1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/Support/CommandLine.h"
87 #include "llvm/Support/Debug.h"
88 #include "llvm/Support/ErrorHandling.h"
89 #include "llvm/Support/MathExtras.h"
90 #include "llvm/Support/raw_ostream.h"
91 #include "llvm/Support/SaveAndRestore.h"
95 #define DEBUG_TYPE "scalar-evolution"
97 STATISTIC(NumArrayLenItCounts,
98 "Number of trip counts computed with array length");
99 STATISTIC(NumTripCountsComputed,
100 "Number of loops with predictable loop counts");
101 STATISTIC(NumTripCountsNotComputed,
102 "Number of loops without predictable loop counts");
103 STATISTIC(NumBruteForceTripCountsComputed,
104 "Number of loops with trip counts computed by force");
106 static cl::opt<unsigned>
107 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
108 cl::desc("Maximum number of iterations SCEV will "
109 "symbolically execute a constant "
113 // FIXME: Enable this with XDEBUG when the test suite is clean.
115 VerifySCEV("verify-scev",
116 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
118 //===----------------------------------------------------------------------===//
119 // SCEV class definitions
120 //===----------------------------------------------------------------------===//
122 //===----------------------------------------------------------------------===//
123 // Implementation of the SCEV class.
126 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
127 void SCEV::dump() const {
133 void SCEV::print(raw_ostream &OS) const {
134 switch (static_cast<SCEVTypes>(getSCEVType())) {
136 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
139 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
140 const SCEV *Op = Trunc->getOperand();
141 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
142 << *Trunc->getType() << ")";
146 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
147 const SCEV *Op = ZExt->getOperand();
148 OS << "(zext " << *Op->getType() << " " << *Op << " to "
149 << *ZExt->getType() << ")";
153 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
154 const SCEV *Op = SExt->getOperand();
155 OS << "(sext " << *Op->getType() << " " << *Op << " to "
156 << *SExt->getType() << ")";
160 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
161 OS << "{" << *AR->getOperand(0);
162 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
163 OS << ",+," << *AR->getOperand(i);
165 if (AR->getNoWrapFlags(FlagNUW))
167 if (AR->getNoWrapFlags(FlagNSW))
169 if (AR->getNoWrapFlags(FlagNW) &&
170 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
172 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
180 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
181 const char *OpStr = nullptr;
182 switch (NAry->getSCEVType()) {
183 case scAddExpr: OpStr = " + "; break;
184 case scMulExpr: OpStr = " * "; break;
185 case scUMaxExpr: OpStr = " umax "; break;
186 case scSMaxExpr: OpStr = " smax "; break;
189 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
192 if (std::next(I) != E)
196 switch (NAry->getSCEVType()) {
199 if (NAry->getNoWrapFlags(FlagNUW))
201 if (NAry->getNoWrapFlags(FlagNSW))
207 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
208 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
212 const SCEVUnknown *U = cast<SCEVUnknown>(this);
214 if (U->isSizeOf(AllocTy)) {
215 OS << "sizeof(" << *AllocTy << ")";
218 if (U->isAlignOf(AllocTy)) {
219 OS << "alignof(" << *AllocTy << ")";
225 if (U->isOffsetOf(CTy, FieldNo)) {
226 OS << "offsetof(" << *CTy << ", ";
227 FieldNo->printAsOperand(OS, false);
232 // Otherwise just print it normally.
233 U->getValue()->printAsOperand(OS, false);
236 case scCouldNotCompute:
237 OS << "***COULDNOTCOMPUTE***";
240 llvm_unreachable("Unknown SCEV kind!");
243 Type *SCEV::getType() const {
244 switch (static_cast<SCEVTypes>(getSCEVType())) {
246 return cast<SCEVConstant>(this)->getType();
250 return cast<SCEVCastExpr>(this)->getType();
255 return cast<SCEVNAryExpr>(this)->getType();
257 return cast<SCEVAddExpr>(this)->getType();
259 return cast<SCEVUDivExpr>(this)->getType();
261 return cast<SCEVUnknown>(this)->getType();
262 case scCouldNotCompute:
263 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
265 llvm_unreachable("Unknown SCEV kind!");
268 bool SCEV::isZero() const {
269 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
270 return SC->getValue()->isZero();
274 bool SCEV::isOne() const {
275 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
276 return SC->getValue()->isOne();
280 bool SCEV::isAllOnesValue() const {
281 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
282 return SC->getValue()->isAllOnesValue();
286 /// isNonConstantNegative - Return true if the specified scev is negated, but
288 bool SCEV::isNonConstantNegative() const {
289 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
290 if (!Mul) return false;
292 // If there is a constant factor, it will be first.
293 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
294 if (!SC) return false;
296 // Return true if the value is negative, this matches things like (-42 * V).
297 return SC->getValue()->getValue().isNegative();
300 SCEVCouldNotCompute::SCEVCouldNotCompute() :
301 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
303 bool SCEVCouldNotCompute::classof(const SCEV *S) {
304 return S->getSCEVType() == scCouldNotCompute;
307 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
309 ID.AddInteger(scConstant);
312 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
313 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
314 UniqueSCEVs.InsertNode(S, IP);
318 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
319 return getConstant(ConstantInt::get(getContext(), Val));
323 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
324 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
325 return getConstant(ConstantInt::get(ITy, V, isSigned));
328 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
329 unsigned SCEVTy, const SCEV *op, Type *ty)
330 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
332 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
333 const SCEV *op, Type *ty)
334 : SCEVCastExpr(ID, scTruncate, op, ty) {
335 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
336 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
337 "Cannot truncate non-integer value!");
340 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
341 const SCEV *op, Type *ty)
342 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
343 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
344 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
345 "Cannot zero extend non-integer value!");
348 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
349 const SCEV *op, Type *ty)
350 : SCEVCastExpr(ID, scSignExtend, op, ty) {
351 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
352 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
353 "Cannot sign extend non-integer value!");
356 void SCEVUnknown::deleted() {
357 // Clear this SCEVUnknown from various maps.
358 SE->forgetMemoizedResults(this);
360 // Remove this SCEVUnknown from the uniquing map.
361 SE->UniqueSCEVs.RemoveNode(this);
363 // Release the value.
367 void SCEVUnknown::allUsesReplacedWith(Value *New) {
368 // Clear this SCEVUnknown from various maps.
369 SE->forgetMemoizedResults(this);
371 // Remove this SCEVUnknown from the uniquing map.
372 SE->UniqueSCEVs.RemoveNode(this);
374 // Update this SCEVUnknown to point to the new value. This is needed
375 // because there may still be outstanding SCEVs which still point to
380 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
381 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
382 if (VCE->getOpcode() == Instruction::PtrToInt)
383 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
384 if (CE->getOpcode() == Instruction::GetElementPtr &&
385 CE->getOperand(0)->isNullValue() &&
386 CE->getNumOperands() == 2)
387 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
389 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
397 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
398 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
399 if (VCE->getOpcode() == Instruction::PtrToInt)
400 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
401 if (CE->getOpcode() == Instruction::GetElementPtr &&
402 CE->getOperand(0)->isNullValue()) {
404 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
405 if (StructType *STy = dyn_cast<StructType>(Ty))
406 if (!STy->isPacked() &&
407 CE->getNumOperands() == 3 &&
408 CE->getOperand(1)->isNullValue()) {
409 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
411 STy->getNumElements() == 2 &&
412 STy->getElementType(0)->isIntegerTy(1)) {
413 AllocTy = STy->getElementType(1);
422 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
423 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
424 if (VCE->getOpcode() == Instruction::PtrToInt)
425 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
426 if (CE->getOpcode() == Instruction::GetElementPtr &&
427 CE->getNumOperands() == 3 &&
428 CE->getOperand(0)->isNullValue() &&
429 CE->getOperand(1)->isNullValue()) {
431 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
432 // Ignore vector types here so that ScalarEvolutionExpander doesn't
433 // emit getelementptrs that index into vectors.
434 if (Ty->isStructTy() || Ty->isArrayTy()) {
436 FieldNo = CE->getOperand(2);
444 //===----------------------------------------------------------------------===//
446 //===----------------------------------------------------------------------===//
449 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
450 /// than the complexity of the RHS. This comparator is used to canonicalize
452 class SCEVComplexityCompare {
453 const LoopInfo *const LI;
455 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
457 // Return true or false if LHS is less than, or at least RHS, respectively.
458 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
459 return compare(LHS, RHS) < 0;
462 // Return negative, zero, or positive, if LHS is less than, equal to, or
463 // greater than RHS, respectively. A three-way result allows recursive
464 // comparisons to be more efficient.
465 int compare(const SCEV *LHS, const SCEV *RHS) const {
466 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
470 // Primarily, sort the SCEVs by their getSCEVType().
471 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
473 return (int)LType - (int)RType;
475 // Aside from the getSCEVType() ordering, the particular ordering
476 // isn't very important except that it's beneficial to be consistent,
477 // so that (a + b) and (b + a) don't end up as different expressions.
478 switch (static_cast<SCEVTypes>(LType)) {
480 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
481 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
483 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
484 // not as complete as it could be.
485 const Value *LV = LU->getValue(), *RV = RU->getValue();
487 // Order pointer values after integer values. This helps SCEVExpander
489 bool LIsPointer = LV->getType()->isPointerTy(),
490 RIsPointer = RV->getType()->isPointerTy();
491 if (LIsPointer != RIsPointer)
492 return (int)LIsPointer - (int)RIsPointer;
494 // Compare getValueID values.
495 unsigned LID = LV->getValueID(),
496 RID = RV->getValueID();
498 return (int)LID - (int)RID;
500 // Sort arguments by their position.
501 if (const Argument *LA = dyn_cast<Argument>(LV)) {
502 const Argument *RA = cast<Argument>(RV);
503 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
504 return (int)LArgNo - (int)RArgNo;
507 // For instructions, compare their loop depth, and their operand
508 // count. This is pretty loose.
509 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
510 const Instruction *RInst = cast<Instruction>(RV);
512 // Compare loop depths.
513 const BasicBlock *LParent = LInst->getParent(),
514 *RParent = RInst->getParent();
515 if (LParent != RParent) {
516 unsigned LDepth = LI->getLoopDepth(LParent),
517 RDepth = LI->getLoopDepth(RParent);
518 if (LDepth != RDepth)
519 return (int)LDepth - (int)RDepth;
522 // Compare the number of operands.
523 unsigned LNumOps = LInst->getNumOperands(),
524 RNumOps = RInst->getNumOperands();
525 return (int)LNumOps - (int)RNumOps;
532 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
533 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
535 // Compare constant values.
536 const APInt &LA = LC->getValue()->getValue();
537 const APInt &RA = RC->getValue()->getValue();
538 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
539 if (LBitWidth != RBitWidth)
540 return (int)LBitWidth - (int)RBitWidth;
541 return LA.ult(RA) ? -1 : 1;
545 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
546 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
548 // Compare addrec loop depths.
549 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
550 if (LLoop != RLoop) {
551 unsigned LDepth = LLoop->getLoopDepth(),
552 RDepth = RLoop->getLoopDepth();
553 if (LDepth != RDepth)
554 return (int)LDepth - (int)RDepth;
557 // Addrec complexity grows with operand count.
558 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
559 if (LNumOps != RNumOps)
560 return (int)LNumOps - (int)RNumOps;
562 // Lexicographically compare.
563 for (unsigned i = 0; i != LNumOps; ++i) {
564 long X = compare(LA->getOperand(i), RA->getOperand(i));
576 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
577 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
579 // Lexicographically compare n-ary expressions.
580 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
581 if (LNumOps != RNumOps)
582 return (int)LNumOps - (int)RNumOps;
584 for (unsigned i = 0; i != LNumOps; ++i) {
587 long X = compare(LC->getOperand(i), RC->getOperand(i));
591 return (int)LNumOps - (int)RNumOps;
595 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
596 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
598 // Lexicographically compare udiv expressions.
599 long X = compare(LC->getLHS(), RC->getLHS());
602 return compare(LC->getRHS(), RC->getRHS());
608 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
609 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
611 // Compare cast expressions by operand.
612 return compare(LC->getOperand(), RC->getOperand());
615 case scCouldNotCompute:
616 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
618 llvm_unreachable("Unknown SCEV kind!");
623 /// GroupByComplexity - Given a list of SCEV objects, order them by their
624 /// complexity, and group objects of the same complexity together by value.
625 /// When this routine is finished, we know that any duplicates in the vector are
626 /// consecutive and that complexity is monotonically increasing.
628 /// Note that we go take special precautions to ensure that we get deterministic
629 /// results from this routine. In other words, we don't want the results of
630 /// this to depend on where the addresses of various SCEV objects happened to
633 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
635 if (Ops.size() < 2) return; // Noop
636 if (Ops.size() == 2) {
637 // This is the common case, which also happens to be trivially simple.
639 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
640 if (SCEVComplexityCompare(LI)(RHS, LHS))
645 // Do the rough sort by complexity.
646 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
648 // Now that we are sorted by complexity, group elements of the same
649 // complexity. Note that this is, at worst, N^2, but the vector is likely to
650 // be extremely short in practice. Note that we take this approach because we
651 // do not want to depend on the addresses of the objects we are grouping.
652 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
653 const SCEV *S = Ops[i];
654 unsigned Complexity = S->getSCEVType();
656 // If there are any objects of the same complexity and same value as this
658 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
659 if (Ops[j] == S) { // Found a duplicate.
660 // Move it to immediately after i'th element.
661 std::swap(Ops[i+1], Ops[j]);
662 ++i; // no need to rescan it.
663 if (i == e-2) return; // Done!
670 struct FindSCEVSize {
672 FindSCEVSize() : Size(0) {}
674 bool follow(const SCEV *S) {
676 // Keep looking at all operands of S.
679 bool isDone() const {
685 // Returns the size of the SCEV S.
686 static inline int sizeOfSCEV(const SCEV *S) {
688 SCEVTraversal<FindSCEVSize> ST(F);
695 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
697 // Computes the Quotient and Remainder of the division of Numerator by
699 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
700 const SCEV *Denominator, const SCEV **Quotient,
701 const SCEV **Remainder) {
702 assert(Numerator && Denominator && "Uninitialized SCEV");
704 SCEVDivision D(SE, Numerator, Denominator);
706 // Check for the trivial case here to avoid having to check for it in the
708 if (Numerator == Denominator) {
714 if (Numerator->isZero()) {
720 // A simple case when N/1. The quotient is N.
721 if (Denominator->isOne()) {
722 *Quotient = Numerator;
727 // Split the Denominator when it is a product.
728 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
730 *Quotient = Numerator;
731 for (const SCEV *Op : T->operands()) {
732 divide(SE, *Quotient, Op, &Q, &R);
735 // Bail out when the Numerator is not divisible by one of the terms of
739 *Remainder = Numerator;
748 *Quotient = D.Quotient;
749 *Remainder = D.Remainder;
752 // Except in the trivial case described above, we do not know how to divide
753 // Expr by Denominator for the following functions with empty implementation.
754 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
755 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
756 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
757 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
758 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
759 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
760 void visitUnknown(const SCEVUnknown *Numerator) {}
761 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
763 void visitConstant(const SCEVConstant *Numerator) {
764 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
765 APInt NumeratorVal = Numerator->getValue()->getValue();
766 APInt DenominatorVal = D->getValue()->getValue();
767 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
768 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
770 if (NumeratorBW > DenominatorBW)
771 DenominatorVal = DenominatorVal.sext(NumeratorBW);
772 else if (NumeratorBW < DenominatorBW)
773 NumeratorVal = NumeratorVal.sext(DenominatorBW);
775 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
776 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
777 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
778 Quotient = SE.getConstant(QuotientVal);
779 Remainder = SE.getConstant(RemainderVal);
784 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
785 const SCEV *StartQ, *StartR, *StepQ, *StepR;
786 if (!Numerator->isAffine())
787 return cannotDivide(Numerator);
788 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
789 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
790 // Bail out if the types do not match.
791 Type *Ty = Denominator->getType();
792 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
793 Ty != StepQ->getType() || Ty != StepR->getType())
794 return cannotDivide(Numerator);
795 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
796 Numerator->getNoWrapFlags());
797 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
798 Numerator->getNoWrapFlags());
801 void visitAddExpr(const SCEVAddExpr *Numerator) {
802 SmallVector<const SCEV *, 2> Qs, Rs;
803 Type *Ty = Denominator->getType();
805 for (const SCEV *Op : Numerator->operands()) {
807 divide(SE, Op, Denominator, &Q, &R);
809 // Bail out if types do not match.
810 if (Ty != Q->getType() || Ty != R->getType())
811 return cannotDivide(Numerator);
817 if (Qs.size() == 1) {
823 Quotient = SE.getAddExpr(Qs);
824 Remainder = SE.getAddExpr(Rs);
827 void visitMulExpr(const SCEVMulExpr *Numerator) {
828 SmallVector<const SCEV *, 2> Qs;
829 Type *Ty = Denominator->getType();
831 bool FoundDenominatorTerm = false;
832 for (const SCEV *Op : Numerator->operands()) {
833 // Bail out if types do not match.
834 if (Ty != Op->getType())
835 return cannotDivide(Numerator);
837 if (FoundDenominatorTerm) {
842 // Check whether Denominator divides one of the product operands.
844 divide(SE, Op, Denominator, &Q, &R);
850 // Bail out if types do not match.
851 if (Ty != Q->getType())
852 return cannotDivide(Numerator);
854 FoundDenominatorTerm = true;
858 if (FoundDenominatorTerm) {
863 Quotient = SE.getMulExpr(Qs);
867 if (!isa<SCEVUnknown>(Denominator))
868 return cannotDivide(Numerator);
870 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
871 ValueToValueMap RewriteMap;
872 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
873 cast<SCEVConstant>(Zero)->getValue();
874 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
876 if (Remainder->isZero()) {
877 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
878 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
879 cast<SCEVConstant>(One)->getValue();
881 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
885 // Quotient is (Numerator - Remainder) divided by Denominator.
887 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
888 // This SCEV does not seem to simplify: fail the division here.
889 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
890 return cannotDivide(Numerator);
891 divide(SE, Diff, Denominator, &Q, &R);
893 return cannotDivide(Numerator);
898 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
899 const SCEV *Denominator)
900 : SE(S), Denominator(Denominator) {
901 Zero = SE.getZero(Denominator->getType());
902 One = SE.getOne(Denominator->getType());
904 // We generally do not know how to divide Expr by Denominator. We
905 // initialize the division to a "cannot divide" state to simplify the rest
907 cannotDivide(Numerator);
910 // Convenience function for giving up on the division. We set the quotient to
911 // be equal to zero and the remainder to be equal to the numerator.
912 void cannotDivide(const SCEV *Numerator) {
914 Remainder = Numerator;
918 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
923 //===----------------------------------------------------------------------===//
924 // Simple SCEV method implementations
925 //===----------------------------------------------------------------------===//
927 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
929 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
932 // Handle the simplest case efficiently.
934 return SE.getTruncateOrZeroExtend(It, ResultTy);
936 // We are using the following formula for BC(It, K):
938 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
940 // Suppose, W is the bitwidth of the return value. We must be prepared for
941 // overflow. Hence, we must assure that the result of our computation is
942 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
943 // safe in modular arithmetic.
945 // However, this code doesn't use exactly that formula; the formula it uses
946 // is something like the following, where T is the number of factors of 2 in
947 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
950 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
952 // This formula is trivially equivalent to the previous formula. However,
953 // this formula can be implemented much more efficiently. The trick is that
954 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
955 // arithmetic. To do exact division in modular arithmetic, all we have
956 // to do is multiply by the inverse. Therefore, this step can be done at
959 // The next issue is how to safely do the division by 2^T. The way this
960 // is done is by doing the multiplication step at a width of at least W + T
961 // bits. This way, the bottom W+T bits of the product are accurate. Then,
962 // when we perform the division by 2^T (which is equivalent to a right shift
963 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
964 // truncated out after the division by 2^T.
966 // In comparison to just directly using the first formula, this technique
967 // is much more efficient; using the first formula requires W * K bits,
968 // but this formula less than W + K bits. Also, the first formula requires
969 // a division step, whereas this formula only requires multiplies and shifts.
971 // It doesn't matter whether the subtraction step is done in the calculation
972 // width or the input iteration count's width; if the subtraction overflows,
973 // the result must be zero anyway. We prefer here to do it in the width of
974 // the induction variable because it helps a lot for certain cases; CodeGen
975 // isn't smart enough to ignore the overflow, which leads to much less
976 // efficient code if the width of the subtraction is wider than the native
979 // (It's possible to not widen at all by pulling out factors of 2 before
980 // the multiplication; for example, K=2 can be calculated as
981 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
982 // extra arithmetic, so it's not an obvious win, and it gets
983 // much more complicated for K > 3.)
985 // Protection from insane SCEVs; this bound is conservative,
986 // but it probably doesn't matter.
988 return SE.getCouldNotCompute();
990 unsigned W = SE.getTypeSizeInBits(ResultTy);
992 // Calculate K! / 2^T and T; we divide out the factors of two before
993 // multiplying for calculating K! / 2^T to avoid overflow.
994 // Other overflow doesn't matter because we only care about the bottom
995 // W bits of the result.
996 APInt OddFactorial(W, 1);
998 for (unsigned i = 3; i <= K; ++i) {
1000 unsigned TwoFactors = Mult.countTrailingZeros();
1002 Mult = Mult.lshr(TwoFactors);
1003 OddFactorial *= Mult;
1006 // We need at least W + T bits for the multiplication step
1007 unsigned CalculationBits = W + T;
1009 // Calculate 2^T, at width T+W.
1010 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1012 // Calculate the multiplicative inverse of K! / 2^T;
1013 // this multiplication factor will perform the exact division by
1015 APInt Mod = APInt::getSignedMinValue(W+1);
1016 APInt MultiplyFactor = OddFactorial.zext(W+1);
1017 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1018 MultiplyFactor = MultiplyFactor.trunc(W);
1020 // Calculate the product, at width T+W
1021 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1023 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1024 for (unsigned i = 1; i != K; ++i) {
1025 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1026 Dividend = SE.getMulExpr(Dividend,
1027 SE.getTruncateOrZeroExtend(S, CalculationTy));
1031 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1033 // Truncate the result, and divide by K! / 2^T.
1035 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1036 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1039 /// evaluateAtIteration - Return the value of this chain of recurrences at
1040 /// the specified iteration number. We can evaluate this recurrence by
1041 /// multiplying each element in the chain by the binomial coefficient
1042 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1044 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1046 /// where BC(It, k) stands for binomial coefficient.
1048 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1049 ScalarEvolution &SE) const {
1050 const SCEV *Result = getStart();
1051 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1052 // The computation is correct in the face of overflow provided that the
1053 // multiplication is performed _after_ the evaluation of the binomial
1055 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1056 if (isa<SCEVCouldNotCompute>(Coeff))
1059 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1064 //===----------------------------------------------------------------------===//
1065 // SCEV Expression folder implementations
1066 //===----------------------------------------------------------------------===//
1068 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1070 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1071 "This is not a truncating conversion!");
1072 assert(isSCEVable(Ty) &&
1073 "This is not a conversion to a SCEVable type!");
1074 Ty = getEffectiveSCEVType(Ty);
1076 FoldingSetNodeID ID;
1077 ID.AddInteger(scTruncate);
1081 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1083 // Fold if the operand is constant.
1084 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1086 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1088 // trunc(trunc(x)) --> trunc(x)
1089 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1090 return getTruncateExpr(ST->getOperand(), Ty);
1092 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1093 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1094 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1096 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1097 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1098 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1100 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1101 // eliminate all the truncates, or we replace other casts with truncates.
1102 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1103 SmallVector<const SCEV *, 4> Operands;
1104 bool hasTrunc = false;
1105 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1106 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1107 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1108 hasTrunc = isa<SCEVTruncateExpr>(S);
1109 Operands.push_back(S);
1112 return getAddExpr(Operands);
1113 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1116 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1117 // eliminate all the truncates, or we replace other casts with truncates.
1118 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1119 SmallVector<const SCEV *, 4> Operands;
1120 bool hasTrunc = false;
1121 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1122 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1123 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1124 hasTrunc = isa<SCEVTruncateExpr>(S);
1125 Operands.push_back(S);
1128 return getMulExpr(Operands);
1129 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1132 // If the input value is a chrec scev, truncate the chrec's operands.
1133 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1134 SmallVector<const SCEV *, 4> Operands;
1135 for (const SCEV *Op : AddRec->operands())
1136 Operands.push_back(getTruncateExpr(Op, Ty));
1137 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1140 // The cast wasn't folded; create an explicit cast node. We can reuse
1141 // the existing insert position since if we get here, we won't have
1142 // made any changes which would invalidate it.
1143 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1145 UniqueSCEVs.InsertNode(S, IP);
1149 // Get the limit of a recurrence such that incrementing by Step cannot cause
1150 // signed overflow as long as the value of the recurrence within the
1151 // loop does not exceed this limit before incrementing.
1152 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1153 ICmpInst::Predicate *Pred,
1154 ScalarEvolution *SE) {
1155 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1156 if (SE->isKnownPositive(Step)) {
1157 *Pred = ICmpInst::ICMP_SLT;
1158 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1159 SE->getSignedRange(Step).getSignedMax());
1161 if (SE->isKnownNegative(Step)) {
1162 *Pred = ICmpInst::ICMP_SGT;
1163 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1164 SE->getSignedRange(Step).getSignedMin());
1169 // Get the limit of a recurrence such that incrementing by Step cannot cause
1170 // unsigned overflow as long as the value of the recurrence within the loop does
1171 // not exceed this limit before incrementing.
1172 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1173 ICmpInst::Predicate *Pred,
1174 ScalarEvolution *SE) {
1175 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1176 *Pred = ICmpInst::ICMP_ULT;
1178 return SE->getConstant(APInt::getMinValue(BitWidth) -
1179 SE->getUnsignedRange(Step).getUnsignedMax());
1184 struct ExtendOpTraitsBase {
1185 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1188 // Used to make code generic over signed and unsigned overflow.
1189 template <typename ExtendOp> struct ExtendOpTraits {
1192 // static const SCEV::NoWrapFlags WrapType;
1194 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1196 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1197 // ICmpInst::Predicate *Pred,
1198 // ScalarEvolution *SE);
1202 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1203 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1205 static const GetExtendExprTy GetExtendExpr;
1207 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1208 ICmpInst::Predicate *Pred,
1209 ScalarEvolution *SE) {
1210 return getSignedOverflowLimitForStep(Step, Pred, SE);
1214 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1215 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1218 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1219 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1221 static const GetExtendExprTy GetExtendExpr;
1223 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1224 ICmpInst::Predicate *Pred,
1225 ScalarEvolution *SE) {
1226 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1230 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1231 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1234 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1235 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1236 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1237 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1238 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1239 // expression "Step + sext/zext(PreIncAR)" is congruent with
1240 // "sext/zext(PostIncAR)"
1241 template <typename ExtendOpTy>
1242 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1243 ScalarEvolution *SE) {
1244 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1245 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1247 const Loop *L = AR->getLoop();
1248 const SCEV *Start = AR->getStart();
1249 const SCEV *Step = AR->getStepRecurrence(*SE);
1251 // Check for a simple looking step prior to loop entry.
1252 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1256 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1257 // subtraction is expensive. For this purpose, perform a quick and dirty
1258 // difference, by checking for Step in the operand list.
1259 SmallVector<const SCEV *, 4> DiffOps;
1260 for (const SCEV *Op : SA->operands())
1262 DiffOps.push_back(Op);
1264 if (DiffOps.size() == SA->getNumOperands())
1267 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1270 // 1. NSW/NUW flags on the step increment.
1271 auto PreStartFlags =
1272 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1273 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1274 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1275 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1277 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1278 // "S+X does not sign/unsign-overflow".
1281 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1282 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1283 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1286 // 2. Direct overflow check on the step operation's expression.
1287 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1288 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1289 const SCEV *OperandExtendedStart =
1290 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1291 (SE->*GetExtendExpr)(Step, WideTy));
1292 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1293 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1294 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1295 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1296 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1297 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1302 // 3. Loop precondition.
1303 ICmpInst::Predicate Pred;
1304 const SCEV *OverflowLimit =
1305 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1307 if (OverflowLimit &&
1308 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1314 // Get the normalized zero or sign extended expression for this AddRec's Start.
1315 template <typename ExtendOpTy>
1316 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1317 ScalarEvolution *SE) {
1318 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1320 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1322 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1324 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1325 (SE->*GetExtendExpr)(PreStart, Ty));
1328 // Try to prove away overflow by looking at "nearby" add recurrences. A
1329 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1330 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1334 // {S,+,X} == {S-T,+,X} + T
1335 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1337 // If ({S-T,+,X} + T) does not overflow ... (1)
1339 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1341 // If {S-T,+,X} does not overflow ... (2)
1343 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1344 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1346 // If (S-T)+T does not overflow ... (3)
1348 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1349 // == {Ext(S),+,Ext(X)} == LHS
1351 // Thus, if (1), (2) and (3) are true for some T, then
1352 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1354 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1355 // does not overflow" restricted to the 0th iteration. Therefore we only need
1356 // to check for (1) and (2).
1358 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1359 // is `Delta` (defined below).
1361 template <typename ExtendOpTy>
1362 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1365 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1367 // We restrict `Start` to a constant to prevent SCEV from spending too much
1368 // time here. It is correct (but more expensive) to continue with a
1369 // non-constant `Start` and do a general SCEV subtraction to compute
1370 // `PreStart` below.
1372 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1376 APInt StartAI = StartC->getValue()->getValue();
1378 for (unsigned Delta : {-2, -1, 1, 2}) {
1379 const SCEV *PreStart = getConstant(StartAI - Delta);
1381 FoldingSetNodeID ID;
1382 ID.AddInteger(scAddRecExpr);
1383 ID.AddPointer(PreStart);
1384 ID.AddPointer(Step);
1388 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1390 // Give up if we don't already have the add recurrence we need because
1391 // actually constructing an add recurrence is relatively expensive.
1392 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1393 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1394 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1395 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1396 DeltaS, &Pred, this);
1397 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1405 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1407 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1408 "This is not an extending conversion!");
1409 assert(isSCEVable(Ty) &&
1410 "This is not a conversion to a SCEVable type!");
1411 Ty = getEffectiveSCEVType(Ty);
1413 // Fold if the operand is constant.
1414 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1416 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1418 // zext(zext(x)) --> zext(x)
1419 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1420 return getZeroExtendExpr(SZ->getOperand(), Ty);
1422 // Before doing any expensive analysis, check to see if we've already
1423 // computed a SCEV for this Op and Ty.
1424 FoldingSetNodeID ID;
1425 ID.AddInteger(scZeroExtend);
1429 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1431 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1432 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1433 // It's possible the bits taken off by the truncate were all zero bits. If
1434 // so, we should be able to simplify this further.
1435 const SCEV *X = ST->getOperand();
1436 ConstantRange CR = getUnsignedRange(X);
1437 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1438 unsigned NewBits = getTypeSizeInBits(Ty);
1439 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1440 CR.zextOrTrunc(NewBits)))
1441 return getTruncateOrZeroExtend(X, Ty);
1444 // If the input value is a chrec scev, and we can prove that the value
1445 // did not overflow the old, smaller, value, we can zero extend all of the
1446 // operands (often constants). This allows analysis of something like
1447 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1448 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1449 if (AR->isAffine()) {
1450 const SCEV *Start = AR->getStart();
1451 const SCEV *Step = AR->getStepRecurrence(*this);
1452 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1453 const Loop *L = AR->getLoop();
1455 // If we have special knowledge that this addrec won't overflow,
1456 // we don't need to do any further analysis.
1457 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1458 return getAddRecExpr(
1459 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1460 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1462 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1463 // Note that this serves two purposes: It filters out loops that are
1464 // simply not analyzable, and it covers the case where this code is
1465 // being called from within backedge-taken count analysis, such that
1466 // attempting to ask for the backedge-taken count would likely result
1467 // in infinite recursion. In the later case, the analysis code will
1468 // cope with a conservative value, and it will take care to purge
1469 // that value once it has finished.
1470 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1471 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1472 // Manually compute the final value for AR, checking for
1475 // Check whether the backedge-taken count can be losslessly casted to
1476 // the addrec's type. The count is always unsigned.
1477 const SCEV *CastedMaxBECount =
1478 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1479 const SCEV *RecastedMaxBECount =
1480 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1481 if (MaxBECount == RecastedMaxBECount) {
1482 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1483 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1484 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1485 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1486 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1487 const SCEV *WideMaxBECount =
1488 getZeroExtendExpr(CastedMaxBECount, WideTy);
1489 const SCEV *OperandExtendedAdd =
1490 getAddExpr(WideStart,
1491 getMulExpr(WideMaxBECount,
1492 getZeroExtendExpr(Step, WideTy)));
1493 if (ZAdd == OperandExtendedAdd) {
1494 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1495 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1496 // Return the expression with the addrec on the outside.
1497 return getAddRecExpr(
1498 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1499 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1501 // Similar to above, only this time treat the step value as signed.
1502 // This covers loops that count down.
1503 OperandExtendedAdd =
1504 getAddExpr(WideStart,
1505 getMulExpr(WideMaxBECount,
1506 getSignExtendExpr(Step, WideTy)));
1507 if (ZAdd == OperandExtendedAdd) {
1508 // Cache knowledge of AR NW, which is propagated to this AddRec.
1509 // Negative step causes unsigned wrap, but it still can't self-wrap.
1510 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1511 // Return the expression with the addrec on the outside.
1512 return getAddRecExpr(
1513 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1514 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1518 // If the backedge is guarded by a comparison with the pre-inc value
1519 // the addrec is safe. Also, if the entry is guarded by a comparison
1520 // with the start value and the backedge is guarded by a comparison
1521 // with the post-inc value, the addrec is safe.
1522 if (isKnownPositive(Step)) {
1523 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1524 getUnsignedRange(Step).getUnsignedMax());
1525 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1526 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1527 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1528 AR->getPostIncExpr(*this), N))) {
1529 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1530 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1531 // Return the expression with the addrec on the outside.
1532 return getAddRecExpr(
1533 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1534 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1536 } else if (isKnownNegative(Step)) {
1537 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1538 getSignedRange(Step).getSignedMin());
1539 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1540 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1541 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1542 AR->getPostIncExpr(*this), N))) {
1543 // Cache knowledge of AR NW, which is propagated to this AddRec.
1544 // Negative step causes unsigned wrap, but it still can't self-wrap.
1545 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1546 // Return the expression with the addrec on the outside.
1547 return getAddRecExpr(
1548 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1549 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1554 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1555 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1556 return getAddRecExpr(
1557 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1558 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1562 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1563 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1564 if (SA->getNoWrapFlags(SCEV::FlagNUW)) {
1565 // If the addition does not unsign overflow then we can, by definition,
1566 // commute the zero extension with the addition operation.
1567 SmallVector<const SCEV *, 4> Ops;
1568 for (const auto *Op : SA->operands())
1569 Ops.push_back(getZeroExtendExpr(Op, Ty));
1570 return getAddExpr(Ops, SCEV::FlagNUW);
1574 // The cast wasn't folded; create an explicit cast node.
1575 // Recompute the insert position, as it may have been invalidated.
1576 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1577 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1579 UniqueSCEVs.InsertNode(S, IP);
1583 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1585 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1586 "This is not an extending conversion!");
1587 assert(isSCEVable(Ty) &&
1588 "This is not a conversion to a SCEVable type!");
1589 Ty = getEffectiveSCEVType(Ty);
1591 // Fold if the operand is constant.
1592 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1594 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1596 // sext(sext(x)) --> sext(x)
1597 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1598 return getSignExtendExpr(SS->getOperand(), Ty);
1600 // sext(zext(x)) --> zext(x)
1601 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1602 return getZeroExtendExpr(SZ->getOperand(), Ty);
1604 // Before doing any expensive analysis, check to see if we've already
1605 // computed a SCEV for this Op and Ty.
1606 FoldingSetNodeID ID;
1607 ID.AddInteger(scSignExtend);
1611 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1613 // If the input value is provably positive, build a zext instead.
1614 if (isKnownNonNegative(Op))
1615 return getZeroExtendExpr(Op, Ty);
1617 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1618 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1619 // It's possible the bits taken off by the truncate were all sign bits. If
1620 // so, we should be able to simplify this further.
1621 const SCEV *X = ST->getOperand();
1622 ConstantRange CR = getSignedRange(X);
1623 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1624 unsigned NewBits = getTypeSizeInBits(Ty);
1625 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1626 CR.sextOrTrunc(NewBits)))
1627 return getTruncateOrSignExtend(X, Ty);
1630 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1631 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1632 if (SA->getNumOperands() == 2) {
1633 auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1634 auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1636 if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1637 const APInt &C1 = SC1->getValue()->getValue();
1638 const APInt &C2 = SC2->getValue()->getValue();
1639 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1640 C2.ugt(C1) && C2.isPowerOf2())
1641 return getAddExpr(getSignExtendExpr(SC1, Ty),
1642 getSignExtendExpr(SMul, Ty));
1647 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1648 if (SA->getNoWrapFlags(SCEV::FlagNSW)) {
1649 // If the addition does not sign overflow then we can, by definition,
1650 // commute the sign extension with the addition operation.
1651 SmallVector<const SCEV *, 4> Ops;
1652 for (const auto *Op : SA->operands())
1653 Ops.push_back(getSignExtendExpr(Op, Ty));
1654 return getAddExpr(Ops, SCEV::FlagNSW);
1657 // If the input value is a chrec scev, and we can prove that the value
1658 // did not overflow the old, smaller, value, we can sign extend all of the
1659 // operands (often constants). This allows analysis of something like
1660 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1661 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1662 if (AR->isAffine()) {
1663 const SCEV *Start = AR->getStart();
1664 const SCEV *Step = AR->getStepRecurrence(*this);
1665 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1666 const Loop *L = AR->getLoop();
1668 // If we have special knowledge that this addrec won't overflow,
1669 // we don't need to do any further analysis.
1670 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1671 return getAddRecExpr(
1672 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1673 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1675 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1676 // Note that this serves two purposes: It filters out loops that are
1677 // simply not analyzable, and it covers the case where this code is
1678 // being called from within backedge-taken count analysis, such that
1679 // attempting to ask for the backedge-taken count would likely result
1680 // in infinite recursion. In the later case, the analysis code will
1681 // cope with a conservative value, and it will take care to purge
1682 // that value once it has finished.
1683 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1684 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1685 // Manually compute the final value for AR, checking for
1688 // Check whether the backedge-taken count can be losslessly casted to
1689 // the addrec's type. The count is always unsigned.
1690 const SCEV *CastedMaxBECount =
1691 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1692 const SCEV *RecastedMaxBECount =
1693 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1694 if (MaxBECount == RecastedMaxBECount) {
1695 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1696 // Check whether Start+Step*MaxBECount has no signed overflow.
1697 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1698 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1699 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1700 const SCEV *WideMaxBECount =
1701 getZeroExtendExpr(CastedMaxBECount, WideTy);
1702 const SCEV *OperandExtendedAdd =
1703 getAddExpr(WideStart,
1704 getMulExpr(WideMaxBECount,
1705 getSignExtendExpr(Step, WideTy)));
1706 if (SAdd == OperandExtendedAdd) {
1707 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1708 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1709 // Return the expression with the addrec on the outside.
1710 return getAddRecExpr(
1711 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1712 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1714 // Similar to above, only this time treat the step value as unsigned.
1715 // This covers loops that count up with an unsigned step.
1716 OperandExtendedAdd =
1717 getAddExpr(WideStart,
1718 getMulExpr(WideMaxBECount,
1719 getZeroExtendExpr(Step, WideTy)));
1720 if (SAdd == OperandExtendedAdd) {
1721 // If AR wraps around then
1723 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1724 // => SAdd != OperandExtendedAdd
1726 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1727 // (SAdd == OperandExtendedAdd => AR is NW)
1729 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1731 // Return the expression with the addrec on the outside.
1732 return getAddRecExpr(
1733 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1734 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1738 // If the backedge is guarded by a comparison with the pre-inc value
1739 // the addrec is safe. Also, if the entry is guarded by a comparison
1740 // with the start value and the backedge is guarded by a comparison
1741 // with the post-inc value, the addrec is safe.
1742 ICmpInst::Predicate Pred;
1743 const SCEV *OverflowLimit =
1744 getSignedOverflowLimitForStep(Step, &Pred, this);
1745 if (OverflowLimit &&
1746 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1747 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1748 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1750 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1751 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1752 return getAddRecExpr(
1753 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1754 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1757 // If Start and Step are constants, check if we can apply this
1759 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1760 auto *SC1 = dyn_cast<SCEVConstant>(Start);
1761 auto *SC2 = dyn_cast<SCEVConstant>(Step);
1763 const APInt &C1 = SC1->getValue()->getValue();
1764 const APInt &C2 = SC2->getValue()->getValue();
1765 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1767 Start = getSignExtendExpr(Start, Ty);
1768 const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1769 AR->getNoWrapFlags());
1770 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1774 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1775 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1776 return getAddRecExpr(
1777 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1778 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1782 // The cast wasn't folded; create an explicit cast node.
1783 // Recompute the insert position, as it may have been invalidated.
1784 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1785 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1787 UniqueSCEVs.InsertNode(S, IP);
1791 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1792 /// unspecified bits out to the given type.
1794 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1796 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1797 "This is not an extending conversion!");
1798 assert(isSCEVable(Ty) &&
1799 "This is not a conversion to a SCEVable type!");
1800 Ty = getEffectiveSCEVType(Ty);
1802 // Sign-extend negative constants.
1803 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1804 if (SC->getValue()->getValue().isNegative())
1805 return getSignExtendExpr(Op, Ty);
1807 // Peel off a truncate cast.
1808 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1809 const SCEV *NewOp = T->getOperand();
1810 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1811 return getAnyExtendExpr(NewOp, Ty);
1812 return getTruncateOrNoop(NewOp, Ty);
1815 // Next try a zext cast. If the cast is folded, use it.
1816 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1817 if (!isa<SCEVZeroExtendExpr>(ZExt))
1820 // Next try a sext cast. If the cast is folded, use it.
1821 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1822 if (!isa<SCEVSignExtendExpr>(SExt))
1825 // Force the cast to be folded into the operands of an addrec.
1826 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1827 SmallVector<const SCEV *, 4> Ops;
1828 for (const SCEV *Op : AR->operands())
1829 Ops.push_back(getAnyExtendExpr(Op, Ty));
1830 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1833 // If the expression is obviously signed, use the sext cast value.
1834 if (isa<SCEVSMaxExpr>(Op))
1837 // Absent any other information, use the zext cast value.
1841 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1842 /// a list of operands to be added under the given scale, update the given
1843 /// map. This is a helper function for getAddRecExpr. As an example of
1844 /// what it does, given a sequence of operands that would form an add
1845 /// expression like this:
1847 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1849 /// where A and B are constants, update the map with these values:
1851 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1853 /// and add 13 + A*B*29 to AccumulatedConstant.
1854 /// This will allow getAddRecExpr to produce this:
1856 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1858 /// This form often exposes folding opportunities that are hidden in
1859 /// the original operand list.
1861 /// Return true iff it appears that any interesting folding opportunities
1862 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1863 /// the common case where no interesting opportunities are present, and
1864 /// is also used as a check to avoid infinite recursion.
1867 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1868 SmallVectorImpl<const SCEV *> &NewOps,
1869 APInt &AccumulatedConstant,
1870 const SCEV *const *Ops, size_t NumOperands,
1872 ScalarEvolution &SE) {
1873 bool Interesting = false;
1875 // Iterate over the add operands. They are sorted, with constants first.
1877 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1879 // Pull a buried constant out to the outside.
1880 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1882 AccumulatedConstant += Scale * C->getValue()->getValue();
1885 // Next comes everything else. We're especially interested in multiplies
1886 // here, but they're in the middle, so just visit the rest with one loop.
1887 for (; i != NumOperands; ++i) {
1888 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1889 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1891 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1892 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1893 // A multiplication of a constant with another add; recurse.
1894 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1896 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1897 Add->op_begin(), Add->getNumOperands(),
1900 // A multiplication of a constant with some other value. Update
1902 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1903 const SCEV *Key = SE.getMulExpr(MulOps);
1904 auto Pair = M.insert(std::make_pair(Key, NewScale));
1906 NewOps.push_back(Pair.first->first);
1908 Pair.first->second += NewScale;
1909 // The map already had an entry for this value, which may indicate
1910 // a folding opportunity.
1915 // An ordinary operand. Update the map.
1916 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1917 M.insert(std::make_pair(Ops[i], Scale));
1919 NewOps.push_back(Pair.first->first);
1921 Pair.first->second += Scale;
1922 // The map already had an entry for this value, which may indicate
1923 // a folding opportunity.
1933 struct APIntCompare {
1934 bool operator()(const APInt &LHS, const APInt &RHS) const {
1935 return LHS.ult(RHS);
1940 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1941 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1942 // can't-overflow flags for the operation if possible.
1943 static SCEV::NoWrapFlags
1944 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1945 const SmallVectorImpl<const SCEV *> &Ops,
1946 SCEV::NoWrapFlags Flags) {
1947 using namespace std::placeholders;
1948 typedef OverflowingBinaryOperator OBO;
1951 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1953 assert(CanAnalyze && "don't call from other places!");
1955 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1956 SCEV::NoWrapFlags SignOrUnsignWrap =
1957 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1959 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1960 auto IsKnownNonNegative =
1961 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1963 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1964 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1966 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1968 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1970 if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
1971 Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
1973 // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
1974 // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
1976 const APInt &C = cast<SCEVConstant>(Ops[0])->getValue()->getValue();
1977 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
1979 ConstantRange::makeNoWrapRegion(Instruction::Add, C, OBO::NoSignedWrap);
1980 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
1981 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
1983 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
1985 ConstantRange::makeNoWrapRegion(Instruction::Add, C,
1986 OBO::NoUnsignedWrap);
1987 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
1988 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
1995 /// getAddExpr - Get a canonical add expression, or something simpler if
1997 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1998 SCEV::NoWrapFlags Flags) {
1999 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2000 "only nuw or nsw allowed");
2001 assert(!Ops.empty() && "Cannot get empty add!");
2002 if (Ops.size() == 1) return Ops[0];
2004 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2005 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2006 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2007 "SCEVAddExpr operand types don't match!");
2010 // Sort by complexity, this groups all similar expression types together.
2011 GroupByComplexity(Ops, &LI);
2013 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2015 // If there are any constants, fold them together.
2017 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2019 assert(Idx < Ops.size());
2020 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2021 // We found two constants, fold them together!
2022 Ops[0] = getConstant(LHSC->getValue()->getValue() +
2023 RHSC->getValue()->getValue());
2024 if (Ops.size() == 2) return Ops[0];
2025 Ops.erase(Ops.begin()+1); // Erase the folded element
2026 LHSC = cast<SCEVConstant>(Ops[0]);
2029 // If we are left with a constant zero being added, strip it off.
2030 if (LHSC->getValue()->isZero()) {
2031 Ops.erase(Ops.begin());
2035 if (Ops.size() == 1) return Ops[0];
2038 // Okay, check to see if the same value occurs in the operand list more than
2039 // once. If so, merge them together into an multiply expression. Since we
2040 // sorted the list, these values are required to be adjacent.
2041 Type *Ty = Ops[0]->getType();
2042 bool FoundMatch = false;
2043 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2044 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2045 // Scan ahead to count how many equal operands there are.
2047 while (i+Count != e && Ops[i+Count] == Ops[i])
2049 // Merge the values into a multiply.
2050 const SCEV *Scale = getConstant(Ty, Count);
2051 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2052 if (Ops.size() == Count)
2055 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2056 --i; e -= Count - 1;
2060 return getAddExpr(Ops, Flags);
2062 // Check for truncates. If all the operands are truncated from the same
2063 // type, see if factoring out the truncate would permit the result to be
2064 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2065 // if the contents of the resulting outer trunc fold to something simple.
2066 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2067 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2068 Type *DstType = Trunc->getType();
2069 Type *SrcType = Trunc->getOperand()->getType();
2070 SmallVector<const SCEV *, 8> LargeOps;
2072 // Check all the operands to see if they can be represented in the
2073 // source type of the truncate.
2074 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2075 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2076 if (T->getOperand()->getType() != SrcType) {
2080 LargeOps.push_back(T->getOperand());
2081 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2082 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2083 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2084 SmallVector<const SCEV *, 8> LargeMulOps;
2085 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2086 if (const SCEVTruncateExpr *T =
2087 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2088 if (T->getOperand()->getType() != SrcType) {
2092 LargeMulOps.push_back(T->getOperand());
2093 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2094 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2101 LargeOps.push_back(getMulExpr(LargeMulOps));
2108 // Evaluate the expression in the larger type.
2109 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2110 // If it folds to something simple, use it. Otherwise, don't.
2111 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2112 return getTruncateExpr(Fold, DstType);
2116 // Skip past any other cast SCEVs.
2117 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2120 // If there are add operands they would be next.
2121 if (Idx < Ops.size()) {
2122 bool DeletedAdd = false;
2123 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2124 // If we have an add, expand the add operands onto the end of the operands
2126 Ops.erase(Ops.begin()+Idx);
2127 Ops.append(Add->op_begin(), Add->op_end());
2131 // If we deleted at least one add, we added operands to the end of the list,
2132 // and they are not necessarily sorted. Recurse to resort and resimplify
2133 // any operands we just acquired.
2135 return getAddExpr(Ops);
2138 // Skip over the add expression until we get to a multiply.
2139 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2142 // Check to see if there are any folding opportunities present with
2143 // operands multiplied by constant values.
2144 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2145 uint64_t BitWidth = getTypeSizeInBits(Ty);
2146 DenseMap<const SCEV *, APInt> M;
2147 SmallVector<const SCEV *, 8> NewOps;
2148 APInt AccumulatedConstant(BitWidth, 0);
2149 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2150 Ops.data(), Ops.size(),
2151 APInt(BitWidth, 1), *this)) {
2152 // Some interesting folding opportunity is present, so its worthwhile to
2153 // re-generate the operands list. Group the operands by constant scale,
2154 // to avoid multiplying by the same constant scale multiple times.
2155 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2156 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
2157 E = NewOps.end(); I != E; ++I)
2158 MulOpLists[M.find(*I)->second].push_back(*I);
2159 // Re-generate the operands list.
2161 if (AccumulatedConstant != 0)
2162 Ops.push_back(getConstant(AccumulatedConstant));
2163 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
2164 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
2166 Ops.push_back(getMulExpr(getConstant(I->first),
2167 getAddExpr(I->second)));
2170 if (Ops.size() == 1)
2172 return getAddExpr(Ops);
2176 // If we are adding something to a multiply expression, make sure the
2177 // something is not already an operand of the multiply. If so, merge it into
2179 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2180 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2181 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2182 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2183 if (isa<SCEVConstant>(MulOpSCEV))
2185 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2186 if (MulOpSCEV == Ops[AddOp]) {
2187 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2188 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2189 if (Mul->getNumOperands() != 2) {
2190 // If the multiply has more than two operands, we must get the
2192 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2193 Mul->op_begin()+MulOp);
2194 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2195 InnerMul = getMulExpr(MulOps);
2197 const SCEV *One = getOne(Ty);
2198 const SCEV *AddOne = getAddExpr(One, InnerMul);
2199 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2200 if (Ops.size() == 2) return OuterMul;
2202 Ops.erase(Ops.begin()+AddOp);
2203 Ops.erase(Ops.begin()+Idx-1);
2205 Ops.erase(Ops.begin()+Idx);
2206 Ops.erase(Ops.begin()+AddOp-1);
2208 Ops.push_back(OuterMul);
2209 return getAddExpr(Ops);
2212 // Check this multiply against other multiplies being added together.
2213 for (unsigned OtherMulIdx = Idx+1;
2214 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2216 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2217 // If MulOp occurs in OtherMul, we can fold the two multiplies
2219 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2220 OMulOp != e; ++OMulOp)
2221 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2222 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2223 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2224 if (Mul->getNumOperands() != 2) {
2225 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2226 Mul->op_begin()+MulOp);
2227 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2228 InnerMul1 = getMulExpr(MulOps);
2230 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2231 if (OtherMul->getNumOperands() != 2) {
2232 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2233 OtherMul->op_begin()+OMulOp);
2234 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2235 InnerMul2 = getMulExpr(MulOps);
2237 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2238 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2239 if (Ops.size() == 2) return OuterMul;
2240 Ops.erase(Ops.begin()+Idx);
2241 Ops.erase(Ops.begin()+OtherMulIdx-1);
2242 Ops.push_back(OuterMul);
2243 return getAddExpr(Ops);
2249 // If there are any add recurrences in the operands list, see if any other
2250 // added values are loop invariant. If so, we can fold them into the
2252 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2255 // Scan over all recurrences, trying to fold loop invariants into them.
2256 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2257 // Scan all of the other operands to this add and add them to the vector if
2258 // they are loop invariant w.r.t. the recurrence.
2259 SmallVector<const SCEV *, 8> LIOps;
2260 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2261 const Loop *AddRecLoop = AddRec->getLoop();
2262 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2263 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2264 LIOps.push_back(Ops[i]);
2265 Ops.erase(Ops.begin()+i);
2269 // If we found some loop invariants, fold them into the recurrence.
2270 if (!LIOps.empty()) {
2271 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2272 LIOps.push_back(AddRec->getStart());
2274 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2276 AddRecOps[0] = getAddExpr(LIOps);
2278 // Build the new addrec. Propagate the NUW and NSW flags if both the
2279 // outer add and the inner addrec are guaranteed to have no overflow.
2280 // Always propagate NW.
2281 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2282 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2284 // If all of the other operands were loop invariant, we are done.
2285 if (Ops.size() == 1) return NewRec;
2287 // Otherwise, add the folded AddRec by the non-invariant parts.
2288 for (unsigned i = 0;; ++i)
2289 if (Ops[i] == AddRec) {
2293 return getAddExpr(Ops);
2296 // Okay, if there weren't any loop invariants to be folded, check to see if
2297 // there are multiple AddRec's with the same loop induction variable being
2298 // added together. If so, we can fold them.
2299 for (unsigned OtherIdx = Idx+1;
2300 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2302 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2303 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2304 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2306 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2308 if (const SCEVAddRecExpr *OtherAddRec =
2309 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2310 if (OtherAddRec->getLoop() == AddRecLoop) {
2311 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2313 if (i >= AddRecOps.size()) {
2314 AddRecOps.append(OtherAddRec->op_begin()+i,
2315 OtherAddRec->op_end());
2318 AddRecOps[i] = getAddExpr(AddRecOps[i],
2319 OtherAddRec->getOperand(i));
2321 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2323 // Step size has changed, so we cannot guarantee no self-wraparound.
2324 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2325 return getAddExpr(Ops);
2328 // Otherwise couldn't fold anything into this recurrence. Move onto the
2332 // Okay, it looks like we really DO need an add expr. Check to see if we
2333 // already have one, otherwise create a new one.
2334 FoldingSetNodeID ID;
2335 ID.AddInteger(scAddExpr);
2336 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2337 ID.AddPointer(Ops[i]);
2340 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2342 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2343 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2344 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2346 UniqueSCEVs.InsertNode(S, IP);
2348 S->setNoWrapFlags(Flags);
2352 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2354 if (j > 1 && k / j != i) Overflow = true;
2358 /// Compute the result of "n choose k", the binomial coefficient. If an
2359 /// intermediate computation overflows, Overflow will be set and the return will
2360 /// be garbage. Overflow is not cleared on absence of overflow.
2361 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2362 // We use the multiplicative formula:
2363 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2364 // At each iteration, we take the n-th term of the numeral and divide by the
2365 // (k-n)th term of the denominator. This division will always produce an
2366 // integral result, and helps reduce the chance of overflow in the
2367 // intermediate computations. However, we can still overflow even when the
2368 // final result would fit.
2370 if (n == 0 || n == k) return 1;
2371 if (k > n) return 0;
2377 for (uint64_t i = 1; i <= k; ++i) {
2378 r = umul_ov(r, n-(i-1), Overflow);
2384 /// Determine if any of the operands in this SCEV are a constant or if
2385 /// any of the add or multiply expressions in this SCEV contain a constant.
2386 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2387 SmallVector<const SCEV *, 4> Ops;
2388 Ops.push_back(StartExpr);
2389 while (!Ops.empty()) {
2390 const SCEV *CurrentExpr = Ops.pop_back_val();
2391 if (isa<SCEVConstant>(*CurrentExpr))
2394 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2395 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2396 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2402 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2404 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2405 SCEV::NoWrapFlags Flags) {
2406 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2407 "only nuw or nsw allowed");
2408 assert(!Ops.empty() && "Cannot get empty mul!");
2409 if (Ops.size() == 1) return Ops[0];
2411 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2412 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2413 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2414 "SCEVMulExpr operand types don't match!");
2417 // Sort by complexity, this groups all similar expression types together.
2418 GroupByComplexity(Ops, &LI);
2420 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2422 // If there are any constants, fold them together.
2424 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2426 // C1*(C2+V) -> C1*C2 + C1*V
2427 if (Ops.size() == 2)
2428 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2429 // If any of Add's ops are Adds or Muls with a constant,
2430 // apply this transformation as well.
2431 if (Add->getNumOperands() == 2)
2432 if (containsConstantSomewhere(Add))
2433 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2434 getMulExpr(LHSC, Add->getOperand(1)));
2437 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2438 // We found two constants, fold them together!
2439 ConstantInt *Fold = ConstantInt::get(getContext(),
2440 LHSC->getValue()->getValue() *
2441 RHSC->getValue()->getValue());
2442 Ops[0] = getConstant(Fold);
2443 Ops.erase(Ops.begin()+1); // Erase the folded element
2444 if (Ops.size() == 1) return Ops[0];
2445 LHSC = cast<SCEVConstant>(Ops[0]);
2448 // If we are left with a constant one being multiplied, strip it off.
2449 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2450 Ops.erase(Ops.begin());
2452 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2453 // If we have a multiply of zero, it will always be zero.
2455 } else if (Ops[0]->isAllOnesValue()) {
2456 // If we have a mul by -1 of an add, try distributing the -1 among the
2458 if (Ops.size() == 2) {
2459 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2460 SmallVector<const SCEV *, 4> NewOps;
2461 bool AnyFolded = false;
2462 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2463 E = Add->op_end(); I != E; ++I) {
2464 const SCEV *Mul = getMulExpr(Ops[0], *I);
2465 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2466 NewOps.push_back(Mul);
2469 return getAddExpr(NewOps);
2470 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2471 // Negation preserves a recurrence's no self-wrap property.
2472 SmallVector<const SCEV *, 4> Operands;
2473 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2474 E = AddRec->op_end(); I != E; ++I) {
2475 Operands.push_back(getMulExpr(Ops[0], *I));
2477 return getAddRecExpr(Operands, AddRec->getLoop(),
2478 AddRec->getNoWrapFlags(SCEV::FlagNW));
2483 if (Ops.size() == 1)
2487 // Skip over the add expression until we get to a multiply.
2488 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2491 // If there are mul operands inline them all into this expression.
2492 if (Idx < Ops.size()) {
2493 bool DeletedMul = false;
2494 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2495 // If we have an mul, expand the mul operands onto the end of the operands
2497 Ops.erase(Ops.begin()+Idx);
2498 Ops.append(Mul->op_begin(), Mul->op_end());
2502 // If we deleted at least one mul, we added operands to the end of the list,
2503 // and they are not necessarily sorted. Recurse to resort and resimplify
2504 // any operands we just acquired.
2506 return getMulExpr(Ops);
2509 // If there are any add recurrences in the operands list, see if any other
2510 // added values are loop invariant. If so, we can fold them into the
2512 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2515 // Scan over all recurrences, trying to fold loop invariants into them.
2516 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2517 // Scan all of the other operands to this mul and add them to the vector if
2518 // they are loop invariant w.r.t. the recurrence.
2519 SmallVector<const SCEV *, 8> LIOps;
2520 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2521 const Loop *AddRecLoop = AddRec->getLoop();
2522 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2523 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2524 LIOps.push_back(Ops[i]);
2525 Ops.erase(Ops.begin()+i);
2529 // If we found some loop invariants, fold them into the recurrence.
2530 if (!LIOps.empty()) {
2531 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2532 SmallVector<const SCEV *, 4> NewOps;
2533 NewOps.reserve(AddRec->getNumOperands());
2534 const SCEV *Scale = getMulExpr(LIOps);
2535 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2536 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2538 // Build the new addrec. Propagate the NUW and NSW flags if both the
2539 // outer mul and the inner addrec are guaranteed to have no overflow.
2541 // No self-wrap cannot be guaranteed after changing the step size, but
2542 // will be inferred if either NUW or NSW is true.
2543 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2544 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2546 // If all of the other operands were loop invariant, we are done.
2547 if (Ops.size() == 1) return NewRec;
2549 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2550 for (unsigned i = 0;; ++i)
2551 if (Ops[i] == AddRec) {
2555 return getMulExpr(Ops);
2558 // Okay, if there weren't any loop invariants to be folded, check to see if
2559 // there are multiple AddRec's with the same loop induction variable being
2560 // multiplied together. If so, we can fold them.
2562 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2563 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2564 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2565 // ]]],+,...up to x=2n}.
2566 // Note that the arguments to choose() are always integers with values
2567 // known at compile time, never SCEV objects.
2569 // The implementation avoids pointless extra computations when the two
2570 // addrec's are of different length (mathematically, it's equivalent to
2571 // an infinite stream of zeros on the right).
2572 bool OpsModified = false;
2573 for (unsigned OtherIdx = Idx+1;
2574 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2576 const SCEVAddRecExpr *OtherAddRec =
2577 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2578 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2581 bool Overflow = false;
2582 Type *Ty = AddRec->getType();
2583 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2584 SmallVector<const SCEV*, 7> AddRecOps;
2585 for (int x = 0, xe = AddRec->getNumOperands() +
2586 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2587 const SCEV *Term = getZero(Ty);
2588 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2589 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2590 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2591 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2592 z < ze && !Overflow; ++z) {
2593 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2595 if (LargerThan64Bits)
2596 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2598 Coeff = Coeff1*Coeff2;
2599 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2600 const SCEV *Term1 = AddRec->getOperand(y-z);
2601 const SCEV *Term2 = OtherAddRec->getOperand(z);
2602 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2605 AddRecOps.push_back(Term);
2608 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2610 if (Ops.size() == 2) return NewAddRec;
2611 Ops[Idx] = NewAddRec;
2612 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2614 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2620 return getMulExpr(Ops);
2622 // Otherwise couldn't fold anything into this recurrence. Move onto the
2626 // Okay, it looks like we really DO need an mul expr. Check to see if we
2627 // already have one, otherwise create a new one.
2628 FoldingSetNodeID ID;
2629 ID.AddInteger(scMulExpr);
2630 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2631 ID.AddPointer(Ops[i]);
2634 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2636 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2637 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2638 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2640 UniqueSCEVs.InsertNode(S, IP);
2642 S->setNoWrapFlags(Flags);
2646 /// getUDivExpr - Get a canonical unsigned division expression, or something
2647 /// simpler if possible.
2648 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2650 assert(getEffectiveSCEVType(LHS->getType()) ==
2651 getEffectiveSCEVType(RHS->getType()) &&
2652 "SCEVUDivExpr operand types don't match!");
2654 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2655 if (RHSC->getValue()->equalsInt(1))
2656 return LHS; // X udiv 1 --> x
2657 // If the denominator is zero, the result of the udiv is undefined. Don't
2658 // try to analyze it, because the resolution chosen here may differ from
2659 // the resolution chosen in other parts of the compiler.
2660 if (!RHSC->getValue()->isZero()) {
2661 // Determine if the division can be folded into the operands of
2663 // TODO: Generalize this to non-constants by using known-bits information.
2664 Type *Ty = LHS->getType();
2665 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2666 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2667 // For non-power-of-two values, effectively round the value up to the
2668 // nearest power of two.
2669 if (!RHSC->getValue()->getValue().isPowerOf2())
2671 IntegerType *ExtTy =
2672 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2673 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2674 if (const SCEVConstant *Step =
2675 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2676 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2677 const APInt &StepInt = Step->getValue()->getValue();
2678 const APInt &DivInt = RHSC->getValue()->getValue();
2679 if (!StepInt.urem(DivInt) &&
2680 getZeroExtendExpr(AR, ExtTy) ==
2681 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2682 getZeroExtendExpr(Step, ExtTy),
2683 AR->getLoop(), SCEV::FlagAnyWrap)) {
2684 SmallVector<const SCEV *, 4> Operands;
2685 for (const SCEV *Op : AR->operands())
2686 Operands.push_back(getUDivExpr(Op, RHS));
2687 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
2689 /// Get a canonical UDivExpr for a recurrence.
2690 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2691 // We can currently only fold X%N if X is constant.
2692 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2693 if (StartC && !DivInt.urem(StepInt) &&
2694 getZeroExtendExpr(AR, ExtTy) ==
2695 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2696 getZeroExtendExpr(Step, ExtTy),
2697 AR->getLoop(), SCEV::FlagAnyWrap)) {
2698 const APInt &StartInt = StartC->getValue()->getValue();
2699 const APInt &StartRem = StartInt.urem(StepInt);
2701 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2702 AR->getLoop(), SCEV::FlagNW);
2705 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2706 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2707 SmallVector<const SCEV *, 4> Operands;
2708 for (const SCEV *Op : M->operands())
2709 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2710 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2711 // Find an operand that's safely divisible.
2712 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2713 const SCEV *Op = M->getOperand(i);
2714 const SCEV *Div = getUDivExpr(Op, RHSC);
2715 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2716 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2719 return getMulExpr(Operands);
2723 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2724 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2725 SmallVector<const SCEV *, 4> Operands;
2726 for (const SCEV *Op : A->operands())
2727 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2728 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2730 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2731 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2732 if (isa<SCEVUDivExpr>(Op) ||
2733 getMulExpr(Op, RHS) != A->getOperand(i))
2735 Operands.push_back(Op);
2737 if (Operands.size() == A->getNumOperands())
2738 return getAddExpr(Operands);
2742 // Fold if both operands are constant.
2743 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2744 Constant *LHSCV = LHSC->getValue();
2745 Constant *RHSCV = RHSC->getValue();
2746 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2752 FoldingSetNodeID ID;
2753 ID.AddInteger(scUDivExpr);
2757 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2758 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2760 UniqueSCEVs.InsertNode(S, IP);
2764 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2765 APInt A = C1->getValue()->getValue().abs();
2766 APInt B = C2->getValue()->getValue().abs();
2767 uint32_t ABW = A.getBitWidth();
2768 uint32_t BBW = B.getBitWidth();
2775 return APIntOps::GreatestCommonDivisor(A, B);
2778 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2779 /// something simpler if possible. There is no representation for an exact udiv
2780 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2781 /// We can't do this when it's not exact because the udiv may be clearing bits.
2782 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2784 // TODO: we could try to find factors in all sorts of things, but for now we
2785 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2786 // end of this file for inspiration.
2788 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2790 return getUDivExpr(LHS, RHS);
2792 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2793 // If the mulexpr multiplies by a constant, then that constant must be the
2794 // first element of the mulexpr.
2795 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2796 if (LHSCst == RHSCst) {
2797 SmallVector<const SCEV *, 2> Operands;
2798 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2799 return getMulExpr(Operands);
2802 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2803 // that there's a factor provided by one of the other terms. We need to
2805 APInt Factor = gcd(LHSCst, RHSCst);
2806 if (!Factor.isIntN(1)) {
2807 LHSCst = cast<SCEVConstant>(
2808 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2809 RHSCst = cast<SCEVConstant>(
2810 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2811 SmallVector<const SCEV *, 2> Operands;
2812 Operands.push_back(LHSCst);
2813 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2814 LHS = getMulExpr(Operands);
2816 Mul = dyn_cast<SCEVMulExpr>(LHS);
2818 return getUDivExactExpr(LHS, RHS);
2823 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2824 if (Mul->getOperand(i) == RHS) {
2825 SmallVector<const SCEV *, 2> Operands;
2826 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2827 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2828 return getMulExpr(Operands);
2832 return getUDivExpr(LHS, RHS);
2835 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2836 /// Simplify the expression as much as possible.
2837 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2839 SCEV::NoWrapFlags Flags) {
2840 SmallVector<const SCEV *, 4> Operands;
2841 Operands.push_back(Start);
2842 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2843 if (StepChrec->getLoop() == L) {
2844 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2845 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2848 Operands.push_back(Step);
2849 return getAddRecExpr(Operands, L, Flags);
2852 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2853 /// Simplify the expression as much as possible.
2855 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2856 const Loop *L, SCEV::NoWrapFlags Flags) {
2857 if (Operands.size() == 1) return Operands[0];
2859 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2860 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2861 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2862 "SCEVAddRecExpr operand types don't match!");
2863 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2864 assert(isLoopInvariant(Operands[i], L) &&
2865 "SCEVAddRecExpr operand is not loop-invariant!");
2868 if (Operands.back()->isZero()) {
2869 Operands.pop_back();
2870 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2873 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2874 // use that information to infer NUW and NSW flags. However, computing a
2875 // BE count requires calling getAddRecExpr, so we may not yet have a
2876 // meaningful BE count at this point (and if we don't, we'd be stuck
2877 // with a SCEVCouldNotCompute as the cached BE count).
2879 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2881 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2882 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2883 const Loop *NestedLoop = NestedAR->getLoop();
2884 if (L->contains(NestedLoop)
2885 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2886 : (!NestedLoop->contains(L) &&
2887 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2888 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2889 NestedAR->op_end());
2890 Operands[0] = NestedAR->getStart();
2891 // AddRecs require their operands be loop-invariant with respect to their
2892 // loops. Don't perform this transformation if it would break this
2895 std::all_of(Operands.begin(), Operands.end(),
2896 [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
2899 // Create a recurrence for the outer loop with the same step size.
2901 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2902 // inner recurrence has the same property.
2903 SCEV::NoWrapFlags OuterFlags =
2904 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2906 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2907 AllInvariant = std::all_of(
2908 NestedOperands.begin(), NestedOperands.end(),
2909 [&](const SCEV *Op) { return isLoopInvariant(Op, NestedLoop); });
2912 // Ok, both add recurrences are valid after the transformation.
2914 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2915 // the outer recurrence has the same property.
2916 SCEV::NoWrapFlags InnerFlags =
2917 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2918 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2921 // Reset Operands to its original state.
2922 Operands[0] = NestedAR;
2926 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2927 // already have one, otherwise create a new one.
2928 FoldingSetNodeID ID;
2929 ID.AddInteger(scAddRecExpr);
2930 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2931 ID.AddPointer(Operands[i]);
2935 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2937 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2938 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2939 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2940 O, Operands.size(), L);
2941 UniqueSCEVs.InsertNode(S, IP);
2943 S->setNoWrapFlags(Flags);
2948 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2949 const SmallVectorImpl<const SCEV *> &IndexExprs,
2951 // getSCEV(Base)->getType() has the same address space as Base->getType()
2952 // because SCEV::getType() preserves the address space.
2953 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2954 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2955 // instruction to its SCEV, because the Instruction may be guarded by control
2956 // flow and the no-overflow bits may not be valid for the expression in any
2957 // context. This can be fixed similarly to how these flags are handled for
2959 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2961 const SCEV *TotalOffset = getZero(IntPtrTy);
2962 // The address space is unimportant. The first thing we do on CurTy is getting
2963 // its element type.
2964 Type *CurTy = PointerType::getUnqual(PointeeType);
2965 for (const SCEV *IndexExpr : IndexExprs) {
2966 // Compute the (potentially symbolic) offset in bytes for this index.
2967 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2968 // For a struct, add the member offset.
2969 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2970 unsigned FieldNo = Index->getZExtValue();
2971 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2973 // Add the field offset to the running total offset.
2974 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2976 // Update CurTy to the type of the field at Index.
2977 CurTy = STy->getTypeAtIndex(Index);
2979 // Update CurTy to its element type.
2980 CurTy = cast<SequentialType>(CurTy)->getElementType();
2981 // For an array, add the element offset, explicitly scaled.
2982 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2983 // Getelementptr indices are signed.
2984 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2986 // Multiply the index by the element size to compute the element offset.
2987 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2989 // Add the element offset to the running total offset.
2990 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2994 // Add the total offset from all the GEP indices to the base.
2995 return getAddExpr(BaseExpr, TotalOffset, Wrap);
2998 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
3000 SmallVector<const SCEV *, 2> Ops;
3003 return getSMaxExpr(Ops);
3007 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3008 assert(!Ops.empty() && "Cannot get empty smax!");
3009 if (Ops.size() == 1) return Ops[0];
3011 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3012 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3013 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3014 "SCEVSMaxExpr operand types don't match!");
3017 // Sort by complexity, this groups all similar expression types together.
3018 GroupByComplexity(Ops, &LI);
3020 // If there are any constants, fold them together.
3022 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3024 assert(Idx < Ops.size());
3025 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3026 // We found two constants, fold them together!
3027 ConstantInt *Fold = ConstantInt::get(getContext(),
3028 APIntOps::smax(LHSC->getValue()->getValue(),
3029 RHSC->getValue()->getValue()));
3030 Ops[0] = getConstant(Fold);
3031 Ops.erase(Ops.begin()+1); // Erase the folded element
3032 if (Ops.size() == 1) return Ops[0];
3033 LHSC = cast<SCEVConstant>(Ops[0]);
3036 // If we are left with a constant minimum-int, strip it off.
3037 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3038 Ops.erase(Ops.begin());
3040 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3041 // If we have an smax with a constant maximum-int, it will always be
3046 if (Ops.size() == 1) return Ops[0];
3049 // Find the first SMax
3050 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3053 // Check to see if one of the operands is an SMax. If so, expand its operands
3054 // onto our operand list, and recurse to simplify.
3055 if (Idx < Ops.size()) {
3056 bool DeletedSMax = false;
3057 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3058 Ops.erase(Ops.begin()+Idx);
3059 Ops.append(SMax->op_begin(), SMax->op_end());
3064 return getSMaxExpr(Ops);
3067 // Okay, check to see if the same value occurs in the operand list twice. If
3068 // so, delete one. Since we sorted the list, these values are required to
3070 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3071 // X smax Y smax Y --> X smax Y
3072 // X smax Y --> X, if X is always greater than Y
3073 if (Ops[i] == Ops[i+1] ||
3074 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3075 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3077 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3078 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3082 if (Ops.size() == 1) return Ops[0];
3084 assert(!Ops.empty() && "Reduced smax down to nothing!");
3086 // Okay, it looks like we really DO need an smax expr. Check to see if we
3087 // already have one, otherwise create a new one.
3088 FoldingSetNodeID ID;
3089 ID.AddInteger(scSMaxExpr);
3090 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3091 ID.AddPointer(Ops[i]);
3093 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3094 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3095 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3096 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3098 UniqueSCEVs.InsertNode(S, IP);
3102 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3104 SmallVector<const SCEV *, 2> Ops;
3107 return getUMaxExpr(Ops);
3111 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3112 assert(!Ops.empty() && "Cannot get empty umax!");
3113 if (Ops.size() == 1) return Ops[0];
3115 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3116 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3117 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3118 "SCEVUMaxExpr operand types don't match!");
3121 // Sort by complexity, this groups all similar expression types together.
3122 GroupByComplexity(Ops, &LI);
3124 // If there are any constants, fold them together.
3126 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3128 assert(Idx < Ops.size());
3129 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3130 // We found two constants, fold them together!
3131 ConstantInt *Fold = ConstantInt::get(getContext(),
3132 APIntOps::umax(LHSC->getValue()->getValue(),
3133 RHSC->getValue()->getValue()));
3134 Ops[0] = getConstant(Fold);
3135 Ops.erase(Ops.begin()+1); // Erase the folded element
3136 if (Ops.size() == 1) return Ops[0];
3137 LHSC = cast<SCEVConstant>(Ops[0]);
3140 // If we are left with a constant minimum-int, strip it off.
3141 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3142 Ops.erase(Ops.begin());
3144 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3145 // If we have an umax with a constant maximum-int, it will always be
3150 if (Ops.size() == 1) return Ops[0];
3153 // Find the first UMax
3154 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3157 // Check to see if one of the operands is a UMax. If so, expand its operands
3158 // onto our operand list, and recurse to simplify.
3159 if (Idx < Ops.size()) {
3160 bool DeletedUMax = false;
3161 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3162 Ops.erase(Ops.begin()+Idx);
3163 Ops.append(UMax->op_begin(), UMax->op_end());
3168 return getUMaxExpr(Ops);
3171 // Okay, check to see if the same value occurs in the operand list twice. If
3172 // so, delete one. Since we sorted the list, these values are required to
3174 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3175 // X umax Y umax Y --> X umax Y
3176 // X umax Y --> X, if X is always greater than Y
3177 if (Ops[i] == Ops[i+1] ||
3178 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3179 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3181 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3182 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3186 if (Ops.size() == 1) return Ops[0];
3188 assert(!Ops.empty() && "Reduced umax down to nothing!");
3190 // Okay, it looks like we really DO need a umax expr. Check to see if we
3191 // already have one, otherwise create a new one.
3192 FoldingSetNodeID ID;
3193 ID.AddInteger(scUMaxExpr);
3194 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3195 ID.AddPointer(Ops[i]);
3197 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3198 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3199 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3200 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3202 UniqueSCEVs.InsertNode(S, IP);
3206 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3208 // ~smax(~x, ~y) == smin(x, y).
3209 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3212 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3214 // ~umax(~x, ~y) == umin(x, y)
3215 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3218 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3219 // We can bypass creating a target-independent
3220 // constant expression and then folding it back into a ConstantInt.
3221 // This is just a compile-time optimization.
3222 return getConstant(IntTy,
3223 F.getParent()->getDataLayout().getTypeAllocSize(AllocTy));
3226 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3229 // We can bypass creating a target-independent
3230 // constant expression and then folding it back into a ConstantInt.
3231 // This is just a compile-time optimization.
3234 F.getParent()->getDataLayout().getStructLayout(STy)->getElementOffset(
3238 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3239 // Don't attempt to do anything other than create a SCEVUnknown object
3240 // here. createSCEV only calls getUnknown after checking for all other
3241 // interesting possibilities, and any other code that calls getUnknown
3242 // is doing so in order to hide a value from SCEV canonicalization.
3244 FoldingSetNodeID ID;
3245 ID.AddInteger(scUnknown);
3248 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3249 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3250 "Stale SCEVUnknown in uniquing map!");
3253 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3255 FirstUnknown = cast<SCEVUnknown>(S);
3256 UniqueSCEVs.InsertNode(S, IP);
3260 //===----------------------------------------------------------------------===//
3261 // Basic SCEV Analysis and PHI Idiom Recognition Code
3264 /// isSCEVable - Test if values of the given type are analyzable within
3265 /// the SCEV framework. This primarily includes integer types, and it
3266 /// can optionally include pointer types if the ScalarEvolution class
3267 /// has access to target-specific information.
3268 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3269 // Integers and pointers are always SCEVable.
3270 return Ty->isIntegerTy() || Ty->isPointerTy();
3273 /// getTypeSizeInBits - Return the size in bits of the specified type,
3274 /// for which isSCEVable must return true.
3275 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3276 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3277 return F.getParent()->getDataLayout().getTypeSizeInBits(Ty);
3280 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3281 /// the given type and which represents how SCEV will treat the given
3282 /// type, for which isSCEVable must return true. For pointer types,
3283 /// this is the pointer-sized integer type.
3284 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3285 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3287 if (Ty->isIntegerTy())
3290 // The only other support type is pointer.
3291 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3292 return F.getParent()->getDataLayout().getIntPtrType(Ty);
3295 const SCEV *ScalarEvolution::getCouldNotCompute() {
3296 return CouldNotCompute.get();
3300 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3301 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3302 // is set iff if find such SCEVUnknown.
3304 struct FindInvalidSCEVUnknown {
3306 FindInvalidSCEVUnknown() { FindOne = false; }
3307 bool follow(const SCEV *S) {
3308 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3312 if (!cast<SCEVUnknown>(S)->getValue())
3319 bool isDone() const { return FindOne; }
3323 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3324 FindInvalidSCEVUnknown F;
3325 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3331 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3332 /// expression and create a new one.
3333 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3334 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3336 const SCEV *S = getExistingSCEV(V);
3339 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3344 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3345 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3347 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3348 if (I != ValueExprMap.end()) {
3349 const SCEV *S = I->second;
3350 if (checkValidity(S))
3352 ValueExprMap.erase(I);
3357 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3359 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3360 SCEV::NoWrapFlags Flags) {
3361 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3363 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3365 Type *Ty = V->getType();
3366 Ty = getEffectiveSCEVType(Ty);
3368 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3371 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3372 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3373 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3375 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3377 Type *Ty = V->getType();
3378 Ty = getEffectiveSCEVType(Ty);
3379 const SCEV *AllOnes =
3380 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3381 return getMinusSCEV(AllOnes, V);
3384 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3385 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3386 SCEV::NoWrapFlags Flags) {
3387 // Fast path: X - X --> 0.
3389 return getZero(LHS->getType());
3391 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3392 // makes it so that we cannot make much use of NUW.
3393 auto AddFlags = SCEV::FlagAnyWrap;
3394 const bool RHSIsNotMinSigned =
3395 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3396 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3397 // Let M be the minimum representable signed value. Then (-1)*RHS
3398 // signed-wraps if and only if RHS is M. That can happen even for
3399 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3400 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3401 // (-1)*RHS, we need to prove that RHS != M.
3403 // If LHS is non-negative and we know that LHS - RHS does not
3404 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3405 // either by proving that RHS > M or that LHS >= 0.
3406 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3407 AddFlags = SCEV::FlagNSW;
3411 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3412 // RHS is NSW and LHS >= 0.
3414 // The difficulty here is that the NSW flag may have been proven
3415 // relative to a loop that is to be found in a recurrence in LHS and
3416 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3417 // larger scope than intended.
3418 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3420 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3423 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3424 /// input value to the specified type. If the type must be extended, it is zero
3427 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3428 Type *SrcTy = V->getType();
3429 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3430 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3431 "Cannot truncate or zero extend with non-integer arguments!");
3432 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3433 return V; // No conversion
3434 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3435 return getTruncateExpr(V, Ty);
3436 return getZeroExtendExpr(V, Ty);
3439 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3440 /// input value to the specified type. If the type must be extended, it is sign
3443 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3445 Type *SrcTy = V->getType();
3446 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3447 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3448 "Cannot truncate or zero extend with non-integer arguments!");
3449 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3450 return V; // No conversion
3451 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3452 return getTruncateExpr(V, Ty);
3453 return getSignExtendExpr(V, Ty);
3456 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3457 /// input value to the specified type. If the type must be extended, it is zero
3458 /// extended. The conversion must not be narrowing.
3460 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3461 Type *SrcTy = V->getType();
3462 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3463 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3464 "Cannot noop or zero extend with non-integer arguments!");
3465 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3466 "getNoopOrZeroExtend cannot truncate!");
3467 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3468 return V; // No conversion
3469 return getZeroExtendExpr(V, Ty);
3472 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3473 /// input value to the specified type. If the type must be extended, it is sign
3474 /// extended. The conversion must not be narrowing.
3476 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3477 Type *SrcTy = V->getType();
3478 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3479 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3480 "Cannot noop or sign extend with non-integer arguments!");
3481 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3482 "getNoopOrSignExtend cannot truncate!");
3483 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3484 return V; // No conversion
3485 return getSignExtendExpr(V, Ty);
3488 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3489 /// the input value to the specified type. If the type must be extended,
3490 /// it is extended with unspecified bits. The conversion must not be
3493 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3494 Type *SrcTy = V->getType();
3495 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3496 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3497 "Cannot noop or any extend with non-integer arguments!");
3498 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3499 "getNoopOrAnyExtend cannot truncate!");
3500 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3501 return V; // No conversion
3502 return getAnyExtendExpr(V, Ty);
3505 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3506 /// input value to the specified type. The conversion must not be widening.
3508 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3509 Type *SrcTy = V->getType();
3510 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3511 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3512 "Cannot truncate or noop with non-integer arguments!");
3513 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3514 "getTruncateOrNoop cannot extend!");
3515 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3516 return V; // No conversion
3517 return getTruncateExpr(V, Ty);
3520 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3521 /// the types using zero-extension, and then perform a umax operation
3523 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3525 const SCEV *PromotedLHS = LHS;
3526 const SCEV *PromotedRHS = RHS;
3528 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3529 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3531 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3533 return getUMaxExpr(PromotedLHS, PromotedRHS);
3536 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3537 /// the types using zero-extension, and then perform a umin operation
3539 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3541 const SCEV *PromotedLHS = LHS;
3542 const SCEV *PromotedRHS = RHS;
3544 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3545 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3547 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3549 return getUMinExpr(PromotedLHS, PromotedRHS);
3552 /// getPointerBase - Transitively follow the chain of pointer-type operands
3553 /// until reaching a SCEV that does not have a single pointer operand. This
3554 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3555 /// but corner cases do exist.
3556 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3557 // A pointer operand may evaluate to a nonpointer expression, such as null.
3558 if (!V->getType()->isPointerTy())
3561 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3562 return getPointerBase(Cast->getOperand());
3563 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3564 const SCEV *PtrOp = nullptr;
3565 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3567 if ((*I)->getType()->isPointerTy()) {
3568 // Cannot find the base of an expression with multiple pointer operands.
3576 return getPointerBase(PtrOp);
3581 /// PushDefUseChildren - Push users of the given Instruction
3582 /// onto the given Worklist.
3584 PushDefUseChildren(Instruction *I,
3585 SmallVectorImpl<Instruction *> &Worklist) {
3586 // Push the def-use children onto the Worklist stack.
3587 for (User *U : I->users())
3588 Worklist.push_back(cast<Instruction>(U));
3591 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3592 /// instructions that depend on the given instruction and removes them from
3593 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3596 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3597 SmallVector<Instruction *, 16> Worklist;
3598 PushDefUseChildren(PN, Worklist);
3600 SmallPtrSet<Instruction *, 8> Visited;
3602 while (!Worklist.empty()) {
3603 Instruction *I = Worklist.pop_back_val();
3604 if (!Visited.insert(I).second)
3607 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
3608 if (It != ValueExprMap.end()) {
3609 const SCEV *Old = It->second;
3611 // Short-circuit the def-use traversal if the symbolic name
3612 // ceases to appear in expressions.
3613 if (Old != SymName && !hasOperand(Old, SymName))
3616 // SCEVUnknown for a PHI either means that it has an unrecognized
3617 // structure, it's a PHI that's in the progress of being computed
3618 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3619 // additional loop trip count information isn't going to change anything.
3620 // In the second case, createNodeForPHI will perform the necessary
3621 // updates on its own when it gets to that point. In the third, we do
3622 // want to forget the SCEVUnknown.
3623 if (!isa<PHINode>(I) ||
3624 !isa<SCEVUnknown>(Old) ||
3625 (I != PN && Old == SymName)) {
3626 forgetMemoizedResults(Old);
3627 ValueExprMap.erase(It);
3631 PushDefUseChildren(I, Worklist);
3635 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
3636 const Loop *L = LI.getLoopFor(PN->getParent());
3637 if (!L || L->getHeader() != PN->getParent())
3640 // The loop may have multiple entrances or multiple exits; we can analyze
3641 // this phi as an addrec if it has a unique entry value and a unique
3643 Value *BEValueV = nullptr, *StartValueV = nullptr;
3644 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3645 Value *V = PN->getIncomingValue(i);
3646 if (L->contains(PN->getIncomingBlock(i))) {
3649 } else if (BEValueV != V) {
3653 } else if (!StartValueV) {
3655 } else if (StartValueV != V) {
3656 StartValueV = nullptr;
3660 if (BEValueV && StartValueV) {
3661 // While we are analyzing this PHI node, handle its value symbolically.
3662 const SCEV *SymbolicName = getUnknown(PN);
3663 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3664 "PHI node already processed?");
3665 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3667 // Using this symbolic name for the PHI, analyze the value coming around
3669 const SCEV *BEValue = getSCEV(BEValueV);
3671 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3672 // has a special value for the first iteration of the loop.
3674 // If the value coming around the backedge is an add with the symbolic
3675 // value we just inserted, then we found a simple induction variable!
3676 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3677 // If there is a single occurrence of the symbolic value, replace it
3678 // with a recurrence.
3679 unsigned FoundIndex = Add->getNumOperands();
3680 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3681 if (Add->getOperand(i) == SymbolicName)
3682 if (FoundIndex == e) {
3687 if (FoundIndex != Add->getNumOperands()) {
3688 // Create an add with everything but the specified operand.
3689 SmallVector<const SCEV *, 8> Ops;
3690 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3691 if (i != FoundIndex)
3692 Ops.push_back(Add->getOperand(i));
3693 const SCEV *Accum = getAddExpr(Ops);
3695 // This is not a valid addrec if the step amount is varying each
3696 // loop iteration, but is not itself an addrec in this loop.
3697 if (isLoopInvariant(Accum, L) ||
3698 (isa<SCEVAddRecExpr>(Accum) &&
3699 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3700 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3702 // If the increment doesn't overflow, then neither the addrec nor
3703 // the post-increment will overflow.
3704 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3705 if (OBO->getOperand(0) == PN) {
3706 if (OBO->hasNoUnsignedWrap())
3707 Flags = setFlags(Flags, SCEV::FlagNUW);
3708 if (OBO->hasNoSignedWrap())
3709 Flags = setFlags(Flags, SCEV::FlagNSW);
3711 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3712 // If the increment is an inbounds GEP, then we know the address
3713 // space cannot be wrapped around. We cannot make any guarantee
3714 // about signed or unsigned overflow because pointers are
3715 // unsigned but we may have a negative index from the base
3716 // pointer. We can guarantee that no unsigned wrap occurs if the
3717 // indices form a positive value.
3718 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3719 Flags = setFlags(Flags, SCEV::FlagNW);
3721 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3722 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3723 Flags = setFlags(Flags, SCEV::FlagNUW);
3726 // We cannot transfer nuw and nsw flags from subtraction
3727 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3731 const SCEV *StartVal = getSCEV(StartValueV);
3732 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3734 // Since the no-wrap flags are on the increment, they apply to the
3735 // post-incremented value as well.
3736 if (isLoopInvariant(Accum, L))
3737 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
3739 // Okay, for the entire analysis of this edge we assumed the PHI
3740 // to be symbolic. We now need to go back and purge all of the
3741 // entries for the scalars that use the symbolic expression.
3742 ForgetSymbolicName(PN, SymbolicName);
3743 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3747 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
3748 // Otherwise, this could be a loop like this:
3749 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3750 // In this case, j = {1,+,1} and BEValue is j.
3751 // Because the other in-value of i (0) fits the evolution of BEValue
3752 // i really is an addrec evolution.
3753 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3754 const SCEV *StartVal = getSCEV(StartValueV);
3756 // If StartVal = j.start - j.stride, we can use StartVal as the
3757 // initial step of the addrec evolution.
3759 getMinusSCEV(AddRec->getOperand(0), AddRec->getOperand(1))) {
3760 // FIXME: For constant StartVal, we should be able to infer
3762 const SCEV *PHISCEV = getAddRecExpr(StartVal, AddRec->getOperand(1),
3763 L, SCEV::FlagAnyWrap);
3765 // Okay, for the entire analysis of this edge we assumed the PHI
3766 // to be symbolic. We now need to go back and purge all of the
3767 // entries for the scalars that use the symbolic expression.
3768 ForgetSymbolicName(PN, SymbolicName);
3769 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3779 // Checks if the SCEV S is available at BB. S is considered available at BB
3780 // if S can be materialized at BB without introducing a fault.
3781 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
3783 struct CheckAvailable {
3784 bool TraversalDone = false;
3785 bool Available = true;
3787 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
3788 BasicBlock *BB = nullptr;
3791 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
3792 : L(L), BB(BB), DT(DT) {}
3794 bool setUnavailable() {
3795 TraversalDone = true;
3800 bool follow(const SCEV *S) {
3801 switch (S->getSCEVType()) {
3802 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
3803 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
3804 // These expressions are available if their operand(s) is/are.
3807 case scAddRecExpr: {
3808 // We allow add recurrences that are on the loop BB is in, or some
3809 // outer loop. This guarantees availability because the value of the
3810 // add recurrence at BB is simply the "current" value of the induction
3811 // variable. We can relax this in the future; for instance an add
3812 // recurrence on a sibling dominating loop is also available at BB.
3813 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
3814 if (L && (ARLoop == L || ARLoop->contains(L)))
3817 return setUnavailable();
3821 // For SCEVUnknown, we check for simple dominance.
3822 const auto *SU = cast<SCEVUnknown>(S);
3823 Value *V = SU->getValue();
3825 if (isa<Argument>(V))
3828 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
3831 return setUnavailable();
3835 case scCouldNotCompute:
3836 // We do not try to smart about these at all.
3837 return setUnavailable();
3839 llvm_unreachable("switch should be fully covered!");
3842 bool isDone() { return TraversalDone; }
3845 CheckAvailable CA(L, BB, DT);
3846 SCEVTraversal<CheckAvailable> ST(CA);
3849 return CA.Available;
3852 // Try to match a control flow sequence that branches out at BI and merges back
3853 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
3855 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
3856 Value *&C, Value *&LHS, Value *&RHS) {
3857 C = BI->getCondition();
3859 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
3860 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
3862 if (!LeftEdge.isSingleEdge())
3865 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
3867 Use &LeftUse = Merge->getOperandUse(0);
3868 Use &RightUse = Merge->getOperandUse(1);
3870 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
3876 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
3885 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
3886 if (PN->getNumIncomingValues() == 2) {
3887 const Loop *L = LI.getLoopFor(PN->getParent());
3891 // br %cond, label %left, label %right
3897 // V = phi [ %x, %left ], [ %y, %right ]
3899 // as "select %cond, %x, %y"
3901 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
3902 assert(IDom && "At least the entry block should dominate PN");
3904 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
3905 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
3907 if (BI && BI->isConditional() &&
3908 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
3909 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
3910 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
3911 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
3917 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3918 if (const SCEV *S = createAddRecFromPHI(PN))
3921 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
3924 // If the PHI has a single incoming value, follow that value, unless the
3925 // PHI's incoming blocks are in a different loop, in which case doing so
3926 // risks breaking LCSSA form. Instcombine would normally zap these, but
3927 // it doesn't have DominatorTree information, so it may miss cases.
3928 if (Value *V = SimplifyInstruction(PN, F.getParent()->getDataLayout(), &TLI,
3930 if (LI.replacementPreservesLCSSAForm(PN, V))
3933 // If it's not a loop phi, we can't handle it yet.
3934 return getUnknown(PN);
3937 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
3941 // Handle "constant" branch or select. This can occur for instance when a
3942 // loop pass transforms an inner loop and moves on to process the outer loop.
3943 if (auto *CI = dyn_cast<ConstantInt>(Cond))
3944 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
3946 // Try to match some simple smax or umax patterns.
3947 auto *ICI = dyn_cast<ICmpInst>(Cond);
3949 return getUnknown(I);
3951 Value *LHS = ICI->getOperand(0);
3952 Value *RHS = ICI->getOperand(1);
3954 switch (ICI->getPredicate()) {
3955 case ICmpInst::ICMP_SLT:
3956 case ICmpInst::ICMP_SLE:
3957 std::swap(LHS, RHS);
3959 case ICmpInst::ICMP_SGT:
3960 case ICmpInst::ICMP_SGE:
3961 // a >s b ? a+x : b+x -> smax(a, b)+x
3962 // a >s b ? b+x : a+x -> smin(a, b)+x
3963 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
3964 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
3965 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
3966 const SCEV *LA = getSCEV(TrueVal);
3967 const SCEV *RA = getSCEV(FalseVal);
3968 const SCEV *LDiff = getMinusSCEV(LA, LS);
3969 const SCEV *RDiff = getMinusSCEV(RA, RS);
3971 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3972 LDiff = getMinusSCEV(LA, RS);
3973 RDiff = getMinusSCEV(RA, LS);
3975 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3978 case ICmpInst::ICMP_ULT:
3979 case ICmpInst::ICMP_ULE:
3980 std::swap(LHS, RHS);
3982 case ICmpInst::ICMP_UGT:
3983 case ICmpInst::ICMP_UGE:
3984 // a >u b ? a+x : b+x -> umax(a, b)+x
3985 // a >u b ? b+x : a+x -> umin(a, b)+x
3986 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
3987 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
3988 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
3989 const SCEV *LA = getSCEV(TrueVal);
3990 const SCEV *RA = getSCEV(FalseVal);
3991 const SCEV *LDiff = getMinusSCEV(LA, LS);
3992 const SCEV *RDiff = getMinusSCEV(RA, RS);
3994 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3995 LDiff = getMinusSCEV(LA, RS);
3996 RDiff = getMinusSCEV(RA, LS);
3998 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4001 case ICmpInst::ICMP_NE:
4002 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4003 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4004 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4005 const SCEV *One = getOne(I->getType());
4006 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4007 const SCEV *LA = getSCEV(TrueVal);
4008 const SCEV *RA = getSCEV(FalseVal);
4009 const SCEV *LDiff = getMinusSCEV(LA, LS);
4010 const SCEV *RDiff = getMinusSCEV(RA, One);
4012 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4015 case ICmpInst::ICMP_EQ:
4016 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4017 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4018 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4019 const SCEV *One = getOne(I->getType());
4020 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4021 const SCEV *LA = getSCEV(TrueVal);
4022 const SCEV *RA = getSCEV(FalseVal);
4023 const SCEV *LDiff = getMinusSCEV(LA, One);
4024 const SCEV *RDiff = getMinusSCEV(RA, LS);
4026 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4033 return getUnknown(I);
4036 /// createNodeForGEP - Expand GEP instructions into add and multiply
4037 /// operations. This allows them to be analyzed by regular SCEV code.
4039 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
4040 Value *Base = GEP->getOperand(0);
4041 // Don't attempt to analyze GEPs over unsized objects.
4042 if (!Base->getType()->getPointerElementType()->isSized())
4043 return getUnknown(GEP);
4045 SmallVector<const SCEV *, 4> IndexExprs;
4046 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4047 IndexExprs.push_back(getSCEV(*Index));
4048 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
4052 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
4053 /// guaranteed to end in (at every loop iteration). It is, at the same time,
4054 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
4055 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
4057 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4058 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4059 return C->getValue()->getValue().countTrailingZeros();
4061 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4062 return std::min(GetMinTrailingZeros(T->getOperand()),
4063 (uint32_t)getTypeSizeInBits(T->getType()));
4065 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4066 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4067 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4068 getTypeSizeInBits(E->getType()) : OpRes;
4071 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4072 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4073 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4074 getTypeSizeInBits(E->getType()) : OpRes;
4077 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4078 // The result is the min of all operands results.
4079 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4080 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4081 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4085 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4086 // The result is the sum of all operands results.
4087 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4088 uint32_t BitWidth = getTypeSizeInBits(M->getType());
4089 for (unsigned i = 1, e = M->getNumOperands();
4090 SumOpRes != BitWidth && i != e; ++i)
4091 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4096 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4097 // The result is the min of all operands results.
4098 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4099 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4100 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4104 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4105 // The result is the min of all operands results.
4106 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4107 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4108 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4112 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4113 // The result is the min of all operands results.
4114 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4115 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4116 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4120 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4121 // For a SCEVUnknown, ask ValueTracking.
4122 unsigned BitWidth = getTypeSizeInBits(U->getType());
4123 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4124 computeKnownBits(U->getValue(), Zeros, Ones, F.getParent()->getDataLayout(),
4125 0, &AC, nullptr, &DT);
4126 return Zeros.countTrailingOnes();
4133 /// GetRangeFromMetadata - Helper method to assign a range to V from
4134 /// metadata present in the IR.
4135 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4136 if (Instruction *I = dyn_cast<Instruction>(V))
4137 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
4138 return getConstantRangeFromMetadata(*MD);
4143 /// getRange - Determine the range for a particular SCEV. If SignHint is
4144 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4145 /// with a "cleaner" unsigned (resp. signed) representation.
4148 ScalarEvolution::getRange(const SCEV *S,
4149 ScalarEvolution::RangeSignHint SignHint) {
4150 DenseMap<const SCEV *, ConstantRange> &Cache =
4151 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4154 // See if we've computed this range already.
4155 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4156 if (I != Cache.end())
4159 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4160 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
4162 unsigned BitWidth = getTypeSizeInBits(S->getType());
4163 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4165 // If the value has known zeros, the maximum value will have those known zeros
4167 uint32_t TZ = GetMinTrailingZeros(S);
4169 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4170 ConservativeResult =
4171 ConstantRange(APInt::getMinValue(BitWidth),
4172 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4174 ConservativeResult = ConstantRange(
4175 APInt::getSignedMinValue(BitWidth),
4176 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4179 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4180 ConstantRange X = getRange(Add->getOperand(0), SignHint);
4181 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4182 X = X.add(getRange(Add->getOperand(i), SignHint));
4183 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4186 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4187 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4188 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4189 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4190 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4193 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4194 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4195 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4196 X = X.smax(getRange(SMax->getOperand(i), SignHint));
4197 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4200 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4201 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4202 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4203 X = X.umax(getRange(UMax->getOperand(i), SignHint));
4204 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4207 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4208 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4209 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4210 return setRange(UDiv, SignHint,
4211 ConservativeResult.intersectWith(X.udiv(Y)));
4214 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4215 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4216 return setRange(ZExt, SignHint,
4217 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4220 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4221 ConstantRange X = getRange(SExt->getOperand(), SignHint);
4222 return setRange(SExt, SignHint,
4223 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4226 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4227 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4228 return setRange(Trunc, SignHint,
4229 ConservativeResult.intersectWith(X.truncate(BitWidth)));
4232 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4233 // If there's no unsigned wrap, the value will never be less than its
4235 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
4236 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4237 if (!C->getValue()->isZero())
4238 ConservativeResult =
4239 ConservativeResult.intersectWith(
4240 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
4242 // If there's no signed wrap, and all the operands have the same sign or
4243 // zero, the value won't ever change sign.
4244 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
4245 bool AllNonNeg = true;
4246 bool AllNonPos = true;
4247 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4248 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4249 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4252 ConservativeResult = ConservativeResult.intersectWith(
4253 ConstantRange(APInt(BitWidth, 0),
4254 APInt::getSignedMinValue(BitWidth)));
4256 ConservativeResult = ConservativeResult.intersectWith(
4257 ConstantRange(APInt::getSignedMinValue(BitWidth),
4258 APInt(BitWidth, 1)));
4261 // TODO: non-affine addrec
4262 if (AddRec->isAffine()) {
4263 Type *Ty = AddRec->getType();
4264 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4265 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4266 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4268 // Check for overflow. This must be done with ConstantRange arithmetic
4269 // because we could be called from within the ScalarEvolution overflow
4272 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4273 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4274 ConstantRange ZExtMaxBECountRange =
4275 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4277 const SCEV *Start = AddRec->getStart();
4278 const SCEV *Step = AddRec->getStepRecurrence(*this);
4279 ConstantRange StepSRange = getSignedRange(Step);
4280 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4282 ConstantRange StartURange = getUnsignedRange(Start);
4283 ConstantRange EndURange =
4284 StartURange.add(MaxBECountRange.multiply(StepSRange));
4286 // Check for unsigned overflow.
4287 ConstantRange ZExtStartURange =
4288 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4289 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4290 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4292 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4293 EndURange.getUnsignedMin());
4294 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4295 EndURange.getUnsignedMax());
4296 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4298 ConservativeResult =
4299 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4302 ConstantRange StartSRange = getSignedRange(Start);
4303 ConstantRange EndSRange =
4304 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4306 // Check for signed overflow. This must be done with ConstantRange
4307 // arithmetic because we could be called from within the ScalarEvolution
4308 // overflow checking code.
4309 ConstantRange SExtStartSRange =
4310 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4311 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4312 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4314 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4315 EndSRange.getSignedMin());
4316 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4317 EndSRange.getSignedMax());
4318 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4320 ConservativeResult =
4321 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4326 return setRange(AddRec, SignHint, ConservativeResult);
4329 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4330 // Check if the IR explicitly contains !range metadata.
4331 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4332 if (MDRange.hasValue())
4333 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4335 // Split here to avoid paying the compile-time cost of calling both
4336 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4338 const DataLayout &DL = F.getParent()->getDataLayout();
4339 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4340 // For a SCEVUnknown, ask ValueTracking.
4341 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4342 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4343 if (Ones != ~Zeros + 1)
4344 ConservativeResult =
4345 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4347 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4348 "generalize as needed!");
4349 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4351 ConservativeResult = ConservativeResult.intersectWith(
4352 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4353 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4356 return setRange(U, SignHint, ConservativeResult);
4359 return setRange(S, SignHint, ConservativeResult);
4362 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4363 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4364 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4366 // Return early if there are no flags to propagate to the SCEV.
4367 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4368 if (BinOp->hasNoUnsignedWrap())
4369 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4370 if (BinOp->hasNoSignedWrap())
4371 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4372 if (Flags == SCEV::FlagAnyWrap) {
4373 return SCEV::FlagAnyWrap;
4376 // Here we check that BinOp is in the header of the innermost loop
4377 // containing BinOp, since we only deal with instructions in the loop
4378 // header. The actual loop we need to check later will come from an add
4379 // recurrence, but getting that requires computing the SCEV of the operands,
4380 // which can be expensive. This check we can do cheaply to rule out some
4382 Loop *innermostContainingLoop = LI.getLoopFor(BinOp->getParent());
4383 if (innermostContainingLoop == nullptr ||
4384 innermostContainingLoop->getHeader() != BinOp->getParent())
4385 return SCEV::FlagAnyWrap;
4387 // Only proceed if we can prove that BinOp does not yield poison.
4388 if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
4390 // At this point we know that if V is executed, then it does not wrap
4391 // according to at least one of NSW or NUW. If V is not executed, then we do
4392 // not know if the calculation that V represents would wrap. Multiple
4393 // instructions can map to the same SCEV. If we apply NSW or NUW from V to
4394 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4395 // derived from other instructions that map to the same SCEV. We cannot make
4396 // that guarantee for cases where V is not executed. So we need to find the
4397 // loop that V is considered in relation to and prove that V is executed for
4398 // every iteration of that loop. That implies that the value that V
4399 // calculates does not wrap anywhere in the loop, so then we can apply the
4400 // flags to the SCEV.
4402 // We check isLoopInvariant to disambiguate in case we are adding two
4403 // recurrences from different loops, so that we know which loop to prove
4404 // that V is executed in.
4405 for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
4406 const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
4407 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4408 const int OtherOpIndex = 1 - OpIndex;
4409 const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
4410 if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
4411 isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
4415 return SCEV::FlagAnyWrap;
4418 /// createSCEV - We know that there is no SCEV for the specified value. Analyze
4421 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4422 if (!isSCEVable(V->getType()))
4423 return getUnknown(V);
4425 unsigned Opcode = Instruction::UserOp1;
4426 if (Instruction *I = dyn_cast<Instruction>(V)) {
4427 Opcode = I->getOpcode();
4429 // Don't attempt to analyze instructions in blocks that aren't
4430 // reachable. Such instructions don't matter, and they aren't required
4431 // to obey basic rules for definitions dominating uses which this
4432 // analysis depends on.
4433 if (!DT.isReachableFromEntry(I->getParent()))
4434 return getUnknown(V);
4435 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4436 Opcode = CE->getOpcode();
4437 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4438 return getConstant(CI);
4439 else if (isa<ConstantPointerNull>(V))
4440 return getZero(V->getType());
4441 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4442 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4444 return getUnknown(V);
4446 Operator *U = cast<Operator>(V);
4448 case Instruction::Add: {
4449 // The simple thing to do would be to just call getSCEV on both operands
4450 // and call getAddExpr with the result. However if we're looking at a
4451 // bunch of things all added together, this can be quite inefficient,
4452 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4453 // Instead, gather up all the operands and make a single getAddExpr call.
4454 // LLVM IR canonical form means we need only traverse the left operands.
4455 SmallVector<const SCEV *, 4> AddOps;
4456 for (Value *Op = U;; Op = U->getOperand(0)) {
4457 U = dyn_cast<Operator>(Op);
4458 unsigned Opcode = U ? U->getOpcode() : 0;
4459 if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
4460 assert(Op != V && "V should be an add");
4461 AddOps.push_back(getSCEV(Op));
4465 if (auto *OpSCEV = getExistingSCEV(U)) {
4466 AddOps.push_back(OpSCEV);
4470 // If a NUW or NSW flag can be applied to the SCEV for this
4471 // addition, then compute the SCEV for this addition by itself
4472 // with a separate call to getAddExpr. We need to do that
4473 // instead of pushing the operands of the addition onto AddOps,
4474 // since the flags are only known to apply to this particular
4475 // addition - they may not apply to other additions that can be
4476 // formed with operands from AddOps.
4477 const SCEV *RHS = getSCEV(U->getOperand(1));
4478 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4479 if (Flags != SCEV::FlagAnyWrap) {
4480 const SCEV *LHS = getSCEV(U->getOperand(0));
4481 if (Opcode == Instruction::Sub)
4482 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4484 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4488 if (Opcode == Instruction::Sub)
4489 AddOps.push_back(getNegativeSCEV(RHS));
4491 AddOps.push_back(RHS);
4493 return getAddExpr(AddOps);
4496 case Instruction::Mul: {
4497 SmallVector<const SCEV *, 4> MulOps;
4498 for (Value *Op = U;; Op = U->getOperand(0)) {
4499 U = dyn_cast<Operator>(Op);
4500 if (!U || U->getOpcode() != Instruction::Mul) {
4501 assert(Op != V && "V should be a mul");
4502 MulOps.push_back(getSCEV(Op));
4506 if (auto *OpSCEV = getExistingSCEV(U)) {
4507 MulOps.push_back(OpSCEV);
4511 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4512 if (Flags != SCEV::FlagAnyWrap) {
4513 MulOps.push_back(getMulExpr(getSCEV(U->getOperand(0)),
4514 getSCEV(U->getOperand(1)), Flags));
4518 MulOps.push_back(getSCEV(U->getOperand(1)));
4520 return getMulExpr(MulOps);
4522 case Instruction::UDiv:
4523 return getUDivExpr(getSCEV(U->getOperand(0)),
4524 getSCEV(U->getOperand(1)));
4525 case Instruction::Sub:
4526 return getMinusSCEV(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)),
4527 getNoWrapFlagsFromUB(U));
4528 case Instruction::And:
4529 // For an expression like x&255 that merely masks off the high bits,
4530 // use zext(trunc(x)) as the SCEV expression.
4531 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4532 if (CI->isNullValue())
4533 return getSCEV(U->getOperand(1));
4534 if (CI->isAllOnesValue())
4535 return getSCEV(U->getOperand(0));
4536 const APInt &A = CI->getValue();
4538 // Instcombine's ShrinkDemandedConstant may strip bits out of
4539 // constants, obscuring what would otherwise be a low-bits mask.
4540 // Use computeKnownBits to compute what ShrinkDemandedConstant
4541 // knew about to reconstruct a low-bits mask value.
4542 unsigned LZ = A.countLeadingZeros();
4543 unsigned TZ = A.countTrailingZeros();
4544 unsigned BitWidth = A.getBitWidth();
4545 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4546 computeKnownBits(U->getOperand(0), KnownZero, KnownOne,
4547 F.getParent()->getDataLayout(), 0, &AC, nullptr, &DT);
4549 APInt EffectiveMask =
4550 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4551 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4552 const SCEV *MulCount = getConstant(
4553 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4557 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4558 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4565 case Instruction::Or:
4566 // If the RHS of the Or is a constant, we may have something like:
4567 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4568 // optimizations will transparently handle this case.
4570 // In order for this transformation to be safe, the LHS must be of the
4571 // form X*(2^n) and the Or constant must be less than 2^n.
4572 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4573 const SCEV *LHS = getSCEV(U->getOperand(0));
4574 const APInt &CIVal = CI->getValue();
4575 if (GetMinTrailingZeros(LHS) >=
4576 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4577 // Build a plain add SCEV.
4578 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4579 // If the LHS of the add was an addrec and it has no-wrap flags,
4580 // transfer the no-wrap flags, since an or won't introduce a wrap.
4581 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4582 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4583 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4584 OldAR->getNoWrapFlags());
4590 case Instruction::Xor:
4591 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4592 // If the RHS of the xor is a signbit, then this is just an add.
4593 // Instcombine turns add of signbit into xor as a strength reduction step.
4594 if (CI->getValue().isSignBit())
4595 return getAddExpr(getSCEV(U->getOperand(0)),
4596 getSCEV(U->getOperand(1)));
4598 // If the RHS of xor is -1, then this is a not operation.
4599 if (CI->isAllOnesValue())
4600 return getNotSCEV(getSCEV(U->getOperand(0)));
4602 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4603 // This is a variant of the check for xor with -1, and it handles
4604 // the case where instcombine has trimmed non-demanded bits out
4605 // of an xor with -1.
4606 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4607 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4608 if (BO->getOpcode() == Instruction::And &&
4609 LCI->getValue() == CI->getValue())
4610 if (const SCEVZeroExtendExpr *Z =
4611 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4612 Type *UTy = U->getType();
4613 const SCEV *Z0 = Z->getOperand();
4614 Type *Z0Ty = Z0->getType();
4615 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4617 // If C is a low-bits mask, the zero extend is serving to
4618 // mask off the high bits. Complement the operand and
4619 // re-apply the zext.
4620 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4621 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4623 // If C is a single bit, it may be in the sign-bit position
4624 // before the zero-extend. In this case, represent the xor
4625 // using an add, which is equivalent, and re-apply the zext.
4626 APInt Trunc = CI->getValue().trunc(Z0TySize);
4627 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4629 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4635 case Instruction::Shl:
4636 // Turn shift left of a constant amount into a multiply.
4637 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4638 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4640 // If the shift count is not less than the bitwidth, the result of
4641 // the shift is undefined. Don't try to analyze it, because the
4642 // resolution chosen here may differ from the resolution chosen in
4643 // other parts of the compiler.
4644 if (SA->getValue().uge(BitWidth))
4647 // It is currently not resolved how to interpret NSW for left
4648 // shift by BitWidth - 1, so we avoid applying flags in that
4649 // case. Remove this check (or this comment) once the situation
4651 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
4652 // and http://reviews.llvm.org/D8890 .
4653 auto Flags = SCEV::FlagAnyWrap;
4654 if (SA->getValue().ult(BitWidth - 1)) Flags = getNoWrapFlagsFromUB(U);
4656 Constant *X = ConstantInt::get(getContext(),
4657 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4658 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X), Flags);
4662 case Instruction::LShr:
4663 // Turn logical shift right of a constant into a unsigned divide.
4664 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4665 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4667 // If the shift count is not less than the bitwidth, the result of
4668 // the shift is undefined. Don't try to analyze it, because the
4669 // resolution chosen here may differ from the resolution chosen in
4670 // other parts of the compiler.
4671 if (SA->getValue().uge(BitWidth))
4674 Constant *X = ConstantInt::get(getContext(),
4675 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4676 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4680 case Instruction::AShr:
4681 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4682 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4683 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4684 if (L->getOpcode() == Instruction::Shl &&
4685 L->getOperand(1) == U->getOperand(1)) {
4686 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4688 // If the shift count is not less than the bitwidth, the result of
4689 // the shift is undefined. Don't try to analyze it, because the
4690 // resolution chosen here may differ from the resolution chosen in
4691 // other parts of the compiler.
4692 if (CI->getValue().uge(BitWidth))
4695 uint64_t Amt = BitWidth - CI->getZExtValue();
4696 if (Amt == BitWidth)
4697 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4699 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4700 IntegerType::get(getContext(),
4706 case Instruction::Trunc:
4707 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4709 case Instruction::ZExt:
4710 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4712 case Instruction::SExt:
4713 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4715 case Instruction::BitCast:
4716 // BitCasts are no-op casts so we just eliminate the cast.
4717 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4718 return getSCEV(U->getOperand(0));
4721 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4722 // lead to pointer expressions which cannot safely be expanded to GEPs,
4723 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4724 // simplifying integer expressions.
4726 case Instruction::GetElementPtr:
4727 return createNodeForGEP(cast<GEPOperator>(U));
4729 case Instruction::PHI:
4730 return createNodeForPHI(cast<PHINode>(U));
4732 case Instruction::Select:
4733 // U can also be a select constant expr, which let fall through. Since
4734 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
4735 // constant expressions cannot have instructions as operands, we'd have
4736 // returned getUnknown for a select constant expressions anyway.
4737 if (isa<Instruction>(U))
4738 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
4739 U->getOperand(1), U->getOperand(2));
4741 default: // We cannot analyze this expression.
4745 return getUnknown(V);
4750 //===----------------------------------------------------------------------===//
4751 // Iteration Count Computation Code
4754 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4755 if (BasicBlock *ExitingBB = L->getExitingBlock())
4756 return getSmallConstantTripCount(L, ExitingBB);
4758 // No trip count information for multiple exits.
4762 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4763 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4764 /// constant. Will also return 0 if the maximum trip count is very large (>=
4767 /// This "trip count" assumes that control exits via ExitingBlock. More
4768 /// precisely, it is the number of times that control may reach ExitingBlock
4769 /// before taking the branch. For loops with multiple exits, it may not be the
4770 /// number times that the loop header executes because the loop may exit
4771 /// prematurely via another branch.
4772 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4773 BasicBlock *ExitingBlock) {
4774 assert(ExitingBlock && "Must pass a non-null exiting block!");
4775 assert(L->isLoopExiting(ExitingBlock) &&
4776 "Exiting block must actually branch out of the loop!");
4777 const SCEVConstant *ExitCount =
4778 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4782 ConstantInt *ExitConst = ExitCount->getValue();
4784 // Guard against huge trip counts.
4785 if (ExitConst->getValue().getActiveBits() > 32)
4788 // In case of integer overflow, this returns 0, which is correct.
4789 return ((unsigned)ExitConst->getZExtValue()) + 1;
4792 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4793 if (BasicBlock *ExitingBB = L->getExitingBlock())
4794 return getSmallConstantTripMultiple(L, ExitingBB);
4796 // No trip multiple information for multiple exits.
4800 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4801 /// trip count of this loop as a normal unsigned value, if possible. This
4802 /// means that the actual trip count is always a multiple of the returned
4803 /// value (don't forget the trip count could very well be zero as well!).
4805 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4806 /// multiple of a constant (which is also the case if the trip count is simply
4807 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4808 /// if the trip count is very large (>= 2^32).
4810 /// As explained in the comments for getSmallConstantTripCount, this assumes
4811 /// that control exits the loop via ExitingBlock.
4813 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4814 BasicBlock *ExitingBlock) {
4815 assert(ExitingBlock && "Must pass a non-null exiting block!");
4816 assert(L->isLoopExiting(ExitingBlock) &&
4817 "Exiting block must actually branch out of the loop!");
4818 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4819 if (ExitCount == getCouldNotCompute())
4822 // Get the trip count from the BE count by adding 1.
4823 const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
4824 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4825 // to factor simple cases.
4826 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4827 TCMul = Mul->getOperand(0);
4829 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4833 ConstantInt *Result = MulC->getValue();
4835 // Guard against huge trip counts (this requires checking
4836 // for zero to handle the case where the trip count == -1 and the
4838 if (!Result || Result->getValue().getActiveBits() > 32 ||
4839 Result->getValue().getActiveBits() == 0)
4842 return (unsigned)Result->getZExtValue();
4845 // getExitCount - Get the expression for the number of loop iterations for which
4846 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4847 // SCEVCouldNotCompute.
4848 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4849 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4852 /// getBackedgeTakenCount - If the specified loop has a predictable
4853 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4854 /// object. The backedge-taken count is the number of times the loop header
4855 /// will be branched to from within the loop. This is one less than the
4856 /// trip count of the loop, since it doesn't count the first iteration,
4857 /// when the header is branched to from outside the loop.
4859 /// Note that it is not valid to call this method on a loop without a
4860 /// loop-invariant backedge-taken count (see
4861 /// hasLoopInvariantBackedgeTakenCount).
4863 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4864 return getBackedgeTakenInfo(L).getExact(this);
4867 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4868 /// return the least SCEV value that is known never to be less than the
4869 /// actual backedge taken count.
4870 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4871 return getBackedgeTakenInfo(L).getMax(this);
4874 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4875 /// onto the given Worklist.
4877 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4878 BasicBlock *Header = L->getHeader();
4880 // Push all Loop-header PHIs onto the Worklist stack.
4881 for (BasicBlock::iterator I = Header->begin();
4882 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4883 Worklist.push_back(PN);
4886 const ScalarEvolution::BackedgeTakenInfo &
4887 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4888 // Initially insert an invalid entry for this loop. If the insertion
4889 // succeeds, proceed to actually compute a backedge-taken count and
4890 // update the value. The temporary CouldNotCompute value tells SCEV
4891 // code elsewhere that it shouldn't attempt to request a new
4892 // backedge-taken count, which could result in infinite recursion.
4893 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4894 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4896 return Pair.first->second;
4898 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
4899 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4900 // must be cleared in this scope.
4901 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
4903 if (Result.getExact(this) != getCouldNotCompute()) {
4904 assert(isLoopInvariant(Result.getExact(this), L) &&
4905 isLoopInvariant(Result.getMax(this), L) &&
4906 "Computed backedge-taken count isn't loop invariant for loop!");
4907 ++NumTripCountsComputed;
4909 else if (Result.getMax(this) == getCouldNotCompute() &&
4910 isa<PHINode>(L->getHeader()->begin())) {
4911 // Only count loops that have phi nodes as not being computable.
4912 ++NumTripCountsNotComputed;
4915 // Now that we know more about the trip count for this loop, forget any
4916 // existing SCEV values for PHI nodes in this loop since they are only
4917 // conservative estimates made without the benefit of trip count
4918 // information. This is similar to the code in forgetLoop, except that
4919 // it handles SCEVUnknown PHI nodes specially.
4920 if (Result.hasAnyInfo()) {
4921 SmallVector<Instruction *, 16> Worklist;
4922 PushLoopPHIs(L, Worklist);
4924 SmallPtrSet<Instruction *, 8> Visited;
4925 while (!Worklist.empty()) {
4926 Instruction *I = Worklist.pop_back_val();
4927 if (!Visited.insert(I).second)
4930 ValueExprMapType::iterator It =
4931 ValueExprMap.find_as(static_cast<Value *>(I));
4932 if (It != ValueExprMap.end()) {
4933 const SCEV *Old = It->second;
4935 // SCEVUnknown for a PHI either means that it has an unrecognized
4936 // structure, or it's a PHI that's in the progress of being computed
4937 // by createNodeForPHI. In the former case, additional loop trip
4938 // count information isn't going to change anything. In the later
4939 // case, createNodeForPHI will perform the necessary updates on its
4940 // own when it gets to that point.
4941 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4942 forgetMemoizedResults(Old);
4943 ValueExprMap.erase(It);
4945 if (PHINode *PN = dyn_cast<PHINode>(I))
4946 ConstantEvolutionLoopExitValue.erase(PN);
4949 PushDefUseChildren(I, Worklist);
4953 // Re-lookup the insert position, since the call to
4954 // computeBackedgeTakenCount above could result in a
4955 // recusive call to getBackedgeTakenInfo (on a different
4956 // loop), which would invalidate the iterator computed
4958 return BackedgeTakenCounts.find(L)->second = Result;
4961 /// forgetLoop - This method should be called by the client when it has
4962 /// changed a loop in a way that may effect ScalarEvolution's ability to
4963 /// compute a trip count, or if the loop is deleted.
4964 void ScalarEvolution::forgetLoop(const Loop *L) {
4965 // Drop any stored trip count value.
4966 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4967 BackedgeTakenCounts.find(L);
4968 if (BTCPos != BackedgeTakenCounts.end()) {
4969 BTCPos->second.clear();
4970 BackedgeTakenCounts.erase(BTCPos);
4973 // Drop information about expressions based on loop-header PHIs.
4974 SmallVector<Instruction *, 16> Worklist;
4975 PushLoopPHIs(L, Worklist);
4977 SmallPtrSet<Instruction *, 8> Visited;
4978 while (!Worklist.empty()) {
4979 Instruction *I = Worklist.pop_back_val();
4980 if (!Visited.insert(I).second)
4983 ValueExprMapType::iterator It =
4984 ValueExprMap.find_as(static_cast<Value *>(I));
4985 if (It != ValueExprMap.end()) {
4986 forgetMemoizedResults(It->second);
4987 ValueExprMap.erase(It);
4988 if (PHINode *PN = dyn_cast<PHINode>(I))
4989 ConstantEvolutionLoopExitValue.erase(PN);
4992 PushDefUseChildren(I, Worklist);
4995 // Forget all contained loops too, to avoid dangling entries in the
4996 // ValuesAtScopes map.
4997 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5001 /// forgetValue - This method should be called by the client when it has
5002 /// changed a value in a way that may effect its value, or which may
5003 /// disconnect it from a def-use chain linking it to a loop.
5004 void ScalarEvolution::forgetValue(Value *V) {
5005 Instruction *I = dyn_cast<Instruction>(V);
5008 // Drop information about expressions based on loop-header PHIs.
5009 SmallVector<Instruction *, 16> Worklist;
5010 Worklist.push_back(I);
5012 SmallPtrSet<Instruction *, 8> Visited;
5013 while (!Worklist.empty()) {
5014 I = Worklist.pop_back_val();
5015 if (!Visited.insert(I).second)
5018 ValueExprMapType::iterator It =
5019 ValueExprMap.find_as(static_cast<Value *>(I));
5020 if (It != ValueExprMap.end()) {
5021 forgetMemoizedResults(It->second);
5022 ValueExprMap.erase(It);
5023 if (PHINode *PN = dyn_cast<PHINode>(I))
5024 ConstantEvolutionLoopExitValue.erase(PN);
5027 PushDefUseChildren(I, Worklist);
5031 /// getExact - Get the exact loop backedge taken count considering all loop
5032 /// exits. A computable result can only be returned for loops with a single
5033 /// exit. Returning the minimum taken count among all exits is incorrect
5034 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
5035 /// assumes that the limit of each loop test is never skipped. This is a valid
5036 /// assumption as long as the loop exits via that test. For precise results, it
5037 /// is the caller's responsibility to specify the relevant loop exit using
5038 /// getExact(ExitingBlock, SE).
5040 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
5041 // If any exits were not computable, the loop is not computable.
5042 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
5044 // We need exactly one computable exit.
5045 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
5046 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
5048 const SCEV *BECount = nullptr;
5049 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5050 ENT != nullptr; ENT = ENT->getNextExit()) {
5052 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5055 BECount = ENT->ExactNotTaken;
5056 else if (BECount != ENT->ExactNotTaken)
5057 return SE->getCouldNotCompute();
5059 assert(BECount && "Invalid not taken count for loop exit");
5063 /// getExact - Get the exact not taken count for this loop exit.
5065 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5066 ScalarEvolution *SE) const {
5067 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5068 ENT != nullptr; ENT = ENT->getNextExit()) {
5070 if (ENT->ExitingBlock == ExitingBlock)
5071 return ENT->ExactNotTaken;
5073 return SE->getCouldNotCompute();
5076 /// getMax - Get the max backedge taken count for the loop.
5078 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5079 return Max ? Max : SE->getCouldNotCompute();
5082 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5083 ScalarEvolution *SE) const {
5084 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
5087 if (!ExitNotTaken.ExitingBlock)
5090 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5091 ENT != nullptr; ENT = ENT->getNextExit()) {
5093 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
5094 && SE->hasOperand(ENT->ExactNotTaken, S)) {
5101 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5102 /// computable exit into a persistent ExitNotTakenInfo array.
5103 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5104 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
5105 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
5108 ExitNotTaken.setIncomplete();
5110 unsigned NumExits = ExitCounts.size();
5111 if (NumExits == 0) return;
5113 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
5114 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
5115 if (NumExits == 1) return;
5117 // Handle the rare case of multiple computable exits.
5118 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
5120 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
5121 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
5122 PrevENT->setNextExit(ENT);
5123 ENT->ExitingBlock = ExitCounts[i].first;
5124 ENT->ExactNotTaken = ExitCounts[i].second;
5128 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
5129 void ScalarEvolution::BackedgeTakenInfo::clear() {
5130 ExitNotTaken.ExitingBlock = nullptr;
5131 ExitNotTaken.ExactNotTaken = nullptr;
5132 delete[] ExitNotTaken.getNextExit();
5135 /// computeBackedgeTakenCount - Compute the number of times the backedge
5136 /// of the specified loop will execute.
5137 ScalarEvolution::BackedgeTakenInfo
5138 ScalarEvolution::computeBackedgeTakenCount(const Loop *L) {
5139 SmallVector<BasicBlock *, 8> ExitingBlocks;
5140 L->getExitingBlocks(ExitingBlocks);
5142 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
5143 bool CouldComputeBECount = true;
5144 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5145 const SCEV *MustExitMaxBECount = nullptr;
5146 const SCEV *MayExitMaxBECount = nullptr;
5148 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5149 // and compute maxBECount.
5150 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5151 BasicBlock *ExitBB = ExitingBlocks[i];
5152 ExitLimit EL = computeExitLimit(L, ExitBB);
5154 // 1. For each exit that can be computed, add an entry to ExitCounts.
5155 // CouldComputeBECount is true only if all exits can be computed.
5156 if (EL.Exact == getCouldNotCompute())
5157 // We couldn't compute an exact value for this exit, so
5158 // we won't be able to compute an exact value for the loop.
5159 CouldComputeBECount = false;
5161 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
5163 // 2. Derive the loop's MaxBECount from each exit's max number of
5164 // non-exiting iterations. Partition the loop exits into two kinds:
5165 // LoopMustExits and LoopMayExits.
5167 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5168 // is a LoopMayExit. If any computable LoopMustExit is found, then
5169 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
5170 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
5171 // considered greater than any computable EL.Max.
5172 if (EL.Max != getCouldNotCompute() && Latch &&
5173 DT.dominates(ExitBB, Latch)) {
5174 if (!MustExitMaxBECount)
5175 MustExitMaxBECount = EL.Max;
5177 MustExitMaxBECount =
5178 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5180 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5181 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5182 MayExitMaxBECount = EL.Max;
5185 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5189 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5190 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5191 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5194 ScalarEvolution::ExitLimit
5195 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
5197 // Okay, we've chosen an exiting block. See what condition causes us to exit
5198 // at this block and remember the exit block and whether all other targets
5199 // lead to the loop header.
5200 bool MustExecuteLoopHeader = true;
5201 BasicBlock *Exit = nullptr;
5202 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5204 if (!L->contains(*SI)) {
5205 if (Exit) // Multiple exit successors.
5206 return getCouldNotCompute();
5208 } else if (*SI != L->getHeader()) {
5209 MustExecuteLoopHeader = false;
5212 // At this point, we know we have a conditional branch that determines whether
5213 // the loop is exited. However, we don't know if the branch is executed each
5214 // time through the loop. If not, then the execution count of the branch will
5215 // not be equal to the trip count of the loop.
5217 // Currently we check for this by checking to see if the Exit branch goes to
5218 // the loop header. If so, we know it will always execute the same number of
5219 // times as the loop. We also handle the case where the exit block *is* the
5220 // loop header. This is common for un-rotated loops.
5222 // If both of those tests fail, walk up the unique predecessor chain to the
5223 // header, stopping if there is an edge that doesn't exit the loop. If the
5224 // header is reached, the execution count of the branch will be equal to the
5225 // trip count of the loop.
5227 // More extensive analysis could be done to handle more cases here.
5229 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5230 // The simple checks failed, try climbing the unique predecessor chain
5231 // up to the header.
5233 for (BasicBlock *BB = ExitingBlock; BB; ) {
5234 BasicBlock *Pred = BB->getUniquePredecessor();
5236 return getCouldNotCompute();
5237 TerminatorInst *PredTerm = Pred->getTerminator();
5238 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5241 // If the predecessor has a successor that isn't BB and isn't
5242 // outside the loop, assume the worst.
5243 if (L->contains(PredSucc))
5244 return getCouldNotCompute();
5246 if (Pred == L->getHeader()) {
5253 return getCouldNotCompute();
5256 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5257 TerminatorInst *Term = ExitingBlock->getTerminator();
5258 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5259 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5260 // Proceed to the next level to examine the exit condition expression.
5261 return computeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5262 BI->getSuccessor(1),
5263 /*ControlsExit=*/IsOnlyExit);
5266 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5267 return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
5268 /*ControlsExit=*/IsOnlyExit);
5270 return getCouldNotCompute();
5273 /// computeExitLimitFromCond - Compute the number of times the
5274 /// backedge of the specified loop will execute if its exit condition
5275 /// were a conditional branch of ExitCond, TBB, and FBB.
5277 /// @param ControlsExit is true if ExitCond directly controls the exit
5278 /// branch. In this case, we can assume that the loop exits only if the
5279 /// condition is true and can infer that failing to meet the condition prior to
5280 /// integer wraparound results in undefined behavior.
5281 ScalarEvolution::ExitLimit
5282 ScalarEvolution::computeExitLimitFromCond(const Loop *L,
5286 bool ControlsExit) {
5287 // Check if the controlling expression for this loop is an And or Or.
5288 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5289 if (BO->getOpcode() == Instruction::And) {
5290 // Recurse on the operands of the and.
5291 bool EitherMayExit = L->contains(TBB);
5292 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5293 ControlsExit && !EitherMayExit);
5294 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5295 ControlsExit && !EitherMayExit);
5296 const SCEV *BECount = getCouldNotCompute();
5297 const SCEV *MaxBECount = getCouldNotCompute();
5298 if (EitherMayExit) {
5299 // Both conditions must be true for the loop to continue executing.
5300 // Choose the less conservative count.
5301 if (EL0.Exact == getCouldNotCompute() ||
5302 EL1.Exact == getCouldNotCompute())
5303 BECount = getCouldNotCompute();
5305 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5306 if (EL0.Max == getCouldNotCompute())
5307 MaxBECount = EL1.Max;
5308 else if (EL1.Max == getCouldNotCompute())
5309 MaxBECount = EL0.Max;
5311 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5313 // Both conditions must be true at the same time for the loop to exit.
5314 // For now, be conservative.
5315 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5316 if (EL0.Max == EL1.Max)
5317 MaxBECount = EL0.Max;
5318 if (EL0.Exact == EL1.Exact)
5319 BECount = EL0.Exact;
5322 return ExitLimit(BECount, MaxBECount);
5324 if (BO->getOpcode() == Instruction::Or) {
5325 // Recurse on the operands of the or.
5326 bool EitherMayExit = L->contains(FBB);
5327 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5328 ControlsExit && !EitherMayExit);
5329 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5330 ControlsExit && !EitherMayExit);
5331 const SCEV *BECount = getCouldNotCompute();
5332 const SCEV *MaxBECount = getCouldNotCompute();
5333 if (EitherMayExit) {
5334 // Both conditions must be false for the loop to continue executing.
5335 // Choose the less conservative count.
5336 if (EL0.Exact == getCouldNotCompute() ||
5337 EL1.Exact == getCouldNotCompute())
5338 BECount = getCouldNotCompute();
5340 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5341 if (EL0.Max == getCouldNotCompute())
5342 MaxBECount = EL1.Max;
5343 else if (EL1.Max == getCouldNotCompute())
5344 MaxBECount = EL0.Max;
5346 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5348 // Both conditions must be false at the same time for the loop to exit.
5349 // For now, be conservative.
5350 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5351 if (EL0.Max == EL1.Max)
5352 MaxBECount = EL0.Max;
5353 if (EL0.Exact == EL1.Exact)
5354 BECount = EL0.Exact;
5357 return ExitLimit(BECount, MaxBECount);
5361 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5362 // Proceed to the next level to examine the icmp.
5363 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5364 return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5366 // Check for a constant condition. These are normally stripped out by
5367 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5368 // preserve the CFG and is temporarily leaving constant conditions
5370 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5371 if (L->contains(FBB) == !CI->getZExtValue())
5372 // The backedge is always taken.
5373 return getCouldNotCompute();
5375 // The backedge is never taken.
5376 return getZero(CI->getType());
5379 // If it's not an integer or pointer comparison then compute it the hard way.
5380 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5383 ScalarEvolution::ExitLimit
5384 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
5388 bool ControlsExit) {
5390 // If the condition was exit on true, convert the condition to exit on false
5391 ICmpInst::Predicate Cond;
5392 if (!L->contains(FBB))
5393 Cond = ExitCond->getPredicate();
5395 Cond = ExitCond->getInversePredicate();
5397 // Handle common loops like: for (X = "string"; *X; ++X)
5398 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5399 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5401 computeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5402 if (ItCnt.hasAnyInfo())
5406 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5407 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5409 // Try to evaluate any dependencies out of the loop.
5410 LHS = getSCEVAtScope(LHS, L);
5411 RHS = getSCEVAtScope(RHS, L);
5413 // At this point, we would like to compute how many iterations of the
5414 // loop the predicate will return true for these inputs.
5415 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5416 // If there is a loop-invariant, force it into the RHS.
5417 std::swap(LHS, RHS);
5418 Cond = ICmpInst::getSwappedPredicate(Cond);
5421 // Simplify the operands before analyzing them.
5422 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5424 // If we have a comparison of a chrec against a constant, try to use value
5425 // ranges to answer this query.
5426 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5427 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5428 if (AddRec->getLoop() == L) {
5429 // Form the constant range.
5430 ConstantRange CompRange(
5431 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5433 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5434 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5438 case ICmpInst::ICMP_NE: { // while (X != Y)
5439 // Convert to: while (X-Y != 0)
5440 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5441 if (EL.hasAnyInfo()) return EL;
5444 case ICmpInst::ICMP_EQ: { // while (X == Y)
5445 // Convert to: while (X-Y == 0)
5446 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5447 if (EL.hasAnyInfo()) return EL;
5450 case ICmpInst::ICMP_SLT:
5451 case ICmpInst::ICMP_ULT: { // while (X < Y)
5452 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5453 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5454 if (EL.hasAnyInfo()) return EL;
5457 case ICmpInst::ICMP_SGT:
5458 case ICmpInst::ICMP_UGT: { // while (X > Y)
5459 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5460 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5461 if (EL.hasAnyInfo()) return EL;
5466 dbgs() << "computeBackedgeTakenCount ";
5467 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5468 dbgs() << "[unsigned] ";
5469 dbgs() << *LHS << " "
5470 << Instruction::getOpcodeName(Instruction::ICmp)
5471 << " " << *RHS << "\n";
5475 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5478 ScalarEvolution::ExitLimit
5479 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
5481 BasicBlock *ExitingBlock,
5482 bool ControlsExit) {
5483 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5485 // Give up if the exit is the default dest of a switch.
5486 if (Switch->getDefaultDest() == ExitingBlock)
5487 return getCouldNotCompute();
5489 assert(L->contains(Switch->getDefaultDest()) &&
5490 "Default case must not exit the loop!");
5491 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5492 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5494 // while (X != Y) --> while (X-Y != 0)
5495 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5496 if (EL.hasAnyInfo())
5499 return getCouldNotCompute();
5502 static ConstantInt *
5503 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5504 ScalarEvolution &SE) {
5505 const SCEV *InVal = SE.getConstant(C);
5506 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5507 assert(isa<SCEVConstant>(Val) &&
5508 "Evaluation of SCEV at constant didn't fold correctly?");
5509 return cast<SCEVConstant>(Val)->getValue();
5512 /// computeLoadConstantCompareExitLimit - Given an exit condition of
5513 /// 'icmp op load X, cst', try to see if we can compute the backedge
5514 /// execution count.
5515 ScalarEvolution::ExitLimit
5516 ScalarEvolution::computeLoadConstantCompareExitLimit(
5520 ICmpInst::Predicate predicate) {
5522 if (LI->isVolatile()) return getCouldNotCompute();
5524 // Check to see if the loaded pointer is a getelementptr of a global.
5525 // TODO: Use SCEV instead of manually grubbing with GEPs.
5526 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5527 if (!GEP) return getCouldNotCompute();
5529 // Make sure that it is really a constant global we are gepping, with an
5530 // initializer, and make sure the first IDX is really 0.
5531 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5532 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5533 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5534 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5535 return getCouldNotCompute();
5537 // Okay, we allow one non-constant index into the GEP instruction.
5538 Value *VarIdx = nullptr;
5539 std::vector<Constant*> Indexes;
5540 unsigned VarIdxNum = 0;
5541 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5542 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5543 Indexes.push_back(CI);
5544 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5545 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5546 VarIdx = GEP->getOperand(i);
5548 Indexes.push_back(nullptr);
5551 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5553 return getCouldNotCompute();
5555 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5556 // Check to see if X is a loop variant variable value now.
5557 const SCEV *Idx = getSCEV(VarIdx);
5558 Idx = getSCEVAtScope(Idx, L);
5560 // We can only recognize very limited forms of loop index expressions, in
5561 // particular, only affine AddRec's like {C1,+,C2}.
5562 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5563 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5564 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5565 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5566 return getCouldNotCompute();
5568 unsigned MaxSteps = MaxBruteForceIterations;
5569 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5570 ConstantInt *ItCst = ConstantInt::get(
5571 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5572 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5574 // Form the GEP offset.
5575 Indexes[VarIdxNum] = Val;
5577 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5579 if (!Result) break; // Cannot compute!
5581 // Evaluate the condition for this iteration.
5582 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5583 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5584 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5586 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5587 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5590 ++NumArrayLenItCounts;
5591 return getConstant(ItCst); // Found terminating iteration!
5594 return getCouldNotCompute();
5598 /// CanConstantFold - Return true if we can constant fold an instruction of the
5599 /// specified type, assuming that all operands were constants.
5600 static bool CanConstantFold(const Instruction *I) {
5601 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5602 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5606 if (const CallInst *CI = dyn_cast<CallInst>(I))
5607 if (const Function *F = CI->getCalledFunction())
5608 return canConstantFoldCallTo(F);
5612 /// Determine whether this instruction can constant evolve within this loop
5613 /// assuming its operands can all constant evolve.
5614 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5615 // An instruction outside of the loop can't be derived from a loop PHI.
5616 if (!L->contains(I)) return false;
5618 if (isa<PHINode>(I)) {
5619 // We don't currently keep track of the control flow needed to evaluate
5620 // PHIs, so we cannot handle PHIs inside of loops.
5621 return L->getHeader() == I->getParent();
5624 // If we won't be able to constant fold this expression even if the operands
5625 // are constants, bail early.
5626 return CanConstantFold(I);
5629 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5630 /// recursing through each instruction operand until reaching a loop header phi.
5632 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5633 DenseMap<Instruction *, PHINode *> &PHIMap) {
5635 // Otherwise, we can evaluate this instruction if all of its operands are
5636 // constant or derived from a PHI node themselves.
5637 PHINode *PHI = nullptr;
5638 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5639 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5641 if (isa<Constant>(*OpI)) continue;
5643 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5644 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5646 PHINode *P = dyn_cast<PHINode>(OpInst);
5648 // If this operand is already visited, reuse the prior result.
5649 // We may have P != PHI if this is the deepest point at which the
5650 // inconsistent paths meet.
5651 P = PHIMap.lookup(OpInst);
5653 // Recurse and memoize the results, whether a phi is found or not.
5654 // This recursive call invalidates pointers into PHIMap.
5655 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5659 return nullptr; // Not evolving from PHI
5660 if (PHI && PHI != P)
5661 return nullptr; // Evolving from multiple different PHIs.
5664 // This is a expression evolving from a constant PHI!
5668 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5669 /// in the loop that V is derived from. We allow arbitrary operations along the
5670 /// way, but the operands of an operation must either be constants or a value
5671 /// derived from a constant PHI. If this expression does not fit with these
5672 /// constraints, return null.
5673 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5674 Instruction *I = dyn_cast<Instruction>(V);
5675 if (!I || !canConstantEvolve(I, L)) return nullptr;
5677 if (PHINode *PN = dyn_cast<PHINode>(I))
5680 // Record non-constant instructions contained by the loop.
5681 DenseMap<Instruction *, PHINode *> PHIMap;
5682 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5685 /// EvaluateExpression - Given an expression that passes the
5686 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5687 /// in the loop has the value PHIVal. If we can't fold this expression for some
5688 /// reason, return null.
5689 static Constant *EvaluateExpression(Value *V, const Loop *L,
5690 DenseMap<Instruction *, Constant *> &Vals,
5691 const DataLayout &DL,
5692 const TargetLibraryInfo *TLI) {
5693 // Convenient constant check, but redundant for recursive calls.
5694 if (Constant *C = dyn_cast<Constant>(V)) return C;
5695 Instruction *I = dyn_cast<Instruction>(V);
5696 if (!I) return nullptr;
5698 if (Constant *C = Vals.lookup(I)) return C;
5700 // An instruction inside the loop depends on a value outside the loop that we
5701 // weren't given a mapping for, or a value such as a call inside the loop.
5702 if (!canConstantEvolve(I, L)) return nullptr;
5704 // An unmapped PHI can be due to a branch or another loop inside this loop,
5705 // or due to this not being the initial iteration through a loop where we
5706 // couldn't compute the evolution of this particular PHI last time.
5707 if (isa<PHINode>(I)) return nullptr;
5709 std::vector<Constant*> Operands(I->getNumOperands());
5711 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5712 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5714 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5715 if (!Operands[i]) return nullptr;
5718 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5720 if (!C) return nullptr;
5724 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5725 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5726 Operands[1], DL, TLI);
5727 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5728 if (!LI->isVolatile())
5729 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5731 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5735 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5736 /// in the header of its containing loop, we know the loop executes a
5737 /// constant number of times, and the PHI node is just a recurrence
5738 /// involving constants, fold it.
5740 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5743 auto I = ConstantEvolutionLoopExitValue.find(PN);
5744 if (I != ConstantEvolutionLoopExitValue.end())
5747 if (BEs.ugt(MaxBruteForceIterations))
5748 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5750 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5752 DenseMap<Instruction *, Constant *> CurrentIterVals;
5753 BasicBlock *Header = L->getHeader();
5754 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5756 BasicBlock *Latch = L->getLoopLatch();
5760 // Since the loop has one latch, the PHI node must have two entries. One
5761 // entry must be a constant (coming in from outside of the loop), and the
5762 // second must be derived from the same PHI.
5764 BasicBlock *NonLatch = Latch == PN->getIncomingBlock(0)
5765 ? PN->getIncomingBlock(1)
5766 : PN->getIncomingBlock(0);
5768 assert(PN->getNumIncomingValues() == 2 && "Follows from having one latch!");
5770 // Note: not all PHI nodes in the same block have to have their incoming
5771 // values in the same order, so we use the basic block to look up the incoming
5772 // value, not an index.
5774 for (auto &I : *Header) {
5775 PHINode *PHI = dyn_cast<PHINode>(&I);
5778 dyn_cast<Constant>(PHI->getIncomingValueForBlock(NonLatch));
5779 if (!StartCST) continue;
5780 CurrentIterVals[PHI] = StartCST;
5782 if (!CurrentIterVals.count(PN))
5783 return RetVal = nullptr;
5785 Value *BEValue = PN->getIncomingValueForBlock(Latch);
5787 // Execute the loop symbolically to determine the exit value.
5788 if (BEs.getActiveBits() >= 32)
5789 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5791 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5792 unsigned IterationNum = 0;
5793 const DataLayout &DL = F.getParent()->getDataLayout();
5794 for (; ; ++IterationNum) {
5795 if (IterationNum == NumIterations)
5796 return RetVal = CurrentIterVals[PN]; // Got exit value!
5798 // Compute the value of the PHIs for the next iteration.
5799 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5800 DenseMap<Instruction *, Constant *> NextIterVals;
5802 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5804 return nullptr; // Couldn't evaluate!
5805 NextIterVals[PN] = NextPHI;
5807 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5809 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5810 // cease to be able to evaluate one of them or if they stop evolving,
5811 // because that doesn't necessarily prevent us from computing PN.
5812 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5813 for (const auto &I : CurrentIterVals) {
5814 PHINode *PHI = dyn_cast<PHINode>(I.first);
5815 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5816 PHIsToCompute.emplace_back(PHI, I.second);
5818 // We use two distinct loops because EvaluateExpression may invalidate any
5819 // iterators into CurrentIterVals.
5820 for (const auto &I : PHIsToCompute) {
5821 PHINode *PHI = I.first;
5822 Constant *&NextPHI = NextIterVals[PHI];
5823 if (!NextPHI) { // Not already computed.
5824 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
5825 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5827 if (NextPHI != I.second)
5828 StoppedEvolving = false;
5831 // If all entries in CurrentIterVals == NextIterVals then we can stop
5832 // iterating, the loop can't continue to change.
5833 if (StoppedEvolving)
5834 return RetVal = CurrentIterVals[PN];
5836 CurrentIterVals.swap(NextIterVals);
5840 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
5843 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5844 if (!PN) return getCouldNotCompute();
5846 // If the loop is canonicalized, the PHI will have exactly two entries.
5847 // That's the only form we support here.
5848 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5850 DenseMap<Instruction *, Constant *> CurrentIterVals;
5851 BasicBlock *Header = L->getHeader();
5852 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5854 BasicBlock *Latch = L->getLoopLatch();
5855 assert(Latch && "Should follow from NumIncomingValues == 2!");
5857 // NonLatch is the preheader, or something equivalent.
5858 BasicBlock *NonLatch = Latch == PN->getIncomingBlock(0)
5859 ? PN->getIncomingBlock(1)
5860 : PN->getIncomingBlock(0);
5862 // Note: not all PHI nodes in the same block have to have their incoming
5863 // values in the same order, so we use the basic block to look up the incoming
5864 // value, not an index.
5866 for (auto &I : *Header) {
5867 PHINode *PHI = dyn_cast<PHINode>(&I);
5871 dyn_cast<Constant>(PHI->getIncomingValueForBlock(NonLatch));
5872 if (!StartCST) continue;
5873 CurrentIterVals[PHI] = StartCST;
5875 if (!CurrentIterVals.count(PN))
5876 return getCouldNotCompute();
5878 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5879 // the loop symbolically to determine when the condition gets a value of
5881 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5882 const DataLayout &DL = F.getParent()->getDataLayout();
5883 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5884 auto *CondVal = dyn_cast_or_null<ConstantInt>(
5885 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
5887 // Couldn't symbolically evaluate.
5888 if (!CondVal) return getCouldNotCompute();
5890 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5891 ++NumBruteForceTripCountsComputed;
5892 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5895 // Update all the PHI nodes for the next iteration.
5896 DenseMap<Instruction *, Constant *> NextIterVals;
5898 // Create a list of which PHIs we need to compute. We want to do this before
5899 // calling EvaluateExpression on them because that may invalidate iterators
5900 // into CurrentIterVals.
5901 SmallVector<PHINode *, 8> PHIsToCompute;
5902 for (const auto &I : CurrentIterVals) {
5903 PHINode *PHI = dyn_cast<PHINode>(I.first);
5904 if (!PHI || PHI->getParent() != Header) continue;
5905 PHIsToCompute.push_back(PHI);
5907 for (PHINode *PHI : PHIsToCompute) {
5908 Constant *&NextPHI = NextIterVals[PHI];
5909 if (NextPHI) continue; // Already computed!
5911 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
5912 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5914 CurrentIterVals.swap(NextIterVals);
5917 // Too many iterations were needed to evaluate.
5918 return getCouldNotCompute();
5921 /// getSCEVAtScope - Return a SCEV expression for the specified value
5922 /// at the specified scope in the program. The L value specifies a loop
5923 /// nest to evaluate the expression at, where null is the top-level or a
5924 /// specified loop is immediately inside of the loop.
5926 /// This method can be used to compute the exit value for a variable defined
5927 /// in a loop by querying what the value will hold in the parent loop.
5929 /// In the case that a relevant loop exit value cannot be computed, the
5930 /// original value V is returned.
5931 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5932 // Check to see if we've folded this expression at this loop before.
5933 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5934 for (unsigned u = 0; u < Values.size(); u++) {
5935 if (Values[u].first == L)
5936 return Values[u].second ? Values[u].second : V;
5938 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5939 // Otherwise compute it.
5940 const SCEV *C = computeSCEVAtScope(V, L);
5941 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5942 for (unsigned u = Values2.size(); u > 0; u--) {
5943 if (Values2[u - 1].first == L) {
5944 Values2[u - 1].second = C;
5951 /// This builds up a Constant using the ConstantExpr interface. That way, we
5952 /// will return Constants for objects which aren't represented by a
5953 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5954 /// Returns NULL if the SCEV isn't representable as a Constant.
5955 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5956 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5957 case scCouldNotCompute:
5961 return cast<SCEVConstant>(V)->getValue();
5963 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5964 case scSignExtend: {
5965 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5966 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5967 return ConstantExpr::getSExt(CastOp, SS->getType());
5970 case scZeroExtend: {
5971 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5972 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5973 return ConstantExpr::getZExt(CastOp, SZ->getType());
5977 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5978 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5979 return ConstantExpr::getTrunc(CastOp, ST->getType());
5983 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5984 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5985 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5986 unsigned AS = PTy->getAddressSpace();
5987 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5988 C = ConstantExpr::getBitCast(C, DestPtrTy);
5990 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5991 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5992 if (!C2) return nullptr;
5995 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5996 unsigned AS = C2->getType()->getPointerAddressSpace();
5998 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5999 // The offsets have been converted to bytes. We can add bytes to an
6000 // i8* by GEP with the byte count in the first index.
6001 C = ConstantExpr::getBitCast(C, DestPtrTy);
6004 // Don't bother trying to sum two pointers. We probably can't
6005 // statically compute a load that results from it anyway.
6006 if (C2->getType()->isPointerTy())
6009 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6010 if (PTy->getElementType()->isStructTy())
6011 C2 = ConstantExpr::getIntegerCast(
6012 C2, Type::getInt32Ty(C->getContext()), true);
6013 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
6015 C = ConstantExpr::getAdd(C, C2);
6022 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
6023 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
6024 // Don't bother with pointers at all.
6025 if (C->getType()->isPointerTy()) return nullptr;
6026 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
6027 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
6028 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
6029 C = ConstantExpr::getMul(C, C2);
6036 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6037 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6038 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6039 if (LHS->getType() == RHS->getType())
6040 return ConstantExpr::getUDiv(LHS, RHS);
6045 break; // TODO: smax, umax.
6050 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6051 if (isa<SCEVConstant>(V)) return V;
6053 // If this instruction is evolved from a constant-evolving PHI, compute the
6054 // exit value from the loop without using SCEVs.
6055 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6056 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6057 const Loop *LI = this->LI[I->getParent()];
6058 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
6059 if (PHINode *PN = dyn_cast<PHINode>(I))
6060 if (PN->getParent() == LI->getHeader()) {
6061 // Okay, there is no closed form solution for the PHI node. Check
6062 // to see if the loop that contains it has a known backedge-taken
6063 // count. If so, we may be able to force computation of the exit
6065 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6066 if (const SCEVConstant *BTCC =
6067 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6068 // Okay, we know how many times the containing loop executes. If
6069 // this is a constant evolving PHI node, get the final value at
6070 // the specified iteration number.
6071 Constant *RV = getConstantEvolutionLoopExitValue(PN,
6072 BTCC->getValue()->getValue(),
6074 if (RV) return getSCEV(RV);
6078 // Okay, this is an expression that we cannot symbolically evaluate
6079 // into a SCEV. Check to see if it's possible to symbolically evaluate
6080 // the arguments into constants, and if so, try to constant propagate the
6081 // result. This is particularly useful for computing loop exit values.
6082 if (CanConstantFold(I)) {
6083 SmallVector<Constant *, 4> Operands;
6084 bool MadeImprovement = false;
6085 for (Value *Op : I->operands()) {
6086 if (Constant *C = dyn_cast<Constant>(Op)) {
6087 Operands.push_back(C);
6091 // If any of the operands is non-constant and if they are
6092 // non-integer and non-pointer, don't even try to analyze them
6093 // with scev techniques.
6094 if (!isSCEVable(Op->getType()))
6097 const SCEV *OrigV = getSCEV(Op);
6098 const SCEV *OpV = getSCEVAtScope(OrigV, L);
6099 MadeImprovement |= OrigV != OpV;
6101 Constant *C = BuildConstantFromSCEV(OpV);
6103 if (C->getType() != Op->getType())
6104 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6108 Operands.push_back(C);
6111 // Check to see if getSCEVAtScope actually made an improvement.
6112 if (MadeImprovement) {
6113 Constant *C = nullptr;
6114 const DataLayout &DL = F.getParent()->getDataLayout();
6115 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6116 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6117 Operands[1], DL, &TLI);
6118 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6119 if (!LI->isVolatile())
6120 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
6122 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
6130 // This is some other type of SCEVUnknown, just return it.
6134 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6135 // Avoid performing the look-up in the common case where the specified
6136 // expression has no loop-variant portions.
6137 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6138 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6139 if (OpAtScope != Comm->getOperand(i)) {
6140 // Okay, at least one of these operands is loop variant but might be
6141 // foldable. Build a new instance of the folded commutative expression.
6142 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6143 Comm->op_begin()+i);
6144 NewOps.push_back(OpAtScope);
6146 for (++i; i != e; ++i) {
6147 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6148 NewOps.push_back(OpAtScope);
6150 if (isa<SCEVAddExpr>(Comm))
6151 return getAddExpr(NewOps);
6152 if (isa<SCEVMulExpr>(Comm))
6153 return getMulExpr(NewOps);
6154 if (isa<SCEVSMaxExpr>(Comm))
6155 return getSMaxExpr(NewOps);
6156 if (isa<SCEVUMaxExpr>(Comm))
6157 return getUMaxExpr(NewOps);
6158 llvm_unreachable("Unknown commutative SCEV type!");
6161 // If we got here, all operands are loop invariant.
6165 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6166 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6167 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6168 if (LHS == Div->getLHS() && RHS == Div->getRHS())
6169 return Div; // must be loop invariant
6170 return getUDivExpr(LHS, RHS);
6173 // If this is a loop recurrence for a loop that does not contain L, then we
6174 // are dealing with the final value computed by the loop.
6175 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6176 // First, attempt to evaluate each operand.
6177 // Avoid performing the look-up in the common case where the specified
6178 // expression has no loop-variant portions.
6179 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6180 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6181 if (OpAtScope == AddRec->getOperand(i))
6184 // Okay, at least one of these operands is loop variant but might be
6185 // foldable. Build a new instance of the folded commutative expression.
6186 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6187 AddRec->op_begin()+i);
6188 NewOps.push_back(OpAtScope);
6189 for (++i; i != e; ++i)
6190 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6192 const SCEV *FoldedRec =
6193 getAddRecExpr(NewOps, AddRec->getLoop(),
6194 AddRec->getNoWrapFlags(SCEV::FlagNW));
6195 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6196 // The addrec may be folded to a nonrecurrence, for example, if the
6197 // induction variable is multiplied by zero after constant folding. Go
6198 // ahead and return the folded value.
6204 // If the scope is outside the addrec's loop, evaluate it by using the
6205 // loop exit value of the addrec.
6206 if (!AddRec->getLoop()->contains(L)) {
6207 // To evaluate this recurrence, we need to know how many times the AddRec
6208 // loop iterates. Compute this now.
6209 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6210 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6212 // Then, evaluate the AddRec.
6213 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6219 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6220 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6221 if (Op == Cast->getOperand())
6222 return Cast; // must be loop invariant
6223 return getZeroExtendExpr(Op, Cast->getType());
6226 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6227 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6228 if (Op == Cast->getOperand())
6229 return Cast; // must be loop invariant
6230 return getSignExtendExpr(Op, Cast->getType());
6233 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6234 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6235 if (Op == Cast->getOperand())
6236 return Cast; // must be loop invariant
6237 return getTruncateExpr(Op, Cast->getType());
6240 llvm_unreachable("Unknown SCEV type!");
6243 /// getSCEVAtScope - This is a convenience function which does
6244 /// getSCEVAtScope(getSCEV(V), L).
6245 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6246 return getSCEVAtScope(getSCEV(V), L);
6249 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6250 /// following equation:
6252 /// A * X = B (mod N)
6254 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6255 /// A and B isn't important.
6257 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6258 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6259 ScalarEvolution &SE) {
6260 uint32_t BW = A.getBitWidth();
6261 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6262 assert(A != 0 && "A must be non-zero.");
6266 // The gcd of A and N may have only one prime factor: 2. The number of
6267 // trailing zeros in A is its multiplicity
6268 uint32_t Mult2 = A.countTrailingZeros();
6271 // 2. Check if B is divisible by D.
6273 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6274 // is not less than multiplicity of this prime factor for D.
6275 if (B.countTrailingZeros() < Mult2)
6276 return SE.getCouldNotCompute();
6278 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6281 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6282 // bit width during computations.
6283 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6284 APInt Mod(BW + 1, 0);
6285 Mod.setBit(BW - Mult2); // Mod = N / D
6286 APInt I = AD.multiplicativeInverse(Mod);
6288 // 4. Compute the minimum unsigned root of the equation:
6289 // I * (B / D) mod (N / D)
6290 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6292 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6294 return SE.getConstant(Result.trunc(BW));
6297 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6298 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6299 /// might be the same) or two SCEVCouldNotCompute objects.
6301 static std::pair<const SCEV *,const SCEV *>
6302 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6303 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6304 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6305 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6306 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6308 // We currently can only solve this if the coefficients are constants.
6309 if (!LC || !MC || !NC) {
6310 const SCEV *CNC = SE.getCouldNotCompute();
6311 return std::make_pair(CNC, CNC);
6314 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6315 const APInt &L = LC->getValue()->getValue();
6316 const APInt &M = MC->getValue()->getValue();
6317 const APInt &N = NC->getValue()->getValue();
6318 APInt Two(BitWidth, 2);
6319 APInt Four(BitWidth, 4);
6322 using namespace APIntOps;
6324 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6325 // The B coefficient is M-N/2
6329 // The A coefficient is N/2
6330 APInt A(N.sdiv(Two));
6332 // Compute the B^2-4ac term.
6335 SqrtTerm -= Four * (A * C);
6337 if (SqrtTerm.isNegative()) {
6338 // The loop is provably infinite.
6339 const SCEV *CNC = SE.getCouldNotCompute();
6340 return std::make_pair(CNC, CNC);
6343 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6344 // integer value or else APInt::sqrt() will assert.
6345 APInt SqrtVal(SqrtTerm.sqrt());
6347 // Compute the two solutions for the quadratic formula.
6348 // The divisions must be performed as signed divisions.
6351 if (TwoA.isMinValue()) {
6352 const SCEV *CNC = SE.getCouldNotCompute();
6353 return std::make_pair(CNC, CNC);
6356 LLVMContext &Context = SE.getContext();
6358 ConstantInt *Solution1 =
6359 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6360 ConstantInt *Solution2 =
6361 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6363 return std::make_pair(SE.getConstant(Solution1),
6364 SE.getConstant(Solution2));
6365 } // end APIntOps namespace
6368 /// HowFarToZero - Return the number of times a backedge comparing the specified
6369 /// value to zero will execute. If not computable, return CouldNotCompute.
6371 /// This is only used for loops with a "x != y" exit test. The exit condition is
6372 /// now expressed as a single expression, V = x-y. So the exit test is
6373 /// effectively V != 0. We know and take advantage of the fact that this
6374 /// expression only being used in a comparison by zero context.
6375 ScalarEvolution::ExitLimit
6376 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6377 // If the value is a constant
6378 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6379 // If the value is already zero, the branch will execute zero times.
6380 if (C->getValue()->isZero()) return C;
6381 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6384 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6385 if (!AddRec || AddRec->getLoop() != L)
6386 return getCouldNotCompute();
6388 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6389 // the quadratic equation to solve it.
6390 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6391 std::pair<const SCEV *,const SCEV *> Roots =
6392 SolveQuadraticEquation(AddRec, *this);
6393 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6394 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6397 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6398 << " sol#2: " << *R2 << "\n";
6400 // Pick the smallest positive root value.
6401 if (ConstantInt *CB =
6402 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6405 if (!CB->getZExtValue())
6406 std::swap(R1, R2); // R1 is the minimum root now.
6408 // We can only use this value if the chrec ends up with an exact zero
6409 // value at this index. When solving for "X*X != 5", for example, we
6410 // should not accept a root of 2.
6411 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6413 return R1; // We found a quadratic root!
6416 return getCouldNotCompute();
6419 // Otherwise we can only handle this if it is affine.
6420 if (!AddRec->isAffine())
6421 return getCouldNotCompute();
6423 // If this is an affine expression, the execution count of this branch is
6424 // the minimum unsigned root of the following equation:
6426 // Start + Step*N = 0 (mod 2^BW)
6430 // Step*N = -Start (mod 2^BW)
6432 // where BW is the common bit width of Start and Step.
6434 // Get the initial value for the loop.
6435 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6436 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6438 // For now we handle only constant steps.
6440 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6441 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6442 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6443 // We have not yet seen any such cases.
6444 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6445 if (!StepC || StepC->getValue()->equalsInt(0))
6446 return getCouldNotCompute();
6448 // For positive steps (counting up until unsigned overflow):
6449 // N = -Start/Step (as unsigned)
6450 // For negative steps (counting down to zero):
6452 // First compute the unsigned distance from zero in the direction of Step.
6453 bool CountDown = StepC->getValue()->getValue().isNegative();
6454 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6456 // Handle unitary steps, which cannot wraparound.
6457 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6458 // N = Distance (as unsigned)
6459 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6460 ConstantRange CR = getUnsignedRange(Start);
6461 const SCEV *MaxBECount;
6462 if (!CountDown && CR.getUnsignedMin().isMinValue())
6463 // When counting up, the worst starting value is 1, not 0.
6464 MaxBECount = CR.getUnsignedMax().isMinValue()
6465 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6466 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6468 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6469 : -CR.getUnsignedMin());
6470 return ExitLimit(Distance, MaxBECount);
6473 // As a special case, handle the instance where Step is a positive power of
6474 // two. In this case, determining whether Step divides Distance evenly can be
6475 // done by counting and comparing the number of trailing zeros of Step and
6478 const APInt &StepV = StepC->getValue()->getValue();
6479 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6480 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6481 // case is not handled as this code is guarded by !CountDown.
6482 if (StepV.isPowerOf2() &&
6483 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
6484 // Here we've constrained the equation to be of the form
6486 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
6488 // where we're operating on a W bit wide integer domain and k is
6489 // non-negative. The smallest unsigned solution for X is the trip count.
6491 // (0) is equivalent to:
6493 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
6494 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
6495 // <=> 2^k * Distance' - X = L * 2^(W - N)
6496 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
6498 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
6501 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
6503 // E.g. say we're solving
6505 // 2 * Val = 2 * X (in i8) ... (3)
6507 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
6509 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
6510 // necessarily the smallest unsigned value of X that satisfies (3).
6511 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
6512 // is i8 1, not i8 -127
6514 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
6516 // Since SCEV does not have a URem node, we construct one using a truncate
6517 // and a zero extend.
6519 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
6520 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
6521 auto *WideTy = Distance->getType();
6523 return getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
6527 // If the condition controls loop exit (the loop exits only if the expression
6528 // is true) and the addition is no-wrap we can use unsigned divide to
6529 // compute the backedge count. In this case, the step may not divide the
6530 // distance, but we don't care because if the condition is "missed" the loop
6531 // will have undefined behavior due to wrapping.
6532 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6534 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6535 return ExitLimit(Exact, Exact);
6538 // Then, try to solve the above equation provided that Start is constant.
6539 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6540 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6541 -StartC->getValue()->getValue(),
6543 return getCouldNotCompute();
6546 /// HowFarToNonZero - Return the number of times a backedge checking the
6547 /// specified value for nonzero will execute. If not computable, return
6549 ScalarEvolution::ExitLimit
6550 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6551 // Loops that look like: while (X == 0) are very strange indeed. We don't
6552 // handle them yet except for the trivial case. This could be expanded in the
6553 // future as needed.
6555 // If the value is a constant, check to see if it is known to be non-zero
6556 // already. If so, the backedge will execute zero times.
6557 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6558 if (!C->getValue()->isNullValue())
6559 return getZero(C->getType());
6560 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6563 // We could implement others, but I really doubt anyone writes loops like
6564 // this, and if they did, they would already be constant folded.
6565 return getCouldNotCompute();
6568 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6569 /// (which may not be an immediate predecessor) which has exactly one
6570 /// successor from which BB is reachable, or null if no such block is
6573 std::pair<BasicBlock *, BasicBlock *>
6574 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6575 // If the block has a unique predecessor, then there is no path from the
6576 // predecessor to the block that does not go through the direct edge
6577 // from the predecessor to the block.
6578 if (BasicBlock *Pred = BB->getSinglePredecessor())
6579 return std::make_pair(Pred, BB);
6581 // A loop's header is defined to be a block that dominates the loop.
6582 // If the header has a unique predecessor outside the loop, it must be
6583 // a block that has exactly one successor that can reach the loop.
6584 if (Loop *L = LI.getLoopFor(BB))
6585 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6587 return std::pair<BasicBlock *, BasicBlock *>();
6590 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6591 /// testing whether two expressions are equal, however for the purposes of
6592 /// looking for a condition guarding a loop, it can be useful to be a little
6593 /// more general, since a front-end may have replicated the controlling
6596 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6597 // Quick check to see if they are the same SCEV.
6598 if (A == B) return true;
6600 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
6601 // Not all instructions that are "identical" compute the same value. For
6602 // instance, two distinct alloca instructions allocating the same type are
6603 // identical and do not read memory; but compute distinct values.
6604 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
6607 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6608 // two different instructions with the same value. Check for this case.
6609 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6610 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6611 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6612 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6613 if (ComputesEqualValues(AI, BI))
6616 // Otherwise assume they may have a different value.
6620 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6621 /// predicate Pred. Return true iff any changes were made.
6623 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6624 const SCEV *&LHS, const SCEV *&RHS,
6626 bool Changed = false;
6628 // If we hit the max recursion limit bail out.
6632 // Canonicalize a constant to the right side.
6633 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6634 // Check for both operands constant.
6635 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6636 if (ConstantExpr::getICmp(Pred,
6638 RHSC->getValue())->isNullValue())
6639 goto trivially_false;
6641 goto trivially_true;
6643 // Otherwise swap the operands to put the constant on the right.
6644 std::swap(LHS, RHS);
6645 Pred = ICmpInst::getSwappedPredicate(Pred);
6649 // If we're comparing an addrec with a value which is loop-invariant in the
6650 // addrec's loop, put the addrec on the left. Also make a dominance check,
6651 // as both operands could be addrecs loop-invariant in each other's loop.
6652 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6653 const Loop *L = AR->getLoop();
6654 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6655 std::swap(LHS, RHS);
6656 Pred = ICmpInst::getSwappedPredicate(Pred);
6661 // If there's a constant operand, canonicalize comparisons with boundary
6662 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6663 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6664 const APInt &RA = RC->getValue()->getValue();
6666 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6667 case ICmpInst::ICMP_EQ:
6668 case ICmpInst::ICMP_NE:
6669 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6671 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6672 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6673 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6674 ME->getOperand(0)->isAllOnesValue()) {
6675 RHS = AE->getOperand(1);
6676 LHS = ME->getOperand(1);
6680 case ICmpInst::ICMP_UGE:
6681 if ((RA - 1).isMinValue()) {
6682 Pred = ICmpInst::ICMP_NE;
6683 RHS = getConstant(RA - 1);
6687 if (RA.isMaxValue()) {
6688 Pred = ICmpInst::ICMP_EQ;
6692 if (RA.isMinValue()) goto trivially_true;
6694 Pred = ICmpInst::ICMP_UGT;
6695 RHS = getConstant(RA - 1);
6698 case ICmpInst::ICMP_ULE:
6699 if ((RA + 1).isMaxValue()) {
6700 Pred = ICmpInst::ICMP_NE;
6701 RHS = getConstant(RA + 1);
6705 if (RA.isMinValue()) {
6706 Pred = ICmpInst::ICMP_EQ;
6710 if (RA.isMaxValue()) goto trivially_true;
6712 Pred = ICmpInst::ICMP_ULT;
6713 RHS = getConstant(RA + 1);
6716 case ICmpInst::ICMP_SGE:
6717 if ((RA - 1).isMinSignedValue()) {
6718 Pred = ICmpInst::ICMP_NE;
6719 RHS = getConstant(RA - 1);
6723 if (RA.isMaxSignedValue()) {
6724 Pred = ICmpInst::ICMP_EQ;
6728 if (RA.isMinSignedValue()) goto trivially_true;
6730 Pred = ICmpInst::ICMP_SGT;
6731 RHS = getConstant(RA - 1);
6734 case ICmpInst::ICMP_SLE:
6735 if ((RA + 1).isMaxSignedValue()) {
6736 Pred = ICmpInst::ICMP_NE;
6737 RHS = getConstant(RA + 1);
6741 if (RA.isMinSignedValue()) {
6742 Pred = ICmpInst::ICMP_EQ;
6746 if (RA.isMaxSignedValue()) goto trivially_true;
6748 Pred = ICmpInst::ICMP_SLT;
6749 RHS = getConstant(RA + 1);
6752 case ICmpInst::ICMP_UGT:
6753 if (RA.isMinValue()) {
6754 Pred = ICmpInst::ICMP_NE;
6758 if ((RA + 1).isMaxValue()) {
6759 Pred = ICmpInst::ICMP_EQ;
6760 RHS = getConstant(RA + 1);
6764 if (RA.isMaxValue()) goto trivially_false;
6766 case ICmpInst::ICMP_ULT:
6767 if (RA.isMaxValue()) {
6768 Pred = ICmpInst::ICMP_NE;
6772 if ((RA - 1).isMinValue()) {
6773 Pred = ICmpInst::ICMP_EQ;
6774 RHS = getConstant(RA - 1);
6778 if (RA.isMinValue()) goto trivially_false;
6780 case ICmpInst::ICMP_SGT:
6781 if (RA.isMinSignedValue()) {
6782 Pred = ICmpInst::ICMP_NE;
6786 if ((RA + 1).isMaxSignedValue()) {
6787 Pred = ICmpInst::ICMP_EQ;
6788 RHS = getConstant(RA + 1);
6792 if (RA.isMaxSignedValue()) goto trivially_false;
6794 case ICmpInst::ICMP_SLT:
6795 if (RA.isMaxSignedValue()) {
6796 Pred = ICmpInst::ICMP_NE;
6800 if ((RA - 1).isMinSignedValue()) {
6801 Pred = ICmpInst::ICMP_EQ;
6802 RHS = getConstant(RA - 1);
6806 if (RA.isMinSignedValue()) goto trivially_false;
6811 // Check for obvious equality.
6812 if (HasSameValue(LHS, RHS)) {
6813 if (ICmpInst::isTrueWhenEqual(Pred))
6814 goto trivially_true;
6815 if (ICmpInst::isFalseWhenEqual(Pred))
6816 goto trivially_false;
6819 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6820 // adding or subtracting 1 from one of the operands.
6822 case ICmpInst::ICMP_SLE:
6823 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6824 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6826 Pred = ICmpInst::ICMP_SLT;
6828 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6829 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6831 Pred = ICmpInst::ICMP_SLT;
6835 case ICmpInst::ICMP_SGE:
6836 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6837 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6839 Pred = ICmpInst::ICMP_SGT;
6841 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6842 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6844 Pred = ICmpInst::ICMP_SGT;
6848 case ICmpInst::ICMP_ULE:
6849 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6850 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6852 Pred = ICmpInst::ICMP_ULT;
6854 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6855 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6857 Pred = ICmpInst::ICMP_ULT;
6861 case ICmpInst::ICMP_UGE:
6862 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6863 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6865 Pred = ICmpInst::ICMP_UGT;
6867 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6868 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6870 Pred = ICmpInst::ICMP_UGT;
6878 // TODO: More simplifications are possible here.
6880 // Recursively simplify until we either hit a recursion limit or nothing
6883 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6889 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6890 Pred = ICmpInst::ICMP_EQ;
6895 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6896 Pred = ICmpInst::ICMP_NE;
6900 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6901 return getSignedRange(S).getSignedMax().isNegative();
6904 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6905 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6908 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6909 return !getSignedRange(S).getSignedMin().isNegative();
6912 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6913 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6916 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6917 return isKnownNegative(S) || isKnownPositive(S);
6920 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6921 const SCEV *LHS, const SCEV *RHS) {
6922 // Canonicalize the inputs first.
6923 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6925 // If LHS or RHS is an addrec, check to see if the condition is true in
6926 // every iteration of the loop.
6927 // If LHS and RHS are both addrec, both conditions must be true in
6928 // every iteration of the loop.
6929 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6930 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6931 bool LeftGuarded = false;
6932 bool RightGuarded = false;
6934 const Loop *L = LAR->getLoop();
6935 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6936 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6937 if (!RAR) return true;
6942 const Loop *L = RAR->getLoop();
6943 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6944 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6945 if (!LAR) return true;
6946 RightGuarded = true;
6949 if (LeftGuarded && RightGuarded)
6952 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
6955 // Otherwise see what can be done with known constant ranges.
6956 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6959 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
6960 ICmpInst::Predicate Pred,
6962 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
6965 // Verify an invariant: inverting the predicate should turn a monotonically
6966 // increasing change to a monotonically decreasing one, and vice versa.
6967 bool IncreasingSwapped;
6968 bool ResultSwapped = isMonotonicPredicateImpl(
6969 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
6971 assert(Result == ResultSwapped && "should be able to analyze both!");
6973 assert(Increasing == !IncreasingSwapped &&
6974 "monotonicity should flip as we flip the predicate");
6980 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
6981 ICmpInst::Predicate Pred,
6984 // A zero step value for LHS means the induction variable is essentially a
6985 // loop invariant value. We don't really depend on the predicate actually
6986 // flipping from false to true (for increasing predicates, and the other way
6987 // around for decreasing predicates), all we care about is that *if* the
6988 // predicate changes then it only changes from false to true.
6990 // A zero step value in itself is not very useful, but there may be places
6991 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
6992 // as general as possible.
6996 return false; // Conservative answer
6998 case ICmpInst::ICMP_UGT:
6999 case ICmpInst::ICMP_UGE:
7000 case ICmpInst::ICMP_ULT:
7001 case ICmpInst::ICMP_ULE:
7002 if (!LHS->getNoWrapFlags(SCEV::FlagNUW))
7005 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
7008 case ICmpInst::ICMP_SGT:
7009 case ICmpInst::ICMP_SGE:
7010 case ICmpInst::ICMP_SLT:
7011 case ICmpInst::ICMP_SLE: {
7012 if (!LHS->getNoWrapFlags(SCEV::FlagNSW))
7015 const SCEV *Step = LHS->getStepRecurrence(*this);
7017 if (isKnownNonNegative(Step)) {
7018 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
7022 if (isKnownNonPositive(Step)) {
7023 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7032 llvm_unreachable("switch has default clause!");
7035 bool ScalarEvolution::isLoopInvariantPredicate(
7036 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7037 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7038 const SCEV *&InvariantRHS) {
7040 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7041 if (!isLoopInvariant(RHS, L)) {
7042 if (!isLoopInvariant(LHS, L))
7045 std::swap(LHS, RHS);
7046 Pred = ICmpInst::getSwappedPredicate(Pred);
7049 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7050 if (!ArLHS || ArLHS->getLoop() != L)
7054 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7057 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7058 // true as the loop iterates, and the backedge is control dependent on
7059 // "ArLHS `Pred` RHS" == true then we can reason as follows:
7061 // * if the predicate was false in the first iteration then the predicate
7062 // is never evaluated again, since the loop exits without taking the
7064 // * if the predicate was true in the first iteration then it will
7065 // continue to be true for all future iterations since it is
7066 // monotonically increasing.
7068 // For both the above possibilities, we can replace the loop varying
7069 // predicate with its value on the first iteration of the loop (which is
7072 // A similar reasoning applies for a monotonically decreasing predicate, by
7073 // replacing true with false and false with true in the above two bullets.
7075 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7077 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7080 InvariantPred = Pred;
7081 InvariantLHS = ArLHS->getStart();
7087 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
7088 const SCEV *LHS, const SCEV *RHS) {
7089 if (HasSameValue(LHS, RHS))
7090 return ICmpInst::isTrueWhenEqual(Pred);
7092 // This code is split out from isKnownPredicate because it is called from
7093 // within isLoopEntryGuardedByCond.
7096 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7097 case ICmpInst::ICMP_SGT:
7098 std::swap(LHS, RHS);
7099 case ICmpInst::ICMP_SLT: {
7100 ConstantRange LHSRange = getSignedRange(LHS);
7101 ConstantRange RHSRange = getSignedRange(RHS);
7102 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
7104 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
7108 case ICmpInst::ICMP_SGE:
7109 std::swap(LHS, RHS);
7110 case ICmpInst::ICMP_SLE: {
7111 ConstantRange LHSRange = getSignedRange(LHS);
7112 ConstantRange RHSRange = getSignedRange(RHS);
7113 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
7115 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
7119 case ICmpInst::ICMP_UGT:
7120 std::swap(LHS, RHS);
7121 case ICmpInst::ICMP_ULT: {
7122 ConstantRange LHSRange = getUnsignedRange(LHS);
7123 ConstantRange RHSRange = getUnsignedRange(RHS);
7124 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
7126 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
7130 case ICmpInst::ICMP_UGE:
7131 std::swap(LHS, RHS);
7132 case ICmpInst::ICMP_ULE: {
7133 ConstantRange LHSRange = getUnsignedRange(LHS);
7134 ConstantRange RHSRange = getUnsignedRange(RHS);
7135 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
7137 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
7141 case ICmpInst::ICMP_NE: {
7142 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
7144 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
7147 const SCEV *Diff = getMinusSCEV(LHS, RHS);
7148 if (isKnownNonZero(Diff))
7152 case ICmpInst::ICMP_EQ:
7153 // The check at the top of the function catches the case where
7154 // the values are known to be equal.
7160 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
7164 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
7165 // Return Y via OutY.
7166 auto MatchBinaryAddToConst =
7167 [this](const SCEV *Result, const SCEV *X, APInt &OutY,
7168 SCEV::NoWrapFlags ExpectedFlags) {
7169 const SCEV *NonConstOp, *ConstOp;
7170 SCEV::NoWrapFlags FlagsPresent;
7172 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
7173 !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
7176 OutY = cast<SCEVConstant>(ConstOp)->getValue()->getValue();
7177 return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
7186 case ICmpInst::ICMP_SGE:
7187 std::swap(LHS, RHS);
7188 case ICmpInst::ICMP_SLE:
7189 // X s<= (X + C)<nsw> if C >= 0
7190 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
7193 // (X + C)<nsw> s<= X if C <= 0
7194 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
7195 !C.isStrictlyPositive())
7198 case ICmpInst::ICMP_SGT:
7199 std::swap(LHS, RHS);
7200 case ICmpInst::ICMP_SLT:
7201 // X s< (X + C)<nsw> if C > 0
7202 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
7203 C.isStrictlyPositive())
7206 // (X + C)<nsw> s< X if C < 0
7207 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
7214 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7217 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
7220 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7221 // the stack can result in exponential time complexity.
7222 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7224 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7226 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7227 // isKnownPredicate. isKnownPredicate is more powerful, but also more
7228 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7229 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
7230 // use isKnownPredicate later if needed.
7231 if (isKnownNonNegative(RHS) &&
7232 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7233 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS))
7239 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7240 /// protected by a conditional between LHS and RHS. This is used to
7241 /// to eliminate casts.
7243 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7244 ICmpInst::Predicate Pred,
7245 const SCEV *LHS, const SCEV *RHS) {
7246 // Interpret a null as meaning no loop, where there is obviously no guard
7247 // (interprocedural conditions notwithstanding).
7248 if (!L) return true;
7250 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7252 BasicBlock *Latch = L->getLoopLatch();
7256 BranchInst *LoopContinuePredicate =
7257 dyn_cast<BranchInst>(Latch->getTerminator());
7258 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7259 isImpliedCond(Pred, LHS, RHS,
7260 LoopContinuePredicate->getCondition(),
7261 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7264 // We don't want more than one activation of the following loops on the stack
7265 // -- that can lead to O(n!) time complexity.
7266 if (WalkingBEDominatingConds)
7269 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7271 // See if we can exploit a trip count to prove the predicate.
7272 const auto &BETakenInfo = getBackedgeTakenInfo(L);
7273 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7274 if (LatchBECount != getCouldNotCompute()) {
7275 // We know that Latch branches back to the loop header exactly
7276 // LatchBECount times. This means the backdege condition at Latch is
7277 // equivalent to "{0,+,1} u< LatchBECount".
7278 Type *Ty = LatchBECount->getType();
7279 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7280 const SCEV *LoopCounter =
7281 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7282 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7287 // Check conditions due to any @llvm.assume intrinsics.
7288 for (auto &AssumeVH : AC.assumptions()) {
7291 auto *CI = cast<CallInst>(AssumeVH);
7292 if (!DT.dominates(CI, Latch->getTerminator()))
7295 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7299 // If the loop is not reachable from the entry block, we risk running into an
7300 // infinite loop as we walk up into the dom tree. These loops do not matter
7301 // anyway, so we just return a conservative answer when we see them.
7302 if (!DT.isReachableFromEntry(L->getHeader()))
7305 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7306 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7308 assert(DTN && "should reach the loop header before reaching the root!");
7310 BasicBlock *BB = DTN->getBlock();
7311 BasicBlock *PBB = BB->getSinglePredecessor();
7315 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7316 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7319 Value *Condition = ContinuePredicate->getCondition();
7321 // If we have an edge `E` within the loop body that dominates the only
7322 // latch, the condition guarding `E` also guards the backedge. This
7323 // reasoning works only for loops with a single latch.
7325 BasicBlockEdge DominatingEdge(PBB, BB);
7326 if (DominatingEdge.isSingleEdge()) {
7327 // We're constructively (and conservatively) enumerating edges within the
7328 // loop body that dominate the latch. The dominator tree better agree
7330 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7332 if (isImpliedCond(Pred, LHS, RHS, Condition,
7333 BB != ContinuePredicate->getSuccessor(0)))
7341 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7342 /// by a conditional between LHS and RHS. This is used to help avoid max
7343 /// expressions in loop trip counts, and to eliminate casts.
7345 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7346 ICmpInst::Predicate Pred,
7347 const SCEV *LHS, const SCEV *RHS) {
7348 // Interpret a null as meaning no loop, where there is obviously no guard
7349 // (interprocedural conditions notwithstanding).
7350 if (!L) return false;
7352 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7354 // Starting at the loop predecessor, climb up the predecessor chain, as long
7355 // as there are predecessors that can be found that have unique successors
7356 // leading to the original header.
7357 for (std::pair<BasicBlock *, BasicBlock *>
7358 Pair(L->getLoopPredecessor(), L->getHeader());
7360 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7362 BranchInst *LoopEntryPredicate =
7363 dyn_cast<BranchInst>(Pair.first->getTerminator());
7364 if (!LoopEntryPredicate ||
7365 LoopEntryPredicate->isUnconditional())
7368 if (isImpliedCond(Pred, LHS, RHS,
7369 LoopEntryPredicate->getCondition(),
7370 LoopEntryPredicate->getSuccessor(0) != Pair.second))
7374 // Check conditions due to any @llvm.assume intrinsics.
7375 for (auto &AssumeVH : AC.assumptions()) {
7378 auto *CI = cast<CallInst>(AssumeVH);
7379 if (!DT.dominates(CI, L->getHeader()))
7382 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7389 /// RAII wrapper to prevent recursive application of isImpliedCond.
7390 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7391 /// currently evaluating isImpliedCond.
7392 struct MarkPendingLoopPredicate {
7394 DenseSet<Value*> &LoopPreds;
7397 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7398 : Cond(C), LoopPreds(LP) {
7399 Pending = !LoopPreds.insert(Cond).second;
7401 ~MarkPendingLoopPredicate() {
7403 LoopPreds.erase(Cond);
7407 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7408 /// and RHS is true whenever the given Cond value evaluates to true.
7409 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7410 const SCEV *LHS, const SCEV *RHS,
7411 Value *FoundCondValue,
7413 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7417 // Recursively handle And and Or conditions.
7418 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7419 if (BO->getOpcode() == Instruction::And) {
7421 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7422 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7423 } else if (BO->getOpcode() == Instruction::Or) {
7425 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7426 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7430 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
7431 if (!ICI) return false;
7433 // Now that we found a conditional branch that dominates the loop or controls
7434 // the loop latch. Check to see if it is the comparison we are looking for.
7435 ICmpInst::Predicate FoundPred;
7437 FoundPred = ICI->getInversePredicate();
7439 FoundPred = ICI->getPredicate();
7441 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
7442 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
7444 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
7447 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
7449 ICmpInst::Predicate FoundPred,
7450 const SCEV *FoundLHS,
7451 const SCEV *FoundRHS) {
7452 // Balance the types.
7453 if (getTypeSizeInBits(LHS->getType()) <
7454 getTypeSizeInBits(FoundLHS->getType())) {
7455 if (CmpInst::isSigned(Pred)) {
7456 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
7457 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
7459 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
7460 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
7462 } else if (getTypeSizeInBits(LHS->getType()) >
7463 getTypeSizeInBits(FoundLHS->getType())) {
7464 if (CmpInst::isSigned(FoundPred)) {
7465 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
7466 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
7468 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
7469 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
7473 // Canonicalize the query to match the way instcombine will have
7474 // canonicalized the comparison.
7475 if (SimplifyICmpOperands(Pred, LHS, RHS))
7477 return CmpInst::isTrueWhenEqual(Pred);
7478 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
7479 if (FoundLHS == FoundRHS)
7480 return CmpInst::isFalseWhenEqual(FoundPred);
7482 // Check to see if we can make the LHS or RHS match.
7483 if (LHS == FoundRHS || RHS == FoundLHS) {
7484 if (isa<SCEVConstant>(RHS)) {
7485 std::swap(FoundLHS, FoundRHS);
7486 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
7488 std::swap(LHS, RHS);
7489 Pred = ICmpInst::getSwappedPredicate(Pred);
7493 // Check whether the found predicate is the same as the desired predicate.
7494 if (FoundPred == Pred)
7495 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7497 // Check whether swapping the found predicate makes it the same as the
7498 // desired predicate.
7499 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
7500 if (isa<SCEVConstant>(RHS))
7501 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
7503 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
7504 RHS, LHS, FoundLHS, FoundRHS);
7507 // Unsigned comparison is the same as signed comparison when both the operands
7508 // are non-negative.
7509 if (CmpInst::isUnsigned(FoundPred) &&
7510 CmpInst::getSignedPredicate(FoundPred) == Pred &&
7511 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
7512 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7514 // Check if we can make progress by sharpening ranges.
7515 if (FoundPred == ICmpInst::ICMP_NE &&
7516 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
7518 const SCEVConstant *C = nullptr;
7519 const SCEV *V = nullptr;
7521 if (isa<SCEVConstant>(FoundLHS)) {
7522 C = cast<SCEVConstant>(FoundLHS);
7525 C = cast<SCEVConstant>(FoundRHS);
7529 // The guarding predicate tells us that C != V. If the known range
7530 // of V is [C, t), we can sharpen the range to [C + 1, t). The
7531 // range we consider has to correspond to same signedness as the
7532 // predicate we're interested in folding.
7534 APInt Min = ICmpInst::isSigned(Pred) ?
7535 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7537 if (Min == C->getValue()->getValue()) {
7538 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7539 // This is true even if (Min + 1) wraps around -- in case of
7540 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7542 APInt SharperMin = Min + 1;
7545 case ICmpInst::ICMP_SGE:
7546 case ICmpInst::ICMP_UGE:
7547 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7549 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7550 getConstant(SharperMin)))
7553 case ICmpInst::ICMP_SGT:
7554 case ICmpInst::ICMP_UGT:
7555 // We know from the range information that (V `Pred` Min ||
7556 // V == Min). We know from the guarding condition that !(V
7557 // == Min). This gives us
7559 // V `Pred` Min || V == Min && !(V == Min)
7562 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7564 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7574 // Check whether the actual condition is beyond sufficient.
7575 if (FoundPred == ICmpInst::ICMP_EQ)
7576 if (ICmpInst::isTrueWhenEqual(Pred))
7577 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7579 if (Pred == ICmpInst::ICMP_NE)
7580 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7581 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7584 // Otherwise assume the worst.
7588 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
7589 const SCEV *&L, const SCEV *&R,
7590 SCEV::NoWrapFlags &Flags) {
7591 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
7592 if (!AE || AE->getNumOperands() != 2)
7595 L = AE->getOperand(0);
7596 R = AE->getOperand(1);
7597 Flags = AE->getNoWrapFlags();
7601 bool ScalarEvolution::computeConstantDifference(const SCEV *Less,
7604 // We avoid subtracting expressions here because this function is usually
7605 // fairly deep in the call stack (i.e. is called many times).
7607 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
7608 const auto *LAR = cast<SCEVAddRecExpr>(Less);
7609 const auto *MAR = cast<SCEVAddRecExpr>(More);
7611 if (LAR->getLoop() != MAR->getLoop())
7614 // We look at affine expressions only; not for correctness but to keep
7615 // getStepRecurrence cheap.
7616 if (!LAR->isAffine() || !MAR->isAffine())
7619 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
7622 Less = LAR->getStart();
7623 More = MAR->getStart();
7628 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
7629 const auto &M = cast<SCEVConstant>(More)->getValue()->getValue();
7630 const auto &L = cast<SCEVConstant>(Less)->getValue()->getValue();
7636 SCEV::NoWrapFlags Flags;
7637 if (splitBinaryAdd(Less, L, R, Flags))
7638 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7640 C = -(LC->getValue()->getValue());
7644 if (splitBinaryAdd(More, L, R, Flags))
7645 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7647 C = LC->getValue()->getValue();
7654 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
7655 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
7656 const SCEV *FoundLHS, const SCEV *FoundRHS) {
7657 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
7660 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7664 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
7665 if (!AddRecFoundLHS)
7668 // We'd like to let SCEV reason about control dependencies, so we constrain
7669 // both the inequalities to be about add recurrences on the same loop. This
7670 // way we can use isLoopEntryGuardedByCond later.
7672 const Loop *L = AddRecFoundLHS->getLoop();
7673 if (L != AddRecLHS->getLoop())
7676 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
7678 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
7681 // Informal proof for (2), assuming (1) [*]:
7683 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
7687 // FoundLHS s< FoundRHS s< INT_MIN - C
7688 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
7689 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
7690 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
7691 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
7692 // <=> FoundLHS + C s< FoundRHS + C
7694 // [*]: (1) can be proved by ruling out overflow.
7696 // [**]: This can be proved by analyzing all the four possibilities:
7697 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
7698 // (A s>= 0, B s>= 0).
7701 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
7702 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
7703 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
7704 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
7705 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
7709 if (!computeConstantDifference(FoundLHS, LHS, LDiff) ||
7710 !computeConstantDifference(FoundRHS, RHS, RDiff) ||
7717 APInt FoundRHSLimit;
7719 if (Pred == CmpInst::ICMP_ULT) {
7720 FoundRHSLimit = -RDiff;
7722 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
7723 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - RDiff;
7726 // Try to prove (1) or (2), as needed.
7727 return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
7728 getConstant(FoundRHSLimit));
7731 /// isImpliedCondOperands - Test whether the condition described by Pred,
7732 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7733 /// and FoundRHS is true.
7734 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7735 const SCEV *LHS, const SCEV *RHS,
7736 const SCEV *FoundLHS,
7737 const SCEV *FoundRHS) {
7738 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7741 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
7744 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7745 FoundLHS, FoundRHS) ||
7746 // ~x < ~y --> x > y
7747 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7748 getNotSCEV(FoundRHS),
7749 getNotSCEV(FoundLHS));
7753 /// If Expr computes ~A, return A else return nullptr
7754 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7755 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7756 if (!Add || Add->getNumOperands() != 2 ||
7757 !Add->getOperand(0)->isAllOnesValue())
7760 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7761 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
7762 !AddRHS->getOperand(0)->isAllOnesValue())
7765 return AddRHS->getOperand(1);
7769 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7770 template<typename MaxExprType>
7771 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7772 const SCEV *Candidate) {
7773 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7774 if (!MaxExpr) return false;
7776 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7777 return It != MaxExpr->op_end();
7781 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7782 template<typename MaxExprType>
7783 static bool IsMinConsistingOf(ScalarEvolution &SE,
7784 const SCEV *MaybeMinExpr,
7785 const SCEV *Candidate) {
7786 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7790 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7793 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
7794 ICmpInst::Predicate Pred,
7795 const SCEV *LHS, const SCEV *RHS) {
7797 // If both sides are affine addrecs for the same loop, with equal
7798 // steps, and we know the recurrences don't wrap, then we only
7799 // need to check the predicate on the starting values.
7801 if (!ICmpInst::isRelational(Pred))
7804 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7807 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7810 if (LAR->getLoop() != RAR->getLoop())
7812 if (!LAR->isAffine() || !RAR->isAffine())
7815 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
7818 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
7819 SCEV::FlagNSW : SCEV::FlagNUW;
7820 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
7823 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
7826 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7828 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7829 ICmpInst::Predicate Pred,
7830 const SCEV *LHS, const SCEV *RHS) {
7835 case ICmpInst::ICMP_SGE:
7836 std::swap(LHS, RHS);
7838 case ICmpInst::ICMP_SLE:
7841 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7843 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7845 case ICmpInst::ICMP_UGE:
7846 std::swap(LHS, RHS);
7848 case ICmpInst::ICMP_ULE:
7851 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7853 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7856 llvm_unreachable("covered switch fell through?!");
7859 /// isImpliedCondOperandsHelper - Test whether the condition described by
7860 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7861 /// FoundLHS, and FoundRHS is true.
7863 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7864 const SCEV *LHS, const SCEV *RHS,
7865 const SCEV *FoundLHS,
7866 const SCEV *FoundRHS) {
7867 auto IsKnownPredicateFull =
7868 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7869 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7870 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
7871 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
7872 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
7876 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7877 case ICmpInst::ICMP_EQ:
7878 case ICmpInst::ICMP_NE:
7879 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7882 case ICmpInst::ICMP_SLT:
7883 case ICmpInst::ICMP_SLE:
7884 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7885 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7888 case ICmpInst::ICMP_SGT:
7889 case ICmpInst::ICMP_SGE:
7890 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7891 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7894 case ICmpInst::ICMP_ULT:
7895 case ICmpInst::ICMP_ULE:
7896 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7897 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7900 case ICmpInst::ICMP_UGT:
7901 case ICmpInst::ICMP_UGE:
7902 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7903 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7911 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
7912 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
7913 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
7916 const SCEV *FoundLHS,
7917 const SCEV *FoundRHS) {
7918 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
7919 // The restriction on `FoundRHS` be lifted easily -- it exists only to
7920 // reduce the compile time impact of this optimization.
7923 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
7924 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
7925 !isa<SCEVConstant>(AddLHS->getOperand(0)))
7928 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
7930 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
7931 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
7932 ConstantRange FoundLHSRange =
7933 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
7935 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
7938 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
7939 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
7941 // We can also compute the range of values for `LHS` that satisfy the
7942 // consequent, "`LHS` `Pred` `RHS`":
7943 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
7944 ConstantRange SatisfyingLHSRange =
7945 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
7947 // The antecedent implies the consequent if every value of `LHS` that
7948 // satisfies the antecedent also satisfies the consequent.
7949 return SatisfyingLHSRange.contains(LHSRange);
7952 // Verify if an linear IV with positive stride can overflow when in a
7953 // less-than comparison, knowing the invariant term of the comparison, the
7954 // stride and the knowledge of NSW/NUW flags on the recurrence.
7955 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7956 bool IsSigned, bool NoWrap) {
7957 if (NoWrap) return false;
7959 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7960 const SCEV *One = getOne(Stride->getType());
7963 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7964 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7965 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7968 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7969 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7972 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7973 APInt MaxValue = APInt::getMaxValue(BitWidth);
7974 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7977 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7978 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7981 // Verify if an linear IV with negative stride can overflow when in a
7982 // greater-than comparison, knowing the invariant term of the comparison,
7983 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7984 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7985 bool IsSigned, bool NoWrap) {
7986 if (NoWrap) return false;
7988 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7989 const SCEV *One = getOne(Stride->getType());
7992 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7993 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7994 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7997 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7998 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
8001 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
8002 APInt MinValue = APInt::getMinValue(BitWidth);
8003 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8006 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
8007 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
8010 // Compute the backedge taken count knowing the interval difference, the
8011 // stride and presence of the equality in the comparison.
8012 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
8014 const SCEV *One = getOne(Step->getType());
8015 Delta = Equality ? getAddExpr(Delta, Step)
8016 : getAddExpr(Delta, getMinusSCEV(Step, One));
8017 return getUDivExpr(Delta, Step);
8020 /// HowManyLessThans - Return the number of times a backedge containing the
8021 /// specified less-than comparison will execute. If not computable, return
8022 /// CouldNotCompute.
8024 /// @param ControlsExit is true when the LHS < RHS condition directly controls
8025 /// the branch (loops exits only if condition is true). In this case, we can use
8026 /// NoWrapFlags to skip overflow checks.
8027 ScalarEvolution::ExitLimit
8028 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
8029 const Loop *L, bool IsSigned,
8030 bool ControlsExit) {
8031 // We handle only IV < Invariant
8032 if (!isLoopInvariant(RHS, L))
8033 return getCouldNotCompute();
8035 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8037 // Avoid weird loops
8038 if (!IV || IV->getLoop() != L || !IV->isAffine())
8039 return getCouldNotCompute();
8041 bool NoWrap = ControlsExit &&
8042 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8044 const SCEV *Stride = IV->getStepRecurrence(*this);
8046 // Avoid negative or zero stride values
8047 if (!isKnownPositive(Stride))
8048 return getCouldNotCompute();
8050 // Avoid proven overflow cases: this will ensure that the backedge taken count
8051 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8052 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8053 // behaviors like the case of C language.
8054 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
8055 return getCouldNotCompute();
8057 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
8058 : ICmpInst::ICMP_ULT;
8059 const SCEV *Start = IV->getStart();
8060 const SCEV *End = RHS;
8061 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
8062 const SCEV *Diff = getMinusSCEV(RHS, Start);
8063 // If we have NoWrap set, then we can assume that the increment won't
8064 // overflow, in which case if RHS - Start is a constant, we don't need to
8065 // do a max operation since we can just figure it out statically
8066 if (NoWrap && isa<SCEVConstant>(Diff)) {
8067 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
8071 End = IsSigned ? getSMaxExpr(RHS, Start)
8072 : getUMaxExpr(RHS, Start);
8075 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
8077 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
8078 : getUnsignedRange(Start).getUnsignedMin();
8080 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8081 : getUnsignedRange(Stride).getUnsignedMin();
8083 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8084 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
8085 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
8087 // Although End can be a MAX expression we estimate MaxEnd considering only
8088 // the case End = RHS. This is safe because in the other case (End - Start)
8089 // is zero, leading to a zero maximum backedge taken count.
8091 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8092 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8094 const SCEV *MaxBECount;
8095 if (isa<SCEVConstant>(BECount))
8096 MaxBECount = BECount;
8098 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8099 getConstant(MinStride), false);
8101 if (isa<SCEVCouldNotCompute>(MaxBECount))
8102 MaxBECount = BECount;
8104 return ExitLimit(BECount, MaxBECount);
8107 ScalarEvolution::ExitLimit
8108 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8109 const Loop *L, bool IsSigned,
8110 bool ControlsExit) {
8111 // We handle only IV > Invariant
8112 if (!isLoopInvariant(RHS, L))
8113 return getCouldNotCompute();
8115 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8117 // Avoid weird loops
8118 if (!IV || IV->getLoop() != L || !IV->isAffine())
8119 return getCouldNotCompute();
8121 bool NoWrap = ControlsExit &&
8122 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8124 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8126 // Avoid negative or zero stride values
8127 if (!isKnownPositive(Stride))
8128 return getCouldNotCompute();
8130 // Avoid proven overflow cases: this will ensure that the backedge taken count
8131 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8132 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8133 // behaviors like the case of C language.
8134 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8135 return getCouldNotCompute();
8137 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8138 : ICmpInst::ICMP_UGT;
8140 const SCEV *Start = IV->getStart();
8141 const SCEV *End = RHS;
8142 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
8143 const SCEV *Diff = getMinusSCEV(RHS, Start);
8144 // If we have NoWrap set, then we can assume that the increment won't
8145 // overflow, in which case if RHS - Start is a constant, we don't need to
8146 // do a max operation since we can just figure it out statically
8147 if (NoWrap && isa<SCEVConstant>(Diff)) {
8148 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
8149 if (!D.isNegative())
8152 End = IsSigned ? getSMinExpr(RHS, Start)
8153 : getUMinExpr(RHS, Start);
8156 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8158 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8159 : getUnsignedRange(Start).getUnsignedMax();
8161 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8162 : getUnsignedRange(Stride).getUnsignedMin();
8164 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8165 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8166 : APInt::getMinValue(BitWidth) + (MinStride - 1);
8168 // Although End can be a MIN expression we estimate MinEnd considering only
8169 // the case End = RHS. This is safe because in the other case (Start - End)
8170 // is zero, leading to a zero maximum backedge taken count.
8172 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8173 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8176 const SCEV *MaxBECount = getCouldNotCompute();
8177 if (isa<SCEVConstant>(BECount))
8178 MaxBECount = BECount;
8180 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8181 getConstant(MinStride), false);
8183 if (isa<SCEVCouldNotCompute>(MaxBECount))
8184 MaxBECount = BECount;
8186 return ExitLimit(BECount, MaxBECount);
8189 /// getNumIterationsInRange - Return the number of iterations of this loop that
8190 /// produce values in the specified constant range. Another way of looking at
8191 /// this is that it returns the first iteration number where the value is not in
8192 /// the condition, thus computing the exit count. If the iteration count can't
8193 /// be computed, an instance of SCEVCouldNotCompute is returned.
8194 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
8195 ScalarEvolution &SE) const {
8196 if (Range.isFullSet()) // Infinite loop.
8197 return SE.getCouldNotCompute();
8199 // If the start is a non-zero constant, shift the range to simplify things.
8200 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8201 if (!SC->getValue()->isZero()) {
8202 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8203 Operands[0] = SE.getZero(SC->getType());
8204 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8205 getNoWrapFlags(FlagNW));
8206 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
8207 return ShiftedAddRec->getNumIterationsInRange(
8208 Range.subtract(SC->getValue()->getValue()), SE);
8209 // This is strange and shouldn't happen.
8210 return SE.getCouldNotCompute();
8213 // The only time we can solve this is when we have all constant indices.
8214 // Otherwise, we cannot determine the overflow conditions.
8215 if (std::any_of(op_begin(), op_end(),
8216 [](const SCEV *Op) { return !isa<SCEVConstant>(Op);}))
8217 return SE.getCouldNotCompute();
8219 // Okay at this point we know that all elements of the chrec are constants and
8220 // that the start element is zero.
8222 // First check to see if the range contains zero. If not, the first
8224 unsigned BitWidth = SE.getTypeSizeInBits(getType());
8225 if (!Range.contains(APInt(BitWidth, 0)))
8226 return SE.getZero(getType());
8229 // If this is an affine expression then we have this situation:
8230 // Solve {0,+,A} in Range === Ax in Range
8232 // We know that zero is in the range. If A is positive then we know that
8233 // the upper value of the range must be the first possible exit value.
8234 // If A is negative then the lower of the range is the last possible loop
8235 // value. Also note that we already checked for a full range.
8236 APInt One(BitWidth,1);
8237 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
8238 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8240 // The exit value should be (End+A)/A.
8241 APInt ExitVal = (End + A).udiv(A);
8242 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8244 // Evaluate at the exit value. If we really did fall out of the valid
8245 // range, then we computed our trip count, otherwise wrap around or other
8246 // things must have happened.
8247 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8248 if (Range.contains(Val->getValue()))
8249 return SE.getCouldNotCompute(); // Something strange happened
8251 // Ensure that the previous value is in the range. This is a sanity check.
8252 assert(Range.contains(
8253 EvaluateConstantChrecAtConstant(this,
8254 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8255 "Linear scev computation is off in a bad way!");
8256 return SE.getConstant(ExitValue);
8257 } else if (isQuadratic()) {
8258 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8259 // quadratic equation to solve it. To do this, we must frame our problem in
8260 // terms of figuring out when zero is crossed, instead of when
8261 // Range.getUpper() is crossed.
8262 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8263 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8264 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
8265 // getNoWrapFlags(FlagNW)
8268 // Next, solve the constructed addrec
8269 std::pair<const SCEV *,const SCEV *> Roots =
8270 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
8271 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
8272 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
8274 // Pick the smallest positive root value.
8275 if (ConstantInt *CB =
8276 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
8277 R1->getValue(), R2->getValue()))) {
8278 if (!CB->getZExtValue())
8279 std::swap(R1, R2); // R1 is the minimum root now.
8281 // Make sure the root is not off by one. The returned iteration should
8282 // not be in the range, but the previous one should be. When solving
8283 // for "X*X < 5", for example, we should not return a root of 2.
8284 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
8287 if (Range.contains(R1Val->getValue())) {
8288 // The next iteration must be out of the range...
8289 ConstantInt *NextVal =
8290 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
8292 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8293 if (!Range.contains(R1Val->getValue()))
8294 return SE.getConstant(NextVal);
8295 return SE.getCouldNotCompute(); // Something strange happened
8298 // If R1 was not in the range, then it is a good return value. Make
8299 // sure that R1-1 WAS in the range though, just in case.
8300 ConstantInt *NextVal =
8301 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
8302 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8303 if (Range.contains(R1Val->getValue()))
8305 return SE.getCouldNotCompute(); // Something strange happened
8310 return SE.getCouldNotCompute();
8316 FindUndefs() : Found(false) {}
8318 bool follow(const SCEV *S) {
8319 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
8320 if (isa<UndefValue>(C->getValue()))
8322 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
8323 if (isa<UndefValue>(C->getValue()))
8327 // Keep looking if we haven't found it yet.
8330 bool isDone() const {
8331 // Stop recursion if we have found an undef.
8337 // Return true when S contains at least an undef value.
8339 containsUndefs(const SCEV *S) {
8341 SCEVTraversal<FindUndefs> ST(F);
8348 // Collect all steps of SCEV expressions.
8349 struct SCEVCollectStrides {
8350 ScalarEvolution &SE;
8351 SmallVectorImpl<const SCEV *> &Strides;
8353 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
8354 : SE(SE), Strides(S) {}
8356 bool follow(const SCEV *S) {
8357 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
8358 Strides.push_back(AR->getStepRecurrence(SE));
8361 bool isDone() const { return false; }
8364 // Collect all SCEVUnknown and SCEVMulExpr expressions.
8365 struct SCEVCollectTerms {
8366 SmallVectorImpl<const SCEV *> &Terms;
8368 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
8371 bool follow(const SCEV *S) {
8372 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
8373 if (!containsUndefs(S))
8376 // Stop recursion: once we collected a term, do not walk its operands.
8383 bool isDone() const { return false; }
8386 // Check if a SCEV contains an AddRecExpr.
8387 struct SCEVHasAddRec {
8388 bool &ContainsAddRec;
8390 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
8391 ContainsAddRec = false;
8394 bool follow(const SCEV *S) {
8395 if (isa<SCEVAddRecExpr>(S)) {
8396 ContainsAddRec = true;
8398 // Stop recursion: once we collected a term, do not walk its operands.
8405 bool isDone() const { return false; }
8408 // Find factors that are multiplied with an expression that (possibly as a
8409 // subexpression) contains an AddRecExpr. In the expression:
8411 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
8413 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
8414 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
8415 // parameters as they form a product with an induction variable.
8417 // This collector expects all array size parameters to be in the same MulExpr.
8418 // It might be necessary to later add support for collecting parameters that are
8419 // spread over different nested MulExpr.
8420 struct SCEVCollectAddRecMultiplies {
8421 SmallVectorImpl<const SCEV *> &Terms;
8422 ScalarEvolution &SE;
8424 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
8425 : Terms(T), SE(SE) {}
8427 bool follow(const SCEV *S) {
8428 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
8429 bool HasAddRec = false;
8430 SmallVector<const SCEV *, 0> Operands;
8431 for (auto Op : Mul->operands()) {
8432 if (isa<SCEVUnknown>(Op)) {
8433 Operands.push_back(Op);
8435 bool ContainsAddRec;
8436 SCEVHasAddRec ContiansAddRec(ContainsAddRec);
8437 visitAll(Op, ContiansAddRec);
8438 HasAddRec |= ContainsAddRec;
8441 if (Operands.size() == 0)
8447 Terms.push_back(SE.getMulExpr(Operands));
8448 // Stop recursion: once we collected a term, do not walk its operands.
8455 bool isDone() const { return false; }
8459 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
8461 /// 1) The strides of AddRec expressions.
8462 /// 2) Unknowns that are multiplied with AddRec expressions.
8463 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
8464 SmallVectorImpl<const SCEV *> &Terms) {
8465 SmallVector<const SCEV *, 4> Strides;
8466 SCEVCollectStrides StrideCollector(*this, Strides);
8467 visitAll(Expr, StrideCollector);
8470 dbgs() << "Strides:\n";
8471 for (const SCEV *S : Strides)
8472 dbgs() << *S << "\n";
8475 for (const SCEV *S : Strides) {
8476 SCEVCollectTerms TermCollector(Terms);
8477 visitAll(S, TermCollector);
8481 dbgs() << "Terms:\n";
8482 for (const SCEV *T : Terms)
8483 dbgs() << *T << "\n";
8486 SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
8487 visitAll(Expr, MulCollector);
8490 static bool findArrayDimensionsRec(ScalarEvolution &SE,
8491 SmallVectorImpl<const SCEV *> &Terms,
8492 SmallVectorImpl<const SCEV *> &Sizes) {
8493 int Last = Terms.size() - 1;
8494 const SCEV *Step = Terms[Last];
8496 // End of recursion.
8498 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
8499 SmallVector<const SCEV *, 2> Qs;
8500 for (const SCEV *Op : M->operands())
8501 if (!isa<SCEVConstant>(Op))
8504 Step = SE.getMulExpr(Qs);
8507 Sizes.push_back(Step);
8511 for (const SCEV *&Term : Terms) {
8512 // Normalize the terms before the next call to findArrayDimensionsRec.
8514 SCEVDivision::divide(SE, Term, Step, &Q, &R);
8516 // Bail out when GCD does not evenly divide one of the terms.
8523 // Remove all SCEVConstants.
8524 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
8525 return isa<SCEVConstant>(E);
8529 if (Terms.size() > 0)
8530 if (!findArrayDimensionsRec(SE, Terms, Sizes))
8533 Sizes.push_back(Step);
8538 struct FindParameter {
8539 bool FoundParameter;
8540 FindParameter() : FoundParameter(false) {}
8542 bool follow(const SCEV *S) {
8543 if (isa<SCEVUnknown>(S)) {
8544 FoundParameter = true;
8545 // Stop recursion: we found a parameter.
8551 bool isDone() const {
8552 // Stop recursion if we have found a parameter.
8553 return FoundParameter;
8558 // Returns true when S contains at least a SCEVUnknown parameter.
8560 containsParameters(const SCEV *S) {
8562 SCEVTraversal<FindParameter> ST(F);
8565 return F.FoundParameter;
8568 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
8570 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
8571 for (const SCEV *T : Terms)
8572 if (containsParameters(T))
8577 // Return the number of product terms in S.
8578 static inline int numberOfTerms(const SCEV *S) {
8579 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
8580 return Expr->getNumOperands();
8584 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
8585 if (isa<SCEVConstant>(T))
8588 if (isa<SCEVUnknown>(T))
8591 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
8592 SmallVector<const SCEV *, 2> Factors;
8593 for (const SCEV *Op : M->operands())
8594 if (!isa<SCEVConstant>(Op))
8595 Factors.push_back(Op);
8597 return SE.getMulExpr(Factors);
8603 /// Return the size of an element read or written by Inst.
8604 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
8606 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
8607 Ty = Store->getValueOperand()->getType();
8608 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
8609 Ty = Load->getType();
8613 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
8614 return getSizeOfExpr(ETy, Ty);
8617 /// Second step of delinearization: compute the array dimensions Sizes from the
8618 /// set of Terms extracted from the memory access function of this SCEVAddRec.
8619 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
8620 SmallVectorImpl<const SCEV *> &Sizes,
8621 const SCEV *ElementSize) const {
8623 if (Terms.size() < 1 || !ElementSize)
8626 // Early return when Terms do not contain parameters: we do not delinearize
8627 // non parametric SCEVs.
8628 if (!containsParameters(Terms))
8632 dbgs() << "Terms:\n";
8633 for (const SCEV *T : Terms)
8634 dbgs() << *T << "\n";
8637 // Remove duplicates.
8638 std::sort(Terms.begin(), Terms.end());
8639 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
8641 // Put larger terms first.
8642 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
8643 return numberOfTerms(LHS) > numberOfTerms(RHS);
8646 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8648 // Try to divide all terms by the element size. If term is not divisible by
8649 // element size, proceed with the original term.
8650 for (const SCEV *&Term : Terms) {
8652 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
8657 SmallVector<const SCEV *, 4> NewTerms;
8659 // Remove constant factors.
8660 for (const SCEV *T : Terms)
8661 if (const SCEV *NewT = removeConstantFactors(SE, T))
8662 NewTerms.push_back(NewT);
8665 dbgs() << "Terms after sorting:\n";
8666 for (const SCEV *T : NewTerms)
8667 dbgs() << *T << "\n";
8670 if (NewTerms.empty() ||
8671 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
8676 // The last element to be pushed into Sizes is the size of an element.
8677 Sizes.push_back(ElementSize);
8680 dbgs() << "Sizes:\n";
8681 for (const SCEV *S : Sizes)
8682 dbgs() << *S << "\n";
8686 /// Third step of delinearization: compute the access functions for the
8687 /// Subscripts based on the dimensions in Sizes.
8688 void ScalarEvolution::computeAccessFunctions(
8689 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
8690 SmallVectorImpl<const SCEV *> &Sizes) {
8692 // Early exit in case this SCEV is not an affine multivariate function.
8696 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
8697 if (!AR->isAffine())
8700 const SCEV *Res = Expr;
8701 int Last = Sizes.size() - 1;
8702 for (int i = Last; i >= 0; i--) {
8704 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
8707 dbgs() << "Res: " << *Res << "\n";
8708 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
8709 dbgs() << "Res divided by Sizes[i]:\n";
8710 dbgs() << "Quotient: " << *Q << "\n";
8711 dbgs() << "Remainder: " << *R << "\n";
8716 // Do not record the last subscript corresponding to the size of elements in
8720 // Bail out if the remainder is too complex.
8721 if (isa<SCEVAddRecExpr>(R)) {
8730 // Record the access function for the current subscript.
8731 Subscripts.push_back(R);
8734 // Also push in last position the remainder of the last division: it will be
8735 // the access function of the innermost dimension.
8736 Subscripts.push_back(Res);
8738 std::reverse(Subscripts.begin(), Subscripts.end());
8741 dbgs() << "Subscripts:\n";
8742 for (const SCEV *S : Subscripts)
8743 dbgs() << *S << "\n";
8747 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
8748 /// sizes of an array access. Returns the remainder of the delinearization that
8749 /// is the offset start of the array. The SCEV->delinearize algorithm computes
8750 /// the multiples of SCEV coefficients: that is a pattern matching of sub
8751 /// expressions in the stride and base of a SCEV corresponding to the
8752 /// computation of a GCD (greatest common divisor) of base and stride. When
8753 /// SCEV->delinearize fails, it returns the SCEV unchanged.
8755 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
8757 /// void foo(long n, long m, long o, double A[n][m][o]) {
8759 /// for (long i = 0; i < n; i++)
8760 /// for (long j = 0; j < m; j++)
8761 /// for (long k = 0; k < o; k++)
8762 /// A[i][j][k] = 1.0;
8765 /// the delinearization input is the following AddRec SCEV:
8767 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
8769 /// From this SCEV, we are able to say that the base offset of the access is %A
8770 /// because it appears as an offset that does not divide any of the strides in
8773 /// CHECK: Base offset: %A
8775 /// and then SCEV->delinearize determines the size of some of the dimensions of
8776 /// the array as these are the multiples by which the strides are happening:
8778 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
8780 /// Note that the outermost dimension remains of UnknownSize because there are
8781 /// no strides that would help identifying the size of the last dimension: when
8782 /// the array has been statically allocated, one could compute the size of that
8783 /// dimension by dividing the overall size of the array by the size of the known
8784 /// dimensions: %m * %o * 8.
8786 /// Finally delinearize provides the access functions for the array reference
8787 /// that does correspond to A[i][j][k] of the above C testcase:
8789 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
8791 /// The testcases are checking the output of a function pass:
8792 /// DelinearizationPass that walks through all loads and stores of a function
8793 /// asking for the SCEV of the memory access with respect to all enclosing
8794 /// loops, calling SCEV->delinearize on that and printing the results.
8796 void ScalarEvolution::delinearize(const SCEV *Expr,
8797 SmallVectorImpl<const SCEV *> &Subscripts,
8798 SmallVectorImpl<const SCEV *> &Sizes,
8799 const SCEV *ElementSize) {
8800 // First step: collect parametric terms.
8801 SmallVector<const SCEV *, 4> Terms;
8802 collectParametricTerms(Expr, Terms);
8807 // Second step: find subscript sizes.
8808 findArrayDimensions(Terms, Sizes, ElementSize);
8813 // Third step: compute the access functions for each subscript.
8814 computeAccessFunctions(Expr, Subscripts, Sizes);
8816 if (Subscripts.empty())
8820 dbgs() << "succeeded to delinearize " << *Expr << "\n";
8821 dbgs() << "ArrayDecl[UnknownSize]";
8822 for (const SCEV *S : Sizes)
8823 dbgs() << "[" << *S << "]";
8825 dbgs() << "\nArrayRef";
8826 for (const SCEV *S : Subscripts)
8827 dbgs() << "[" << *S << "]";
8832 //===----------------------------------------------------------------------===//
8833 // SCEVCallbackVH Class Implementation
8834 //===----------------------------------------------------------------------===//
8836 void ScalarEvolution::SCEVCallbackVH::deleted() {
8837 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8838 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
8839 SE->ConstantEvolutionLoopExitValue.erase(PN);
8840 SE->ValueExprMap.erase(getValPtr());
8841 // this now dangles!
8844 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
8845 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8847 // Forget all the expressions associated with users of the old value,
8848 // so that future queries will recompute the expressions using the new
8850 Value *Old = getValPtr();
8851 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
8852 SmallPtrSet<User *, 8> Visited;
8853 while (!Worklist.empty()) {
8854 User *U = Worklist.pop_back_val();
8855 // Deleting the Old value will cause this to dangle. Postpone
8856 // that until everything else is done.
8859 if (!Visited.insert(U).second)
8861 if (PHINode *PN = dyn_cast<PHINode>(U))
8862 SE->ConstantEvolutionLoopExitValue.erase(PN);
8863 SE->ValueExprMap.erase(U);
8864 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
8866 // Delete the Old value.
8867 if (PHINode *PN = dyn_cast<PHINode>(Old))
8868 SE->ConstantEvolutionLoopExitValue.erase(PN);
8869 SE->ValueExprMap.erase(Old);
8870 // this now dangles!
8873 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
8874 : CallbackVH(V), SE(se) {}
8876 //===----------------------------------------------------------------------===//
8877 // ScalarEvolution Class Implementation
8878 //===----------------------------------------------------------------------===//
8880 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
8881 AssumptionCache &AC, DominatorTree &DT,
8883 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
8884 CouldNotCompute(new SCEVCouldNotCompute()),
8885 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
8886 ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
8887 FirstUnknown(nullptr) {}
8889 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
8890 : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
8891 CouldNotCompute(std::move(Arg.CouldNotCompute)),
8892 ValueExprMap(std::move(Arg.ValueExprMap)),
8893 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
8894 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
8895 ConstantEvolutionLoopExitValue(
8896 std::move(Arg.ConstantEvolutionLoopExitValue)),
8897 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
8898 LoopDispositions(std::move(Arg.LoopDispositions)),
8899 BlockDispositions(std::move(Arg.BlockDispositions)),
8900 UnsignedRanges(std::move(Arg.UnsignedRanges)),
8901 SignedRanges(std::move(Arg.SignedRanges)),
8902 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
8903 SCEVAllocator(std::move(Arg.SCEVAllocator)),
8904 FirstUnknown(Arg.FirstUnknown) {
8905 Arg.FirstUnknown = nullptr;
8908 ScalarEvolution::~ScalarEvolution() {
8909 // Iterate through all the SCEVUnknown instances and call their
8910 // destructors, so that they release their references to their values.
8911 for (SCEVUnknown *U = FirstUnknown; U;) {
8912 SCEVUnknown *Tmp = U;
8914 Tmp->~SCEVUnknown();
8916 FirstUnknown = nullptr;
8918 ValueExprMap.clear();
8920 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
8921 // that a loop had multiple computable exits.
8922 for (auto &BTCI : BackedgeTakenCounts)
8923 BTCI.second.clear();
8925 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
8926 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
8927 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
8930 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8931 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8934 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8936 // Print all inner loops first
8937 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8938 PrintLoopInfo(OS, SE, *I);
8941 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8944 SmallVector<BasicBlock *, 8> ExitBlocks;
8945 L->getExitBlocks(ExitBlocks);
8946 if (ExitBlocks.size() != 1)
8947 OS << "<multiple exits> ";
8949 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8950 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8952 OS << "Unpredictable backedge-taken count. ";
8957 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8960 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8961 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8963 OS << "Unpredictable max backedge-taken count. ";
8969 void ScalarEvolution::print(raw_ostream &OS) const {
8970 // ScalarEvolution's implementation of the print method is to print
8971 // out SCEV values of all instructions that are interesting. Doing
8972 // this potentially causes it to create new SCEV objects though,
8973 // which technically conflicts with the const qualifier. This isn't
8974 // observable from outside the class though, so casting away the
8975 // const isn't dangerous.
8976 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8978 OS << "Classifying expressions for: ";
8979 F.printAsOperand(OS, /*PrintType=*/false);
8981 for (Instruction &I : instructions(F))
8982 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
8985 const SCEV *SV = SE.getSCEV(&I);
8987 if (!isa<SCEVCouldNotCompute>(SV)) {
8989 SE.getUnsignedRange(SV).print(OS);
8991 SE.getSignedRange(SV).print(OS);
8994 const Loop *L = LI.getLoopFor(I.getParent());
8996 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
9000 if (!isa<SCEVCouldNotCompute>(AtUse)) {
9002 SE.getUnsignedRange(AtUse).print(OS);
9004 SE.getSignedRange(AtUse).print(OS);
9009 OS << "\t\t" "Exits: ";
9010 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
9011 if (!SE.isLoopInvariant(ExitValue, L)) {
9012 OS << "<<Unknown>>";
9021 OS << "Determining loop execution counts for: ";
9022 F.printAsOperand(OS, /*PrintType=*/false);
9024 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
9025 PrintLoopInfo(OS, &SE, *I);
9028 ScalarEvolution::LoopDisposition
9029 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
9030 auto &Values = LoopDispositions[S];
9031 for (auto &V : Values) {
9032 if (V.getPointer() == L)
9035 Values.emplace_back(L, LoopVariant);
9036 LoopDisposition D = computeLoopDisposition(S, L);
9037 auto &Values2 = LoopDispositions[S];
9038 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9039 if (V.getPointer() == L) {
9047 ScalarEvolution::LoopDisposition
9048 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
9049 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9051 return LoopInvariant;
9055 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
9056 case scAddRecExpr: {
9057 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9059 // If L is the addrec's loop, it's computable.
9060 if (AR->getLoop() == L)
9061 return LoopComputable;
9063 // Add recurrences are never invariant in the function-body (null loop).
9067 // This recurrence is variant w.r.t. L if L contains AR's loop.
9068 if (L->contains(AR->getLoop()))
9071 // This recurrence is invariant w.r.t. L if AR's loop contains L.
9072 if (AR->getLoop()->contains(L))
9073 return LoopInvariant;
9075 // This recurrence is variant w.r.t. L if any of its operands
9077 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
9079 if (!isLoopInvariant(*I, L))
9082 // Otherwise it's loop-invariant.
9083 return LoopInvariant;
9089 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9090 bool HasVarying = false;
9091 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
9093 LoopDisposition D = getLoopDisposition(*I, L);
9094 if (D == LoopVariant)
9096 if (D == LoopComputable)
9099 return HasVarying ? LoopComputable : LoopInvariant;
9102 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9103 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
9104 if (LD == LoopVariant)
9106 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
9107 if (RD == LoopVariant)
9109 return (LD == LoopInvariant && RD == LoopInvariant) ?
9110 LoopInvariant : LoopComputable;
9113 // All non-instruction values are loop invariant. All instructions are loop
9114 // invariant if they are not contained in the specified loop.
9115 // Instructions are never considered invariant in the function body
9116 // (null loop) because they are defined within the "loop".
9117 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
9118 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
9119 return LoopInvariant;
9120 case scCouldNotCompute:
9121 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9123 llvm_unreachable("Unknown SCEV kind!");
9126 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
9127 return getLoopDisposition(S, L) == LoopInvariant;
9130 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
9131 return getLoopDisposition(S, L) == LoopComputable;
9134 ScalarEvolution::BlockDisposition
9135 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9136 auto &Values = BlockDispositions[S];
9137 for (auto &V : Values) {
9138 if (V.getPointer() == BB)
9141 Values.emplace_back(BB, DoesNotDominateBlock);
9142 BlockDisposition D = computeBlockDisposition(S, BB);
9143 auto &Values2 = BlockDispositions[S];
9144 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9145 if (V.getPointer() == BB) {
9153 ScalarEvolution::BlockDisposition
9154 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9155 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9157 return ProperlyDominatesBlock;
9161 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
9162 case scAddRecExpr: {
9163 // This uses a "dominates" query instead of "properly dominates" query
9164 // to test for proper dominance too, because the instruction which
9165 // produces the addrec's value is a PHI, and a PHI effectively properly
9166 // dominates its entire containing block.
9167 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9168 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9169 return DoesNotDominateBlock;
9171 // FALL THROUGH into SCEVNAryExpr handling.
9176 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9178 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
9180 BlockDisposition D = getBlockDisposition(*I, BB);
9181 if (D == DoesNotDominateBlock)
9182 return DoesNotDominateBlock;
9183 if (D == DominatesBlock)
9186 return Proper ? ProperlyDominatesBlock : DominatesBlock;
9189 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9190 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9191 BlockDisposition LD = getBlockDisposition(LHS, BB);
9192 if (LD == DoesNotDominateBlock)
9193 return DoesNotDominateBlock;
9194 BlockDisposition RD = getBlockDisposition(RHS, BB);
9195 if (RD == DoesNotDominateBlock)
9196 return DoesNotDominateBlock;
9197 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9198 ProperlyDominatesBlock : DominatesBlock;
9201 if (Instruction *I =
9202 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9203 if (I->getParent() == BB)
9204 return DominatesBlock;
9205 if (DT.properlyDominates(I->getParent(), BB))
9206 return ProperlyDominatesBlock;
9207 return DoesNotDominateBlock;
9209 return ProperlyDominatesBlock;
9210 case scCouldNotCompute:
9211 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9213 llvm_unreachable("Unknown SCEV kind!");
9216 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9217 return getBlockDisposition(S, BB) >= DominatesBlock;
9220 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9221 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9225 // Search for a SCEV expression node within an expression tree.
9226 // Implements SCEVTraversal::Visitor.
9231 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
9233 bool follow(const SCEV *S) {
9234 IsFound |= (S == Node);
9237 bool isDone() const { return IsFound; }
9241 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9242 SCEVSearch Search(Op);
9243 visitAll(S, Search);
9244 return Search.IsFound;
9247 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9248 ValuesAtScopes.erase(S);
9249 LoopDispositions.erase(S);
9250 BlockDispositions.erase(S);
9251 UnsignedRanges.erase(S);
9252 SignedRanges.erase(S);
9254 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
9255 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
9256 BackedgeTakenInfo &BEInfo = I->second;
9257 if (BEInfo.hasOperand(S, this)) {
9259 BackedgeTakenCounts.erase(I++);
9266 typedef DenseMap<const Loop *, std::string> VerifyMap;
9268 /// replaceSubString - Replaces all occurrences of From in Str with To.
9269 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9271 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9272 Str.replace(Pos, From.size(), To.data(), To.size());
9277 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9279 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9280 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
9281 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
9283 std::string &S = Map[L];
9285 raw_string_ostream OS(S);
9286 SE.getBackedgeTakenCount(L)->print(OS);
9288 // false and 0 are semantically equivalent. This can happen in dead loops.
9289 replaceSubString(OS.str(), "false", "0");
9290 // Remove wrap flags, their use in SCEV is highly fragile.
9291 // FIXME: Remove this when SCEV gets smarter about them.
9292 replaceSubString(OS.str(), "<nw>", "");
9293 replaceSubString(OS.str(), "<nsw>", "");
9294 replaceSubString(OS.str(), "<nuw>", "");
9299 void ScalarEvolution::verify() const {
9300 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9302 // Gather stringified backedge taken counts for all loops using SCEV's caches.
9303 // FIXME: It would be much better to store actual values instead of strings,
9304 // but SCEV pointers will change if we drop the caches.
9305 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9306 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9307 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9309 // Gather stringified backedge taken counts for all loops using a fresh
9310 // ScalarEvolution object.
9311 ScalarEvolution SE2(F, TLI, AC, DT, LI);
9312 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9313 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9315 // Now compare whether they're the same with and without caches. This allows
9316 // verifying that no pass changed the cache.
9317 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
9318 "New loops suddenly appeared!");
9320 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
9321 OldE = BackedgeDumpsOld.end(),
9322 NewI = BackedgeDumpsNew.begin();
9323 OldI != OldE; ++OldI, ++NewI) {
9324 assert(OldI->first == NewI->first && "Loop order changed!");
9326 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
9328 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
9329 // means that a pass is buggy or SCEV has to learn a new pattern but is
9330 // usually not harmful.
9331 if (OldI->second != NewI->second &&
9332 OldI->second.find("undef") == std::string::npos &&
9333 NewI->second.find("undef") == std::string::npos &&
9334 OldI->second != "***COULDNOTCOMPUTE***" &&
9335 NewI->second != "***COULDNOTCOMPUTE***") {
9336 dbgs() << "SCEVValidator: SCEV for loop '"
9337 << OldI->first->getHeader()->getName()
9338 << "' changed from '" << OldI->second
9339 << "' to '" << NewI->second << "'!\n";
9344 // TODO: Verify more things.
9347 char ScalarEvolutionAnalysis::PassID;
9349 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
9350 AnalysisManager<Function> *AM) {
9351 return ScalarEvolution(F, AM->getResult<TargetLibraryAnalysis>(F),
9352 AM->getResult<AssumptionAnalysis>(F),
9353 AM->getResult<DominatorTreeAnalysis>(F),
9354 AM->getResult<LoopAnalysis>(F));
9358 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> *AM) {
9359 AM->getResult<ScalarEvolutionAnalysis>(F).print(OS);
9360 return PreservedAnalyses::all();
9363 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
9364 "Scalar Evolution Analysis", false, true)
9365 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
9366 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
9367 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
9368 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
9369 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
9370 "Scalar Evolution Analysis", false, true)
9371 char ScalarEvolutionWrapperPass::ID = 0;
9373 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
9374 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
9377 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
9378 SE.reset(new ScalarEvolution(
9379 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
9380 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
9381 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
9382 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
9386 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
9388 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
9392 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
9399 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
9400 AU.setPreservesAll();
9401 AU.addRequiredTransitive<AssumptionCacheTracker>();
9402 AU.addRequiredTransitive<LoopInfoWrapperPass>();
9403 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
9404 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();