariant. All instructions are loop
9279 // invariant if they are not contained in the specified loop.
9280 // Instructions are never considered invariant in the function body
9281 // (null loop) because they are defined within the "loop".
9282 if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
9283 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
9284 return LoopInvariant;
9285 case scCouldNotCompute:
9286 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9288 llvm_unreachable("Unknown SCEV kind!");
9291 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
9292 return getLoopDisposition(S, L) == LoopInvariant;
9295 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
9296 return getLoopDisposition(S, L) == LoopComputable;
9299 ScalarEvolution::BlockDisposition
9300 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9301 auto &Values = BlockDispositions[S];
9302 for (auto &V : Values) {
9303 if (V.getPointer() == BB)
9306 Values.emplace_back(BB, DoesNotDominateBlock);
9307 BlockDisposition D = computeBlockDisposition(S, BB);
9308 auto &Values2 = BlockDispositions[S];
9309 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9310 if (V.getPointer() == BB) {
9318 ScalarEvolution::BlockDisposition
9319 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9320 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9322 return ProperlyDominatesBlock;
9326 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
9327 case scAddRecExpr: {
9328 // This uses a "dominates" query instead of "properly dominates" query
9329 // to test for proper dominance too, because the instruction which
9330 // produces the addrec's value is a PHI, and a PHI effectively properly
9331 // dominates its entire containing block.
9332 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9333 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9334 return DoesNotDominateBlock;
9336 // FALL THROUGH into SCEVNAryExpr handling.
9341 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9343 for (const SCEV *NAryOp : NAry->operands()) {
9344 BlockDisposition D = getBlockDisposition(NAryOp, BB);
9345 if (D == DoesNotDominateBlock)
9346 return DoesNotDominateBlock;
9347 if (D == DominatesBlock)
9350 return Proper ? ProperlyDominatesBlock : DominatesBlock;
9353 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9354 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9355 BlockDisposition LD = getBlockDisposition(LHS, BB);
9356 if (LD == DoesNotDominateBlock)
9357 return DoesNotDominateBlock;
9358 BlockDisposition RD = getBlockDisposition(RHS, BB);
9359 if (RD == DoesNotDominateBlock)
9360 return DoesNotDominateBlock;
9361 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9362 ProperlyDominatesBlock : DominatesBlock;
9365 if (Instruction *I =
9366 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9367 if (I->getParent() == BB)
9368 return DominatesBlock;
9369 if (DT.properlyDominates(I->getParent(), BB))
9370 return ProperlyDominatesBlock;
9371 return DoesNotDominateBlock;
9373 return ProperlyDominatesBlock;
9374 case scCouldNotCompute:
9375 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9377 llvm_unreachable("Unknown SCEV kind!");
9380 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9381 return getBlockDisposition(S, BB) >= DominatesBlock;
9384 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9385 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9388 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9389 // Search for a SCEV expression node within an expression tree.
9390 // Implements SCEVTraversal::Visitor.
9395 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
9397 bool follow(const SCEV *S) {
9398 IsFound |= (S == Node);
9401 bool isDone() const { return IsFound; }
9404 SCEVSearch Search(Op);
9405 visitAll(S, Search);
9406 return Search.IsFound;
9409 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9410 ValuesAtScopes.erase(S);
9411 LoopDispositions.erase(S);
9412 BlockDispositions.erase(S);
9413 UnsignedRanges.erase(S);
9414 SignedRanges.erase(S);
9416 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
9417 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
9418 BackedgeTakenInfo &BEInfo = I->second;
9419 if (BEInfo.hasOperand(S, this)) {
9421 BackedgeTakenCounts.erase(I++);
9428 typedef DenseMap<const Loop *, std::string> VerifyMap;
9430 /// replaceSubString - Replaces all occurrences of From in Str with To.
9431 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9433 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9434 Str.replace(Pos, From.size(), To.data(), To.size());
9439 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9441 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9442 std::string &S = Map[L];
9444 raw_string_ostream OS(S);
9445 SE.getBackedgeTakenCount(L)->print(OS);
9447 // false and 0 are semantically equivalent. This can happen in dead loops.
9448 replaceSubString(OS.str(), "false", "0");
9449 // Remove wrap flags, their use in SCEV is highly fragile.
9450 // FIXME: Remove this when SCEV gets smarter about them.
9451 replaceSubString(OS.str(), "<nw>", "");
9452 replaceSubString(OS.str(), "<nsw>", "");
9453 replaceSubString(OS.str(), "<nuw>", "");
9456 for (auto *R : reverse(*L))
9457 getLoopBackedgeTakenCounts(R, Map, SE); // recurse.
9460 void ScalarEvolution::verify() const {
9461 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9463 // Gather stringified backedge taken counts for all loops using SCEV's caches.
9464 // FIXME: It would be much better to store actual values instead of strings,
9465 // but SCEV pointers will change if we drop the caches.
9466 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9467 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9468 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9470 // Gather stringified backedge taken counts for all loops using a fresh
9471 // ScalarEvolution object.
9472 ScalarEvolution SE2(F, TLI, AC, DT, LI);
9473 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9474 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9476 // Now compare whether they're the same with and without caches. This allows
9477 // verifying that no pass changed the cache.
9478 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
9479 "New loops suddenly appeared!");
9481 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
9482 OldE = BackedgeDumpsOld.end(),
9483 NewI = BackedgeDumpsNew.begin();
9484 OldI != OldE; ++OldI, ++NewI) {
9485 assert(OldI->first == NewI->first && "Loop order changed!");
9487 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
9489 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
9490 // means that a pass is buggy or SCEV has to learn a new pattern but is
9491 // usually not harmful.
9492 if (OldI->second != NewI->second &&
9493 OldI->second.find("undef") == std::string::npos &&
9494 NewI->second.find("undef") == std::string::npos &&
9495 OldI->second != "***COULDNOTCOMPUTE***" &&
9496 NewI->second != "***COULDNOTCOMPUTE***") {
9497 dbgs() << "SCEVValidator: SCEV for loop '"
9498 << OldI->first->getHeader()->getName()
9499 << "' changed from '" << OldI->second
9500 << "' to '" << NewI->second << "'!\n";
9505 // TODO: Verify more things.
9508 char ScalarEvolutionAnalysis::PassID;
9510 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
9511 AnalysisManager<Function> *AM) {
9512 return ScalarEvolution(F, AM->getResult<TargetLibraryAnalysis>(F),
9513 AM->getResult<AssumptionAnalysis>(F),
9514 AM->getResult<DominatorTreeAnalysis>(F),
9515 AM->getResult<LoopAnalysis>(F));
9519 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> *AM) {
9520 AM->getResult<ScalarEvolutionAnalysis>(F).print(OS);
9521 return PreservedAnalyses::all();
9524 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
9525 "Scalar Evolution Analysis", false, true)
9526 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
9527 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
9528 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
9529 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
9530 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
9531 "Scalar Evolution Analysis", false, true)
9532 char ScalarEvolutionWrapperPass::ID = 0;
9534 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
9535 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
9538 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
9539 SE.reset(new ScalarEvolution(
9540 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
9541 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
9542 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
9543 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
9547 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
9549 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
9553 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
9560 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
9561 AU.setPreservesAll();
9562 AU.addRequiredTransitive<AssumptionCacheTracker>();
9563 AU.addRequiredTransitive<LoopInfoWrapperPass>();
9564 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
9565 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
9568 const SCEVPredicate *
9569 ScalarEvolution::getEqualPredicate(const SCEVUnknown *LHS,
9570 const SCEVConstant *RHS) {
9571 FoldingSetNodeID ID;
9572 // Unique this node based on the arguments
9573 ID.AddInteger(SCEVPredicate::P_Equal);
9577 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
9579 SCEVEqualPredicate *Eq = new (SCEVAllocator)
9580 SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
9581 UniquePreds.InsertNode(Eq, IP);
9586 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
9588 static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE,
9589 SCEVUnionPredicate &A) {
9590 SCEVPredicateRewriter Rewriter(SE, A);
9591 return Rewriter.visit(Scev);
9594 SCEVPredicateRewriter(ScalarEvolution &SE, SCEVUnionPredicate &P)
9595 : SCEVRewriteVisitor(SE), P(P) {}
9597 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
9598 auto ExprPreds = P.getPredicatesForExpr(Expr);
9599 for (auto *Pred : ExprPreds)
9600 if (const auto *IPred = dyn_cast<const SCEVEqualPredicate>(Pred))
9601 if (IPred->getLHS() == Expr)
9602 return IPred->getRHS();
9608 SCEVUnionPredicate &P;
9610 } // end anonymous namespace
9612 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *Scev,
9613 SCEVUnionPredicate &Preds) {
9614 return SCEVPredicateRewriter::rewrite(Scev, *this, Preds);
9618 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
9619 SCEVPredicateKind Kind)
9620 : FastID(ID), Kind(Kind) {}
9622 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
9623 const SCEVUnknown *LHS,
9624 const SCEVConstant *RHS)
9625 : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {}
9627 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
9628 const auto *Op = dyn_cast<const SCEVEqualPredicate>(N);
9633 return Op->LHS == LHS && Op->RHS == RHS;
9636 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
9638 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
9640 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
9641 OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
9644 /// Union predicates don't get cached so create a dummy set ID for it.
9645 SCEVUnionPredicate::SCEVUnionPredicate()
9646 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
9648 bool SCEVUnionPredicate::isAlwaysTrue() const {
9649 return all_of(Preds,
9650 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
9653 ArrayRef<const SCEVPredicate *>
9654 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
9655 auto I = SCEVToPreds.find(Expr);
9656 if (I == SCEVToPreds.end())
9657 return ArrayRef<const SCEVPredicate *>();
9661 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
9662 if (const auto *Set = dyn_cast<const SCEVUnionPredicate>(N))
9663 return all_of(Set->Preds,
9664 [this](const SCEVPredicate *I) { return this->implies(I); });
9666 auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
9667 if (ScevPredsIt == SCEVToPreds.end())
9669 auto &SCEVPreds = ScevPredsIt->second;
9671 return any_of(SCEVPreds,
9672 [N](const SCEVPredicate *I) { return I->implies(N); });
9675 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
9677 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
9678 for (auto Pred : Preds)
9679 Pred->print(OS, Depth);
9682 void SCEVUnionPredicate::add(const SCEVPredicate *N) {
9683 if (const auto *Set = dyn_cast<const SCEVUnionPredicate>(N)) {
9684 for (auto Pred : Set->Preds)
9692 const SCEV *Key = N->getExpr();
9693 assert(Key && "Only SCEVUnionPredicate doesn't have an "
9694 " associated expression!");
9696 SCEVToPreds[Key].push_back(N);
9700 PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE)
9701 : SE(SE), Generation(0) {}
9703 const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
9704 const SCEV *Expr = SE.getSCEV(V);
9705 RewriteEntry &Entry = RewriteMap[Expr];
9707 // If we already have an entry and the version matches, return it.
9708 if (Entry.second && Generation == Entry.first)
9709 return Entry.second;
9711 // We found an entry but it's stale. Rewrite the stale entry
9712 // acording to the current predicate.
9714 Expr = Entry.second;
9716 const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, Preds);
9717 Entry = {Generation, NewSCEV};
9722 void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
9723 if (Preds.implies(&Pred))
9729 const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
9733 void PredicatedScalarEvolution::updateGeneration() {
9734 // If the generation number wrapped recompute everything.
9735 if (++Generation == 0) {
9736 for (auto &II : RewriteMap) {
9737 const SCEV *Rewritten = II.second.second;
9738 II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, Preds)};