1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/Support/CommandLine.h"
87 #include "llvm/Support/Debug.h"
88 #include "llvm/Support/ErrorHandling.h"
89 #include "llvm/Support/MathExtras.h"
90 #include "llvm/Support/raw_ostream.h"
91 #include "llvm/Support/SaveAndRestore.h"
95 #define DEBUG_TYPE "scalar-evolution"
97 STATISTIC(NumArrayLenItCounts,
98 "Number of trip counts computed with array length");
99 STATISTIC(NumTripCountsComputed,
100 "Number of loops with predictable loop counts");
101 STATISTIC(NumTripCountsNotComputed,
102 "Number of loops without predictable loop counts");
103 STATISTIC(NumBruteForceTripCountsComputed,
104 "Number of loops with trip counts computed by force");
106 static cl::opt<unsigned>
107 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
108 cl::desc("Maximum number of iterations SCEV will "
109 "symbolically execute a constant "
113 // FIXME: Enable this with XDEBUG when the test suite is clean.
115 VerifySCEV("verify-scev",
116 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
118 //===----------------------------------------------------------------------===//
119 // SCEV class definitions
120 //===----------------------------------------------------------------------===//
122 //===----------------------------------------------------------------------===//
123 // Implementation of the SCEV class.
126 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
127 void SCEV::dump() const {
133 void SCEV::print(raw_ostream &OS) const {
134 switch (static_cast<SCEVTypes>(getSCEVType())) {
136 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
139 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
140 const SCEV *Op = Trunc->getOperand();
141 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
142 << *Trunc->getType() << ")";
146 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
147 const SCEV *Op = ZExt->getOperand();
148 OS << "(zext " << *Op->getType() << " " << *Op << " to "
149 << *ZExt->getType() << ")";
153 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
154 const SCEV *Op = SExt->getOperand();
155 OS << "(sext " << *Op->getType() << " " << *Op << " to "
156 << *SExt->getType() << ")";
160 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
161 OS << "{" << *AR->getOperand(0);
162 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
163 OS << ",+," << *AR->getOperand(i);
165 if (AR->getNoWrapFlags(FlagNUW))
167 if (AR->getNoWrapFlags(FlagNSW))
169 if (AR->getNoWrapFlags(FlagNW) &&
170 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
172 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
180 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
181 const char *OpStr = nullptr;
182 switch (NAry->getSCEVType()) {
183 case scAddExpr: OpStr = " + "; break;
184 case scMulExpr: OpStr = " * "; break;
185 case scUMaxExpr: OpStr = " umax "; break;
186 case scSMaxExpr: OpStr = " smax "; break;
189 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
192 if (std::next(I) != E)
196 switch (NAry->getSCEVType()) {
199 if (NAry->getNoWrapFlags(FlagNUW))
201 if (NAry->getNoWrapFlags(FlagNSW))
207 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
208 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
212 const SCEVUnknown *U = cast<SCEVUnknown>(this);
214 if (U->isSizeOf(AllocTy)) {
215 OS << "sizeof(" << *AllocTy << ")";
218 if (U->isAlignOf(AllocTy)) {
219 OS << "alignof(" << *AllocTy << ")";
225 if (U->isOffsetOf(CTy, FieldNo)) {
226 OS << "offsetof(" << *CTy << ", ";
227 FieldNo->printAsOperand(OS, false);
232 // Otherwise just print it normally.
233 U->getValue()->printAsOperand(OS, false);
236 case scCouldNotCompute:
237 OS << "***COULDNOTCOMPUTE***";
240 llvm_unreachable("Unknown SCEV kind!");
243 Type *SCEV::getType() const {
244 switch (static_cast<SCEVTypes>(getSCEVType())) {
246 return cast<SCEVConstant>(this)->getType();
250 return cast<SCEVCastExpr>(this)->getType();
255 return cast<SCEVNAryExpr>(this)->getType();
257 return cast<SCEVAddExpr>(this)->getType();
259 return cast<SCEVUDivExpr>(this)->getType();
261 return cast<SCEVUnknown>(this)->getType();
262 case scCouldNotCompute:
263 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
265 llvm_unreachable("Unknown SCEV kind!");
268 bool SCEV::isZero() const {
269 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
270 return SC->getValue()->isZero();
274 bool SCEV::isOne() const {
275 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
276 return SC->getValue()->isOne();
280 bool SCEV::isAllOnesValue() const {
281 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
282 return SC->getValue()->isAllOnesValue();
286 /// isNonConstantNegative - Return true if the specified scev is negated, but
288 bool SCEV::isNonConstantNegative() const {
289 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
290 if (!Mul) return false;
292 // If there is a constant factor, it will be first.
293 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
294 if (!SC) return false;
296 // Return true if the value is negative, this matches things like (-42 * V).
297 return SC->getValue()->getValue().isNegative();
300 SCEVCouldNotCompute::SCEVCouldNotCompute() :
301 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
303 bool SCEVCouldNotCompute::classof(const SCEV *S) {
304 return S->getSCEVType() == scCouldNotCompute;
307 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
309 ID.AddInteger(scConstant);
312 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
313 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
314 UniqueSCEVs.InsertNode(S, IP);
318 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
319 return getConstant(ConstantInt::get(getContext(), Val));
323 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
324 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
325 return getConstant(ConstantInt::get(ITy, V, isSigned));
328 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
329 unsigned SCEVTy, const SCEV *op, Type *ty)
330 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
332 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
333 const SCEV *op, Type *ty)
334 : SCEVCastExpr(ID, scTruncate, op, ty) {
335 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
336 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
337 "Cannot truncate non-integer value!");
340 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
341 const SCEV *op, Type *ty)
342 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
343 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
344 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
345 "Cannot zero extend non-integer value!");
348 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
349 const SCEV *op, Type *ty)
350 : SCEVCastExpr(ID, scSignExtend, op, ty) {
351 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
352 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
353 "Cannot sign extend non-integer value!");
356 void SCEVUnknown::deleted() {
357 // Clear this SCEVUnknown from various maps.
358 SE->forgetMemoizedResults(this);
360 // Remove this SCEVUnknown from the uniquing map.
361 SE->UniqueSCEVs.RemoveNode(this);
363 // Release the value.
367 void SCEVUnknown::allUsesReplacedWith(Value *New) {
368 // Clear this SCEVUnknown from various maps.
369 SE->forgetMemoizedResults(this);
371 // Remove this SCEVUnknown from the uniquing map.
372 SE->UniqueSCEVs.RemoveNode(this);
374 // Update this SCEVUnknown to point to the new value. This is needed
375 // because there may still be outstanding SCEVs which still point to
380 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
381 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
382 if (VCE->getOpcode() == Instruction::PtrToInt)
383 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
384 if (CE->getOpcode() == Instruction::GetElementPtr &&
385 CE->getOperand(0)->isNullValue() &&
386 CE->getNumOperands() == 2)
387 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
389 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
397 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
398 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
399 if (VCE->getOpcode() == Instruction::PtrToInt)
400 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
401 if (CE->getOpcode() == Instruction::GetElementPtr &&
402 CE->getOperand(0)->isNullValue()) {
404 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
405 if (StructType *STy = dyn_cast<StructType>(Ty))
406 if (!STy->isPacked() &&
407 CE->getNumOperands() == 3 &&
408 CE->getOperand(1)->isNullValue()) {
409 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
411 STy->getNumElements() == 2 &&
412 STy->getElementType(0)->isIntegerTy(1)) {
413 AllocTy = STy->getElementType(1);
422 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
423 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
424 if (VCE->getOpcode() == Instruction::PtrToInt)
425 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
426 if (CE->getOpcode() == Instruction::GetElementPtr &&
427 CE->getNumOperands() == 3 &&
428 CE->getOperand(0)->isNullValue() &&
429 CE->getOperand(1)->isNullValue()) {
431 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
432 // Ignore vector types here so that ScalarEvolutionExpander doesn't
433 // emit getelementptrs that index into vectors.
434 if (Ty->isStructTy() || Ty->isArrayTy()) {
436 FieldNo = CE->getOperand(2);
444 //===----------------------------------------------------------------------===//
446 //===----------------------------------------------------------------------===//
449 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
450 /// than the complexity of the RHS. This comparator is used to canonicalize
452 class SCEVComplexityCompare {
453 const LoopInfo *const LI;
455 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
457 // Return true or false if LHS is less than, or at least RHS, respectively.
458 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
459 return compare(LHS, RHS) < 0;
462 // Return negative, zero, or positive, if LHS is less than, equal to, or
463 // greater than RHS, respectively. A three-way result allows recursive
464 // comparisons to be more efficient.
465 int compare(const SCEV *LHS, const SCEV *RHS) const {
466 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
470 // Primarily, sort the SCEVs by their getSCEVType().
471 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
473 return (int)LType - (int)RType;
475 // Aside from the getSCEVType() ordering, the particular ordering
476 // isn't very important except that it's beneficial to be consistent,
477 // so that (a + b) and (b + a) don't end up as different expressions.
478 switch (static_cast<SCEVTypes>(LType)) {
480 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
481 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
483 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
484 // not as complete as it could be.
485 const Value *LV = LU->getValue(), *RV = RU->getValue();
487 // Order pointer values after integer values. This helps SCEVExpander
489 bool LIsPointer = LV->getType()->isPointerTy(),
490 RIsPointer = RV->getType()->isPointerTy();
491 if (LIsPointer != RIsPointer)
492 return (int)LIsPointer - (int)RIsPointer;
494 // Compare getValueID values.
495 unsigned LID = LV->getValueID(),
496 RID = RV->getValueID();
498 return (int)LID - (int)RID;
500 // Sort arguments by their position.
501 if (const Argument *LA = dyn_cast<Argument>(LV)) {
502 const Argument *RA = cast<Argument>(RV);
503 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
504 return (int)LArgNo - (int)RArgNo;
507 // For instructions, compare their loop depth, and their operand
508 // count. This is pretty loose.
509 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
510 const Instruction *RInst = cast<Instruction>(RV);
512 // Compare loop depths.
513 const BasicBlock *LParent = LInst->getParent(),
514 *RParent = RInst->getParent();
515 if (LParent != RParent) {
516 unsigned LDepth = LI->getLoopDepth(LParent),
517 RDepth = LI->getLoopDepth(RParent);
518 if (LDepth != RDepth)
519 return (int)LDepth - (int)RDepth;
522 // Compare the number of operands.
523 unsigned LNumOps = LInst->getNumOperands(),
524 RNumOps = RInst->getNumOperands();
525 return (int)LNumOps - (int)RNumOps;
532 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
533 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
535 // Compare constant values.
536 const APInt &LA = LC->getValue()->getValue();
537 const APInt &RA = RC->getValue()->getValue();
538 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
539 if (LBitWidth != RBitWidth)
540 return (int)LBitWidth - (int)RBitWidth;
541 return LA.ult(RA) ? -1 : 1;
545 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
546 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
548 // Compare addrec loop depths.
549 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
550 if (LLoop != RLoop) {
551 unsigned LDepth = LLoop->getLoopDepth(),
552 RDepth = RLoop->getLoopDepth();
553 if (LDepth != RDepth)
554 return (int)LDepth - (int)RDepth;
557 // Addrec complexity grows with operand count.
558 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
559 if (LNumOps != RNumOps)
560 return (int)LNumOps - (int)RNumOps;
562 // Lexicographically compare.
563 for (unsigned i = 0; i != LNumOps; ++i) {
564 long X = compare(LA->getOperand(i), RA->getOperand(i));
576 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
577 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
579 // Lexicographically compare n-ary expressions.
580 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
581 if (LNumOps != RNumOps)
582 return (int)LNumOps - (int)RNumOps;
584 for (unsigned i = 0; i != LNumOps; ++i) {
587 long X = compare(LC->getOperand(i), RC->getOperand(i));
591 return (int)LNumOps - (int)RNumOps;
595 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
596 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
598 // Lexicographically compare udiv expressions.
599 long X = compare(LC->getLHS(), RC->getLHS());
602 return compare(LC->getRHS(), RC->getRHS());
608 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
609 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
611 // Compare cast expressions by operand.
612 return compare(LC->getOperand(), RC->getOperand());
615 case scCouldNotCompute:
616 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
618 llvm_unreachable("Unknown SCEV kind!");
623 /// GroupByComplexity - Given a list of SCEV objects, order them by their
624 /// complexity, and group objects of the same complexity together by value.
625 /// When this routine is finished, we know that any duplicates in the vector are
626 /// consecutive and that complexity is monotonically increasing.
628 /// Note that we go take special precautions to ensure that we get deterministic
629 /// results from this routine. In other words, we don't want the results of
630 /// this to depend on where the addresses of various SCEV objects happened to
633 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
635 if (Ops.size() < 2) return; // Noop
636 if (Ops.size() == 2) {
637 // This is the common case, which also happens to be trivially simple.
639 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
640 if (SCEVComplexityCompare(LI)(RHS, LHS))
645 // Do the rough sort by complexity.
646 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
648 // Now that we are sorted by complexity, group elements of the same
649 // complexity. Note that this is, at worst, N^2, but the vector is likely to
650 // be extremely short in practice. Note that we take this approach because we
651 // do not want to depend on the addresses of the objects we are grouping.
652 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
653 const SCEV *S = Ops[i];
654 unsigned Complexity = S->getSCEVType();
656 // If there are any objects of the same complexity and same value as this
658 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
659 if (Ops[j] == S) { // Found a duplicate.
660 // Move it to immediately after i'th element.
661 std::swap(Ops[i+1], Ops[j]);
662 ++i; // no need to rescan it.
663 if (i == e-2) return; // Done!
670 struct FindSCEVSize {
672 FindSCEVSize() : Size(0) {}
674 bool follow(const SCEV *S) {
676 // Keep looking at all operands of S.
679 bool isDone() const {
685 // Returns the size of the SCEV S.
686 static inline int sizeOfSCEV(const SCEV *S) {
688 SCEVTraversal<FindSCEVSize> ST(F);
695 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
697 // Computes the Quotient and Remainder of the division of Numerator by
699 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
700 const SCEV *Denominator, const SCEV **Quotient,
701 const SCEV **Remainder) {
702 assert(Numerator && Denominator && "Uninitialized SCEV");
704 SCEVDivision D(SE, Numerator, Denominator);
706 // Check for the trivial case here to avoid having to check for it in the
708 if (Numerator == Denominator) {
714 if (Numerator->isZero()) {
720 // A simple case when N/1. The quotient is N.
721 if (Denominator->isOne()) {
722 *Quotient = Numerator;
727 // Split the Denominator when it is a product.
728 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
730 *Quotient = Numerator;
731 for (const SCEV *Op : T->operands()) {
732 divide(SE, *Quotient, Op, &Q, &R);
735 // Bail out when the Numerator is not divisible by one of the terms of
739 *Remainder = Numerator;
748 *Quotient = D.Quotient;
749 *Remainder = D.Remainder;
752 // Except in the trivial case described above, we do not know how to divide
753 // Expr by Denominator for the following functions with empty implementation.
754 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
755 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
756 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
757 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
758 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
759 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
760 void visitUnknown(const SCEVUnknown *Numerator) {}
761 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
763 void visitConstant(const SCEVConstant *Numerator) {
764 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
765 APInt NumeratorVal = Numerator->getValue()->getValue();
766 APInt DenominatorVal = D->getValue()->getValue();
767 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
768 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
770 if (NumeratorBW > DenominatorBW)
771 DenominatorVal = DenominatorVal.sext(NumeratorBW);
772 else if (NumeratorBW < DenominatorBW)
773 NumeratorVal = NumeratorVal.sext(DenominatorBW);
775 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
776 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
777 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
778 Quotient = SE.getConstant(QuotientVal);
779 Remainder = SE.getConstant(RemainderVal);
784 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
785 const SCEV *StartQ, *StartR, *StepQ, *StepR;
786 if (!Numerator->isAffine())
787 return cannotDivide(Numerator);
788 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
789 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
790 // Bail out if the types do not match.
791 Type *Ty = Denominator->getType();
792 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
793 Ty != StepQ->getType() || Ty != StepR->getType())
794 return cannotDivide(Numerator);
795 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
796 Numerator->getNoWrapFlags());
797 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
798 Numerator->getNoWrapFlags());
801 void visitAddExpr(const SCEVAddExpr *Numerator) {
802 SmallVector<const SCEV *, 2> Qs, Rs;
803 Type *Ty = Denominator->getType();
805 for (const SCEV *Op : Numerator->operands()) {
807 divide(SE, Op, Denominator, &Q, &R);
809 // Bail out if types do not match.
810 if (Ty != Q->getType() || Ty != R->getType())
811 return cannotDivide(Numerator);
817 if (Qs.size() == 1) {
823 Quotient = SE.getAddExpr(Qs);
824 Remainder = SE.getAddExpr(Rs);
827 void visitMulExpr(const SCEVMulExpr *Numerator) {
828 SmallVector<const SCEV *, 2> Qs;
829 Type *Ty = Denominator->getType();
831 bool FoundDenominatorTerm = false;
832 for (const SCEV *Op : Numerator->operands()) {
833 // Bail out if types do not match.
834 if (Ty != Op->getType())
835 return cannotDivide(Numerator);
837 if (FoundDenominatorTerm) {
842 // Check whether Denominator divides one of the product operands.
844 divide(SE, Op, Denominator, &Q, &R);
850 // Bail out if types do not match.
851 if (Ty != Q->getType())
852 return cannotDivide(Numerator);
854 FoundDenominatorTerm = true;
858 if (FoundDenominatorTerm) {
863 Quotient = SE.getMulExpr(Qs);
867 if (!isa<SCEVUnknown>(Denominator))
868 return cannotDivide(Numerator);
870 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
871 ValueToValueMap RewriteMap;
872 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
873 cast<SCEVConstant>(Zero)->getValue();
874 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
876 if (Remainder->isZero()) {
877 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
878 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
879 cast<SCEVConstant>(One)->getValue();
881 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
885 // Quotient is (Numerator - Remainder) divided by Denominator.
887 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
888 // This SCEV does not seem to simplify: fail the division here.
889 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
890 return cannotDivide(Numerator);
891 divide(SE, Diff, Denominator, &Q, &R);
893 return cannotDivide(Numerator);
898 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
899 const SCEV *Denominator)
900 : SE(S), Denominator(Denominator) {
901 Zero = SE.getZero(Denominator->getType());
902 One = SE.getOne(Denominator->getType());
904 // We generally do not know how to divide Expr by Denominator. We
905 // initialize the division to a "cannot divide" state to simplify the rest
907 cannotDivide(Numerator);
910 // Convenience function for giving up on the division. We set the quotient to
911 // be equal to zero and the remainder to be equal to the numerator.
912 void cannotDivide(const SCEV *Numerator) {
914 Remainder = Numerator;
918 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
923 //===----------------------------------------------------------------------===//
924 // Simple SCEV method implementations
925 //===----------------------------------------------------------------------===//
927 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
929 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
932 // Handle the simplest case efficiently.
934 return SE.getTruncateOrZeroExtend(It, ResultTy);
936 // We are using the following formula for BC(It, K):
938 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
940 // Suppose, W is the bitwidth of the return value. We must be prepared for
941 // overflow. Hence, we must assure that the result of our computation is
942 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
943 // safe in modular arithmetic.
945 // However, this code doesn't use exactly that formula; the formula it uses
946 // is something like the following, where T is the number of factors of 2 in
947 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
950 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
952 // This formula is trivially equivalent to the previous formula. However,
953 // this formula can be implemented much more efficiently. The trick is that
954 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
955 // arithmetic. To do exact division in modular arithmetic, all we have
956 // to do is multiply by the inverse. Therefore, this step can be done at
959 // The next issue is how to safely do the division by 2^T. The way this
960 // is done is by doing the multiplication step at a width of at least W + T
961 // bits. This way, the bottom W+T bits of the product are accurate. Then,
962 // when we perform the division by 2^T (which is equivalent to a right shift
963 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
964 // truncated out after the division by 2^T.
966 // In comparison to just directly using the first formula, this technique
967 // is much more efficient; using the first formula requires W * K bits,
968 // but this formula less than W + K bits. Also, the first formula requires
969 // a division step, whereas this formula only requires multiplies and shifts.
971 // It doesn't matter whether the subtraction step is done in the calculation
972 // width or the input iteration count's width; if the subtraction overflows,
973 // the result must be zero anyway. We prefer here to do it in the width of
974 // the induction variable because it helps a lot for certain cases; CodeGen
975 // isn't smart enough to ignore the overflow, which leads to much less
976 // efficient code if the width of the subtraction is wider than the native
979 // (It's possible to not widen at all by pulling out factors of 2 before
980 // the multiplication; for example, K=2 can be calculated as
981 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
982 // extra arithmetic, so it's not an obvious win, and it gets
983 // much more complicated for K > 3.)
985 // Protection from insane SCEVs; this bound is conservative,
986 // but it probably doesn't matter.
988 return SE.getCouldNotCompute();
990 unsigned W = SE.getTypeSizeInBits(ResultTy);
992 // Calculate K! / 2^T and T; we divide out the factors of two before
993 // multiplying for calculating K! / 2^T to avoid overflow.
994 // Other overflow doesn't matter because we only care about the bottom
995 // W bits of the result.
996 APInt OddFactorial(W, 1);
998 for (unsigned i = 3; i <= K; ++i) {
1000 unsigned TwoFactors = Mult.countTrailingZeros();
1002 Mult = Mult.lshr(TwoFactors);
1003 OddFactorial *= Mult;
1006 // We need at least W + T bits for the multiplication step
1007 unsigned CalculationBits = W + T;
1009 // Calculate 2^T, at width T+W.
1010 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1012 // Calculate the multiplicative inverse of K! / 2^T;
1013 // this multiplication factor will perform the exact division by
1015 APInt Mod = APInt::getSignedMinValue(W+1);
1016 APInt MultiplyFactor = OddFactorial.zext(W+1);
1017 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1018 MultiplyFactor = MultiplyFactor.trunc(W);
1020 // Calculate the product, at width T+W
1021 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1023 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1024 for (unsigned i = 1; i != K; ++i) {
1025 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1026 Dividend = SE.getMulExpr(Dividend,
1027 SE.getTruncateOrZeroExtend(S, CalculationTy));
1031 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1033 // Truncate the result, and divide by K! / 2^T.
1035 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1036 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1039 /// evaluateAtIteration - Return the value of this chain of recurrences at
1040 /// the specified iteration number. We can evaluate this recurrence by
1041 /// multiplying each element in the chain by the binomial coefficient
1042 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1044 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1046 /// where BC(It, k) stands for binomial coefficient.
1048 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1049 ScalarEvolution &SE) const {
1050 const SCEV *Result = getStart();
1051 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1052 // The computation is correct in the face of overflow provided that the
1053 // multiplication is performed _after_ the evaluation of the binomial
1055 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1056 if (isa<SCEVCouldNotCompute>(Coeff))
1059 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1064 //===----------------------------------------------------------------------===//
1065 // SCEV Expression folder implementations
1066 //===----------------------------------------------------------------------===//
1068 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1070 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1071 "This is not a truncating conversion!");
1072 assert(isSCEVable(Ty) &&
1073 "This is not a conversion to a SCEVable type!");
1074 Ty = getEffectiveSCEVType(Ty);
1076 FoldingSetNodeID ID;
1077 ID.AddInteger(scTruncate);
1081 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1083 // Fold if the operand is constant.
1084 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1086 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1088 // trunc(trunc(x)) --> trunc(x)
1089 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1090 return getTruncateExpr(ST->getOperand(), Ty);
1092 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1093 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1094 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1096 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1097 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1098 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1100 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1101 // eliminate all the truncates, or we replace other casts with truncates.
1102 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1103 SmallVector<const SCEV *, 4> Operands;
1104 bool hasTrunc = false;
1105 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1106 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1107 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1108 hasTrunc = isa<SCEVTruncateExpr>(S);
1109 Operands.push_back(S);
1112 return getAddExpr(Operands);
1113 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1116 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1117 // eliminate all the truncates, or we replace other casts with truncates.
1118 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1119 SmallVector<const SCEV *, 4> Operands;
1120 bool hasTrunc = false;
1121 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1122 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1123 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1124 hasTrunc = isa<SCEVTruncateExpr>(S);
1125 Operands.push_back(S);
1128 return getMulExpr(Operands);
1129 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1132 // If the input value is a chrec scev, truncate the chrec's operands.
1133 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1134 SmallVector<const SCEV *, 4> Operands;
1135 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1136 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
1137 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1140 // The cast wasn't folded; create an explicit cast node. We can reuse
1141 // the existing insert position since if we get here, we won't have
1142 // made any changes which would invalidate it.
1143 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1145 UniqueSCEVs.InsertNode(S, IP);
1149 // Get the limit of a recurrence such that incrementing by Step cannot cause
1150 // signed overflow as long as the value of the recurrence within the
1151 // loop does not exceed this limit before incrementing.
1152 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1153 ICmpInst::Predicate *Pred,
1154 ScalarEvolution *SE) {
1155 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1156 if (SE->isKnownPositive(Step)) {
1157 *Pred = ICmpInst::ICMP_SLT;
1158 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1159 SE->getSignedRange(Step).getSignedMax());
1161 if (SE->isKnownNegative(Step)) {
1162 *Pred = ICmpInst::ICMP_SGT;
1163 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1164 SE->getSignedRange(Step).getSignedMin());
1169 // Get the limit of a recurrence such that incrementing by Step cannot cause
1170 // unsigned overflow as long as the value of the recurrence within the loop does
1171 // not exceed this limit before incrementing.
1172 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1173 ICmpInst::Predicate *Pred,
1174 ScalarEvolution *SE) {
1175 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1176 *Pred = ICmpInst::ICMP_ULT;
1178 return SE->getConstant(APInt::getMinValue(BitWidth) -
1179 SE->getUnsignedRange(Step).getUnsignedMax());
1184 struct ExtendOpTraitsBase {
1185 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1188 // Used to make code generic over signed and unsigned overflow.
1189 template <typename ExtendOp> struct ExtendOpTraits {
1192 // static const SCEV::NoWrapFlags WrapType;
1194 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1196 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1197 // ICmpInst::Predicate *Pred,
1198 // ScalarEvolution *SE);
1202 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1203 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1205 static const GetExtendExprTy GetExtendExpr;
1207 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1208 ICmpInst::Predicate *Pred,
1209 ScalarEvolution *SE) {
1210 return getSignedOverflowLimitForStep(Step, Pred, SE);
1214 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1215 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1218 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1219 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1221 static const GetExtendExprTy GetExtendExpr;
1223 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1224 ICmpInst::Predicate *Pred,
1225 ScalarEvolution *SE) {
1226 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1230 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1231 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1234 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1235 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1236 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1237 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1238 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1239 // expression "Step + sext/zext(PreIncAR)" is congruent with
1240 // "sext/zext(PostIncAR)"
1241 template <typename ExtendOpTy>
1242 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1243 ScalarEvolution *SE) {
1244 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1245 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1247 const Loop *L = AR->getLoop();
1248 const SCEV *Start = AR->getStart();
1249 const SCEV *Step = AR->getStepRecurrence(*SE);
1251 // Check for a simple looking step prior to loop entry.
1252 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1256 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1257 // subtraction is expensive. For this purpose, perform a quick and dirty
1258 // difference, by checking for Step in the operand list.
1259 SmallVector<const SCEV *, 4> DiffOps;
1260 for (const SCEV *Op : SA->operands())
1262 DiffOps.push_back(Op);
1264 if (DiffOps.size() == SA->getNumOperands())
1267 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1270 // 1. NSW/NUW flags on the step increment.
1271 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1272 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1273 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1275 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1276 // "S+X does not sign/unsign-overflow".
1279 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1280 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1281 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1284 // 2. Direct overflow check on the step operation's expression.
1285 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1286 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1287 const SCEV *OperandExtendedStart =
1288 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1289 (SE->*GetExtendExpr)(Step, WideTy));
1290 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1291 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1292 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1293 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1294 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1295 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1300 // 3. Loop precondition.
1301 ICmpInst::Predicate Pred;
1302 const SCEV *OverflowLimit =
1303 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1305 if (OverflowLimit &&
1306 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1312 // Get the normalized zero or sign extended expression for this AddRec's Start.
1313 template <typename ExtendOpTy>
1314 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1315 ScalarEvolution *SE) {
1316 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1318 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1320 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1322 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1323 (SE->*GetExtendExpr)(PreStart, Ty));
1326 // Try to prove away overflow by looking at "nearby" add recurrences. A
1327 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1328 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1332 // {S,+,X} == {S-T,+,X} + T
1333 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1335 // If ({S-T,+,X} + T) does not overflow ... (1)
1337 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1339 // If {S-T,+,X} does not overflow ... (2)
1341 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1342 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1344 // If (S-T)+T does not overflow ... (3)
1346 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1347 // == {Ext(S),+,Ext(X)} == LHS
1349 // Thus, if (1), (2) and (3) are true for some T, then
1350 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1352 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1353 // does not overflow" restricted to the 0th iteration. Therefore we only need
1354 // to check for (1) and (2).
1356 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1357 // is `Delta` (defined below).
1359 template <typename ExtendOpTy>
1360 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1363 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1365 // We restrict `Start` to a constant to prevent SCEV from spending too much
1366 // time here. It is correct (but more expensive) to continue with a
1367 // non-constant `Start` and do a general SCEV subtraction to compute
1368 // `PreStart` below.
1370 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1374 APInt StartAI = StartC->getValue()->getValue();
1376 for (unsigned Delta : {-2, -1, 1, 2}) {
1377 const SCEV *PreStart = getConstant(StartAI - Delta);
1379 // Give up if we don't already have the add recurrence we need because
1380 // actually constructing an add recurrence is relatively expensive.
1381 const SCEVAddRecExpr *PreAR = [&]() {
1382 FoldingSetNodeID ID;
1383 ID.AddInteger(scAddRecExpr);
1384 ID.AddPointer(PreStart);
1385 ID.AddPointer(Step);
1388 return static_cast<SCEVAddRecExpr *>(
1389 this->UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1392 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1393 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1394 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1395 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1396 DeltaS, &Pred, this);
1397 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1405 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1407 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1408 "This is not an extending conversion!");
1409 assert(isSCEVable(Ty) &&
1410 "This is not a conversion to a SCEVable type!");
1411 Ty = getEffectiveSCEVType(Ty);
1413 // Fold if the operand is constant.
1414 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1416 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1418 // zext(zext(x)) --> zext(x)
1419 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1420 return getZeroExtendExpr(SZ->getOperand(), Ty);
1422 // Before doing any expensive analysis, check to see if we've already
1423 // computed a SCEV for this Op and Ty.
1424 FoldingSetNodeID ID;
1425 ID.AddInteger(scZeroExtend);
1429 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1431 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1432 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1433 // It's possible the bits taken off by the truncate were all zero bits. If
1434 // so, we should be able to simplify this further.
1435 const SCEV *X = ST->getOperand();
1436 ConstantRange CR = getUnsignedRange(X);
1437 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1438 unsigned NewBits = getTypeSizeInBits(Ty);
1439 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1440 CR.zextOrTrunc(NewBits)))
1441 return getTruncateOrZeroExtend(X, Ty);
1444 // If the input value is a chrec scev, and we can prove that the value
1445 // did not overflow the old, smaller, value, we can zero extend all of the
1446 // operands (often constants). This allows analysis of something like
1447 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1448 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1449 if (AR->isAffine()) {
1450 const SCEV *Start = AR->getStart();
1451 const SCEV *Step = AR->getStepRecurrence(*this);
1452 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1453 const Loop *L = AR->getLoop();
1455 // If we have special knowledge that this addrec won't overflow,
1456 // we don't need to do any further analysis.
1457 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1458 return getAddRecExpr(
1459 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1460 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1462 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1463 // Note that this serves two purposes: It filters out loops that are
1464 // simply not analyzable, and it covers the case where this code is
1465 // being called from within backedge-taken count analysis, such that
1466 // attempting to ask for the backedge-taken count would likely result
1467 // in infinite recursion. In the later case, the analysis code will
1468 // cope with a conservative value, and it will take care to purge
1469 // that value once it has finished.
1470 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1471 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1472 // Manually compute the final value for AR, checking for
1475 // Check whether the backedge-taken count can be losslessly casted to
1476 // the addrec's type. The count is always unsigned.
1477 const SCEV *CastedMaxBECount =
1478 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1479 const SCEV *RecastedMaxBECount =
1480 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1481 if (MaxBECount == RecastedMaxBECount) {
1482 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1483 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1484 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1485 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1486 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1487 const SCEV *WideMaxBECount =
1488 getZeroExtendExpr(CastedMaxBECount, WideTy);
1489 const SCEV *OperandExtendedAdd =
1490 getAddExpr(WideStart,
1491 getMulExpr(WideMaxBECount,
1492 getZeroExtendExpr(Step, WideTy)));
1493 if (ZAdd == OperandExtendedAdd) {
1494 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1495 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1496 // Return the expression with the addrec on the outside.
1497 return getAddRecExpr(
1498 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1499 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1501 // Similar to above, only this time treat the step value as signed.
1502 // This covers loops that count down.
1503 OperandExtendedAdd =
1504 getAddExpr(WideStart,
1505 getMulExpr(WideMaxBECount,
1506 getSignExtendExpr(Step, WideTy)));
1507 if (ZAdd == OperandExtendedAdd) {
1508 // Cache knowledge of AR NW, which is propagated to this AddRec.
1509 // Negative step causes unsigned wrap, but it still can't self-wrap.
1510 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1511 // Return the expression with the addrec on the outside.
1512 return getAddRecExpr(
1513 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1514 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1518 // If the backedge is guarded by a comparison with the pre-inc value
1519 // the addrec is safe. Also, if the entry is guarded by a comparison
1520 // with the start value and the backedge is guarded by a comparison
1521 // with the post-inc value, the addrec is safe.
1522 if (isKnownPositive(Step)) {
1523 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1524 getUnsignedRange(Step).getUnsignedMax());
1525 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1526 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1527 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1528 AR->getPostIncExpr(*this), N))) {
1529 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1530 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1531 // Return the expression with the addrec on the outside.
1532 return getAddRecExpr(
1533 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1534 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1536 } else if (isKnownNegative(Step)) {
1537 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1538 getSignedRange(Step).getSignedMin());
1539 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1540 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1541 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1542 AR->getPostIncExpr(*this), N))) {
1543 // Cache knowledge of AR NW, which is propagated to this AddRec.
1544 // Negative step causes unsigned wrap, but it still can't self-wrap.
1545 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1546 // Return the expression with the addrec on the outside.
1547 return getAddRecExpr(
1548 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1549 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1554 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1555 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1556 return getAddRecExpr(
1557 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1558 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1562 // The cast wasn't folded; create an explicit cast node.
1563 // Recompute the insert position, as it may have been invalidated.
1564 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1565 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1567 UniqueSCEVs.InsertNode(S, IP);
1571 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1573 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1574 "This is not an extending conversion!");
1575 assert(isSCEVable(Ty) &&
1576 "This is not a conversion to a SCEVable type!");
1577 Ty = getEffectiveSCEVType(Ty);
1579 // Fold if the operand is constant.
1580 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1582 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1584 // sext(sext(x)) --> sext(x)
1585 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1586 return getSignExtendExpr(SS->getOperand(), Ty);
1588 // sext(zext(x)) --> zext(x)
1589 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1590 return getZeroExtendExpr(SZ->getOperand(), Ty);
1592 // Before doing any expensive analysis, check to see if we've already
1593 // computed a SCEV for this Op and Ty.
1594 FoldingSetNodeID ID;
1595 ID.AddInteger(scSignExtend);
1599 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1601 // If the input value is provably positive, build a zext instead.
1602 if (isKnownNonNegative(Op))
1603 return getZeroExtendExpr(Op, Ty);
1605 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1606 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1607 // It's possible the bits taken off by the truncate were all sign bits. If
1608 // so, we should be able to simplify this further.
1609 const SCEV *X = ST->getOperand();
1610 ConstantRange CR = getSignedRange(X);
1611 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1612 unsigned NewBits = getTypeSizeInBits(Ty);
1613 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1614 CR.sextOrTrunc(NewBits)))
1615 return getTruncateOrSignExtend(X, Ty);
1618 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1619 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1620 if (SA->getNumOperands() == 2) {
1621 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1622 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1624 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1625 const APInt &C1 = SC1->getValue()->getValue();
1626 const APInt &C2 = SC2->getValue()->getValue();
1627 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1628 C2.ugt(C1) && C2.isPowerOf2())
1629 return getAddExpr(getSignExtendExpr(SC1, Ty),
1630 getSignExtendExpr(SMul, Ty));
1635 // If the input value is a chrec scev, and we can prove that the value
1636 // did not overflow the old, smaller, value, we can sign extend all of the
1637 // operands (often constants). This allows analysis of something like
1638 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1639 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1640 if (AR->isAffine()) {
1641 const SCEV *Start = AR->getStart();
1642 const SCEV *Step = AR->getStepRecurrence(*this);
1643 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1644 const Loop *L = AR->getLoop();
1646 // If we have special knowledge that this addrec won't overflow,
1647 // we don't need to do any further analysis.
1648 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1649 return getAddRecExpr(
1650 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1651 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1653 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1654 // Note that this serves two purposes: It filters out loops that are
1655 // simply not analyzable, and it covers the case where this code is
1656 // being called from within backedge-taken count analysis, such that
1657 // attempting to ask for the backedge-taken count would likely result
1658 // in infinite recursion. In the later case, the analysis code will
1659 // cope with a conservative value, and it will take care to purge
1660 // that value once it has finished.
1661 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1662 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1663 // Manually compute the final value for AR, checking for
1666 // Check whether the backedge-taken count can be losslessly casted to
1667 // the addrec's type. The count is always unsigned.
1668 const SCEV *CastedMaxBECount =
1669 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1670 const SCEV *RecastedMaxBECount =
1671 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1672 if (MaxBECount == RecastedMaxBECount) {
1673 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1674 // Check whether Start+Step*MaxBECount has no signed overflow.
1675 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1676 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1677 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1678 const SCEV *WideMaxBECount =
1679 getZeroExtendExpr(CastedMaxBECount, WideTy);
1680 const SCEV *OperandExtendedAdd =
1681 getAddExpr(WideStart,
1682 getMulExpr(WideMaxBECount,
1683 getSignExtendExpr(Step, WideTy)));
1684 if (SAdd == OperandExtendedAdd) {
1685 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1686 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1687 // Return the expression with the addrec on the outside.
1688 return getAddRecExpr(
1689 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1690 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1692 // Similar to above, only this time treat the step value as unsigned.
1693 // This covers loops that count up with an unsigned step.
1694 OperandExtendedAdd =
1695 getAddExpr(WideStart,
1696 getMulExpr(WideMaxBECount,
1697 getZeroExtendExpr(Step, WideTy)));
1698 if (SAdd == OperandExtendedAdd) {
1699 // If AR wraps around then
1701 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1702 // => SAdd != OperandExtendedAdd
1704 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1705 // (SAdd == OperandExtendedAdd => AR is NW)
1707 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1709 // Return the expression with the addrec on the outside.
1710 return getAddRecExpr(
1711 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1712 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1716 // If the backedge is guarded by a comparison with the pre-inc value
1717 // the addrec is safe. Also, if the entry is guarded by a comparison
1718 // with the start value and the backedge is guarded by a comparison
1719 // with the post-inc value, the addrec is safe.
1720 ICmpInst::Predicate Pred;
1721 const SCEV *OverflowLimit =
1722 getSignedOverflowLimitForStep(Step, &Pred, this);
1723 if (OverflowLimit &&
1724 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1725 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1726 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1728 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1729 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1730 return getAddRecExpr(
1731 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1732 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1735 // If Start and Step are constants, check if we can apply this
1737 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1738 auto SC1 = dyn_cast<SCEVConstant>(Start);
1739 auto SC2 = dyn_cast<SCEVConstant>(Step);
1741 const APInt &C1 = SC1->getValue()->getValue();
1742 const APInt &C2 = SC2->getValue()->getValue();
1743 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1745 Start = getSignExtendExpr(Start, Ty);
1746 const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1747 AR->getNoWrapFlags());
1748 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1752 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1753 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1754 return getAddRecExpr(
1755 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1756 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1760 // The cast wasn't folded; create an explicit cast node.
1761 // Recompute the insert position, as it may have been invalidated.
1762 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1763 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1765 UniqueSCEVs.InsertNode(S, IP);
1769 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1770 /// unspecified bits out to the given type.
1772 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1774 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1775 "This is not an extending conversion!");
1776 assert(isSCEVable(Ty) &&
1777 "This is not a conversion to a SCEVable type!");
1778 Ty = getEffectiveSCEVType(Ty);
1780 // Sign-extend negative constants.
1781 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1782 if (SC->getValue()->getValue().isNegative())
1783 return getSignExtendExpr(Op, Ty);
1785 // Peel off a truncate cast.
1786 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1787 const SCEV *NewOp = T->getOperand();
1788 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1789 return getAnyExtendExpr(NewOp, Ty);
1790 return getTruncateOrNoop(NewOp, Ty);
1793 // Next try a zext cast. If the cast is folded, use it.
1794 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1795 if (!isa<SCEVZeroExtendExpr>(ZExt))
1798 // Next try a sext cast. If the cast is folded, use it.
1799 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1800 if (!isa<SCEVSignExtendExpr>(SExt))
1803 // Force the cast to be folded into the operands of an addrec.
1804 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1805 SmallVector<const SCEV *, 4> Ops;
1806 for (const SCEV *Op : AR->operands())
1807 Ops.push_back(getAnyExtendExpr(Op, Ty));
1808 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1811 // If the expression is obviously signed, use the sext cast value.
1812 if (isa<SCEVSMaxExpr>(Op))
1815 // Absent any other information, use the zext cast value.
1819 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1820 /// a list of operands to be added under the given scale, update the given
1821 /// map. This is a helper function for getAddRecExpr. As an example of
1822 /// what it does, given a sequence of operands that would form an add
1823 /// expression like this:
1825 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1827 /// where A and B are constants, update the map with these values:
1829 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1831 /// and add 13 + A*B*29 to AccumulatedConstant.
1832 /// This will allow getAddRecExpr to produce this:
1834 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1836 /// This form often exposes folding opportunities that are hidden in
1837 /// the original operand list.
1839 /// Return true iff it appears that any interesting folding opportunities
1840 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1841 /// the common case where no interesting opportunities are present, and
1842 /// is also used as a check to avoid infinite recursion.
1845 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1846 SmallVectorImpl<const SCEV *> &NewOps,
1847 APInt &AccumulatedConstant,
1848 const SCEV *const *Ops, size_t NumOperands,
1850 ScalarEvolution &SE) {
1851 bool Interesting = false;
1853 // Iterate over the add operands. They are sorted, with constants first.
1855 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1857 // Pull a buried constant out to the outside.
1858 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1860 AccumulatedConstant += Scale * C->getValue()->getValue();
1863 // Next comes everything else. We're especially interested in multiplies
1864 // here, but they're in the middle, so just visit the rest with one loop.
1865 for (; i != NumOperands; ++i) {
1866 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1867 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1869 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1870 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1871 // A multiplication of a constant with another add; recurse.
1872 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1874 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1875 Add->op_begin(), Add->getNumOperands(),
1878 // A multiplication of a constant with some other value. Update
1880 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1881 const SCEV *Key = SE.getMulExpr(MulOps);
1882 auto Pair = M.insert(std::make_pair(Key, NewScale));
1884 NewOps.push_back(Pair.first->first);
1886 Pair.first->second += NewScale;
1887 // The map already had an entry for this value, which may indicate
1888 // a folding opportunity.
1893 // An ordinary operand. Update the map.
1894 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1895 M.insert(std::make_pair(Ops[i], Scale));
1897 NewOps.push_back(Pair.first->first);
1899 Pair.first->second += Scale;
1900 // The map already had an entry for this value, which may indicate
1901 // a folding opportunity.
1911 struct APIntCompare {
1912 bool operator()(const APInt &LHS, const APInt &RHS) const {
1913 return LHS.ult(RHS);
1918 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1919 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1920 // can't-overflow flags for the operation if possible.
1921 static SCEV::NoWrapFlags
1922 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1923 const SmallVectorImpl<const SCEV *> &Ops,
1924 SCEV::NoWrapFlags OldFlags) {
1925 using namespace std::placeholders;
1928 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1930 assert(CanAnalyze && "don't call from other places!");
1932 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1933 SCEV::NoWrapFlags SignOrUnsignWrap =
1934 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1936 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1937 auto IsKnownNonNegative =
1938 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1940 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1941 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1942 return ScalarEvolution::setFlags(OldFlags,
1943 (SCEV::NoWrapFlags)SignOrUnsignMask);
1948 /// getAddExpr - Get a canonical add expression, or something simpler if
1950 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1951 SCEV::NoWrapFlags Flags) {
1952 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1953 "only nuw or nsw allowed");
1954 assert(!Ops.empty() && "Cannot get empty add!");
1955 if (Ops.size() == 1) return Ops[0];
1957 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1958 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1959 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1960 "SCEVAddExpr operand types don't match!");
1963 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1965 // Sort by complexity, this groups all similar expression types together.
1966 GroupByComplexity(Ops, &LI);
1968 // If there are any constants, fold them together.
1970 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1972 assert(Idx < Ops.size());
1973 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1974 // We found two constants, fold them together!
1975 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1976 RHSC->getValue()->getValue());
1977 if (Ops.size() == 2) return Ops[0];
1978 Ops.erase(Ops.begin()+1); // Erase the folded element
1979 LHSC = cast<SCEVConstant>(Ops[0]);
1982 // If we are left with a constant zero being added, strip it off.
1983 if (LHSC->getValue()->isZero()) {
1984 Ops.erase(Ops.begin());
1988 if (Ops.size() == 1) return Ops[0];
1991 // Okay, check to see if the same value occurs in the operand list more than
1992 // once. If so, merge them together into an multiply expression. Since we
1993 // sorted the list, these values are required to be adjacent.
1994 Type *Ty = Ops[0]->getType();
1995 bool FoundMatch = false;
1996 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1997 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1998 // Scan ahead to count how many equal operands there are.
2000 while (i+Count != e && Ops[i+Count] == Ops[i])
2002 // Merge the values into a multiply.
2003 const SCEV *Scale = getConstant(Ty, Count);
2004 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2005 if (Ops.size() == Count)
2008 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2009 --i; e -= Count - 1;
2013 return getAddExpr(Ops, Flags);
2015 // Check for truncates. If all the operands are truncated from the same
2016 // type, see if factoring out the truncate would permit the result to be
2017 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2018 // if the contents of the resulting outer trunc fold to something simple.
2019 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2020 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2021 Type *DstType = Trunc->getType();
2022 Type *SrcType = Trunc->getOperand()->getType();
2023 SmallVector<const SCEV *, 8> LargeOps;
2025 // Check all the operands to see if they can be represented in the
2026 // source type of the truncate.
2027 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2028 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2029 if (T->getOperand()->getType() != SrcType) {
2033 LargeOps.push_back(T->getOperand());
2034 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2035 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2036 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2037 SmallVector<const SCEV *, 8> LargeMulOps;
2038 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2039 if (const SCEVTruncateExpr *T =
2040 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2041 if (T->getOperand()->getType() != SrcType) {
2045 LargeMulOps.push_back(T->getOperand());
2046 } else if (const SCEVConstant *C =
2047 dyn_cast<SCEVConstant>(M->getOperand(j))) {
2048 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2055 LargeOps.push_back(getMulExpr(LargeMulOps));
2062 // Evaluate the expression in the larger type.
2063 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2064 // If it folds to something simple, use it. Otherwise, don't.
2065 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2066 return getTruncateExpr(Fold, DstType);
2070 // Skip past any other cast SCEVs.
2071 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2074 // If there are add operands they would be next.
2075 if (Idx < Ops.size()) {
2076 bool DeletedAdd = false;
2077 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2078 // If we have an add, expand the add operands onto the end of the operands
2080 Ops.erase(Ops.begin()+Idx);
2081 Ops.append(Add->op_begin(), Add->op_end());
2085 // If we deleted at least one add, we added operands to the end of the list,
2086 // and they are not necessarily sorted. Recurse to resort and resimplify
2087 // any operands we just acquired.
2089 return getAddExpr(Ops);
2092 // Skip over the add expression until we get to a multiply.
2093 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2096 // Check to see if there are any folding opportunities present with
2097 // operands multiplied by constant values.
2098 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2099 uint64_t BitWidth = getTypeSizeInBits(Ty);
2100 DenseMap<const SCEV *, APInt> M;
2101 SmallVector<const SCEV *, 8> NewOps;
2102 APInt AccumulatedConstant(BitWidth, 0);
2103 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2104 Ops.data(), Ops.size(),
2105 APInt(BitWidth, 1), *this)) {
2106 // Some interesting folding opportunity is present, so its worthwhile to
2107 // re-generate the operands list. Group the operands by constant scale,
2108 // to avoid multiplying by the same constant scale multiple times.
2109 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2110 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
2111 E = NewOps.end(); I != E; ++I)
2112 MulOpLists[M.find(*I)->second].push_back(*I);
2113 // Re-generate the operands list.
2115 if (AccumulatedConstant != 0)
2116 Ops.push_back(getConstant(AccumulatedConstant));
2117 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
2118 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
2120 Ops.push_back(getMulExpr(getConstant(I->first),
2121 getAddExpr(I->second)));
2124 if (Ops.size() == 1)
2126 return getAddExpr(Ops);
2130 // If we are adding something to a multiply expression, make sure the
2131 // something is not already an operand of the multiply. If so, merge it into
2133 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2134 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2135 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2136 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2137 if (isa<SCEVConstant>(MulOpSCEV))
2139 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2140 if (MulOpSCEV == Ops[AddOp]) {
2141 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2142 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2143 if (Mul->getNumOperands() != 2) {
2144 // If the multiply has more than two operands, we must get the
2146 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2147 Mul->op_begin()+MulOp);
2148 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2149 InnerMul = getMulExpr(MulOps);
2151 const SCEV *One = getOne(Ty);
2152 const SCEV *AddOne = getAddExpr(One, InnerMul);
2153 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2154 if (Ops.size() == 2) return OuterMul;
2156 Ops.erase(Ops.begin()+AddOp);
2157 Ops.erase(Ops.begin()+Idx-1);
2159 Ops.erase(Ops.begin()+Idx);
2160 Ops.erase(Ops.begin()+AddOp-1);
2162 Ops.push_back(OuterMul);
2163 return getAddExpr(Ops);
2166 // Check this multiply against other multiplies being added together.
2167 for (unsigned OtherMulIdx = Idx+1;
2168 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2170 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2171 // If MulOp occurs in OtherMul, we can fold the two multiplies
2173 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2174 OMulOp != e; ++OMulOp)
2175 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2176 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2177 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2178 if (Mul->getNumOperands() != 2) {
2179 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2180 Mul->op_begin()+MulOp);
2181 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2182 InnerMul1 = getMulExpr(MulOps);
2184 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2185 if (OtherMul->getNumOperands() != 2) {
2186 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2187 OtherMul->op_begin()+OMulOp);
2188 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2189 InnerMul2 = getMulExpr(MulOps);
2191 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2192 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2193 if (Ops.size() == 2) return OuterMul;
2194 Ops.erase(Ops.begin()+Idx);
2195 Ops.erase(Ops.begin()+OtherMulIdx-1);
2196 Ops.push_back(OuterMul);
2197 return getAddExpr(Ops);
2203 // If there are any add recurrences in the operands list, see if any other
2204 // added values are loop invariant. If so, we can fold them into the
2206 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2209 // Scan over all recurrences, trying to fold loop invariants into them.
2210 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2211 // Scan all of the other operands to this add and add them to the vector if
2212 // they are loop invariant w.r.t. the recurrence.
2213 SmallVector<const SCEV *, 8> LIOps;
2214 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2215 const Loop *AddRecLoop = AddRec->getLoop();
2216 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2217 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2218 LIOps.push_back(Ops[i]);
2219 Ops.erase(Ops.begin()+i);
2223 // If we found some loop invariants, fold them into the recurrence.
2224 if (!LIOps.empty()) {
2225 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2226 LIOps.push_back(AddRec->getStart());
2228 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2230 AddRecOps[0] = getAddExpr(LIOps);
2232 // Build the new addrec. Propagate the NUW and NSW flags if both the
2233 // outer add and the inner addrec are guaranteed to have no overflow.
2234 // Always propagate NW.
2235 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2236 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2238 // If all of the other operands were loop invariant, we are done.
2239 if (Ops.size() == 1) return NewRec;
2241 // Otherwise, add the folded AddRec by the non-invariant parts.
2242 for (unsigned i = 0;; ++i)
2243 if (Ops[i] == AddRec) {
2247 return getAddExpr(Ops);
2250 // Okay, if there weren't any loop invariants to be folded, check to see if
2251 // there are multiple AddRec's with the same loop induction variable being
2252 // added together. If so, we can fold them.
2253 for (unsigned OtherIdx = Idx+1;
2254 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2256 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2257 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2258 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2260 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2262 if (const SCEVAddRecExpr *OtherAddRec =
2263 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2264 if (OtherAddRec->getLoop() == AddRecLoop) {
2265 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2267 if (i >= AddRecOps.size()) {
2268 AddRecOps.append(OtherAddRec->op_begin()+i,
2269 OtherAddRec->op_end());
2272 AddRecOps[i] = getAddExpr(AddRecOps[i],
2273 OtherAddRec->getOperand(i));
2275 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2277 // Step size has changed, so we cannot guarantee no self-wraparound.
2278 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2279 return getAddExpr(Ops);
2282 // Otherwise couldn't fold anything into this recurrence. Move onto the
2286 // Okay, it looks like we really DO need an add expr. Check to see if we
2287 // already have one, otherwise create a new one.
2288 FoldingSetNodeID ID;
2289 ID.AddInteger(scAddExpr);
2290 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2291 ID.AddPointer(Ops[i]);
2294 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2296 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2297 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2298 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2300 UniqueSCEVs.InsertNode(S, IP);
2302 S->setNoWrapFlags(Flags);
2306 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2308 if (j > 1 && k / j != i) Overflow = true;
2312 /// Compute the result of "n choose k", the binomial coefficient. If an
2313 /// intermediate computation overflows, Overflow will be set and the return will
2314 /// be garbage. Overflow is not cleared on absence of overflow.
2315 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2316 // We use the multiplicative formula:
2317 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2318 // At each iteration, we take the n-th term of the numeral and divide by the
2319 // (k-n)th term of the denominator. This division will always produce an
2320 // integral result, and helps reduce the chance of overflow in the
2321 // intermediate computations. However, we can still overflow even when the
2322 // final result would fit.
2324 if (n == 0 || n == k) return 1;
2325 if (k > n) return 0;
2331 for (uint64_t i = 1; i <= k; ++i) {
2332 r = umul_ov(r, n-(i-1), Overflow);
2338 /// Determine if any of the operands in this SCEV are a constant or if
2339 /// any of the add or multiply expressions in this SCEV contain a constant.
2340 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2341 SmallVector<const SCEV *, 4> Ops;
2342 Ops.push_back(StartExpr);
2343 while (!Ops.empty()) {
2344 const SCEV *CurrentExpr = Ops.pop_back_val();
2345 if (isa<SCEVConstant>(*CurrentExpr))
2348 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2349 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2350 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2356 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2358 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2359 SCEV::NoWrapFlags Flags) {
2360 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2361 "only nuw or nsw allowed");
2362 assert(!Ops.empty() && "Cannot get empty mul!");
2363 if (Ops.size() == 1) return Ops[0];
2365 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2366 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2367 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2368 "SCEVMulExpr operand types don't match!");
2371 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2373 // Sort by complexity, this groups all similar expression types together.
2374 GroupByComplexity(Ops, &LI);
2376 // If there are any constants, fold them together.
2378 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2380 // C1*(C2+V) -> C1*C2 + C1*V
2381 if (Ops.size() == 2)
2382 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2383 // If any of Add's ops are Adds or Muls with a constant,
2384 // apply this transformation as well.
2385 if (Add->getNumOperands() == 2)
2386 if (containsConstantSomewhere(Add))
2387 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2388 getMulExpr(LHSC, Add->getOperand(1)));
2391 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2392 // We found two constants, fold them together!
2393 ConstantInt *Fold = ConstantInt::get(getContext(),
2394 LHSC->getValue()->getValue() *
2395 RHSC->getValue()->getValue());
2396 Ops[0] = getConstant(Fold);
2397 Ops.erase(Ops.begin()+1); // Erase the folded element
2398 if (Ops.size() == 1) return Ops[0];
2399 LHSC = cast<SCEVConstant>(Ops[0]);
2402 // If we are left with a constant one being multiplied, strip it off.
2403 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2404 Ops.erase(Ops.begin());
2406 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2407 // If we have a multiply of zero, it will always be zero.
2409 } else if (Ops[0]->isAllOnesValue()) {
2410 // If we have a mul by -1 of an add, try distributing the -1 among the
2412 if (Ops.size() == 2) {
2413 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2414 SmallVector<const SCEV *, 4> NewOps;
2415 bool AnyFolded = false;
2416 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2417 E = Add->op_end(); I != E; ++I) {
2418 const SCEV *Mul = getMulExpr(Ops[0], *I);
2419 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2420 NewOps.push_back(Mul);
2423 return getAddExpr(NewOps);
2425 else if (const SCEVAddRecExpr *
2426 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2427 // Negation preserves a recurrence's no self-wrap property.
2428 SmallVector<const SCEV *, 4> Operands;
2429 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2430 E = AddRec->op_end(); I != E; ++I) {
2431 Operands.push_back(getMulExpr(Ops[0], *I));
2433 return getAddRecExpr(Operands, AddRec->getLoop(),
2434 AddRec->getNoWrapFlags(SCEV::FlagNW));
2439 if (Ops.size() == 1)
2443 // Skip over the add expression until we get to a multiply.
2444 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2447 // If there are mul operands inline them all into this expression.
2448 if (Idx < Ops.size()) {
2449 bool DeletedMul = false;
2450 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2451 // If we have an mul, expand the mul operands onto the end of the operands
2453 Ops.erase(Ops.begin()+Idx);
2454 Ops.append(Mul->op_begin(), Mul->op_end());
2458 // If we deleted at least one mul, we added operands to the end of the list,
2459 // and they are not necessarily sorted. Recurse to resort and resimplify
2460 // any operands we just acquired.
2462 return getMulExpr(Ops);
2465 // If there are any add recurrences in the operands list, see if any other
2466 // added values are loop invariant. If so, we can fold them into the
2468 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2471 // Scan over all recurrences, trying to fold loop invariants into them.
2472 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2473 // Scan all of the other operands to this mul and add them to the vector if
2474 // they are loop invariant w.r.t. the recurrence.
2475 SmallVector<const SCEV *, 8> LIOps;
2476 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2477 const Loop *AddRecLoop = AddRec->getLoop();
2478 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2479 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2480 LIOps.push_back(Ops[i]);
2481 Ops.erase(Ops.begin()+i);
2485 // If we found some loop invariants, fold them into the recurrence.
2486 if (!LIOps.empty()) {
2487 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2488 SmallVector<const SCEV *, 4> NewOps;
2489 NewOps.reserve(AddRec->getNumOperands());
2490 const SCEV *Scale = getMulExpr(LIOps);
2491 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2492 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2494 // Build the new addrec. Propagate the NUW and NSW flags if both the
2495 // outer mul and the inner addrec are guaranteed to have no overflow.
2497 // No self-wrap cannot be guaranteed after changing the step size, but
2498 // will be inferred if either NUW or NSW is true.
2499 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2500 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2502 // If all of the other operands were loop invariant, we are done.
2503 if (Ops.size() == 1) return NewRec;
2505 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2506 for (unsigned i = 0;; ++i)
2507 if (Ops[i] == AddRec) {
2511 return getMulExpr(Ops);
2514 // Okay, if there weren't any loop invariants to be folded, check to see if
2515 // there are multiple AddRec's with the same loop induction variable being
2516 // multiplied together. If so, we can fold them.
2518 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2519 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2520 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2521 // ]]],+,...up to x=2n}.
2522 // Note that the arguments to choose() are always integers with values
2523 // known at compile time, never SCEV objects.
2525 // The implementation avoids pointless extra computations when the two
2526 // addrec's are of different length (mathematically, it's equivalent to
2527 // an infinite stream of zeros on the right).
2528 bool OpsModified = false;
2529 for (unsigned OtherIdx = Idx+1;
2530 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2532 const SCEVAddRecExpr *OtherAddRec =
2533 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2534 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2537 bool Overflow = false;
2538 Type *Ty = AddRec->getType();
2539 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2540 SmallVector<const SCEV*, 7> AddRecOps;
2541 for (int x = 0, xe = AddRec->getNumOperands() +
2542 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2543 const SCEV *Term = getZero(Ty);
2544 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2545 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2546 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2547 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2548 z < ze && !Overflow; ++z) {
2549 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2551 if (LargerThan64Bits)
2552 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2554 Coeff = Coeff1*Coeff2;
2555 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2556 const SCEV *Term1 = AddRec->getOperand(y-z);
2557 const SCEV *Term2 = OtherAddRec->getOperand(z);
2558 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2561 AddRecOps.push_back(Term);
2564 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2566 if (Ops.size() == 2) return NewAddRec;
2567 Ops[Idx] = NewAddRec;
2568 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2570 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2576 return getMulExpr(Ops);
2578 // Otherwise couldn't fold anything into this recurrence. Move onto the
2582 // Okay, it looks like we really DO need an mul expr. Check to see if we
2583 // already have one, otherwise create a new one.
2584 FoldingSetNodeID ID;
2585 ID.AddInteger(scMulExpr);
2586 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2587 ID.AddPointer(Ops[i]);
2590 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2592 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2593 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2594 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2596 UniqueSCEVs.InsertNode(S, IP);
2598 S->setNoWrapFlags(Flags);
2602 /// getUDivExpr - Get a canonical unsigned division expression, or something
2603 /// simpler if possible.
2604 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2606 assert(getEffectiveSCEVType(LHS->getType()) ==
2607 getEffectiveSCEVType(RHS->getType()) &&
2608 "SCEVUDivExpr operand types don't match!");
2610 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2611 if (RHSC->getValue()->equalsInt(1))
2612 return LHS; // X udiv 1 --> x
2613 // If the denominator is zero, the result of the udiv is undefined. Don't
2614 // try to analyze it, because the resolution chosen here may differ from
2615 // the resolution chosen in other parts of the compiler.
2616 if (!RHSC->getValue()->isZero()) {
2617 // Determine if the division can be folded into the operands of
2619 // TODO: Generalize this to non-constants by using known-bits information.
2620 Type *Ty = LHS->getType();
2621 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2622 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2623 // For non-power-of-two values, effectively round the value up to the
2624 // nearest power of two.
2625 if (!RHSC->getValue()->getValue().isPowerOf2())
2627 IntegerType *ExtTy =
2628 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2629 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2630 if (const SCEVConstant *Step =
2631 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2632 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2633 const APInt &StepInt = Step->getValue()->getValue();
2634 const APInt &DivInt = RHSC->getValue()->getValue();
2635 if (!StepInt.urem(DivInt) &&
2636 getZeroExtendExpr(AR, ExtTy) ==
2637 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2638 getZeroExtendExpr(Step, ExtTy),
2639 AR->getLoop(), SCEV::FlagAnyWrap)) {
2640 SmallVector<const SCEV *, 4> Operands;
2641 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2642 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2643 return getAddRecExpr(Operands, AR->getLoop(),
2646 /// Get a canonical UDivExpr for a recurrence.
2647 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2648 // We can currently only fold X%N if X is constant.
2649 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2650 if (StartC && !DivInt.urem(StepInt) &&
2651 getZeroExtendExpr(AR, ExtTy) ==
2652 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2653 getZeroExtendExpr(Step, ExtTy),
2654 AR->getLoop(), SCEV::FlagAnyWrap)) {
2655 const APInt &StartInt = StartC->getValue()->getValue();
2656 const APInt &StartRem = StartInt.urem(StepInt);
2658 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2659 AR->getLoop(), SCEV::FlagNW);
2662 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2663 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2664 SmallVector<const SCEV *, 4> Operands;
2665 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2666 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2667 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2668 // Find an operand that's safely divisible.
2669 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2670 const SCEV *Op = M->getOperand(i);
2671 const SCEV *Div = getUDivExpr(Op, RHSC);
2672 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2673 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2676 return getMulExpr(Operands);
2680 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2681 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2682 SmallVector<const SCEV *, 4> Operands;
2683 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2684 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2685 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2687 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2688 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2689 if (isa<SCEVUDivExpr>(Op) ||
2690 getMulExpr(Op, RHS) != A->getOperand(i))
2692 Operands.push_back(Op);
2694 if (Operands.size() == A->getNumOperands())
2695 return getAddExpr(Operands);
2699 // Fold if both operands are constant.
2700 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2701 Constant *LHSCV = LHSC->getValue();
2702 Constant *RHSCV = RHSC->getValue();
2703 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2709 FoldingSetNodeID ID;
2710 ID.AddInteger(scUDivExpr);
2714 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2715 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2717 UniqueSCEVs.InsertNode(S, IP);
2721 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2722 APInt A = C1->getValue()->getValue().abs();
2723 APInt B = C2->getValue()->getValue().abs();
2724 uint32_t ABW = A.getBitWidth();
2725 uint32_t BBW = B.getBitWidth();
2732 return APIntOps::GreatestCommonDivisor(A, B);
2735 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2736 /// something simpler if possible. There is no representation for an exact udiv
2737 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2738 /// We can't do this when it's not exact because the udiv may be clearing bits.
2739 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2741 // TODO: we could try to find factors in all sorts of things, but for now we
2742 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2743 // end of this file for inspiration.
2745 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2747 return getUDivExpr(LHS, RHS);
2749 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2750 // If the mulexpr multiplies by a constant, then that constant must be the
2751 // first element of the mulexpr.
2752 if (const SCEVConstant *LHSCst =
2753 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2754 if (LHSCst == RHSCst) {
2755 SmallVector<const SCEV *, 2> Operands;
2756 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2757 return getMulExpr(Operands);
2760 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2761 // that there's a factor provided by one of the other terms. We need to
2763 APInt Factor = gcd(LHSCst, RHSCst);
2764 if (!Factor.isIntN(1)) {
2765 LHSCst = cast<SCEVConstant>(
2766 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2767 RHSCst = cast<SCEVConstant>(
2768 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2769 SmallVector<const SCEV *, 2> Operands;
2770 Operands.push_back(LHSCst);
2771 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2772 LHS = getMulExpr(Operands);
2774 Mul = dyn_cast<SCEVMulExpr>(LHS);
2776 return getUDivExactExpr(LHS, RHS);
2781 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2782 if (Mul->getOperand(i) == RHS) {
2783 SmallVector<const SCEV *, 2> Operands;
2784 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2785 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2786 return getMulExpr(Operands);
2790 return getUDivExpr(LHS, RHS);
2793 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2794 /// Simplify the expression as much as possible.
2795 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2797 SCEV::NoWrapFlags Flags) {
2798 SmallVector<const SCEV *, 4> Operands;
2799 Operands.push_back(Start);
2800 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2801 if (StepChrec->getLoop() == L) {
2802 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2803 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2806 Operands.push_back(Step);
2807 return getAddRecExpr(Operands, L, Flags);
2810 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2811 /// Simplify the expression as much as possible.
2813 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2814 const Loop *L, SCEV::NoWrapFlags Flags) {
2815 if (Operands.size() == 1) return Operands[0];
2817 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2818 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2819 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2820 "SCEVAddRecExpr operand types don't match!");
2821 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2822 assert(isLoopInvariant(Operands[i], L) &&
2823 "SCEVAddRecExpr operand is not loop-invariant!");
2826 if (Operands.back()->isZero()) {
2827 Operands.pop_back();
2828 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2831 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2832 // use that information to infer NUW and NSW flags. However, computing a
2833 // BE count requires calling getAddRecExpr, so we may not yet have a
2834 // meaningful BE count at this point (and if we don't, we'd be stuck
2835 // with a SCEVCouldNotCompute as the cached BE count).
2837 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2839 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2840 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2841 const Loop *NestedLoop = NestedAR->getLoop();
2842 if (L->contains(NestedLoop)
2843 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2844 : (!NestedLoop->contains(L) &&
2845 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2846 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2847 NestedAR->op_end());
2848 Operands[0] = NestedAR->getStart();
2849 // AddRecs require their operands be loop-invariant with respect to their
2850 // loops. Don't perform this transformation if it would break this
2852 bool AllInvariant = true;
2853 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2854 if (!isLoopInvariant(Operands[i], L)) {
2855 AllInvariant = false;
2859 // Create a recurrence for the outer loop with the same step size.
2861 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2862 // inner recurrence has the same property.
2863 SCEV::NoWrapFlags OuterFlags =
2864 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2866 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2867 AllInvariant = true;
2868 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2869 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2870 AllInvariant = false;
2874 // Ok, both add recurrences are valid after the transformation.
2876 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2877 // the outer recurrence has the same property.
2878 SCEV::NoWrapFlags InnerFlags =
2879 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2880 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2883 // Reset Operands to its original state.
2884 Operands[0] = NestedAR;
2888 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2889 // already have one, otherwise create a new one.
2890 FoldingSetNodeID ID;
2891 ID.AddInteger(scAddRecExpr);
2892 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2893 ID.AddPointer(Operands[i]);
2897 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2899 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2900 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2901 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2902 O, Operands.size(), L);
2903 UniqueSCEVs.InsertNode(S, IP);
2905 S->setNoWrapFlags(Flags);
2910 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2911 const SmallVectorImpl<const SCEV *> &IndexExprs,
2913 // getSCEV(Base)->getType() has the same address space as Base->getType()
2914 // because SCEV::getType() preserves the address space.
2915 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2916 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2917 // instruction to its SCEV, because the Instruction may be guarded by control
2918 // flow and the no-overflow bits may not be valid for the expression in any
2919 // context. This can be fixed similarly to how these flags are handled for
2921 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2923 const SCEV *TotalOffset = getZero(IntPtrTy);
2924 // The address space is unimportant. The first thing we do on CurTy is getting
2925 // its element type.
2926 Type *CurTy = PointerType::getUnqual(PointeeType);
2927 for (const SCEV *IndexExpr : IndexExprs) {
2928 // Compute the (potentially symbolic) offset in bytes for this index.
2929 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2930 // For a struct, add the member offset.
2931 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2932 unsigned FieldNo = Index->getZExtValue();
2933 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2935 // Add the field offset to the running total offset.
2936 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2938 // Update CurTy to the type of the field at Index.
2939 CurTy = STy->getTypeAtIndex(Index);
2941 // Update CurTy to its element type.
2942 CurTy = cast<SequentialType>(CurTy)->getElementType();
2943 // For an array, add the element offset, explicitly scaled.
2944 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2945 // Getelementptr indices are signed.
2946 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2948 // Multiply the index by the element size to compute the element offset.
2949 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2951 // Add the element offset to the running total offset.
2952 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2956 // Add the total offset from all the GEP indices to the base.
2957 return getAddExpr(BaseExpr, TotalOffset, Wrap);
2960 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2962 SmallVector<const SCEV *, 2> Ops;
2965 return getSMaxExpr(Ops);
2969 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2970 assert(!Ops.empty() && "Cannot get empty smax!");
2971 if (Ops.size() == 1) return Ops[0];
2973 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2974 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2975 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2976 "SCEVSMaxExpr operand types don't match!");
2979 // Sort by complexity, this groups all similar expression types together.
2980 GroupByComplexity(Ops, &LI);
2982 // If there are any constants, fold them together.
2984 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2986 assert(Idx < Ops.size());
2987 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2988 // We found two constants, fold them together!
2989 ConstantInt *Fold = ConstantInt::get(getContext(),
2990 APIntOps::smax(LHSC->getValue()->getValue(),
2991 RHSC->getValue()->getValue()));
2992 Ops[0] = getConstant(Fold);
2993 Ops.erase(Ops.begin()+1); // Erase the folded element
2994 if (Ops.size() == 1) return Ops[0];
2995 LHSC = cast<SCEVConstant>(Ops[0]);
2998 // If we are left with a constant minimum-int, strip it off.
2999 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3000 Ops.erase(Ops.begin());
3002 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3003 // If we have an smax with a constant maximum-int, it will always be
3008 if (Ops.size() == 1) return Ops[0];
3011 // Find the first SMax
3012 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3015 // Check to see if one of the operands is an SMax. If so, expand its operands
3016 // onto our operand list, and recurse to simplify.
3017 if (Idx < Ops.size()) {
3018 bool DeletedSMax = false;
3019 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3020 Ops.erase(Ops.begin()+Idx);
3021 Ops.append(SMax->op_begin(), SMax->op_end());
3026 return getSMaxExpr(Ops);
3029 // Okay, check to see if the same value occurs in the operand list twice. If
3030 // so, delete one. Since we sorted the list, these values are required to
3032 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3033 // X smax Y smax Y --> X smax Y
3034 // X smax Y --> X, if X is always greater than Y
3035 if (Ops[i] == Ops[i+1] ||
3036 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3037 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3039 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3040 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3044 if (Ops.size() == 1) return Ops[0];
3046 assert(!Ops.empty() && "Reduced smax down to nothing!");
3048 // Okay, it looks like we really DO need an smax expr. Check to see if we
3049 // already have one, otherwise create a new one.
3050 FoldingSetNodeID ID;
3051 ID.AddInteger(scSMaxExpr);
3052 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3053 ID.AddPointer(Ops[i]);
3055 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3056 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3057 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3058 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3060 UniqueSCEVs.InsertNode(S, IP);
3064 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3066 SmallVector<const SCEV *, 2> Ops;
3069 return getUMaxExpr(Ops);
3073 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3074 assert(!Ops.empty() && "Cannot get empty umax!");
3075 if (Ops.size() == 1) return Ops[0];
3077 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3078 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3079 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3080 "SCEVUMaxExpr operand types don't match!");
3083 // Sort by complexity, this groups all similar expression types together.
3084 GroupByComplexity(Ops, &LI);
3086 // If there are any constants, fold them together.
3088 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3090 assert(Idx < Ops.size());
3091 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3092 // We found two constants, fold them together!
3093 ConstantInt *Fold = ConstantInt::get(getContext(),
3094 APIntOps::umax(LHSC->getValue()->getValue(),
3095 RHSC->getValue()->getValue()));
3096 Ops[0] = getConstant(Fold);
3097 Ops.erase(Ops.begin()+1); // Erase the folded element
3098 if (Ops.size() == 1) return Ops[0];
3099 LHSC = cast<SCEVConstant>(Ops[0]);
3102 // If we are left with a constant minimum-int, strip it off.
3103 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3104 Ops.erase(Ops.begin());
3106 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3107 // If we have an umax with a constant maximum-int, it will always be
3112 if (Ops.size() == 1) return Ops[0];
3115 // Find the first UMax
3116 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3119 // Check to see if one of the operands is a UMax. If so, expand its operands
3120 // onto our operand list, and recurse to simplify.
3121 if (Idx < Ops.size()) {
3122 bool DeletedUMax = false;
3123 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3124 Ops.erase(Ops.begin()+Idx);
3125 Ops.append(UMax->op_begin(), UMax->op_end());
3130 return getUMaxExpr(Ops);
3133 // Okay, check to see if the same value occurs in the operand list twice. If
3134 // so, delete one. Since we sorted the list, these values are required to
3136 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3137 // X umax Y umax Y --> X umax Y
3138 // X umax Y --> X, if X is always greater than Y
3139 if (Ops[i] == Ops[i+1] ||
3140 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3141 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3143 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3144 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3148 if (Ops.size() == 1) return Ops[0];
3150 assert(!Ops.empty() && "Reduced umax down to nothing!");
3152 // Okay, it looks like we really DO need a umax expr. Check to see if we
3153 // already have one, otherwise create a new one.
3154 FoldingSetNodeID ID;
3155 ID.AddInteger(scUMaxExpr);
3156 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3157 ID.AddPointer(Ops[i]);
3159 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3160 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3161 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3162 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3164 UniqueSCEVs.InsertNode(S, IP);
3168 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3170 // ~smax(~x, ~y) == smin(x, y).
3171 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3174 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3176 // ~umax(~x, ~y) == umin(x, y)
3177 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3180 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3181 // We can bypass creating a target-independent
3182 // constant expression and then folding it back into a ConstantInt.
3183 // This is just a compile-time optimization.
3184 return getConstant(IntTy,
3185 F.getParent()->getDataLayout().getTypeAllocSize(AllocTy));
3188 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3191 // We can bypass creating a target-independent
3192 // constant expression and then folding it back into a ConstantInt.
3193 // This is just a compile-time optimization.
3196 F.getParent()->getDataLayout().getStructLayout(STy)->getElementOffset(
3200 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3201 // Don't attempt to do anything other than create a SCEVUnknown object
3202 // here. createSCEV only calls getUnknown after checking for all other
3203 // interesting possibilities, and any other code that calls getUnknown
3204 // is doing so in order to hide a value from SCEV canonicalization.
3206 FoldingSetNodeID ID;
3207 ID.AddInteger(scUnknown);
3210 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3211 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3212 "Stale SCEVUnknown in uniquing map!");
3215 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3217 FirstUnknown = cast<SCEVUnknown>(S);
3218 UniqueSCEVs.InsertNode(S, IP);
3222 //===----------------------------------------------------------------------===//
3223 // Basic SCEV Analysis and PHI Idiom Recognition Code
3226 /// isSCEVable - Test if values of the given type are analyzable within
3227 /// the SCEV framework. This primarily includes integer types, and it
3228 /// can optionally include pointer types if the ScalarEvolution class
3229 /// has access to target-specific information.
3230 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3231 // Integers and pointers are always SCEVable.
3232 return Ty->isIntegerTy() || Ty->isPointerTy();
3235 /// getTypeSizeInBits - Return the size in bits of the specified type,
3236 /// for which isSCEVable must return true.
3237 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3238 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3239 return F.getParent()->getDataLayout().getTypeSizeInBits(Ty);
3242 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3243 /// the given type and which represents how SCEV will treat the given
3244 /// type, for which isSCEVable must return true. For pointer types,
3245 /// this is the pointer-sized integer type.
3246 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3247 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3249 if (Ty->isIntegerTy()) {
3253 // The only other support type is pointer.
3254 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3255 return F.getParent()->getDataLayout().getIntPtrType(Ty);
3258 const SCEV *ScalarEvolution::getCouldNotCompute() {
3259 return CouldNotCompute.get();
3263 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3264 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3265 // is set iff if find such SCEVUnknown.
3267 struct FindInvalidSCEVUnknown {
3269 FindInvalidSCEVUnknown() { FindOne = false; }
3270 bool follow(const SCEV *S) {
3271 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3275 if (!cast<SCEVUnknown>(S)->getValue())
3282 bool isDone() const { return FindOne; }
3286 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3287 FindInvalidSCEVUnknown F;
3288 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3294 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3295 /// expression and create a new one.
3296 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3297 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3299 const SCEV *S = getExistingSCEV(V);
3302 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3307 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3308 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3310 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3311 if (I != ValueExprMap.end()) {
3312 const SCEV *S = I->second;
3313 if (checkValidity(S))
3315 ValueExprMap.erase(I);
3320 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3322 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3323 SCEV::NoWrapFlags Flags) {
3324 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3326 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3328 Type *Ty = V->getType();
3329 Ty = getEffectiveSCEVType(Ty);
3331 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3334 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3335 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3336 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3338 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3340 Type *Ty = V->getType();
3341 Ty = getEffectiveSCEVType(Ty);
3342 const SCEV *AllOnes =
3343 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3344 return getMinusSCEV(AllOnes, V);
3347 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3348 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3349 SCEV::NoWrapFlags Flags) {
3350 // Fast path: X - X --> 0.
3352 return getZero(LHS->getType());
3354 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3355 // makes it so that we cannot make much use of NUW.
3356 auto AddFlags = SCEV::FlagAnyWrap;
3357 const bool RHSIsNotMinSigned =
3358 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3359 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3360 // Let M be the minimum representable signed value. Then (-1)*RHS
3361 // signed-wraps if and only if RHS is M. That can happen even for
3362 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3363 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3364 // (-1)*RHS, we need to prove that RHS != M.
3366 // If LHS is non-negative and we know that LHS - RHS does not
3367 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3368 // either by proving that RHS > M or that LHS >= 0.
3369 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3370 AddFlags = SCEV::FlagNSW;
3374 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3375 // RHS is NSW and LHS >= 0.
3377 // The difficulty here is that the NSW flag may have been proven
3378 // relative to a loop that is to be found in a recurrence in LHS and
3379 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3380 // larger scope than intended.
3381 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3383 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3386 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3387 /// input value to the specified type. If the type must be extended, it is zero
3390 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3391 Type *SrcTy = V->getType();
3392 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3393 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3394 "Cannot truncate or zero extend with non-integer arguments!");
3395 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3396 return V; // No conversion
3397 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3398 return getTruncateExpr(V, Ty);
3399 return getZeroExtendExpr(V, Ty);
3402 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3403 /// input value to the specified type. If the type must be extended, it is sign
3406 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3408 Type *SrcTy = V->getType();
3409 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3410 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3411 "Cannot truncate or zero extend with non-integer arguments!");
3412 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3413 return V; // No conversion
3414 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3415 return getTruncateExpr(V, Ty);
3416 return getSignExtendExpr(V, Ty);
3419 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3420 /// input value to the specified type. If the type must be extended, it is zero
3421 /// extended. The conversion must not be narrowing.
3423 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3424 Type *SrcTy = V->getType();
3425 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3426 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3427 "Cannot noop or zero extend with non-integer arguments!");
3428 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3429 "getNoopOrZeroExtend cannot truncate!");
3430 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3431 return V; // No conversion
3432 return getZeroExtendExpr(V, Ty);
3435 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3436 /// input value to the specified type. If the type must be extended, it is sign
3437 /// extended. The conversion must not be narrowing.
3439 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3440 Type *SrcTy = V->getType();
3441 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3442 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3443 "Cannot noop or sign extend with non-integer arguments!");
3444 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3445 "getNoopOrSignExtend cannot truncate!");
3446 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3447 return V; // No conversion
3448 return getSignExtendExpr(V, Ty);
3451 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3452 /// the input value to the specified type. If the type must be extended,
3453 /// it is extended with unspecified bits. The conversion must not be
3456 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3457 Type *SrcTy = V->getType();
3458 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3459 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3460 "Cannot noop or any extend with non-integer arguments!");
3461 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3462 "getNoopOrAnyExtend cannot truncate!");
3463 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3464 return V; // No conversion
3465 return getAnyExtendExpr(V, Ty);
3468 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3469 /// input value to the specified type. The conversion must not be widening.
3471 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3472 Type *SrcTy = V->getType();
3473 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3474 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3475 "Cannot truncate or noop with non-integer arguments!");
3476 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3477 "getTruncateOrNoop cannot extend!");
3478 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3479 return V; // No conversion
3480 return getTruncateExpr(V, Ty);
3483 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3484 /// the types using zero-extension, and then perform a umax operation
3486 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3488 const SCEV *PromotedLHS = LHS;
3489 const SCEV *PromotedRHS = RHS;
3491 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3492 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3494 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3496 return getUMaxExpr(PromotedLHS, PromotedRHS);
3499 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3500 /// the types using zero-extension, and then perform a umin operation
3502 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3504 const SCEV *PromotedLHS = LHS;
3505 const SCEV *PromotedRHS = RHS;
3507 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3508 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3510 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3512 return getUMinExpr(PromotedLHS, PromotedRHS);
3515 /// getPointerBase - Transitively follow the chain of pointer-type operands
3516 /// until reaching a SCEV that does not have a single pointer operand. This
3517 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3518 /// but corner cases do exist.
3519 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3520 // A pointer operand may evaluate to a nonpointer expression, such as null.
3521 if (!V->getType()->isPointerTy())
3524 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3525 return getPointerBase(Cast->getOperand());
3527 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3528 const SCEV *PtrOp = nullptr;
3529 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3531 if ((*I)->getType()->isPointerTy()) {
3532 // Cannot find the base of an expression with multiple pointer operands.
3540 return getPointerBase(PtrOp);
3545 /// PushDefUseChildren - Push users of the given Instruction
3546 /// onto the given Worklist.
3548 PushDefUseChildren(Instruction *I,
3549 SmallVectorImpl<Instruction *> &Worklist) {
3550 // Push the def-use children onto the Worklist stack.
3551 for (User *U : I->users())
3552 Worklist.push_back(cast<Instruction>(U));
3555 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3556 /// instructions that depend on the given instruction and removes them from
3557 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3560 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3561 SmallVector<Instruction *, 16> Worklist;
3562 PushDefUseChildren(PN, Worklist);
3564 SmallPtrSet<Instruction *, 8> Visited;
3566 while (!Worklist.empty()) {
3567 Instruction *I = Worklist.pop_back_val();
3568 if (!Visited.insert(I).second)
3571 ValueExprMapType::iterator It =
3572 ValueExprMap.find_as(static_cast<Value *>(I));
3573 if (It != ValueExprMap.end()) {
3574 const SCEV *Old = It->second;
3576 // Short-circuit the def-use traversal if the symbolic name
3577 // ceases to appear in expressions.
3578 if (Old != SymName && !hasOperand(Old, SymName))
3581 // SCEVUnknown for a PHI either means that it has an unrecognized
3582 // structure, it's a PHI that's in the progress of being computed
3583 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3584 // additional loop trip count information isn't going to change anything.
3585 // In the second case, createNodeForPHI will perform the necessary
3586 // updates on its own when it gets to that point. In the third, we do
3587 // want to forget the SCEVUnknown.
3588 if (!isa<PHINode>(I) ||
3589 !isa<SCEVUnknown>(Old) ||
3590 (I != PN && Old == SymName)) {
3591 forgetMemoizedResults(Old);
3592 ValueExprMap.erase(It);
3596 PushDefUseChildren(I, Worklist);
3600 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
3601 const Loop *L = LI.getLoopFor(PN->getParent());
3602 if (!L || L->getHeader() != PN->getParent())
3605 // The loop may have multiple entrances or multiple exits; we can analyze
3606 // this phi as an addrec if it has a unique entry value and a unique
3608 Value *BEValueV = nullptr, *StartValueV = nullptr;
3609 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3610 Value *V = PN->getIncomingValue(i);
3611 if (L->contains(PN->getIncomingBlock(i))) {
3614 } else if (BEValueV != V) {
3618 } else if (!StartValueV) {
3620 } else if (StartValueV != V) {
3621 StartValueV = nullptr;
3625 if (BEValueV && StartValueV) {
3626 // While we are analyzing this PHI node, handle its value symbolically.
3627 const SCEV *SymbolicName = getUnknown(PN);
3628 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3629 "PHI node already processed?");
3630 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3632 // Using this symbolic name for the PHI, analyze the value coming around
3634 const SCEV *BEValue = getSCEV(BEValueV);
3636 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3637 // has a special value for the first iteration of the loop.
3639 // If the value coming around the backedge is an add with the symbolic
3640 // value we just inserted, then we found a simple induction variable!
3641 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3642 // If there is a single occurrence of the symbolic value, replace it
3643 // with a recurrence.
3644 unsigned FoundIndex = Add->getNumOperands();
3645 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3646 if (Add->getOperand(i) == SymbolicName)
3647 if (FoundIndex == e) {
3652 if (FoundIndex != Add->getNumOperands()) {
3653 // Create an add with everything but the specified operand.
3654 SmallVector<const SCEV *, 8> Ops;
3655 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3656 if (i != FoundIndex)
3657 Ops.push_back(Add->getOperand(i));
3658 const SCEV *Accum = getAddExpr(Ops);
3660 // This is not a valid addrec if the step amount is varying each
3661 // loop iteration, but is not itself an addrec in this loop.
3662 if (isLoopInvariant(Accum, L) ||
3663 (isa<SCEVAddRecExpr>(Accum) &&
3664 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3665 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3667 // If the increment doesn't overflow, then neither the addrec nor
3668 // the post-increment will overflow.
3669 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3670 if (OBO->getOperand(0) == PN) {
3671 if (OBO->hasNoUnsignedWrap())
3672 Flags = setFlags(Flags, SCEV::FlagNUW);
3673 if (OBO->hasNoSignedWrap())
3674 Flags = setFlags(Flags, SCEV::FlagNSW);
3676 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3677 // If the increment is an inbounds GEP, then we know the address
3678 // space cannot be wrapped around. We cannot make any guarantee
3679 // about signed or unsigned overflow because pointers are
3680 // unsigned but we may have a negative index from the base
3681 // pointer. We can guarantee that no unsigned wrap occurs if the
3682 // indices form a positive value.
3683 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3684 Flags = setFlags(Flags, SCEV::FlagNW);
3686 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3687 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3688 Flags = setFlags(Flags, SCEV::FlagNUW);
3691 // We cannot transfer nuw and nsw flags from subtraction
3692 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3696 const SCEV *StartVal = getSCEV(StartValueV);
3697 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3699 // Since the no-wrap flags are on the increment, they apply to the
3700 // post-incremented value as well.
3701 if (isLoopInvariant(Accum, L))
3702 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
3704 // Okay, for the entire analysis of this edge we assumed the PHI
3705 // to be symbolic. We now need to go back and purge all of the
3706 // entries for the scalars that use the symbolic expression.
3707 ForgetSymbolicName(PN, SymbolicName);
3708 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3712 } else if (const SCEVAddRecExpr *AddRec =
3713 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3714 // Otherwise, this could be a loop like this:
3715 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3716 // In this case, j = {1,+,1} and BEValue is j.
3717 // Because the other in-value of i (0) fits the evolution of BEValue
3718 // i really is an addrec evolution.
3719 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3720 const SCEV *StartVal = getSCEV(StartValueV);
3722 // If StartVal = j.start - j.stride, we can use StartVal as the
3723 // initial step of the addrec evolution.
3725 getMinusSCEV(AddRec->getOperand(0), AddRec->getOperand(1))) {
3726 // FIXME: For constant StartVal, we should be able to infer
3728 const SCEV *PHISCEV = getAddRecExpr(StartVal, AddRec->getOperand(1),
3729 L, SCEV::FlagAnyWrap);
3731 // Okay, for the entire analysis of this edge we assumed the PHI
3732 // to be symbolic. We now need to go back and purge all of the
3733 // entries for the scalars that use the symbolic expression.
3734 ForgetSymbolicName(PN, SymbolicName);
3735 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3745 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
3746 const Loop *L = LI.getLoopFor(PN->getParent());
3748 // Try to match a control flow sequence that branches out at BI and merges
3749 // back at Merge into a "C ? LHS : RHS" select pattern. Return true on a
3750 // successful match.
3751 auto BrPHIToSelect = [&](BranchInst *BI, PHINode *Merge, Value *&C,
3752 Value *&LHS, Value *&RHS) {
3753 C = BI->getCondition();
3755 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
3756 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
3758 if (!LeftEdge.isSingleEdge())
3761 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
3763 Use &LeftUse = Merge->getOperandUse(0);
3764 Use &RightUse = Merge->getOperandUse(1);
3766 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
3772 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
3781 // Checks if the SCEV S is available at BB. S is considered available at BB
3782 // if S can be materialized at BB without introducing a fault.
3783 auto IsAvailableOnEntry = [&](const SCEV *S, BasicBlock *BB) {
3784 struct CheckAvailable {
3785 bool TraversalDone = false;
3786 bool Available = true;
3788 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
3789 BasicBlock *BB = nullptr;
3792 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
3793 : L(L), BB(BB), DT(DT) {}
3795 bool setUnavailable() {
3796 TraversalDone = true;
3801 bool follow(const SCEV *S) {
3802 switch (S->getSCEVType()) {
3803 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
3804 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
3805 // These expressions are available if their operand(s) is/are.
3808 case scAddRecExpr: {
3809 // We allow add recurrences that are on the loop BB is in, or some
3810 // outer loop. This guarantees availability because the value of the
3811 // add recurrence at BB is simply the "current" value of the induction
3812 // variable. We can relax this in the future; for instance an add
3813 // recurrence on a sibling dominating loop is also available at BB.
3814 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
3815 if (L && (ARLoop == L || ARLoop->contains(L)))
3818 return setUnavailable();
3822 // For SCEVUnknown, we check for simple dominance.
3823 const auto *SU = cast<SCEVUnknown>(S);
3824 Value *V = SU->getValue();
3826 if (isa<Argument>(V))
3829 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
3832 return setUnavailable();
3836 case scCouldNotCompute:
3837 // We do not try to smart about these at all.
3838 return setUnavailable();
3840 llvm_unreachable("switch should be fully covered!");
3843 bool isDone() { return TraversalDone; }
3846 CheckAvailable CA(L, BB, DT);
3847 SCEVTraversal<CheckAvailable> ST(CA);
3850 return CA.Available;
3853 if (PN->getNumIncomingValues() == 2) {
3856 // br %cond, label %left, label %right
3862 // V = phi [ %x, %left ], [ %y, %right ]
3864 // as "select %cond, %x, %y"
3866 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
3867 assert(IDom && "At least the entry block should dominate PN");
3869 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
3870 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
3872 if (BI && BI->isConditional() && BrPHIToSelect(BI, PN, Cond, LHS, RHS) &&
3873 IsAvailableOnEntry(getSCEV(LHS), PN->getParent()) &&
3874 IsAvailableOnEntry(getSCEV(RHS), PN->getParent()))
3875 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
3881 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3882 if (const SCEV *S = createAddRecFromPHI(PN))
3885 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
3888 // If the PHI has a single incoming value, follow that value, unless the
3889 // PHI's incoming blocks are in a different loop, in which case doing so
3890 // risks breaking LCSSA form. Instcombine would normally zap these, but
3891 // it doesn't have DominatorTree information, so it may miss cases.
3892 if (Value *V = SimplifyInstruction(PN, F.getParent()->getDataLayout(), &TLI,
3894 if (LI.replacementPreservesLCSSAForm(PN, V))
3897 // If it's not a loop phi, we can't handle it yet.
3898 return getUnknown(PN);
3901 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
3905 // Try to match some simple smax or umax patterns.
3906 auto *ICI = dyn_cast<ICmpInst>(Cond);
3908 return getUnknown(I);
3910 Value *LHS = ICI->getOperand(0);
3911 Value *RHS = ICI->getOperand(1);
3913 switch (ICI->getPredicate()) {
3914 case ICmpInst::ICMP_SLT:
3915 case ICmpInst::ICMP_SLE:
3916 std::swap(LHS, RHS);
3918 case ICmpInst::ICMP_SGT:
3919 case ICmpInst::ICMP_SGE:
3920 // a >s b ? a+x : b+x -> smax(a, b)+x
3921 // a >s b ? b+x : a+x -> smin(a, b)+x
3922 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
3923 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
3924 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
3925 const SCEV *LA = getSCEV(TrueVal);
3926 const SCEV *RA = getSCEV(FalseVal);
3927 const SCEV *LDiff = getMinusSCEV(LA, LS);
3928 const SCEV *RDiff = getMinusSCEV(RA, RS);
3930 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3931 LDiff = getMinusSCEV(LA, RS);
3932 RDiff = getMinusSCEV(RA, LS);
3934 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3937 case ICmpInst::ICMP_ULT:
3938 case ICmpInst::ICMP_ULE:
3939 std::swap(LHS, RHS);
3941 case ICmpInst::ICMP_UGT:
3942 case ICmpInst::ICMP_UGE:
3943 // a >u b ? a+x : b+x -> umax(a, b)+x
3944 // a >u b ? b+x : a+x -> umin(a, b)+x
3945 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
3946 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
3947 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
3948 const SCEV *LA = getSCEV(TrueVal);
3949 const SCEV *RA = getSCEV(FalseVal);
3950 const SCEV *LDiff = getMinusSCEV(LA, LS);
3951 const SCEV *RDiff = getMinusSCEV(RA, RS);
3953 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3954 LDiff = getMinusSCEV(LA, RS);
3955 RDiff = getMinusSCEV(RA, LS);
3957 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3960 case ICmpInst::ICMP_NE:
3961 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3962 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
3963 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
3964 const SCEV *One = getOne(I->getType());
3965 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), 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, One);
3971 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3974 case ICmpInst::ICMP_EQ:
3975 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3976 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
3977 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
3978 const SCEV *One = getOne(I->getType());
3979 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
3980 const SCEV *LA = getSCEV(TrueVal);
3981 const SCEV *RA = getSCEV(FalseVal);
3982 const SCEV *LDiff = getMinusSCEV(LA, One);
3983 const SCEV *RDiff = getMinusSCEV(RA, LS);
3985 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3992 return getUnknown(I);
3995 /// createNodeForGEP - Expand GEP instructions into add and multiply
3996 /// operations. This allows them to be analyzed by regular SCEV code.
3998 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3999 Value *Base = GEP->getOperand(0);
4000 // Don't attempt to analyze GEPs over unsized objects.
4001 if (!Base->getType()->getPointerElementType()->isSized())
4002 return getUnknown(GEP);
4004 SmallVector<const SCEV *, 4> IndexExprs;
4005 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4006 IndexExprs.push_back(getSCEV(*Index));
4007 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
4011 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
4012 /// guaranteed to end in (at every loop iteration). It is, at the same time,
4013 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
4014 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
4016 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4017 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4018 return C->getValue()->getValue().countTrailingZeros();
4020 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4021 return std::min(GetMinTrailingZeros(T->getOperand()),
4022 (uint32_t)getTypeSizeInBits(T->getType()));
4024 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4025 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4026 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4027 getTypeSizeInBits(E->getType()) : OpRes;
4030 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4031 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4032 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4033 getTypeSizeInBits(E->getType()) : OpRes;
4036 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4037 // The result is the min of all operands results.
4038 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4039 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4040 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4044 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4045 // The result is the sum of all operands results.
4046 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4047 uint32_t BitWidth = getTypeSizeInBits(M->getType());
4048 for (unsigned i = 1, e = M->getNumOperands();
4049 SumOpRes != BitWidth && i != e; ++i)
4050 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4055 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4056 // The result is the min of all operands results.
4057 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4058 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4059 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4063 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4064 // The result is the min of all operands results.
4065 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4066 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4067 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4071 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4072 // The result is the min of all operands results.
4073 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4074 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4075 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4079 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4080 // For a SCEVUnknown, ask ValueTracking.
4081 unsigned BitWidth = getTypeSizeInBits(U->getType());
4082 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4083 computeKnownBits(U->getValue(), Zeros, Ones, F.getParent()->getDataLayout(),
4084 0, &AC, nullptr, &DT);
4085 return Zeros.countTrailingOnes();
4092 /// GetRangeFromMetadata - Helper method to assign a range to V from
4093 /// metadata present in the IR.
4094 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4095 if (Instruction *I = dyn_cast<Instruction>(V)) {
4096 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
4097 ConstantRange TotalRange(
4098 cast<IntegerType>(I->getType())->getBitWidth(), false);
4100 unsigned NumRanges = MD->getNumOperands() / 2;
4101 assert(NumRanges >= 1);
4103 for (unsigned i = 0; i < NumRanges; ++i) {
4104 ConstantInt *Lower =
4105 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
4106 ConstantInt *Upper =
4107 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
4108 ConstantRange Range(Lower->getValue(), Upper->getValue());
4109 TotalRange = TotalRange.unionWith(Range);
4119 /// getRange - Determine the range for a particular SCEV. If SignHint is
4120 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4121 /// with a "cleaner" unsigned (resp. signed) representation.
4124 ScalarEvolution::getRange(const SCEV *S,
4125 ScalarEvolution::RangeSignHint SignHint) {
4126 DenseMap<const SCEV *, ConstantRange> &Cache =
4127 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4130 // See if we've computed this range already.
4131 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4132 if (I != Cache.end())
4135 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4136 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
4138 unsigned BitWidth = getTypeSizeInBits(S->getType());
4139 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4141 // If the value has known zeros, the maximum value will have those known zeros
4143 uint32_t TZ = GetMinTrailingZeros(S);
4145 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4146 ConservativeResult =
4147 ConstantRange(APInt::getMinValue(BitWidth),
4148 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4150 ConservativeResult = ConstantRange(
4151 APInt::getSignedMinValue(BitWidth),
4152 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4155 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4156 ConstantRange X = getRange(Add->getOperand(0), SignHint);
4157 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4158 X = X.add(getRange(Add->getOperand(i), SignHint));
4159 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4162 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4163 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4164 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4165 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4166 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4169 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4170 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4171 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4172 X = X.smax(getRange(SMax->getOperand(i), SignHint));
4173 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4176 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4177 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4178 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4179 X = X.umax(getRange(UMax->getOperand(i), SignHint));
4180 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4183 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4184 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4185 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4186 return setRange(UDiv, SignHint,
4187 ConservativeResult.intersectWith(X.udiv(Y)));
4190 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4191 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4192 return setRange(ZExt, SignHint,
4193 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4196 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4197 ConstantRange X = getRange(SExt->getOperand(), SignHint);
4198 return setRange(SExt, SignHint,
4199 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4202 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4203 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4204 return setRange(Trunc, SignHint,
4205 ConservativeResult.intersectWith(X.truncate(BitWidth)));
4208 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4209 // If there's no unsigned wrap, the value will never be less than its
4211 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
4212 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4213 if (!C->getValue()->isZero())
4214 ConservativeResult =
4215 ConservativeResult.intersectWith(
4216 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
4218 // If there's no signed wrap, and all the operands have the same sign or
4219 // zero, the value won't ever change sign.
4220 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
4221 bool AllNonNeg = true;
4222 bool AllNonPos = true;
4223 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4224 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4225 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4228 ConservativeResult = ConservativeResult.intersectWith(
4229 ConstantRange(APInt(BitWidth, 0),
4230 APInt::getSignedMinValue(BitWidth)));
4232 ConservativeResult = ConservativeResult.intersectWith(
4233 ConstantRange(APInt::getSignedMinValue(BitWidth),
4234 APInt(BitWidth, 1)));
4237 // TODO: non-affine addrec
4238 if (AddRec->isAffine()) {
4239 Type *Ty = AddRec->getType();
4240 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4241 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4242 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4244 // Check for overflow. This must be done with ConstantRange arithmetic
4245 // because we could be called from within the ScalarEvolution overflow
4248 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4249 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4250 ConstantRange ZExtMaxBECountRange =
4251 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4253 const SCEV *Start = AddRec->getStart();
4254 const SCEV *Step = AddRec->getStepRecurrence(*this);
4255 ConstantRange StepSRange = getSignedRange(Step);
4256 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4258 ConstantRange StartURange = getUnsignedRange(Start);
4259 ConstantRange EndURange =
4260 StartURange.add(MaxBECountRange.multiply(StepSRange));
4262 // Check for unsigned overflow.
4263 ConstantRange ZExtStartURange =
4264 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4265 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4266 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4268 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4269 EndURange.getUnsignedMin());
4270 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4271 EndURange.getUnsignedMax());
4272 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4274 ConservativeResult =
4275 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4278 ConstantRange StartSRange = getSignedRange(Start);
4279 ConstantRange EndSRange =
4280 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4282 // Check for signed overflow. This must be done with ConstantRange
4283 // arithmetic because we could be called from within the ScalarEvolution
4284 // overflow checking code.
4285 ConstantRange SExtStartSRange =
4286 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4287 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4288 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4290 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4291 EndSRange.getSignedMin());
4292 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4293 EndSRange.getSignedMax());
4294 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4296 ConservativeResult =
4297 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4302 return setRange(AddRec, SignHint, ConservativeResult);
4305 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4306 // Check if the IR explicitly contains !range metadata.
4307 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4308 if (MDRange.hasValue())
4309 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4311 // Split here to avoid paying the compile-time cost of calling both
4312 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4314 const DataLayout &DL = F.getParent()->getDataLayout();
4315 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4316 // For a SCEVUnknown, ask ValueTracking.
4317 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4318 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4319 if (Ones != ~Zeros + 1)
4320 ConservativeResult =
4321 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4323 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4324 "generalize as needed!");
4325 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4327 ConservativeResult = ConservativeResult.intersectWith(
4328 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4329 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4332 return setRange(U, SignHint, ConservativeResult);
4335 return setRange(S, SignHint, ConservativeResult);
4338 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4339 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4340 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4342 // Return early if there are no flags to propagate to the SCEV.
4343 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4344 if (BinOp->hasNoUnsignedWrap())
4345 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4346 if (BinOp->hasNoSignedWrap())
4347 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4348 if (Flags == SCEV::FlagAnyWrap) {
4349 return SCEV::FlagAnyWrap;
4352 // Here we check that BinOp is in the header of the innermost loop
4353 // containing BinOp, since we only deal with instructions in the loop
4354 // header. The actual loop we need to check later will come from an add
4355 // recurrence, but getting that requires computing the SCEV of the operands,
4356 // which can be expensive. This check we can do cheaply to rule out some
4358 Loop *innermostContainingLoop = LI.getLoopFor(BinOp->getParent());
4359 if (innermostContainingLoop == nullptr ||
4360 innermostContainingLoop->getHeader() != BinOp->getParent())
4361 return SCEV::FlagAnyWrap;
4363 // Only proceed if we can prove that BinOp does not yield poison.
4364 if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
4366 // At this point we know that if V is executed, then it does not wrap
4367 // according to at least one of NSW or NUW. If V is not executed, then we do
4368 // not know if the calculation that V represents would wrap. Multiple
4369 // instructions can map to the same SCEV. If we apply NSW or NUW from V to
4370 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4371 // derived from other instructions that map to the same SCEV. We cannot make
4372 // that guarantee for cases where V is not executed. So we need to find the
4373 // loop that V is considered in relation to and prove that V is executed for
4374 // every iteration of that loop. That implies that the value that V
4375 // calculates does not wrap anywhere in the loop, so then we can apply the
4376 // flags to the SCEV.
4378 // We check isLoopInvariant to disambiguate in case we are adding two
4379 // recurrences from different loops, so that we know which loop to prove
4380 // that V is executed in.
4381 for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
4382 const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
4383 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4384 const int OtherOpIndex = 1 - OpIndex;
4385 const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
4386 if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
4387 isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
4391 return SCEV::FlagAnyWrap;
4394 /// createSCEV - We know that there is no SCEV for the specified value. Analyze
4397 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4398 if (!isSCEVable(V->getType()))
4399 return getUnknown(V);
4401 unsigned Opcode = Instruction::UserOp1;
4402 if (Instruction *I = dyn_cast<Instruction>(V)) {
4403 Opcode = I->getOpcode();
4405 // Don't attempt to analyze instructions in blocks that aren't
4406 // reachable. Such instructions don't matter, and they aren't required
4407 // to obey basic rules for definitions dominating uses which this
4408 // analysis depends on.
4409 if (!DT.isReachableFromEntry(I->getParent()))
4410 return getUnknown(V);
4411 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4412 Opcode = CE->getOpcode();
4413 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4414 return getConstant(CI);
4415 else if (isa<ConstantPointerNull>(V))
4416 return getZero(V->getType());
4417 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4418 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4420 return getUnknown(V);
4422 Operator *U = cast<Operator>(V);
4424 case Instruction::Add: {
4425 // The simple thing to do would be to just call getSCEV on both operands
4426 // and call getAddExpr with the result. However if we're looking at a
4427 // bunch of things all added together, this can be quite inefficient,
4428 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4429 // Instead, gather up all the operands and make a single getAddExpr call.
4430 // LLVM IR canonical form means we need only traverse the left operands.
4431 SmallVector<const SCEV *, 4> AddOps;
4432 for (Value *Op = U;; Op = U->getOperand(0)) {
4433 U = dyn_cast<Operator>(Op);
4434 unsigned Opcode = U ? U->getOpcode() : 0;
4435 if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
4436 assert(Op != V && "V should be an add");
4437 AddOps.push_back(getSCEV(Op));
4441 if (auto *OpSCEV = getExistingSCEV(U)) {
4442 AddOps.push_back(OpSCEV);
4446 // If a NUW or NSW flag can be applied to the SCEV for this
4447 // addition, then compute the SCEV for this addition by itself
4448 // with a separate call to getAddExpr. We need to do that
4449 // instead of pushing the operands of the addition onto AddOps,
4450 // since the flags are only known to apply to this particular
4451 // addition - they may not apply to other additions that can be
4452 // formed with operands from AddOps.
4453 const SCEV *RHS = getSCEV(U->getOperand(1));
4454 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4455 if (Flags != SCEV::FlagAnyWrap) {
4456 const SCEV *LHS = getSCEV(U->getOperand(0));
4457 if (Opcode == Instruction::Sub)
4458 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4460 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4464 if (Opcode == Instruction::Sub)
4465 AddOps.push_back(getNegativeSCEV(RHS));
4467 AddOps.push_back(RHS);
4469 return getAddExpr(AddOps);
4472 case Instruction::Mul: {
4473 SmallVector<const SCEV *, 4> MulOps;
4474 for (Value *Op = U;; Op = U->getOperand(0)) {
4475 U = dyn_cast<Operator>(Op);
4476 if (!U || U->getOpcode() != Instruction::Mul) {
4477 assert(Op != V && "V should be a mul");
4478 MulOps.push_back(getSCEV(Op));
4482 if (auto *OpSCEV = getExistingSCEV(U)) {
4483 MulOps.push_back(OpSCEV);
4487 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4488 if (Flags != SCEV::FlagAnyWrap) {
4489 MulOps.push_back(getMulExpr(getSCEV(U->getOperand(0)),
4490 getSCEV(U->getOperand(1)), Flags));
4494 MulOps.push_back(getSCEV(U->getOperand(1)));
4496 return getMulExpr(MulOps);
4498 case Instruction::UDiv:
4499 return getUDivExpr(getSCEV(U->getOperand(0)),
4500 getSCEV(U->getOperand(1)));
4501 case Instruction::Sub:
4502 return getMinusSCEV(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)),
4503 getNoWrapFlagsFromUB(U));
4504 case Instruction::And:
4505 // For an expression like x&255 that merely masks off the high bits,
4506 // use zext(trunc(x)) as the SCEV expression.
4507 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4508 if (CI->isNullValue())
4509 return getSCEV(U->getOperand(1));
4510 if (CI->isAllOnesValue())
4511 return getSCEV(U->getOperand(0));
4512 const APInt &A = CI->getValue();
4514 // Instcombine's ShrinkDemandedConstant may strip bits out of
4515 // constants, obscuring what would otherwise be a low-bits mask.
4516 // Use computeKnownBits to compute what ShrinkDemandedConstant
4517 // knew about to reconstruct a low-bits mask value.
4518 unsigned LZ = A.countLeadingZeros();
4519 unsigned TZ = A.countTrailingZeros();
4520 unsigned BitWidth = A.getBitWidth();
4521 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4522 computeKnownBits(U->getOperand(0), KnownZero, KnownOne,
4523 F.getParent()->getDataLayout(), 0, &AC, nullptr, &DT);
4525 APInt EffectiveMask =
4526 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4527 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4528 const SCEV *MulCount = getConstant(
4529 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4533 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4534 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4541 case Instruction::Or:
4542 // If the RHS of the Or is a constant, we may have something like:
4543 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4544 // optimizations will transparently handle this case.
4546 // In order for this transformation to be safe, the LHS must be of the
4547 // form X*(2^n) and the Or constant must be less than 2^n.
4548 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4549 const SCEV *LHS = getSCEV(U->getOperand(0));
4550 const APInt &CIVal = CI->getValue();
4551 if (GetMinTrailingZeros(LHS) >=
4552 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4553 // Build a plain add SCEV.
4554 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4555 // If the LHS of the add was an addrec and it has no-wrap flags,
4556 // transfer the no-wrap flags, since an or won't introduce a wrap.
4557 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4558 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4559 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4560 OldAR->getNoWrapFlags());
4566 case Instruction::Xor:
4567 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4568 // If the RHS of the xor is a signbit, then this is just an add.
4569 // Instcombine turns add of signbit into xor as a strength reduction step.
4570 if (CI->getValue().isSignBit())
4571 return getAddExpr(getSCEV(U->getOperand(0)),
4572 getSCEV(U->getOperand(1)));
4574 // If the RHS of xor is -1, then this is a not operation.
4575 if (CI->isAllOnesValue())
4576 return getNotSCEV(getSCEV(U->getOperand(0)));
4578 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4579 // This is a variant of the check for xor with -1, and it handles
4580 // the case where instcombine has trimmed non-demanded bits out
4581 // of an xor with -1.
4582 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4583 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4584 if (BO->getOpcode() == Instruction::And &&
4585 LCI->getValue() == CI->getValue())
4586 if (const SCEVZeroExtendExpr *Z =
4587 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4588 Type *UTy = U->getType();
4589 const SCEV *Z0 = Z->getOperand();
4590 Type *Z0Ty = Z0->getType();
4591 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4593 // If C is a low-bits mask, the zero extend is serving to
4594 // mask off the high bits. Complement the operand and
4595 // re-apply the zext.
4596 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4597 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4599 // If C is a single bit, it may be in the sign-bit position
4600 // before the zero-extend. In this case, represent the xor
4601 // using an add, which is equivalent, and re-apply the zext.
4602 APInt Trunc = CI->getValue().trunc(Z0TySize);
4603 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4605 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4611 case Instruction::Shl:
4612 // Turn shift left of a constant amount into a multiply.
4613 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4614 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4616 // If the shift count is not less than the bitwidth, the result of
4617 // the shift is undefined. Don't try to analyze it, because the
4618 // resolution chosen here may differ from the resolution chosen in
4619 // other parts of the compiler.
4620 if (SA->getValue().uge(BitWidth))
4623 // It is currently not resolved how to interpret NSW for left
4624 // shift by BitWidth - 1, so we avoid applying flags in that
4625 // case. Remove this check (or this comment) once the situation
4627 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
4628 // and http://reviews.llvm.org/D8890 .
4629 auto Flags = SCEV::FlagAnyWrap;
4630 if (SA->getValue().ult(BitWidth - 1)) Flags = getNoWrapFlagsFromUB(U);
4632 Constant *X = ConstantInt::get(getContext(),
4633 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4634 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X), Flags);
4638 case Instruction::LShr:
4639 // Turn logical shift right of a constant into a unsigned divide.
4640 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4641 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4643 // If the shift count is not less than the bitwidth, the result of
4644 // the shift is undefined. Don't try to analyze it, because the
4645 // resolution chosen here may differ from the resolution chosen in
4646 // other parts of the compiler.
4647 if (SA->getValue().uge(BitWidth))
4650 Constant *X = ConstantInt::get(getContext(),
4651 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4652 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4656 case Instruction::AShr:
4657 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4658 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4659 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4660 if (L->getOpcode() == Instruction::Shl &&
4661 L->getOperand(1) == U->getOperand(1)) {
4662 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4664 // If the shift count is not less than the bitwidth, the result of
4665 // the shift is undefined. Don't try to analyze it, because the
4666 // resolution chosen here may differ from the resolution chosen in
4667 // other parts of the compiler.
4668 if (CI->getValue().uge(BitWidth))
4671 uint64_t Amt = BitWidth - CI->getZExtValue();
4672 if (Amt == BitWidth)
4673 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4675 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4676 IntegerType::get(getContext(),
4682 case Instruction::Trunc:
4683 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4685 case Instruction::ZExt:
4686 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4688 case Instruction::SExt:
4689 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4691 case Instruction::BitCast:
4692 // BitCasts are no-op casts so we just eliminate the cast.
4693 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4694 return getSCEV(U->getOperand(0));
4697 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4698 // lead to pointer expressions which cannot safely be expanded to GEPs,
4699 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4700 // simplifying integer expressions.
4702 case Instruction::GetElementPtr:
4703 return createNodeForGEP(cast<GEPOperator>(U));
4705 case Instruction::PHI:
4706 return createNodeForPHI(cast<PHINode>(U));
4708 case Instruction::Select:
4709 // U can also be a select constant expr, which let fall through. Since
4710 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
4711 // constant expressions cannot have instructions as operands, we'd have
4712 // returned getUnknown for a select constant expressions anyway.
4713 if (isa<Instruction>(U))
4714 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
4715 U->getOperand(1), U->getOperand(2));
4717 default: // We cannot analyze this expression.
4721 return getUnknown(V);
4726 //===----------------------------------------------------------------------===//
4727 // Iteration Count Computation Code
4730 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4731 if (BasicBlock *ExitingBB = L->getExitingBlock())
4732 return getSmallConstantTripCount(L, ExitingBB);
4734 // No trip count information for multiple exits.
4738 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4739 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4740 /// constant. Will also return 0 if the maximum trip count is very large (>=
4743 /// This "trip count" assumes that control exits via ExitingBlock. More
4744 /// precisely, it is the number of times that control may reach ExitingBlock
4745 /// before taking the branch. For loops with multiple exits, it may not be the
4746 /// number times that the loop header executes because the loop may exit
4747 /// prematurely via another branch.
4748 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4749 BasicBlock *ExitingBlock) {
4750 assert(ExitingBlock && "Must pass a non-null exiting block!");
4751 assert(L->isLoopExiting(ExitingBlock) &&
4752 "Exiting block must actually branch out of the loop!");
4753 const SCEVConstant *ExitCount =
4754 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4758 ConstantInt *ExitConst = ExitCount->getValue();
4760 // Guard against huge trip counts.
4761 if (ExitConst->getValue().getActiveBits() > 32)
4764 // In case of integer overflow, this returns 0, which is correct.
4765 return ((unsigned)ExitConst->getZExtValue()) + 1;
4768 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4769 if (BasicBlock *ExitingBB = L->getExitingBlock())
4770 return getSmallConstantTripMultiple(L, ExitingBB);
4772 // No trip multiple information for multiple exits.
4776 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4777 /// trip count of this loop as a normal unsigned value, if possible. This
4778 /// means that the actual trip count is always a multiple of the returned
4779 /// value (don't forget the trip count could very well be zero as well!).
4781 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4782 /// multiple of a constant (which is also the case if the trip count is simply
4783 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4784 /// if the trip count is very large (>= 2^32).
4786 /// As explained in the comments for getSmallConstantTripCount, this assumes
4787 /// that control exits the loop via ExitingBlock.
4789 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4790 BasicBlock *ExitingBlock) {
4791 assert(ExitingBlock && "Must pass a non-null exiting block!");
4792 assert(L->isLoopExiting(ExitingBlock) &&
4793 "Exiting block must actually branch out of the loop!");
4794 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4795 if (ExitCount == getCouldNotCompute())
4798 // Get the trip count from the BE count by adding 1.
4799 const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
4800 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4801 // to factor simple cases.
4802 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4803 TCMul = Mul->getOperand(0);
4805 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4809 ConstantInt *Result = MulC->getValue();
4811 // Guard against huge trip counts (this requires checking
4812 // for zero to handle the case where the trip count == -1 and the
4814 if (!Result || Result->getValue().getActiveBits() > 32 ||
4815 Result->getValue().getActiveBits() == 0)
4818 return (unsigned)Result->getZExtValue();
4821 // getExitCount - Get the expression for the number of loop iterations for which
4822 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4823 // SCEVCouldNotCompute.
4824 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4825 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4828 /// getBackedgeTakenCount - If the specified loop has a predictable
4829 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4830 /// object. The backedge-taken count is the number of times the loop header
4831 /// will be branched to from within the loop. This is one less than the
4832 /// trip count of the loop, since it doesn't count the first iteration,
4833 /// when the header is branched to from outside the loop.
4835 /// Note that it is not valid to call this method on a loop without a
4836 /// loop-invariant backedge-taken count (see
4837 /// hasLoopInvariantBackedgeTakenCount).
4839 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4840 return getBackedgeTakenInfo(L).getExact(this);
4843 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4844 /// return the least SCEV value that is known never to be less than the
4845 /// actual backedge taken count.
4846 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4847 return getBackedgeTakenInfo(L).getMax(this);
4850 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4851 /// onto the given Worklist.
4853 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4854 BasicBlock *Header = L->getHeader();
4856 // Push all Loop-header PHIs onto the Worklist stack.
4857 for (BasicBlock::iterator I = Header->begin();
4858 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4859 Worklist.push_back(PN);
4862 const ScalarEvolution::BackedgeTakenInfo &
4863 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4864 // Initially insert an invalid entry for this loop. If the insertion
4865 // succeeds, proceed to actually compute a backedge-taken count and
4866 // update the value. The temporary CouldNotCompute value tells SCEV
4867 // code elsewhere that it shouldn't attempt to request a new
4868 // backedge-taken count, which could result in infinite recursion.
4869 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4870 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4872 return Pair.first->second;
4874 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4875 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4876 // must be cleared in this scope.
4877 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4879 if (Result.getExact(this) != getCouldNotCompute()) {
4880 assert(isLoopInvariant(Result.getExact(this), L) &&
4881 isLoopInvariant(Result.getMax(this), L) &&
4882 "Computed backedge-taken count isn't loop invariant for loop!");
4883 ++NumTripCountsComputed;
4885 else if (Result.getMax(this) == getCouldNotCompute() &&
4886 isa<PHINode>(L->getHeader()->begin())) {
4887 // Only count loops that have phi nodes as not being computable.
4888 ++NumTripCountsNotComputed;
4891 // Now that we know more about the trip count for this loop, forget any
4892 // existing SCEV values for PHI nodes in this loop since they are only
4893 // conservative estimates made without the benefit of trip count
4894 // information. This is similar to the code in forgetLoop, except that
4895 // it handles SCEVUnknown PHI nodes specially.
4896 if (Result.hasAnyInfo()) {
4897 SmallVector<Instruction *, 16> Worklist;
4898 PushLoopPHIs(L, Worklist);
4900 SmallPtrSet<Instruction *, 8> Visited;
4901 while (!Worklist.empty()) {
4902 Instruction *I = Worklist.pop_back_val();
4903 if (!Visited.insert(I).second)
4906 ValueExprMapType::iterator It =
4907 ValueExprMap.find_as(static_cast<Value *>(I));
4908 if (It != ValueExprMap.end()) {
4909 const SCEV *Old = It->second;
4911 // SCEVUnknown for a PHI either means that it has an unrecognized
4912 // structure, or it's a PHI that's in the progress of being computed
4913 // by createNodeForPHI. In the former case, additional loop trip
4914 // count information isn't going to change anything. In the later
4915 // case, createNodeForPHI will perform the necessary updates on its
4916 // own when it gets to that point.
4917 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4918 forgetMemoizedResults(Old);
4919 ValueExprMap.erase(It);
4921 if (PHINode *PN = dyn_cast<PHINode>(I))
4922 ConstantEvolutionLoopExitValue.erase(PN);
4925 PushDefUseChildren(I, Worklist);
4929 // Re-lookup the insert position, since the call to
4930 // ComputeBackedgeTakenCount above could result in a
4931 // recusive call to getBackedgeTakenInfo (on a different
4932 // loop), which would invalidate the iterator computed
4934 return BackedgeTakenCounts.find(L)->second = Result;
4937 /// forgetLoop - This method should be called by the client when it has
4938 /// changed a loop in a way that may effect ScalarEvolution's ability to
4939 /// compute a trip count, or if the loop is deleted.
4940 void ScalarEvolution::forgetLoop(const Loop *L) {
4941 // Drop any stored trip count value.
4942 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4943 BackedgeTakenCounts.find(L);
4944 if (BTCPos != BackedgeTakenCounts.end()) {
4945 BTCPos->second.clear();
4946 BackedgeTakenCounts.erase(BTCPos);
4949 // Drop information about expressions based on loop-header PHIs.
4950 SmallVector<Instruction *, 16> Worklist;
4951 PushLoopPHIs(L, Worklist);
4953 SmallPtrSet<Instruction *, 8> Visited;
4954 while (!Worklist.empty()) {
4955 Instruction *I = Worklist.pop_back_val();
4956 if (!Visited.insert(I).second)
4959 ValueExprMapType::iterator It =
4960 ValueExprMap.find_as(static_cast<Value *>(I));
4961 if (It != ValueExprMap.end()) {
4962 forgetMemoizedResults(It->second);
4963 ValueExprMap.erase(It);
4964 if (PHINode *PN = dyn_cast<PHINode>(I))
4965 ConstantEvolutionLoopExitValue.erase(PN);
4968 PushDefUseChildren(I, Worklist);
4971 // Forget all contained loops too, to avoid dangling entries in the
4972 // ValuesAtScopes map.
4973 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4977 /// forgetValue - This method should be called by the client when it has
4978 /// changed a value in a way that may effect its value, or which may
4979 /// disconnect it from a def-use chain linking it to a loop.
4980 void ScalarEvolution::forgetValue(Value *V) {
4981 Instruction *I = dyn_cast<Instruction>(V);
4984 // Drop information about expressions based on loop-header PHIs.
4985 SmallVector<Instruction *, 16> Worklist;
4986 Worklist.push_back(I);
4988 SmallPtrSet<Instruction *, 8> Visited;
4989 while (!Worklist.empty()) {
4990 I = Worklist.pop_back_val();
4991 if (!Visited.insert(I).second)
4994 ValueExprMapType::iterator It =
4995 ValueExprMap.find_as(static_cast<Value *>(I));
4996 if (It != ValueExprMap.end()) {
4997 forgetMemoizedResults(It->second);
4998 ValueExprMap.erase(It);
4999 if (PHINode *PN = dyn_cast<PHINode>(I))
5000 ConstantEvolutionLoopExitValue.erase(PN);
5003 PushDefUseChildren(I, Worklist);
5007 /// getExact - Get the exact loop backedge taken count considering all loop
5008 /// exits. A computable result can only be returned for loops with a single
5009 /// exit. Returning the minimum taken count among all exits is incorrect
5010 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
5011 /// assumes that the limit of each loop test is never skipped. This is a valid
5012 /// assumption as long as the loop exits via that test. For precise results, it
5013 /// is the caller's responsibility to specify the relevant loop exit using
5014 /// getExact(ExitingBlock, SE).
5016 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
5017 // If any exits were not computable, the loop is not computable.
5018 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
5020 // We need exactly one computable exit.
5021 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
5022 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
5024 const SCEV *BECount = nullptr;
5025 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5026 ENT != nullptr; ENT = ENT->getNextExit()) {
5028 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5031 BECount = ENT->ExactNotTaken;
5032 else if (BECount != ENT->ExactNotTaken)
5033 return SE->getCouldNotCompute();
5035 assert(BECount && "Invalid not taken count for loop exit");
5039 /// getExact - Get the exact not taken count for this loop exit.
5041 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5042 ScalarEvolution *SE) const {
5043 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5044 ENT != nullptr; ENT = ENT->getNextExit()) {
5046 if (ENT->ExitingBlock == ExitingBlock)
5047 return ENT->ExactNotTaken;
5049 return SE->getCouldNotCompute();
5052 /// getMax - Get the max backedge taken count for the loop.
5054 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5055 return Max ? Max : SE->getCouldNotCompute();
5058 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5059 ScalarEvolution *SE) const {
5060 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
5063 if (!ExitNotTaken.ExitingBlock)
5066 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5067 ENT != nullptr; ENT = ENT->getNextExit()) {
5069 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
5070 && SE->hasOperand(ENT->ExactNotTaken, S)) {
5077 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5078 /// computable exit into a persistent ExitNotTakenInfo array.
5079 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5080 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
5081 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
5084 ExitNotTaken.setIncomplete();
5086 unsigned NumExits = ExitCounts.size();
5087 if (NumExits == 0) return;
5089 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
5090 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
5091 if (NumExits == 1) return;
5093 // Handle the rare case of multiple computable exits.
5094 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
5096 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
5097 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
5098 PrevENT->setNextExit(ENT);
5099 ENT->ExitingBlock = ExitCounts[i].first;
5100 ENT->ExactNotTaken = ExitCounts[i].second;
5104 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
5105 void ScalarEvolution::BackedgeTakenInfo::clear() {
5106 ExitNotTaken.ExitingBlock = nullptr;
5107 ExitNotTaken.ExactNotTaken = nullptr;
5108 delete[] ExitNotTaken.getNextExit();
5111 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
5112 /// of the specified loop will execute.
5113 ScalarEvolution::BackedgeTakenInfo
5114 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
5115 SmallVector<BasicBlock *, 8> ExitingBlocks;
5116 L->getExitingBlocks(ExitingBlocks);
5118 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
5119 bool CouldComputeBECount = true;
5120 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5121 const SCEV *MustExitMaxBECount = nullptr;
5122 const SCEV *MayExitMaxBECount = nullptr;
5124 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5125 // and compute maxBECount.
5126 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5127 BasicBlock *ExitBB = ExitingBlocks[i];
5128 ExitLimit EL = ComputeExitLimit(L, ExitBB);
5130 // 1. For each exit that can be computed, add an entry to ExitCounts.
5131 // CouldComputeBECount is true only if all exits can be computed.
5132 if (EL.Exact == getCouldNotCompute())
5133 // We couldn't compute an exact value for this exit, so
5134 // we won't be able to compute an exact value for the loop.
5135 CouldComputeBECount = false;
5137 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
5139 // 2. Derive the loop's MaxBECount from each exit's max number of
5140 // non-exiting iterations. Partition the loop exits into two kinds:
5141 // LoopMustExits and LoopMayExits.
5143 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5144 // is a LoopMayExit. If any computable LoopMustExit is found, then
5145 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
5146 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
5147 // considered greater than any computable EL.Max.
5148 if (EL.Max != getCouldNotCompute() && Latch &&
5149 DT.dominates(ExitBB, Latch)) {
5150 if (!MustExitMaxBECount)
5151 MustExitMaxBECount = EL.Max;
5153 MustExitMaxBECount =
5154 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5156 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5157 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5158 MayExitMaxBECount = EL.Max;
5161 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5165 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5166 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5167 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5170 /// ComputeExitLimit - Compute the number of times the backedge of the specified
5171 /// loop will execute if it exits via the specified block.
5172 ScalarEvolution::ExitLimit
5173 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
5175 // Okay, we've chosen an exiting block. See what condition causes us to
5176 // exit at this block and remember the exit block and whether all other targets
5177 // lead to the loop header.
5178 bool MustExecuteLoopHeader = true;
5179 BasicBlock *Exit = nullptr;
5180 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5182 if (!L->contains(*SI)) {
5183 if (Exit) // Multiple exit successors.
5184 return getCouldNotCompute();
5186 } else if (*SI != L->getHeader()) {
5187 MustExecuteLoopHeader = false;
5190 // At this point, we know we have a conditional branch that determines whether
5191 // the loop is exited. However, we don't know if the branch is executed each
5192 // time through the loop. If not, then the execution count of the branch will
5193 // not be equal to the trip count of the loop.
5195 // Currently we check for this by checking to see if the Exit branch goes to
5196 // the loop header. If so, we know it will always execute the same number of
5197 // times as the loop. We also handle the case where the exit block *is* the
5198 // loop header. This is common for un-rotated loops.
5200 // If both of those tests fail, walk up the unique predecessor chain to the
5201 // header, stopping if there is an edge that doesn't exit the loop. If the
5202 // header is reached, the execution count of the branch will be equal to the
5203 // trip count of the loop.
5205 // More extensive analysis could be done to handle more cases here.
5207 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5208 // The simple checks failed, try climbing the unique predecessor chain
5209 // up to the header.
5211 for (BasicBlock *BB = ExitingBlock; BB; ) {
5212 BasicBlock *Pred = BB->getUniquePredecessor();
5214 return getCouldNotCompute();
5215 TerminatorInst *PredTerm = Pred->getTerminator();
5216 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5219 // If the predecessor has a successor that isn't BB and isn't
5220 // outside the loop, assume the worst.
5221 if (L->contains(PredSucc))
5222 return getCouldNotCompute();
5224 if (Pred == L->getHeader()) {
5231 return getCouldNotCompute();
5234 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5235 TerminatorInst *Term = ExitingBlock->getTerminator();
5236 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5237 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5238 // Proceed to the next level to examine the exit condition expression.
5239 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5240 BI->getSuccessor(1),
5241 /*ControlsExit=*/IsOnlyExit);
5244 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5245 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
5246 /*ControlsExit=*/IsOnlyExit);
5248 return getCouldNotCompute();
5251 /// ComputeExitLimitFromCond - Compute the number of times the
5252 /// backedge of the specified loop will execute if its exit condition
5253 /// were a conditional branch of ExitCond, TBB, and FBB.
5255 /// @param ControlsExit is true if ExitCond directly controls the exit
5256 /// branch. In this case, we can assume that the loop exits only if the
5257 /// condition is true and can infer that failing to meet the condition prior to
5258 /// integer wraparound results in undefined behavior.
5259 ScalarEvolution::ExitLimit
5260 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
5264 bool ControlsExit) {
5265 // Check if the controlling expression for this loop is an And or Or.
5266 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5267 if (BO->getOpcode() == Instruction::And) {
5268 // Recurse on the operands of the and.
5269 bool EitherMayExit = L->contains(TBB);
5270 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5271 ControlsExit && !EitherMayExit);
5272 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5273 ControlsExit && !EitherMayExit);
5274 const SCEV *BECount = getCouldNotCompute();
5275 const SCEV *MaxBECount = getCouldNotCompute();
5276 if (EitherMayExit) {
5277 // Both conditions must be true for the loop to continue executing.
5278 // Choose the less conservative count.
5279 if (EL0.Exact == getCouldNotCompute() ||
5280 EL1.Exact == getCouldNotCompute())
5281 BECount = getCouldNotCompute();
5283 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5284 if (EL0.Max == getCouldNotCompute())
5285 MaxBECount = EL1.Max;
5286 else if (EL1.Max == getCouldNotCompute())
5287 MaxBECount = EL0.Max;
5289 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5291 // Both conditions must be true at the same time for the loop to exit.
5292 // For now, be conservative.
5293 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5294 if (EL0.Max == EL1.Max)
5295 MaxBECount = EL0.Max;
5296 if (EL0.Exact == EL1.Exact)
5297 BECount = EL0.Exact;
5300 return ExitLimit(BECount, MaxBECount);
5302 if (BO->getOpcode() == Instruction::Or) {
5303 // Recurse on the operands of the or.
5304 bool EitherMayExit = L->contains(FBB);
5305 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5306 ControlsExit && !EitherMayExit);
5307 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5308 ControlsExit && !EitherMayExit);
5309 const SCEV *BECount = getCouldNotCompute();
5310 const SCEV *MaxBECount = getCouldNotCompute();
5311 if (EitherMayExit) {
5312 // Both conditions must be false for the loop to continue executing.
5313 // Choose the less conservative count.
5314 if (EL0.Exact == getCouldNotCompute() ||
5315 EL1.Exact == getCouldNotCompute())
5316 BECount = getCouldNotCompute();
5318 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5319 if (EL0.Max == getCouldNotCompute())
5320 MaxBECount = EL1.Max;
5321 else if (EL1.Max == getCouldNotCompute())
5322 MaxBECount = EL0.Max;
5324 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5326 // Both conditions must be false at the same time for the loop to exit.
5327 // For now, be conservative.
5328 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5329 if (EL0.Max == EL1.Max)
5330 MaxBECount = EL0.Max;
5331 if (EL0.Exact == EL1.Exact)
5332 BECount = EL0.Exact;
5335 return ExitLimit(BECount, MaxBECount);
5339 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5340 // Proceed to the next level to examine the icmp.
5341 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5342 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5344 // Check for a constant condition. These are normally stripped out by
5345 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5346 // preserve the CFG and is temporarily leaving constant conditions
5348 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5349 if (L->contains(FBB) == !CI->getZExtValue())
5350 // The backedge is always taken.
5351 return getCouldNotCompute();
5353 // The backedge is never taken.
5354 return getZero(CI->getType());
5357 // If it's not an integer or pointer comparison then compute it the hard way.
5358 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5361 /// ComputeExitLimitFromICmp - Compute the number of times the
5362 /// backedge of the specified loop will execute if its exit condition
5363 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5364 ScalarEvolution::ExitLimit
5365 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5369 bool ControlsExit) {
5371 // If the condition was exit on true, convert the condition to exit on false
5372 ICmpInst::Predicate Cond;
5373 if (!L->contains(FBB))
5374 Cond = ExitCond->getPredicate();
5376 Cond = ExitCond->getInversePredicate();
5378 // Handle common loops like: for (X = "string"; *X; ++X)
5379 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5380 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5382 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5383 if (ItCnt.hasAnyInfo())
5387 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5388 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5390 // Try to evaluate any dependencies out of the loop.
5391 LHS = getSCEVAtScope(LHS, L);
5392 RHS = getSCEVAtScope(RHS, L);
5394 // At this point, we would like to compute how many iterations of the
5395 // loop the predicate will return true for these inputs.
5396 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5397 // If there is a loop-invariant, force it into the RHS.
5398 std::swap(LHS, RHS);
5399 Cond = ICmpInst::getSwappedPredicate(Cond);
5402 // Simplify the operands before analyzing them.
5403 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5405 // If we have a comparison of a chrec against a constant, try to use value
5406 // ranges to answer this query.
5407 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5408 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5409 if (AddRec->getLoop() == L) {
5410 // Form the constant range.
5411 ConstantRange CompRange(
5412 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5414 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5415 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5419 case ICmpInst::ICMP_NE: { // while (X != Y)
5420 // Convert to: while (X-Y != 0)
5421 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5422 if (EL.hasAnyInfo()) return EL;
5425 case ICmpInst::ICMP_EQ: { // while (X == Y)
5426 // Convert to: while (X-Y == 0)
5427 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5428 if (EL.hasAnyInfo()) return EL;
5431 case ICmpInst::ICMP_SLT:
5432 case ICmpInst::ICMP_ULT: { // while (X < Y)
5433 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5434 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5435 if (EL.hasAnyInfo()) return EL;
5438 case ICmpInst::ICMP_SGT:
5439 case ICmpInst::ICMP_UGT: { // while (X > Y)
5440 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5441 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5442 if (EL.hasAnyInfo()) return EL;
5447 dbgs() << "ComputeBackedgeTakenCount ";
5448 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5449 dbgs() << "[unsigned] ";
5450 dbgs() << *LHS << " "
5451 << Instruction::getOpcodeName(Instruction::ICmp)
5452 << " " << *RHS << "\n";
5456 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5459 ScalarEvolution::ExitLimit
5460 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5462 BasicBlock *ExitingBlock,
5463 bool ControlsExit) {
5464 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5466 // Give up if the exit is the default dest of a switch.
5467 if (Switch->getDefaultDest() == ExitingBlock)
5468 return getCouldNotCompute();
5470 assert(L->contains(Switch->getDefaultDest()) &&
5471 "Default case must not exit the loop!");
5472 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5473 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5475 // while (X != Y) --> while (X-Y != 0)
5476 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5477 if (EL.hasAnyInfo())
5480 return getCouldNotCompute();
5483 static ConstantInt *
5484 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5485 ScalarEvolution &SE) {
5486 const SCEV *InVal = SE.getConstant(C);
5487 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5488 assert(isa<SCEVConstant>(Val) &&
5489 "Evaluation of SCEV at constant didn't fold correctly?");
5490 return cast<SCEVConstant>(Val)->getValue();
5493 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5494 /// 'icmp op load X, cst', try to see if we can compute the backedge
5495 /// execution count.
5496 ScalarEvolution::ExitLimit
5497 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5501 ICmpInst::Predicate predicate) {
5503 if (LI->isVolatile()) return getCouldNotCompute();
5505 // Check to see if the loaded pointer is a getelementptr of a global.
5506 // TODO: Use SCEV instead of manually grubbing with GEPs.
5507 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5508 if (!GEP) return getCouldNotCompute();
5510 // Make sure that it is really a constant global we are gepping, with an
5511 // initializer, and make sure the first IDX is really 0.
5512 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5513 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5514 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5515 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5516 return getCouldNotCompute();
5518 // Okay, we allow one non-constant index into the GEP instruction.
5519 Value *VarIdx = nullptr;
5520 std::vector<Constant*> Indexes;
5521 unsigned VarIdxNum = 0;
5522 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5523 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5524 Indexes.push_back(CI);
5525 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5526 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5527 VarIdx = GEP->getOperand(i);
5529 Indexes.push_back(nullptr);
5532 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5534 return getCouldNotCompute();
5536 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5537 // Check to see if X is a loop variant variable value now.
5538 const SCEV *Idx = getSCEV(VarIdx);
5539 Idx = getSCEVAtScope(Idx, L);
5541 // We can only recognize very limited forms of loop index expressions, in
5542 // particular, only affine AddRec's like {C1,+,C2}.
5543 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5544 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5545 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5546 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5547 return getCouldNotCompute();
5549 unsigned MaxSteps = MaxBruteForceIterations;
5550 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5551 ConstantInt *ItCst = ConstantInt::get(
5552 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5553 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5555 // Form the GEP offset.
5556 Indexes[VarIdxNum] = Val;
5558 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5560 if (!Result) break; // Cannot compute!
5562 // Evaluate the condition for this iteration.
5563 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5564 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5565 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5567 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5568 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5571 ++NumArrayLenItCounts;
5572 return getConstant(ItCst); // Found terminating iteration!
5575 return getCouldNotCompute();
5579 /// CanConstantFold - Return true if we can constant fold an instruction of the
5580 /// specified type, assuming that all operands were constants.
5581 static bool CanConstantFold(const Instruction *I) {
5582 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5583 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5587 if (const CallInst *CI = dyn_cast<CallInst>(I))
5588 if (const Function *F = CI->getCalledFunction())
5589 return canConstantFoldCallTo(F);
5593 /// Determine whether this instruction can constant evolve within this loop
5594 /// assuming its operands can all constant evolve.
5595 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5596 // An instruction outside of the loop can't be derived from a loop PHI.
5597 if (!L->contains(I)) return false;
5599 if (isa<PHINode>(I)) {
5600 // We don't currently keep track of the control flow needed to evaluate
5601 // PHIs, so we cannot handle PHIs inside of loops.
5602 return L->getHeader() == I->getParent();
5605 // If we won't be able to constant fold this expression even if the operands
5606 // are constants, bail early.
5607 return CanConstantFold(I);
5610 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5611 /// recursing through each instruction operand until reaching a loop header phi.
5613 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5614 DenseMap<Instruction *, PHINode *> &PHIMap) {
5616 // Otherwise, we can evaluate this instruction if all of its operands are
5617 // constant or derived from a PHI node themselves.
5618 PHINode *PHI = nullptr;
5619 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5620 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5622 if (isa<Constant>(*OpI)) continue;
5624 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5625 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5627 PHINode *P = dyn_cast<PHINode>(OpInst);
5629 // If this operand is already visited, reuse the prior result.
5630 // We may have P != PHI if this is the deepest point at which the
5631 // inconsistent paths meet.
5632 P = PHIMap.lookup(OpInst);
5634 // Recurse and memoize the results, whether a phi is found or not.
5635 // This recursive call invalidates pointers into PHIMap.
5636 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5640 return nullptr; // Not evolving from PHI
5641 if (PHI && PHI != P)
5642 return nullptr; // Evolving from multiple different PHIs.
5645 // This is a expression evolving from a constant PHI!
5649 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5650 /// in the loop that V is derived from. We allow arbitrary operations along the
5651 /// way, but the operands of an operation must either be constants or a value
5652 /// derived from a constant PHI. If this expression does not fit with these
5653 /// constraints, return null.
5654 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5655 Instruction *I = dyn_cast<Instruction>(V);
5656 if (!I || !canConstantEvolve(I, L)) return nullptr;
5658 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5662 // Record non-constant instructions contained by the loop.
5663 DenseMap<Instruction *, PHINode *> PHIMap;
5664 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5667 /// EvaluateExpression - Given an expression that passes the
5668 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5669 /// in the loop has the value PHIVal. If we can't fold this expression for some
5670 /// reason, return null.
5671 static Constant *EvaluateExpression(Value *V, const Loop *L,
5672 DenseMap<Instruction *, Constant *> &Vals,
5673 const DataLayout &DL,
5674 const TargetLibraryInfo *TLI) {
5675 // Convenient constant check, but redundant for recursive calls.
5676 if (Constant *C = dyn_cast<Constant>(V)) return C;
5677 Instruction *I = dyn_cast<Instruction>(V);
5678 if (!I) return nullptr;
5680 if (Constant *C = Vals.lookup(I)) return C;
5682 // An instruction inside the loop depends on a value outside the loop that we
5683 // weren't given a mapping for, or a value such as a call inside the loop.
5684 if (!canConstantEvolve(I, L)) return nullptr;
5686 // An unmapped PHI can be due to a branch or another loop inside this loop,
5687 // or due to this not being the initial iteration through a loop where we
5688 // couldn't compute the evolution of this particular PHI last time.
5689 if (isa<PHINode>(I)) return nullptr;
5691 std::vector<Constant*> Operands(I->getNumOperands());
5693 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5694 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5696 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5697 if (!Operands[i]) return nullptr;
5700 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5702 if (!C) return nullptr;
5706 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5707 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5708 Operands[1], DL, TLI);
5709 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5710 if (!LI->isVolatile())
5711 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5713 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5717 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5718 /// in the header of its containing loop, we know the loop executes a
5719 /// constant number of times, and the PHI node is just a recurrence
5720 /// involving constants, fold it.
5722 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5725 DenseMap<PHINode*, Constant*>::const_iterator I =
5726 ConstantEvolutionLoopExitValue.find(PN);
5727 if (I != ConstantEvolutionLoopExitValue.end())
5730 if (BEs.ugt(MaxBruteForceIterations))
5731 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5733 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5735 DenseMap<Instruction *, Constant *> CurrentIterVals;
5736 BasicBlock *Header = L->getHeader();
5737 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5739 // Since the loop is canonicalized, the PHI node must have two entries. One
5740 // entry must be a constant (coming in from outside of the loop), and the
5741 // second must be derived from the same PHI.
5742 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5743 PHINode *PHI = nullptr;
5744 for (BasicBlock::iterator I = Header->begin();
5745 (PHI = dyn_cast<PHINode>(I)); ++I) {
5746 Constant *StartCST =
5747 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5748 if (!StartCST) continue;
5749 CurrentIterVals[PHI] = StartCST;
5751 if (!CurrentIterVals.count(PN))
5752 return RetVal = nullptr;
5754 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5756 // Execute the loop symbolically to determine the exit value.
5757 if (BEs.getActiveBits() >= 32)
5758 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5760 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5761 unsigned IterationNum = 0;
5762 const DataLayout &DL = F.getParent()->getDataLayout();
5763 for (; ; ++IterationNum) {
5764 if (IterationNum == NumIterations)
5765 return RetVal = CurrentIterVals[PN]; // Got exit value!
5767 // Compute the value of the PHIs for the next iteration.
5768 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5769 DenseMap<Instruction *, Constant *> NextIterVals;
5771 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5773 return nullptr; // Couldn't evaluate!
5774 NextIterVals[PN] = NextPHI;
5776 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5778 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5779 // cease to be able to evaluate one of them or if they stop evolving,
5780 // because that doesn't necessarily prevent us from computing PN.
5781 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5782 for (DenseMap<Instruction *, Constant *>::const_iterator
5783 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5784 PHINode *PHI = dyn_cast<PHINode>(I->first);
5785 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5786 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5788 // We use two distinct loops because EvaluateExpression may invalidate any
5789 // iterators into CurrentIterVals.
5790 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5791 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5792 PHINode *PHI = I->first;
5793 Constant *&NextPHI = NextIterVals[PHI];
5794 if (!NextPHI) { // Not already computed.
5795 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5796 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5798 if (NextPHI != I->second)
5799 StoppedEvolving = false;
5802 // If all entries in CurrentIterVals == NextIterVals then we can stop
5803 // iterating, the loop can't continue to change.
5804 if (StoppedEvolving)
5805 return RetVal = CurrentIterVals[PN];
5807 CurrentIterVals.swap(NextIterVals);
5811 /// ComputeExitCountExhaustively - If the loop is known to execute a
5812 /// constant number of times (the condition evolves only from constants),
5813 /// try to evaluate a few iterations of the loop until we get the exit
5814 /// condition gets a value of ExitWhen (true or false). If we cannot
5815 /// evaluate the trip count of the loop, return getCouldNotCompute().
5816 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5819 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5820 if (!PN) return getCouldNotCompute();
5822 // If the loop is canonicalized, the PHI will have exactly two entries.
5823 // That's the only form we support here.
5824 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5826 DenseMap<Instruction *, Constant *> CurrentIterVals;
5827 BasicBlock *Header = L->getHeader();
5828 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5830 // One entry must be a constant (coming in from outside of the loop), and the
5831 // second must be derived from the same PHI.
5832 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5833 PHINode *PHI = nullptr;
5834 for (BasicBlock::iterator I = Header->begin();
5835 (PHI = dyn_cast<PHINode>(I)); ++I) {
5836 Constant *StartCST =
5837 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5838 if (!StartCST) continue;
5839 CurrentIterVals[PHI] = StartCST;
5841 if (!CurrentIterVals.count(PN))
5842 return getCouldNotCompute();
5844 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5845 // the loop symbolically to determine when the condition gets a value of
5847 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5848 const DataLayout &DL = F.getParent()->getDataLayout();
5849 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5850 ConstantInt *CondVal = dyn_cast_or_null<ConstantInt>(
5851 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
5853 // Couldn't symbolically evaluate.
5854 if (!CondVal) return getCouldNotCompute();
5856 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5857 ++NumBruteForceTripCountsComputed;
5858 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5861 // Update all the PHI nodes for the next iteration.
5862 DenseMap<Instruction *, Constant *> NextIterVals;
5864 // Create a list of which PHIs we need to compute. We want to do this before
5865 // calling EvaluateExpression on them because that may invalidate iterators
5866 // into CurrentIterVals.
5867 SmallVector<PHINode *, 8> PHIsToCompute;
5868 for (DenseMap<Instruction *, Constant *>::const_iterator
5869 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5870 PHINode *PHI = dyn_cast<PHINode>(I->first);
5871 if (!PHI || PHI->getParent() != Header) continue;
5872 PHIsToCompute.push_back(PHI);
5874 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5875 E = PHIsToCompute.end(); I != E; ++I) {
5877 Constant *&NextPHI = NextIterVals[PHI];
5878 if (NextPHI) continue; // Already computed!
5880 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5881 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5883 CurrentIterVals.swap(NextIterVals);
5886 // Too many iterations were needed to evaluate.
5887 return getCouldNotCompute();
5890 /// getSCEVAtScope - Return a SCEV expression for the specified value
5891 /// at the specified scope in the program. The L value specifies a loop
5892 /// nest to evaluate the expression at, where null is the top-level or a
5893 /// specified loop is immediately inside of the loop.
5895 /// This method can be used to compute the exit value for a variable defined
5896 /// in a loop by querying what the value will hold in the parent loop.
5898 /// In the case that a relevant loop exit value cannot be computed, the
5899 /// original value V is returned.
5900 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5901 // Check to see if we've folded this expression at this loop before.
5902 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5903 for (unsigned u = 0; u < Values.size(); u++) {
5904 if (Values[u].first == L)
5905 return Values[u].second ? Values[u].second : V;
5907 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5908 // Otherwise compute it.
5909 const SCEV *C = computeSCEVAtScope(V, L);
5910 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5911 for (unsigned u = Values2.size(); u > 0; u--) {
5912 if (Values2[u - 1].first == L) {
5913 Values2[u - 1].second = C;
5920 /// This builds up a Constant using the ConstantExpr interface. That way, we
5921 /// will return Constants for objects which aren't represented by a
5922 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5923 /// Returns NULL if the SCEV isn't representable as a Constant.
5924 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5925 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5926 case scCouldNotCompute:
5930 return cast<SCEVConstant>(V)->getValue();
5932 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5933 case scSignExtend: {
5934 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5935 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5936 return ConstantExpr::getSExt(CastOp, SS->getType());
5939 case scZeroExtend: {
5940 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5941 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5942 return ConstantExpr::getZExt(CastOp, SZ->getType());
5946 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5947 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5948 return ConstantExpr::getTrunc(CastOp, ST->getType());
5952 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5953 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5954 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5955 unsigned AS = PTy->getAddressSpace();
5956 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5957 C = ConstantExpr::getBitCast(C, DestPtrTy);
5959 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5960 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5961 if (!C2) return nullptr;
5964 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5965 unsigned AS = C2->getType()->getPointerAddressSpace();
5967 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5968 // The offsets have been converted to bytes. We can add bytes to an
5969 // i8* by GEP with the byte count in the first index.
5970 C = ConstantExpr::getBitCast(C, DestPtrTy);
5973 // Don't bother trying to sum two pointers. We probably can't
5974 // statically compute a load that results from it anyway.
5975 if (C2->getType()->isPointerTy())
5978 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5979 if (PTy->getElementType()->isStructTy())
5980 C2 = ConstantExpr::getIntegerCast(
5981 C2, Type::getInt32Ty(C->getContext()), true);
5982 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
5984 C = ConstantExpr::getAdd(C, C2);
5991 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5992 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5993 // Don't bother with pointers at all.
5994 if (C->getType()->isPointerTy()) return nullptr;
5995 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5996 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5997 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5998 C = ConstantExpr::getMul(C, C2);
6005 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6006 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6007 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6008 if (LHS->getType() == RHS->getType())
6009 return ConstantExpr::getUDiv(LHS, RHS);
6014 break; // TODO: smax, umax.
6019 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6020 if (isa<SCEVConstant>(V)) return V;
6022 // If this instruction is evolved from a constant-evolving PHI, compute the
6023 // exit value from the loop without using SCEVs.
6024 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6025 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6026 const Loop *LI = this->LI[I->getParent()];
6027 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
6028 if (PHINode *PN = dyn_cast<PHINode>(I))
6029 if (PN->getParent() == LI->getHeader()) {
6030 // Okay, there is no closed form solution for the PHI node. Check
6031 // to see if the loop that contains it has a known backedge-taken
6032 // count. If so, we may be able to force computation of the exit
6034 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6035 if (const SCEVConstant *BTCC =
6036 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6037 // Okay, we know how many times the containing loop executes. If
6038 // this is a constant evolving PHI node, get the final value at
6039 // the specified iteration number.
6040 Constant *RV = getConstantEvolutionLoopExitValue(PN,
6041 BTCC->getValue()->getValue(),
6043 if (RV) return getSCEV(RV);
6047 // Okay, this is an expression that we cannot symbolically evaluate
6048 // into a SCEV. Check to see if it's possible to symbolically evaluate
6049 // the arguments into constants, and if so, try to constant propagate the
6050 // result. This is particularly useful for computing loop exit values.
6051 if (CanConstantFold(I)) {
6052 SmallVector<Constant *, 4> Operands;
6053 bool MadeImprovement = false;
6054 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
6055 Value *Op = I->getOperand(i);
6056 if (Constant *C = dyn_cast<Constant>(Op)) {
6057 Operands.push_back(C);
6061 // If any of the operands is non-constant and if they are
6062 // non-integer and non-pointer, don't even try to analyze them
6063 // with scev techniques.
6064 if (!isSCEVable(Op->getType()))
6067 const SCEV *OrigV = getSCEV(Op);
6068 const SCEV *OpV = getSCEVAtScope(OrigV, L);
6069 MadeImprovement |= OrigV != OpV;
6071 Constant *C = BuildConstantFromSCEV(OpV);
6073 if (C->getType() != Op->getType())
6074 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6078 Operands.push_back(C);
6081 // Check to see if getSCEVAtScope actually made an improvement.
6082 if (MadeImprovement) {
6083 Constant *C = nullptr;
6084 const DataLayout &DL = F.getParent()->getDataLayout();
6085 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6086 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6087 Operands[1], DL, &TLI);
6088 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6089 if (!LI->isVolatile())
6090 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
6092 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
6100 // This is some other type of SCEVUnknown, just return it.
6104 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6105 // Avoid performing the look-up in the common case where the specified
6106 // expression has no loop-variant portions.
6107 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6108 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6109 if (OpAtScope != Comm->getOperand(i)) {
6110 // Okay, at least one of these operands is loop variant but might be
6111 // foldable. Build a new instance of the folded commutative expression.
6112 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6113 Comm->op_begin()+i);
6114 NewOps.push_back(OpAtScope);
6116 for (++i; i != e; ++i) {
6117 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6118 NewOps.push_back(OpAtScope);
6120 if (isa<SCEVAddExpr>(Comm))
6121 return getAddExpr(NewOps);
6122 if (isa<SCEVMulExpr>(Comm))
6123 return getMulExpr(NewOps);
6124 if (isa<SCEVSMaxExpr>(Comm))
6125 return getSMaxExpr(NewOps);
6126 if (isa<SCEVUMaxExpr>(Comm))
6127 return getUMaxExpr(NewOps);
6128 llvm_unreachable("Unknown commutative SCEV type!");
6131 // If we got here, all operands are loop invariant.
6135 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6136 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6137 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6138 if (LHS == Div->getLHS() && RHS == Div->getRHS())
6139 return Div; // must be loop invariant
6140 return getUDivExpr(LHS, RHS);
6143 // If this is a loop recurrence for a loop that does not contain L, then we
6144 // are dealing with the final value computed by the loop.
6145 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6146 // First, attempt to evaluate each operand.
6147 // Avoid performing the look-up in the common case where the specified
6148 // expression has no loop-variant portions.
6149 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6150 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6151 if (OpAtScope == AddRec->getOperand(i))
6154 // Okay, at least one of these operands is loop variant but might be
6155 // foldable. Build a new instance of the folded commutative expression.
6156 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6157 AddRec->op_begin()+i);
6158 NewOps.push_back(OpAtScope);
6159 for (++i; i != e; ++i)
6160 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6162 const SCEV *FoldedRec =
6163 getAddRecExpr(NewOps, AddRec->getLoop(),
6164 AddRec->getNoWrapFlags(SCEV::FlagNW));
6165 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6166 // The addrec may be folded to a nonrecurrence, for example, if the
6167 // induction variable is multiplied by zero after constant folding. Go
6168 // ahead and return the folded value.
6174 // If the scope is outside the addrec's loop, evaluate it by using the
6175 // loop exit value of the addrec.
6176 if (!AddRec->getLoop()->contains(L)) {
6177 // To evaluate this recurrence, we need to know how many times the AddRec
6178 // loop iterates. Compute this now.
6179 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6180 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6182 // Then, evaluate the AddRec.
6183 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6189 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6190 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6191 if (Op == Cast->getOperand())
6192 return Cast; // must be loop invariant
6193 return getZeroExtendExpr(Op, Cast->getType());
6196 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6197 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6198 if (Op == Cast->getOperand())
6199 return Cast; // must be loop invariant
6200 return getSignExtendExpr(Op, Cast->getType());
6203 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6204 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6205 if (Op == Cast->getOperand())
6206 return Cast; // must be loop invariant
6207 return getTruncateExpr(Op, Cast->getType());
6210 llvm_unreachable("Unknown SCEV type!");
6213 /// getSCEVAtScope - This is a convenience function which does
6214 /// getSCEVAtScope(getSCEV(V), L).
6215 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6216 return getSCEVAtScope(getSCEV(V), L);
6219 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6220 /// following equation:
6222 /// A * X = B (mod N)
6224 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6225 /// A and B isn't important.
6227 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6228 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6229 ScalarEvolution &SE) {
6230 uint32_t BW = A.getBitWidth();
6231 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6232 assert(A != 0 && "A must be non-zero.");
6236 // The gcd of A and N may have only one prime factor: 2. The number of
6237 // trailing zeros in A is its multiplicity
6238 uint32_t Mult2 = A.countTrailingZeros();
6241 // 2. Check if B is divisible by D.
6243 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6244 // is not less than multiplicity of this prime factor for D.
6245 if (B.countTrailingZeros() < Mult2)
6246 return SE.getCouldNotCompute();
6248 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6251 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6252 // bit width during computations.
6253 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6254 APInt Mod(BW + 1, 0);
6255 Mod.setBit(BW - Mult2); // Mod = N / D
6256 APInt I = AD.multiplicativeInverse(Mod);
6258 // 4. Compute the minimum unsigned root of the equation:
6259 // I * (B / D) mod (N / D)
6260 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6262 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6264 return SE.getConstant(Result.trunc(BW));
6267 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6268 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6269 /// might be the same) or two SCEVCouldNotCompute objects.
6271 static std::pair<const SCEV *,const SCEV *>
6272 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6273 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6274 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6275 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6276 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6278 // We currently can only solve this if the coefficients are constants.
6279 if (!LC || !MC || !NC) {
6280 const SCEV *CNC = SE.getCouldNotCompute();
6281 return std::make_pair(CNC, CNC);
6284 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6285 const APInt &L = LC->getValue()->getValue();
6286 const APInt &M = MC->getValue()->getValue();
6287 const APInt &N = NC->getValue()->getValue();
6288 APInt Two(BitWidth, 2);
6289 APInt Four(BitWidth, 4);
6292 using namespace APIntOps;
6294 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6295 // The B coefficient is M-N/2
6299 // The A coefficient is N/2
6300 APInt A(N.sdiv(Two));
6302 // Compute the B^2-4ac term.
6305 SqrtTerm -= Four * (A * C);
6307 if (SqrtTerm.isNegative()) {
6308 // The loop is provably infinite.
6309 const SCEV *CNC = SE.getCouldNotCompute();
6310 return std::make_pair(CNC, CNC);
6313 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6314 // integer value or else APInt::sqrt() will assert.
6315 APInt SqrtVal(SqrtTerm.sqrt());
6317 // Compute the two solutions for the quadratic formula.
6318 // The divisions must be performed as signed divisions.
6321 if (TwoA.isMinValue()) {
6322 const SCEV *CNC = SE.getCouldNotCompute();
6323 return std::make_pair(CNC, CNC);
6326 LLVMContext &Context = SE.getContext();
6328 ConstantInt *Solution1 =
6329 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6330 ConstantInt *Solution2 =
6331 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6333 return std::make_pair(SE.getConstant(Solution1),
6334 SE.getConstant(Solution2));
6335 } // end APIntOps namespace
6338 /// HowFarToZero - Return the number of times a backedge comparing the specified
6339 /// value to zero will execute. If not computable, return CouldNotCompute.
6341 /// This is only used for loops with a "x != y" exit test. The exit condition is
6342 /// now expressed as a single expression, V = x-y. So the exit test is
6343 /// effectively V != 0. We know and take advantage of the fact that this
6344 /// expression only being used in a comparison by zero context.
6345 ScalarEvolution::ExitLimit
6346 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6347 // If the value is a constant
6348 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6349 // If the value is already zero, the branch will execute zero times.
6350 if (C->getValue()->isZero()) return C;
6351 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6354 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6355 if (!AddRec || AddRec->getLoop() != L)
6356 return getCouldNotCompute();
6358 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6359 // the quadratic equation to solve it.
6360 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6361 std::pair<const SCEV *,const SCEV *> Roots =
6362 SolveQuadraticEquation(AddRec, *this);
6363 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6364 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6367 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6368 << " sol#2: " << *R2 << "\n";
6370 // Pick the smallest positive root value.
6371 if (ConstantInt *CB =
6372 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6375 if (!CB->getZExtValue())
6376 std::swap(R1, R2); // R1 is the minimum root now.
6378 // We can only use this value if the chrec ends up with an exact zero
6379 // value at this index. When solving for "X*X != 5", for example, we
6380 // should not accept a root of 2.
6381 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6383 return R1; // We found a quadratic root!
6386 return getCouldNotCompute();
6389 // Otherwise we can only handle this if it is affine.
6390 if (!AddRec->isAffine())
6391 return getCouldNotCompute();
6393 // If this is an affine expression, the execution count of this branch is
6394 // the minimum unsigned root of the following equation:
6396 // Start + Step*N = 0 (mod 2^BW)
6400 // Step*N = -Start (mod 2^BW)
6402 // where BW is the common bit width of Start and Step.
6404 // Get the initial value for the loop.
6405 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6406 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6408 // For now we handle only constant steps.
6410 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6411 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6412 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6413 // We have not yet seen any such cases.
6414 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6415 if (!StepC || StepC->getValue()->equalsInt(0))
6416 return getCouldNotCompute();
6418 // For positive steps (counting up until unsigned overflow):
6419 // N = -Start/Step (as unsigned)
6420 // For negative steps (counting down to zero):
6422 // First compute the unsigned distance from zero in the direction of Step.
6423 bool CountDown = StepC->getValue()->getValue().isNegative();
6424 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6426 // Handle unitary steps, which cannot wraparound.
6427 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6428 // N = Distance (as unsigned)
6429 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6430 ConstantRange CR = getUnsignedRange(Start);
6431 const SCEV *MaxBECount;
6432 if (!CountDown && CR.getUnsignedMin().isMinValue())
6433 // When counting up, the worst starting value is 1, not 0.
6434 MaxBECount = CR.getUnsignedMax().isMinValue()
6435 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6436 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6438 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6439 : -CR.getUnsignedMin());
6440 return ExitLimit(Distance, MaxBECount);
6443 // As a special case, handle the instance where Step is a positive power of
6444 // two. In this case, determining whether Step divides Distance evenly can be
6445 // done by counting and comparing the number of trailing zeros of Step and
6448 const APInt &StepV = StepC->getValue()->getValue();
6449 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6450 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6451 // case is not handled as this code is guarded by !CountDown.
6452 if (StepV.isPowerOf2() &&
6453 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
6454 // Here we've constrained the equation to be of the form
6456 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
6458 // where we're operating on a W bit wide integer domain and k is
6459 // non-negative. The smallest unsigned solution for X is the trip count.
6461 // (0) is equivalent to:
6463 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
6464 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
6465 // <=> 2^k * Distance' - X = L * 2^(W - N)
6466 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
6468 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
6471 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
6473 // E.g. say we're solving
6475 // 2 * Val = 2 * X (in i8) ... (3)
6477 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
6479 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
6480 // necessarily the smallest unsigned value of X that satisfies (3).
6481 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
6482 // is i8 1, not i8 -127
6484 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
6486 // Since SCEV does not have a URem node, we construct one using a truncate
6487 // and a zero extend.
6489 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
6490 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
6491 auto *WideTy = Distance->getType();
6493 return getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
6497 // If the condition controls loop exit (the loop exits only if the expression
6498 // is true) and the addition is no-wrap we can use unsigned divide to
6499 // compute the backedge count. In this case, the step may not divide the
6500 // distance, but we don't care because if the condition is "missed" the loop
6501 // will have undefined behavior due to wrapping.
6502 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6504 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6505 return ExitLimit(Exact, Exact);
6508 // Then, try to solve the above equation provided that Start is constant.
6509 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6510 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6511 -StartC->getValue()->getValue(),
6513 return getCouldNotCompute();
6516 /// HowFarToNonZero - Return the number of times a backedge checking the
6517 /// specified value for nonzero will execute. If not computable, return
6519 ScalarEvolution::ExitLimit
6520 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6521 // Loops that look like: while (X == 0) are very strange indeed. We don't
6522 // handle them yet except for the trivial case. This could be expanded in the
6523 // future as needed.
6525 // If the value is a constant, check to see if it is known to be non-zero
6526 // already. If so, the backedge will execute zero times.
6527 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6528 if (!C->getValue()->isNullValue())
6529 return getZero(C->getType());
6530 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6533 // We could implement others, but I really doubt anyone writes loops like
6534 // this, and if they did, they would already be constant folded.
6535 return getCouldNotCompute();
6538 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6539 /// (which may not be an immediate predecessor) which has exactly one
6540 /// successor from which BB is reachable, or null if no such block is
6543 std::pair<BasicBlock *, BasicBlock *>
6544 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6545 // If the block has a unique predecessor, then there is no path from the
6546 // predecessor to the block that does not go through the direct edge
6547 // from the predecessor to the block.
6548 if (BasicBlock *Pred = BB->getSinglePredecessor())
6549 return std::make_pair(Pred, BB);
6551 // A loop's header is defined to be a block that dominates the loop.
6552 // If the header has a unique predecessor outside the loop, it must be
6553 // a block that has exactly one successor that can reach the loop.
6554 if (Loop *L = LI.getLoopFor(BB))
6555 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6557 return std::pair<BasicBlock *, BasicBlock *>();
6560 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6561 /// testing whether two expressions are equal, however for the purposes of
6562 /// looking for a condition guarding a loop, it can be useful to be a little
6563 /// more general, since a front-end may have replicated the controlling
6566 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6567 // Quick check to see if they are the same SCEV.
6568 if (A == B) return true;
6570 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
6571 // Not all instructions that are "identical" compute the same value. For
6572 // instance, two distinct alloca instructions allocating the same type are
6573 // identical and do not read memory; but compute distinct values.
6574 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
6577 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6578 // two different instructions with the same value. Check for this case.
6579 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6580 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6581 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6582 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6583 if (ComputesEqualValues(AI, BI))
6586 // Otherwise assume they may have a different value.
6590 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6591 /// predicate Pred. Return true iff any changes were made.
6593 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6594 const SCEV *&LHS, const SCEV *&RHS,
6596 bool Changed = false;
6598 // If we hit the max recursion limit bail out.
6602 // Canonicalize a constant to the right side.
6603 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6604 // Check for both operands constant.
6605 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6606 if (ConstantExpr::getICmp(Pred,
6608 RHSC->getValue())->isNullValue())
6609 goto trivially_false;
6611 goto trivially_true;
6613 // Otherwise swap the operands to put the constant on the right.
6614 std::swap(LHS, RHS);
6615 Pred = ICmpInst::getSwappedPredicate(Pred);
6619 // If we're comparing an addrec with a value which is loop-invariant in the
6620 // addrec's loop, put the addrec on the left. Also make a dominance check,
6621 // as both operands could be addrecs loop-invariant in each other's loop.
6622 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6623 const Loop *L = AR->getLoop();
6624 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6625 std::swap(LHS, RHS);
6626 Pred = ICmpInst::getSwappedPredicate(Pred);
6631 // If there's a constant operand, canonicalize comparisons with boundary
6632 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6633 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6634 const APInt &RA = RC->getValue()->getValue();
6636 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6637 case ICmpInst::ICMP_EQ:
6638 case ICmpInst::ICMP_NE:
6639 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6641 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6642 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6643 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6644 ME->getOperand(0)->isAllOnesValue()) {
6645 RHS = AE->getOperand(1);
6646 LHS = ME->getOperand(1);
6650 case ICmpInst::ICMP_UGE:
6651 if ((RA - 1).isMinValue()) {
6652 Pred = ICmpInst::ICMP_NE;
6653 RHS = getConstant(RA - 1);
6657 if (RA.isMaxValue()) {
6658 Pred = ICmpInst::ICMP_EQ;
6662 if (RA.isMinValue()) goto trivially_true;
6664 Pred = ICmpInst::ICMP_UGT;
6665 RHS = getConstant(RA - 1);
6668 case ICmpInst::ICMP_ULE:
6669 if ((RA + 1).isMaxValue()) {
6670 Pred = ICmpInst::ICMP_NE;
6671 RHS = getConstant(RA + 1);
6675 if (RA.isMinValue()) {
6676 Pred = ICmpInst::ICMP_EQ;
6680 if (RA.isMaxValue()) goto trivially_true;
6682 Pred = ICmpInst::ICMP_ULT;
6683 RHS = getConstant(RA + 1);
6686 case ICmpInst::ICMP_SGE:
6687 if ((RA - 1).isMinSignedValue()) {
6688 Pred = ICmpInst::ICMP_NE;
6689 RHS = getConstant(RA - 1);
6693 if (RA.isMaxSignedValue()) {
6694 Pred = ICmpInst::ICMP_EQ;
6698 if (RA.isMinSignedValue()) goto trivially_true;
6700 Pred = ICmpInst::ICMP_SGT;
6701 RHS = getConstant(RA - 1);
6704 case ICmpInst::ICMP_SLE:
6705 if ((RA + 1).isMaxSignedValue()) {
6706 Pred = ICmpInst::ICMP_NE;
6707 RHS = getConstant(RA + 1);
6711 if (RA.isMinSignedValue()) {
6712 Pred = ICmpInst::ICMP_EQ;
6716 if (RA.isMaxSignedValue()) goto trivially_true;
6718 Pred = ICmpInst::ICMP_SLT;
6719 RHS = getConstant(RA + 1);
6722 case ICmpInst::ICMP_UGT:
6723 if (RA.isMinValue()) {
6724 Pred = ICmpInst::ICMP_NE;
6728 if ((RA + 1).isMaxValue()) {
6729 Pred = ICmpInst::ICMP_EQ;
6730 RHS = getConstant(RA + 1);
6734 if (RA.isMaxValue()) goto trivially_false;
6736 case ICmpInst::ICMP_ULT:
6737 if (RA.isMaxValue()) {
6738 Pred = ICmpInst::ICMP_NE;
6742 if ((RA - 1).isMinValue()) {
6743 Pred = ICmpInst::ICMP_EQ;
6744 RHS = getConstant(RA - 1);
6748 if (RA.isMinValue()) goto trivially_false;
6750 case ICmpInst::ICMP_SGT:
6751 if (RA.isMinSignedValue()) {
6752 Pred = ICmpInst::ICMP_NE;
6756 if ((RA + 1).isMaxSignedValue()) {
6757 Pred = ICmpInst::ICMP_EQ;
6758 RHS = getConstant(RA + 1);
6762 if (RA.isMaxSignedValue()) goto trivially_false;
6764 case ICmpInst::ICMP_SLT:
6765 if (RA.isMaxSignedValue()) {
6766 Pred = ICmpInst::ICMP_NE;
6770 if ((RA - 1).isMinSignedValue()) {
6771 Pred = ICmpInst::ICMP_EQ;
6772 RHS = getConstant(RA - 1);
6776 if (RA.isMinSignedValue()) goto trivially_false;
6781 // Check for obvious equality.
6782 if (HasSameValue(LHS, RHS)) {
6783 if (ICmpInst::isTrueWhenEqual(Pred))
6784 goto trivially_true;
6785 if (ICmpInst::isFalseWhenEqual(Pred))
6786 goto trivially_false;
6789 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6790 // adding or subtracting 1 from one of the operands.
6792 case ICmpInst::ICMP_SLE:
6793 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6794 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6796 Pred = ICmpInst::ICMP_SLT;
6798 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6799 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6801 Pred = ICmpInst::ICMP_SLT;
6805 case ICmpInst::ICMP_SGE:
6806 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6807 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6809 Pred = ICmpInst::ICMP_SGT;
6811 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6812 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6814 Pred = ICmpInst::ICMP_SGT;
6818 case ICmpInst::ICMP_ULE:
6819 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6820 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6822 Pred = ICmpInst::ICMP_ULT;
6824 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6825 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6827 Pred = ICmpInst::ICMP_ULT;
6831 case ICmpInst::ICMP_UGE:
6832 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6833 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6835 Pred = ICmpInst::ICMP_UGT;
6837 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6838 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6840 Pred = ICmpInst::ICMP_UGT;
6848 // TODO: More simplifications are possible here.
6850 // Recursively simplify until we either hit a recursion limit or nothing
6853 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6859 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6860 Pred = ICmpInst::ICMP_EQ;
6865 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6866 Pred = ICmpInst::ICMP_NE;
6870 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6871 return getSignedRange(S).getSignedMax().isNegative();
6874 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6875 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6878 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6879 return !getSignedRange(S).getSignedMin().isNegative();
6882 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6883 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6886 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6887 return isKnownNegative(S) || isKnownPositive(S);
6890 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6891 const SCEV *LHS, const SCEV *RHS) {
6892 // Canonicalize the inputs first.
6893 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6895 // If LHS or RHS is an addrec, check to see if the condition is true in
6896 // every iteration of the loop.
6897 // If LHS and RHS are both addrec, both conditions must be true in
6898 // every iteration of the loop.
6899 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6900 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6901 bool LeftGuarded = false;
6902 bool RightGuarded = false;
6904 const Loop *L = LAR->getLoop();
6905 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6906 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6907 if (!RAR) return true;
6912 const Loop *L = RAR->getLoop();
6913 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6914 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6915 if (!LAR) return true;
6916 RightGuarded = true;
6919 if (LeftGuarded && RightGuarded)
6922 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
6925 // Otherwise see what can be done with known constant ranges.
6926 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6929 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
6930 ICmpInst::Predicate Pred,
6932 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
6935 // Verify an invariant: inverting the predicate should turn a monotonically
6936 // increasing change to a monotonically decreasing one, and vice versa.
6937 bool IncreasingSwapped;
6938 bool ResultSwapped = isMonotonicPredicateImpl(
6939 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
6941 assert(Result == ResultSwapped && "should be able to analyze both!");
6943 assert(Increasing == !IncreasingSwapped &&
6944 "monotonicity should flip as we flip the predicate");
6950 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
6951 ICmpInst::Predicate Pred,
6954 // A zero step value for LHS means the induction variable is essentially a
6955 // loop invariant value. We don't really depend on the predicate actually
6956 // flipping from false to true (for increasing predicates, and the other way
6957 // around for decreasing predicates), all we care about is that *if* the
6958 // predicate changes then it only changes from false to true.
6960 // A zero step value in itself is not very useful, but there may be places
6961 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
6962 // as general as possible.
6966 return false; // Conservative answer
6968 case ICmpInst::ICMP_UGT:
6969 case ICmpInst::ICMP_UGE:
6970 case ICmpInst::ICMP_ULT:
6971 case ICmpInst::ICMP_ULE:
6972 if (!LHS->getNoWrapFlags(SCEV::FlagNUW))
6975 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
6978 case ICmpInst::ICMP_SGT:
6979 case ICmpInst::ICMP_SGE:
6980 case ICmpInst::ICMP_SLT:
6981 case ICmpInst::ICMP_SLE: {
6982 if (!LHS->getNoWrapFlags(SCEV::FlagNSW))
6985 const SCEV *Step = LHS->getStepRecurrence(*this);
6987 if (isKnownNonNegative(Step)) {
6988 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
6992 if (isKnownNonPositive(Step)) {
6993 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7002 llvm_unreachable("switch has default clause!");
7005 bool ScalarEvolution::isLoopInvariantPredicate(
7006 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7007 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7008 const SCEV *&InvariantRHS) {
7010 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7011 if (!isLoopInvariant(RHS, L)) {
7012 if (!isLoopInvariant(LHS, L))
7015 std::swap(LHS, RHS);
7016 Pred = ICmpInst::getSwappedPredicate(Pred);
7019 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7020 if (!ArLHS || ArLHS->getLoop() != L)
7024 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7027 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7028 // true as the loop iterates, and the backedge is control dependent on
7029 // "ArLHS `Pred` RHS" == true then we can reason as follows:
7031 // * if the predicate was false in the first iteration then the predicate
7032 // is never evaluated again, since the loop exits without taking the
7034 // * if the predicate was true in the first iteration then it will
7035 // continue to be true for all future iterations since it is
7036 // monotonically increasing.
7038 // For both the above possibilities, we can replace the loop varying
7039 // predicate with its value on the first iteration of the loop (which is
7042 // A similar reasoning applies for a monotonically decreasing predicate, by
7043 // replacing true with false and false with true in the above two bullets.
7045 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7047 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7050 InvariantPred = Pred;
7051 InvariantLHS = ArLHS->getStart();
7057 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
7058 const SCEV *LHS, const SCEV *RHS) {
7059 if (HasSameValue(LHS, RHS))
7060 return ICmpInst::isTrueWhenEqual(Pred);
7062 // This code is split out from isKnownPredicate because it is called from
7063 // within isLoopEntryGuardedByCond.
7066 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7067 case ICmpInst::ICMP_SGT:
7068 std::swap(LHS, RHS);
7069 case ICmpInst::ICMP_SLT: {
7070 ConstantRange LHSRange = getSignedRange(LHS);
7071 ConstantRange RHSRange = getSignedRange(RHS);
7072 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
7074 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
7078 case ICmpInst::ICMP_SGE:
7079 std::swap(LHS, RHS);
7080 case ICmpInst::ICMP_SLE: {
7081 ConstantRange LHSRange = getSignedRange(LHS);
7082 ConstantRange RHSRange = getSignedRange(RHS);
7083 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
7085 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
7089 case ICmpInst::ICMP_UGT:
7090 std::swap(LHS, RHS);
7091 case ICmpInst::ICMP_ULT: {
7092 ConstantRange LHSRange = getUnsignedRange(LHS);
7093 ConstantRange RHSRange = getUnsignedRange(RHS);
7094 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
7096 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
7100 case ICmpInst::ICMP_UGE:
7101 std::swap(LHS, RHS);
7102 case ICmpInst::ICMP_ULE: {
7103 ConstantRange LHSRange = getUnsignedRange(LHS);
7104 ConstantRange RHSRange = getUnsignedRange(RHS);
7105 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
7107 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
7111 case ICmpInst::ICMP_NE: {
7112 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
7114 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
7117 const SCEV *Diff = getMinusSCEV(LHS, RHS);
7118 if (isKnownNonZero(Diff))
7122 case ICmpInst::ICMP_EQ:
7123 // The check at the top of the function catches the case where
7124 // the values are known to be equal.
7130 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7133 if (ProvingSplitPredicate)
7136 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7137 // the stack can result in exponential time complexity.
7138 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7140 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7142 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7143 // isKnownPredicate. isKnownPredicate is more powerful, but also more
7144 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7145 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
7146 // use isKnownPredicate later if needed.
7147 if (Pred == ICmpInst::ICMP_ULT && isKnownNonNegative(RHS) &&
7148 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7149 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS))
7155 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7156 /// protected by a conditional between LHS and RHS. This is used to
7157 /// to eliminate casts.
7159 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7160 ICmpInst::Predicate Pred,
7161 const SCEV *LHS, const SCEV *RHS) {
7162 // Interpret a null as meaning no loop, where there is obviously no guard
7163 // (interprocedural conditions notwithstanding).
7164 if (!L) return true;
7166 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7168 BasicBlock *Latch = L->getLoopLatch();
7172 BranchInst *LoopContinuePredicate =
7173 dyn_cast<BranchInst>(Latch->getTerminator());
7174 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7175 isImpliedCond(Pred, LHS, RHS,
7176 LoopContinuePredicate->getCondition(),
7177 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7180 // We don't want more than one activation of the following loops on the stack
7181 // -- that can lead to O(n!) time complexity.
7182 if (WalkingBEDominatingConds)
7185 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7187 // See if we can exploit a trip count to prove the predicate.
7188 const auto &BETakenInfo = getBackedgeTakenInfo(L);
7189 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7190 if (LatchBECount != getCouldNotCompute()) {
7191 // We know that Latch branches back to the loop header exactly
7192 // LatchBECount times. This means the backdege condition at Latch is
7193 // equivalent to "{0,+,1} u< LatchBECount".
7194 Type *Ty = LatchBECount->getType();
7195 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7196 const SCEV *LoopCounter =
7197 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7198 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7203 // Check conditions due to any @llvm.assume intrinsics.
7204 for (auto &AssumeVH : AC.assumptions()) {
7207 auto *CI = cast<CallInst>(AssumeVH);
7208 if (!DT.dominates(CI, Latch->getTerminator()))
7211 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7215 // If the loop is not reachable from the entry block, we risk running into an
7216 // infinite loop as we walk up into the dom tree. These loops do not matter
7217 // anyway, so we just return a conservative answer when we see them.
7218 if (!DT.isReachableFromEntry(L->getHeader()))
7221 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7222 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7224 assert(DTN && "should reach the loop header before reaching the root!");
7226 BasicBlock *BB = DTN->getBlock();
7227 BasicBlock *PBB = BB->getSinglePredecessor();
7231 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7232 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7235 Value *Condition = ContinuePredicate->getCondition();
7237 // If we have an edge `E` within the loop body that dominates the only
7238 // latch, the condition guarding `E` also guards the backedge. This
7239 // reasoning works only for loops with a single latch.
7241 BasicBlockEdge DominatingEdge(PBB, BB);
7242 if (DominatingEdge.isSingleEdge()) {
7243 // We're constructively (and conservatively) enumerating edges within the
7244 // loop body that dominate the latch. The dominator tree better agree
7246 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7248 if (isImpliedCond(Pred, LHS, RHS, Condition,
7249 BB != ContinuePredicate->getSuccessor(0)))
7257 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7258 /// by a conditional between LHS and RHS. This is used to help avoid max
7259 /// expressions in loop trip counts, and to eliminate casts.
7261 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7262 ICmpInst::Predicate Pred,
7263 const SCEV *LHS, const SCEV *RHS) {
7264 // Interpret a null as meaning no loop, where there is obviously no guard
7265 // (interprocedural conditions notwithstanding).
7266 if (!L) return false;
7268 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7270 // Starting at the loop predecessor, climb up the predecessor chain, as long
7271 // as there are predecessors that can be found that have unique successors
7272 // leading to the original header.
7273 for (std::pair<BasicBlock *, BasicBlock *>
7274 Pair(L->getLoopPredecessor(), L->getHeader());
7276 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7278 BranchInst *LoopEntryPredicate =
7279 dyn_cast<BranchInst>(Pair.first->getTerminator());
7280 if (!LoopEntryPredicate ||
7281 LoopEntryPredicate->isUnconditional())
7284 if (isImpliedCond(Pred, LHS, RHS,
7285 LoopEntryPredicate->getCondition(),
7286 LoopEntryPredicate->getSuccessor(0) != Pair.second))
7290 // Check conditions due to any @llvm.assume intrinsics.
7291 for (auto &AssumeVH : AC.assumptions()) {
7294 auto *CI = cast<CallInst>(AssumeVH);
7295 if (!DT.dominates(CI, L->getHeader()))
7298 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7305 /// RAII wrapper to prevent recursive application of isImpliedCond.
7306 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7307 /// currently evaluating isImpliedCond.
7308 struct MarkPendingLoopPredicate {
7310 DenseSet<Value*> &LoopPreds;
7313 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7314 : Cond(C), LoopPreds(LP) {
7315 Pending = !LoopPreds.insert(Cond).second;
7317 ~MarkPendingLoopPredicate() {
7319 LoopPreds.erase(Cond);
7323 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7324 /// and RHS is true whenever the given Cond value evaluates to true.
7325 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7326 const SCEV *LHS, const SCEV *RHS,
7327 Value *FoundCondValue,
7329 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7333 // Recursively handle And and Or conditions.
7334 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7335 if (BO->getOpcode() == Instruction::And) {
7337 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7338 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7339 } else if (BO->getOpcode() == Instruction::Or) {
7341 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7342 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7346 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
7347 if (!ICI) return false;
7349 // Now that we found a conditional branch that dominates the loop or controls
7350 // the loop latch. Check to see if it is the comparison we are looking for.
7351 ICmpInst::Predicate FoundPred;
7353 FoundPred = ICI->getInversePredicate();
7355 FoundPred = ICI->getPredicate();
7357 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
7358 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
7360 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
7363 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
7365 ICmpInst::Predicate FoundPred,
7366 const SCEV *FoundLHS,
7367 const SCEV *FoundRHS) {
7368 // Balance the types.
7369 if (getTypeSizeInBits(LHS->getType()) <
7370 getTypeSizeInBits(FoundLHS->getType())) {
7371 if (CmpInst::isSigned(Pred)) {
7372 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
7373 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
7375 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
7376 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
7378 } else if (getTypeSizeInBits(LHS->getType()) >
7379 getTypeSizeInBits(FoundLHS->getType())) {
7380 if (CmpInst::isSigned(FoundPred)) {
7381 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
7382 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
7384 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
7385 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
7389 // Canonicalize the query to match the way instcombine will have
7390 // canonicalized the comparison.
7391 if (SimplifyICmpOperands(Pred, LHS, RHS))
7393 return CmpInst::isTrueWhenEqual(Pred);
7394 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
7395 if (FoundLHS == FoundRHS)
7396 return CmpInst::isFalseWhenEqual(FoundPred);
7398 // Check to see if we can make the LHS or RHS match.
7399 if (LHS == FoundRHS || RHS == FoundLHS) {
7400 if (isa<SCEVConstant>(RHS)) {
7401 std::swap(FoundLHS, FoundRHS);
7402 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
7404 std::swap(LHS, RHS);
7405 Pred = ICmpInst::getSwappedPredicate(Pred);
7409 // Check whether the found predicate is the same as the desired predicate.
7410 if (FoundPred == Pred)
7411 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7413 // Check whether swapping the found predicate makes it the same as the
7414 // desired predicate.
7415 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
7416 if (isa<SCEVConstant>(RHS))
7417 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
7419 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
7420 RHS, LHS, FoundLHS, FoundRHS);
7423 // Check if we can make progress by sharpening ranges.
7424 if (FoundPred == ICmpInst::ICMP_NE &&
7425 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
7427 const SCEVConstant *C = nullptr;
7428 const SCEV *V = nullptr;
7430 if (isa<SCEVConstant>(FoundLHS)) {
7431 C = cast<SCEVConstant>(FoundLHS);
7434 C = cast<SCEVConstant>(FoundRHS);
7438 // The guarding predicate tells us that C != V. If the known range
7439 // of V is [C, t), we can sharpen the range to [C + 1, t). The
7440 // range we consider has to correspond to same signedness as the
7441 // predicate we're interested in folding.
7443 APInt Min = ICmpInst::isSigned(Pred) ?
7444 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7446 if (Min == C->getValue()->getValue()) {
7447 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7448 // This is true even if (Min + 1) wraps around -- in case of
7449 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7451 APInt SharperMin = Min + 1;
7454 case ICmpInst::ICMP_SGE:
7455 case ICmpInst::ICMP_UGE:
7456 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7458 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7459 getConstant(SharperMin)))
7462 case ICmpInst::ICMP_SGT:
7463 case ICmpInst::ICMP_UGT:
7464 // We know from the range information that (V `Pred` Min ||
7465 // V == Min). We know from the guarding condition that !(V
7466 // == Min). This gives us
7468 // V `Pred` Min || V == Min && !(V == Min)
7471 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7473 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7483 // Check whether the actual condition is beyond sufficient.
7484 if (FoundPred == ICmpInst::ICMP_EQ)
7485 if (ICmpInst::isTrueWhenEqual(Pred))
7486 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7488 if (Pred == ICmpInst::ICMP_NE)
7489 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7490 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7493 // Otherwise assume the worst.
7497 // Return true if More == (Less + C), where C is a constant.
7498 static bool IsConstDiff(ScalarEvolution &SE, const SCEV *Less, const SCEV *More,
7500 // We avoid subtracting expressions here because this function is usually
7501 // fairly deep in the call stack (i.e. is called many times).
7503 auto SplitBinaryAdd = [](const SCEV *Expr, const SCEV *&L, const SCEV *&R) {
7504 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
7505 if (!AE || AE->getNumOperands() != 2)
7508 L = AE->getOperand(0);
7509 R = AE->getOperand(1);
7513 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
7514 const auto *LAR = cast<SCEVAddRecExpr>(Less);
7515 const auto *MAR = cast<SCEVAddRecExpr>(More);
7517 if (LAR->getLoop() != MAR->getLoop())
7520 // We look at affine expressions only; not for correctness but to keep
7521 // getStepRecurrence cheap.
7522 if (!LAR->isAffine() || !MAR->isAffine())
7525 if (LAR->getStepRecurrence(SE) != MAR->getStepRecurrence(SE))
7528 Less = LAR->getStart();
7529 More = MAR->getStart();
7534 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
7535 const auto &M = cast<SCEVConstant>(More)->getValue()->getValue();
7536 const auto &L = cast<SCEVConstant>(Less)->getValue()->getValue();
7542 if (SplitBinaryAdd(Less, L, R))
7543 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7545 C = -(LC->getValue()->getValue());
7549 if (SplitBinaryAdd(More, L, R))
7550 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7552 C = LC->getValue()->getValue();
7559 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
7560 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
7561 const SCEV *FoundLHS, const SCEV *FoundRHS) {
7562 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
7565 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7569 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
7570 if (!AddRecFoundLHS)
7573 // We'd like to let SCEV reason about control dependencies, so we constrain
7574 // both the inequalities to be about add recurrences on the same loop. This
7575 // way we can use isLoopEntryGuardedByCond later.
7577 const Loop *L = AddRecFoundLHS->getLoop();
7578 if (L != AddRecLHS->getLoop())
7581 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
7583 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
7586 // Informal proof for (2), assuming (1) [*]:
7588 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
7592 // FoundLHS s< FoundRHS s< INT_MIN - C
7593 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
7594 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
7595 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
7596 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
7597 // <=> FoundLHS + C s< FoundRHS + C
7599 // [*]: (1) can be proved by ruling out overflow.
7601 // [**]: This can be proved by analyzing all the four possibilities:
7602 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
7603 // (A s>= 0, B s>= 0).
7606 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
7607 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
7608 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
7609 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
7610 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
7614 if (!IsConstDiff(*this, FoundLHS, LHS, LDiff) ||
7615 !IsConstDiff(*this, FoundRHS, RHS, RDiff) ||
7622 APInt FoundRHSLimit;
7624 if (Pred == CmpInst::ICMP_ULT) {
7625 FoundRHSLimit = -RDiff;
7627 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
7628 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - RDiff;
7631 // Try to prove (1) or (2), as needed.
7632 return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
7633 getConstant(FoundRHSLimit));
7636 /// isImpliedCondOperands - Test whether the condition described by Pred,
7637 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7638 /// and FoundRHS is true.
7639 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7640 const SCEV *LHS, const SCEV *RHS,
7641 const SCEV *FoundLHS,
7642 const SCEV *FoundRHS) {
7643 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7646 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
7649 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7650 FoundLHS, FoundRHS) ||
7651 // ~x < ~y --> x > y
7652 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7653 getNotSCEV(FoundRHS),
7654 getNotSCEV(FoundLHS));
7658 /// If Expr computes ~A, return A else return nullptr
7659 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7660 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7661 if (!Add || Add->getNumOperands() != 2) return nullptr;
7663 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
7664 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
7667 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7668 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
7670 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
7671 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
7674 return AddRHS->getOperand(1);
7678 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7679 template<typename MaxExprType>
7680 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7681 const SCEV *Candidate) {
7682 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7683 if (!MaxExpr) return false;
7685 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7686 return It != MaxExpr->op_end();
7690 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7691 template<typename MaxExprType>
7692 static bool IsMinConsistingOf(ScalarEvolution &SE,
7693 const SCEV *MaybeMinExpr,
7694 const SCEV *Candidate) {
7695 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7699 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7702 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
7703 ICmpInst::Predicate Pred,
7704 const SCEV *LHS, const SCEV *RHS) {
7706 // If both sides are affine addrecs for the same loop, with equal
7707 // steps, and we know the recurrences don't wrap, then we only
7708 // need to check the predicate on the starting values.
7710 if (!ICmpInst::isRelational(Pred))
7713 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7716 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7719 if (LAR->getLoop() != RAR->getLoop())
7721 if (!LAR->isAffine() || !RAR->isAffine())
7724 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
7727 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
7728 SCEV::FlagNSW : SCEV::FlagNUW;
7729 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
7732 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
7735 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7737 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7738 ICmpInst::Predicate Pred,
7739 const SCEV *LHS, const SCEV *RHS) {
7744 case ICmpInst::ICMP_SGE:
7745 std::swap(LHS, RHS);
7747 case ICmpInst::ICMP_SLE:
7750 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7752 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7754 case ICmpInst::ICMP_UGE:
7755 std::swap(LHS, RHS);
7757 case ICmpInst::ICMP_ULE:
7760 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7762 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7765 llvm_unreachable("covered switch fell through?!");
7768 /// isImpliedCondOperandsHelper - Test whether the condition described by
7769 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7770 /// FoundLHS, and FoundRHS is true.
7772 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7773 const SCEV *LHS, const SCEV *RHS,
7774 const SCEV *FoundLHS,
7775 const SCEV *FoundRHS) {
7776 auto IsKnownPredicateFull =
7777 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7778 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7779 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
7780 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS);
7784 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7785 case ICmpInst::ICMP_EQ:
7786 case ICmpInst::ICMP_NE:
7787 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7790 case ICmpInst::ICMP_SLT:
7791 case ICmpInst::ICMP_SLE:
7792 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7793 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7796 case ICmpInst::ICMP_SGT:
7797 case ICmpInst::ICMP_SGE:
7798 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7799 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7802 case ICmpInst::ICMP_ULT:
7803 case ICmpInst::ICMP_ULE:
7804 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7805 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7808 case ICmpInst::ICMP_UGT:
7809 case ICmpInst::ICMP_UGE:
7810 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7811 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7819 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
7820 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
7821 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
7824 const SCEV *FoundLHS,
7825 const SCEV *FoundRHS) {
7826 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
7827 // The restriction on `FoundRHS` be lifted easily -- it exists only to
7828 // reduce the compile time impact of this optimization.
7831 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
7832 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
7833 !isa<SCEVConstant>(AddLHS->getOperand(0)))
7836 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
7838 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
7839 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
7840 ConstantRange FoundLHSRange =
7841 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
7843 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
7846 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
7847 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
7849 // We can also compute the range of values for `LHS` that satisfy the
7850 // consequent, "`LHS` `Pred` `RHS`":
7851 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
7852 ConstantRange SatisfyingLHSRange =
7853 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
7855 // The antecedent implies the consequent if every value of `LHS` that
7856 // satisfies the antecedent also satisfies the consequent.
7857 return SatisfyingLHSRange.contains(LHSRange);
7860 // Verify if an linear IV with positive stride can overflow when in a
7861 // less-than comparison, knowing the invariant term of the comparison, the
7862 // stride and the knowledge of NSW/NUW flags on the recurrence.
7863 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7864 bool IsSigned, bool NoWrap) {
7865 if (NoWrap) return false;
7867 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7868 const SCEV *One = getOne(Stride->getType());
7871 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7872 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7873 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7876 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7877 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7880 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7881 APInt MaxValue = APInt::getMaxValue(BitWidth);
7882 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7885 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7886 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7889 // Verify if an linear IV with negative stride can overflow when in a
7890 // greater-than comparison, knowing the invariant term of the comparison,
7891 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7892 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7893 bool IsSigned, bool NoWrap) {
7894 if (NoWrap) return false;
7896 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7897 const SCEV *One = getOne(Stride->getType());
7900 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7901 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7902 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7905 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7906 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7909 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7910 APInt MinValue = APInt::getMinValue(BitWidth);
7911 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7914 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7915 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7918 // Compute the backedge taken count knowing the interval difference, the
7919 // stride and presence of the equality in the comparison.
7920 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7922 const SCEV *One = getOne(Step->getType());
7923 Delta = Equality ? getAddExpr(Delta, Step)
7924 : getAddExpr(Delta, getMinusSCEV(Step, One));
7925 return getUDivExpr(Delta, Step);
7928 /// HowManyLessThans - Return the number of times a backedge containing the
7929 /// specified less-than comparison will execute. If not computable, return
7930 /// CouldNotCompute.
7932 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7933 /// the branch (loops exits only if condition is true). In this case, we can use
7934 /// NoWrapFlags to skip overflow checks.
7935 ScalarEvolution::ExitLimit
7936 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7937 const Loop *L, bool IsSigned,
7938 bool ControlsExit) {
7939 // We handle only IV < Invariant
7940 if (!isLoopInvariant(RHS, L))
7941 return getCouldNotCompute();
7943 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7945 // Avoid weird loops
7946 if (!IV || IV->getLoop() != L || !IV->isAffine())
7947 return getCouldNotCompute();
7949 bool NoWrap = ControlsExit &&
7950 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7952 const SCEV *Stride = IV->getStepRecurrence(*this);
7954 // Avoid negative or zero stride values
7955 if (!isKnownPositive(Stride))
7956 return getCouldNotCompute();
7958 // Avoid proven overflow cases: this will ensure that the backedge taken count
7959 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7960 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7961 // behaviors like the case of C language.
7962 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7963 return getCouldNotCompute();
7965 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7966 : ICmpInst::ICMP_ULT;
7967 const SCEV *Start = IV->getStart();
7968 const SCEV *End = RHS;
7969 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7970 const SCEV *Diff = getMinusSCEV(RHS, Start);
7971 // If we have NoWrap set, then we can assume that the increment won't
7972 // overflow, in which case if RHS - Start is a constant, we don't need to
7973 // do a max operation since we can just figure it out statically
7974 if (NoWrap && isa<SCEVConstant>(Diff)) {
7975 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7979 End = IsSigned ? getSMaxExpr(RHS, Start)
7980 : getUMaxExpr(RHS, Start);
7983 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7985 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7986 : getUnsignedRange(Start).getUnsignedMin();
7988 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7989 : getUnsignedRange(Stride).getUnsignedMin();
7991 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7992 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7993 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7995 // Although End can be a MAX expression we estimate MaxEnd considering only
7996 // the case End = RHS. This is safe because in the other case (End - Start)
7997 // is zero, leading to a zero maximum backedge taken count.
7999 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8000 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8002 const SCEV *MaxBECount;
8003 if (isa<SCEVConstant>(BECount))
8004 MaxBECount = BECount;
8006 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8007 getConstant(MinStride), false);
8009 if (isa<SCEVCouldNotCompute>(MaxBECount))
8010 MaxBECount = BECount;
8012 return ExitLimit(BECount, MaxBECount);
8015 ScalarEvolution::ExitLimit
8016 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8017 const Loop *L, bool IsSigned,
8018 bool ControlsExit) {
8019 // We handle only IV > Invariant
8020 if (!isLoopInvariant(RHS, L))
8021 return getCouldNotCompute();
8023 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8025 // Avoid weird loops
8026 if (!IV || IV->getLoop() != L || !IV->isAffine())
8027 return getCouldNotCompute();
8029 bool NoWrap = ControlsExit &&
8030 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8032 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8034 // Avoid negative or zero stride values
8035 if (!isKnownPositive(Stride))
8036 return getCouldNotCompute();
8038 // Avoid proven overflow cases: this will ensure that the backedge taken count
8039 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8040 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8041 // behaviors like the case of C language.
8042 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8043 return getCouldNotCompute();
8045 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8046 : ICmpInst::ICMP_UGT;
8048 const SCEV *Start = IV->getStart();
8049 const SCEV *End = RHS;
8050 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
8051 const SCEV *Diff = getMinusSCEV(RHS, Start);
8052 // If we have NoWrap set, then we can assume that the increment won't
8053 // overflow, in which case if RHS - Start is a constant, we don't need to
8054 // do a max operation since we can just figure it out statically
8055 if (NoWrap && isa<SCEVConstant>(Diff)) {
8056 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
8057 if (!D.isNegative())
8060 End = IsSigned ? getSMinExpr(RHS, Start)
8061 : getUMinExpr(RHS, Start);
8064 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8066 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8067 : getUnsignedRange(Start).getUnsignedMax();
8069 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8070 : getUnsignedRange(Stride).getUnsignedMin();
8072 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8073 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8074 : APInt::getMinValue(BitWidth) + (MinStride - 1);
8076 // Although End can be a MIN expression we estimate MinEnd considering only
8077 // the case End = RHS. This is safe because in the other case (Start - End)
8078 // is zero, leading to a zero maximum backedge taken count.
8080 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8081 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8084 const SCEV *MaxBECount = getCouldNotCompute();
8085 if (isa<SCEVConstant>(BECount))
8086 MaxBECount = BECount;
8088 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8089 getConstant(MinStride), false);
8091 if (isa<SCEVCouldNotCompute>(MaxBECount))
8092 MaxBECount = BECount;
8094 return ExitLimit(BECount, MaxBECount);
8097 /// getNumIterationsInRange - Return the number of iterations of this loop that
8098 /// produce values in the specified constant range. Another way of looking at
8099 /// this is that it returns the first iteration number where the value is not in
8100 /// the condition, thus computing the exit count. If the iteration count can't
8101 /// be computed, an instance of SCEVCouldNotCompute is returned.
8102 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
8103 ScalarEvolution &SE) const {
8104 if (Range.isFullSet()) // Infinite loop.
8105 return SE.getCouldNotCompute();
8107 // If the start is a non-zero constant, shift the range to simplify things.
8108 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8109 if (!SC->getValue()->isZero()) {
8110 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8111 Operands[0] = SE.getZero(SC->getType());
8112 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8113 getNoWrapFlags(FlagNW));
8114 if (const SCEVAddRecExpr *ShiftedAddRec =
8115 dyn_cast<SCEVAddRecExpr>(Shifted))
8116 return ShiftedAddRec->getNumIterationsInRange(
8117 Range.subtract(SC->getValue()->getValue()), SE);
8118 // This is strange and shouldn't happen.
8119 return SE.getCouldNotCompute();
8122 // The only time we can solve this is when we have all constant indices.
8123 // Otherwise, we cannot determine the overflow conditions.
8124 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
8125 if (!isa<SCEVConstant>(getOperand(i)))
8126 return SE.getCouldNotCompute();
8129 // Okay at this point we know that all elements of the chrec are constants and
8130 // that the start element is zero.
8132 // First check to see if the range contains zero. If not, the first
8134 unsigned BitWidth = SE.getTypeSizeInBits(getType());
8135 if (!Range.contains(APInt(BitWidth, 0)))
8136 return SE.getZero(getType());
8139 // If this is an affine expression then we have this situation:
8140 // Solve {0,+,A} in Range === Ax in Range
8142 // We know that zero is in the range. If A is positive then we know that
8143 // the upper value of the range must be the first possible exit value.
8144 // If A is negative then the lower of the range is the last possible loop
8145 // value. Also note that we already checked for a full range.
8146 APInt One(BitWidth,1);
8147 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
8148 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8150 // The exit value should be (End+A)/A.
8151 APInt ExitVal = (End + A).udiv(A);
8152 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8154 // Evaluate at the exit value. If we really did fall out of the valid
8155 // range, then we computed our trip count, otherwise wrap around or other
8156 // things must have happened.
8157 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8158 if (Range.contains(Val->getValue()))
8159 return SE.getCouldNotCompute(); // Something strange happened
8161 // Ensure that the previous value is in the range. This is a sanity check.
8162 assert(Range.contains(
8163 EvaluateConstantChrecAtConstant(this,
8164 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8165 "Linear scev computation is off in a bad way!");
8166 return SE.getConstant(ExitValue);
8167 } else if (isQuadratic()) {
8168 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8169 // quadratic equation to solve it. To do this, we must frame our problem in
8170 // terms of figuring out when zero is crossed, instead of when
8171 // Range.getUpper() is crossed.
8172 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8173 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8174 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
8175 // getNoWrapFlags(FlagNW)
8178 // Next, solve the constructed addrec
8179 std::pair<const SCEV *,const SCEV *> Roots =
8180 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
8181 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
8182 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
8184 // Pick the smallest positive root value.
8185 if (ConstantInt *CB =
8186 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
8187 R1->getValue(), R2->getValue()))) {
8188 if (!CB->getZExtValue())
8189 std::swap(R1, R2); // R1 is the minimum root now.
8191 // Make sure the root is not off by one. The returned iteration should
8192 // not be in the range, but the previous one should be. When solving
8193 // for "X*X < 5", for example, we should not return a root of 2.
8194 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
8197 if (Range.contains(R1Val->getValue())) {
8198 // The next iteration must be out of the range...
8199 ConstantInt *NextVal =
8200 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
8202 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8203 if (!Range.contains(R1Val->getValue()))
8204 return SE.getConstant(NextVal);
8205 return SE.getCouldNotCompute(); // Something strange happened
8208 // If R1 was not in the range, then it is a good return value. Make
8209 // sure that R1-1 WAS in the range though, just in case.
8210 ConstantInt *NextVal =
8211 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
8212 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8213 if (Range.contains(R1Val->getValue()))
8215 return SE.getCouldNotCompute(); // Something strange happened
8220 return SE.getCouldNotCompute();
8226 FindUndefs() : Found(false) {}
8228 bool follow(const SCEV *S) {
8229 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
8230 if (isa<UndefValue>(C->getValue()))
8232 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
8233 if (isa<UndefValue>(C->getValue()))
8237 // Keep looking if we haven't found it yet.
8240 bool isDone() const {
8241 // Stop recursion if we have found an undef.
8247 // Return true when S contains at least an undef value.
8249 containsUndefs(const SCEV *S) {
8251 SCEVTraversal<FindUndefs> ST(F);
8258 // Collect all steps of SCEV expressions.
8259 struct SCEVCollectStrides {
8260 ScalarEvolution &SE;
8261 SmallVectorImpl<const SCEV *> &Strides;
8263 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
8264 : SE(SE), Strides(S) {}
8266 bool follow(const SCEV *S) {
8267 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
8268 Strides.push_back(AR->getStepRecurrence(SE));
8271 bool isDone() const { return false; }
8274 // Collect all SCEVUnknown and SCEVMulExpr expressions.
8275 struct SCEVCollectTerms {
8276 SmallVectorImpl<const SCEV *> &Terms;
8278 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
8281 bool follow(const SCEV *S) {
8282 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
8283 if (!containsUndefs(S))
8286 // Stop recursion: once we collected a term, do not walk its operands.
8293 bool isDone() const { return false; }
8297 /// Find parametric terms in this SCEVAddRecExpr.
8298 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
8299 SmallVectorImpl<const SCEV *> &Terms) {
8300 SmallVector<const SCEV *, 4> Strides;
8301 SCEVCollectStrides StrideCollector(*this, Strides);
8302 visitAll(Expr, StrideCollector);
8305 dbgs() << "Strides:\n";
8306 for (const SCEV *S : Strides)
8307 dbgs() << *S << "\n";
8310 for (const SCEV *S : Strides) {
8311 SCEVCollectTerms TermCollector(Terms);
8312 visitAll(S, TermCollector);
8316 dbgs() << "Terms:\n";
8317 for (const SCEV *T : Terms)
8318 dbgs() << *T << "\n";
8322 static bool findArrayDimensionsRec(ScalarEvolution &SE,
8323 SmallVectorImpl<const SCEV *> &Terms,
8324 SmallVectorImpl<const SCEV *> &Sizes) {
8325 int Last = Terms.size() - 1;
8326 const SCEV *Step = Terms[Last];
8328 // End of recursion.
8330 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
8331 SmallVector<const SCEV *, 2> Qs;
8332 for (const SCEV *Op : M->operands())
8333 if (!isa<SCEVConstant>(Op))
8336 Step = SE.getMulExpr(Qs);
8339 Sizes.push_back(Step);
8343 for (const SCEV *&Term : Terms) {
8344 // Normalize the terms before the next call to findArrayDimensionsRec.
8346 SCEVDivision::divide(SE, Term, Step, &Q, &R);
8348 // Bail out when GCD does not evenly divide one of the terms.
8355 // Remove all SCEVConstants.
8356 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
8357 return isa<SCEVConstant>(E);
8361 if (Terms.size() > 0)
8362 if (!findArrayDimensionsRec(SE, Terms, Sizes))
8365 Sizes.push_back(Step);
8370 struct FindParameter {
8371 bool FoundParameter;
8372 FindParameter() : FoundParameter(false) {}
8374 bool follow(const SCEV *S) {
8375 if (isa<SCEVUnknown>(S)) {
8376 FoundParameter = true;
8377 // Stop recursion: we found a parameter.
8383 bool isDone() const {
8384 // Stop recursion if we have found a parameter.
8385 return FoundParameter;
8390 // Returns true when S contains at least a SCEVUnknown parameter.
8392 containsParameters(const SCEV *S) {
8394 SCEVTraversal<FindParameter> ST(F);
8397 return F.FoundParameter;
8400 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
8402 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
8403 for (const SCEV *T : Terms)
8404 if (containsParameters(T))
8409 // Return the number of product terms in S.
8410 static inline int numberOfTerms(const SCEV *S) {
8411 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
8412 return Expr->getNumOperands();
8416 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
8417 if (isa<SCEVConstant>(T))
8420 if (isa<SCEVUnknown>(T))
8423 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
8424 SmallVector<const SCEV *, 2> Factors;
8425 for (const SCEV *Op : M->operands())
8426 if (!isa<SCEVConstant>(Op))
8427 Factors.push_back(Op);
8429 return SE.getMulExpr(Factors);
8435 /// Return the size of an element read or written by Inst.
8436 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
8438 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
8439 Ty = Store->getValueOperand()->getType();
8440 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
8441 Ty = Load->getType();
8445 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
8446 return getSizeOfExpr(ETy, Ty);
8449 /// Second step of delinearization: compute the array dimensions Sizes from the
8450 /// set of Terms extracted from the memory access function of this SCEVAddRec.
8451 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
8452 SmallVectorImpl<const SCEV *> &Sizes,
8453 const SCEV *ElementSize) const {
8455 if (Terms.size() < 1 || !ElementSize)
8458 // Early return when Terms do not contain parameters: we do not delinearize
8459 // non parametric SCEVs.
8460 if (!containsParameters(Terms))
8464 dbgs() << "Terms:\n";
8465 for (const SCEV *T : Terms)
8466 dbgs() << *T << "\n";
8469 // Remove duplicates.
8470 std::sort(Terms.begin(), Terms.end());
8471 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
8473 // Put larger terms first.
8474 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
8475 return numberOfTerms(LHS) > numberOfTerms(RHS);
8478 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8480 // Divide all terms by the element size.
8481 for (const SCEV *&Term : Terms) {
8483 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
8487 SmallVector<const SCEV *, 4> NewTerms;
8489 // Remove constant factors.
8490 for (const SCEV *T : Terms)
8491 if (const SCEV *NewT = removeConstantFactors(SE, T))
8492 NewTerms.push_back(NewT);
8495 dbgs() << "Terms after sorting:\n";
8496 for (const SCEV *T : NewTerms)
8497 dbgs() << *T << "\n";
8500 if (NewTerms.empty() ||
8501 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
8506 // The last element to be pushed into Sizes is the size of an element.
8507 Sizes.push_back(ElementSize);
8510 dbgs() << "Sizes:\n";
8511 for (const SCEV *S : Sizes)
8512 dbgs() << *S << "\n";
8516 /// Third step of delinearization: compute the access functions for the
8517 /// Subscripts based on the dimensions in Sizes.
8518 void ScalarEvolution::computeAccessFunctions(
8519 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
8520 SmallVectorImpl<const SCEV *> &Sizes) {
8522 // Early exit in case this SCEV is not an affine multivariate function.
8526 if (auto AR = dyn_cast<SCEVAddRecExpr>(Expr))
8527 if (!AR->isAffine())
8530 const SCEV *Res = Expr;
8531 int Last = Sizes.size() - 1;
8532 for (int i = Last; i >= 0; i--) {
8534 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
8537 dbgs() << "Res: " << *Res << "\n";
8538 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
8539 dbgs() << "Res divided by Sizes[i]:\n";
8540 dbgs() << "Quotient: " << *Q << "\n";
8541 dbgs() << "Remainder: " << *R << "\n";
8546 // Do not record the last subscript corresponding to the size of elements in
8550 // Bail out if the remainder is too complex.
8551 if (isa<SCEVAddRecExpr>(R)) {
8560 // Record the access function for the current subscript.
8561 Subscripts.push_back(R);
8564 // Also push in last position the remainder of the last division: it will be
8565 // the access function of the innermost dimension.
8566 Subscripts.push_back(Res);
8568 std::reverse(Subscripts.begin(), Subscripts.end());
8571 dbgs() << "Subscripts:\n";
8572 for (const SCEV *S : Subscripts)
8573 dbgs() << *S << "\n";
8577 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
8578 /// sizes of an array access. Returns the remainder of the delinearization that
8579 /// is the offset start of the array. The SCEV->delinearize algorithm computes
8580 /// the multiples of SCEV coefficients: that is a pattern matching of sub
8581 /// expressions in the stride and base of a SCEV corresponding to the
8582 /// computation of a GCD (greatest common divisor) of base and stride. When
8583 /// SCEV->delinearize fails, it returns the SCEV unchanged.
8585 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
8587 /// void foo(long n, long m, long o, double A[n][m][o]) {
8589 /// for (long i = 0; i < n; i++)
8590 /// for (long j = 0; j < m; j++)
8591 /// for (long k = 0; k < o; k++)
8592 /// A[i][j][k] = 1.0;
8595 /// the delinearization input is the following AddRec SCEV:
8597 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
8599 /// From this SCEV, we are able to say that the base offset of the access is %A
8600 /// because it appears as an offset that does not divide any of the strides in
8603 /// CHECK: Base offset: %A
8605 /// and then SCEV->delinearize determines the size of some of the dimensions of
8606 /// the array as these are the multiples by which the strides are happening:
8608 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
8610 /// Note that the outermost dimension remains of UnknownSize because there are
8611 /// no strides that would help identifying the size of the last dimension: when
8612 /// the array has been statically allocated, one could compute the size of that
8613 /// dimension by dividing the overall size of the array by the size of the known
8614 /// dimensions: %m * %o * 8.
8616 /// Finally delinearize provides the access functions for the array reference
8617 /// that does correspond to A[i][j][k] of the above C testcase:
8619 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
8621 /// The testcases are checking the output of a function pass:
8622 /// DelinearizationPass that walks through all loads and stores of a function
8623 /// asking for the SCEV of the memory access with respect to all enclosing
8624 /// loops, calling SCEV->delinearize on that and printing the results.
8626 void ScalarEvolution::delinearize(const SCEV *Expr,
8627 SmallVectorImpl<const SCEV *> &Subscripts,
8628 SmallVectorImpl<const SCEV *> &Sizes,
8629 const SCEV *ElementSize) {
8630 // First step: collect parametric terms.
8631 SmallVector<const SCEV *, 4> Terms;
8632 collectParametricTerms(Expr, Terms);
8637 // Second step: find subscript sizes.
8638 findArrayDimensions(Terms, Sizes, ElementSize);
8643 // Third step: compute the access functions for each subscript.
8644 computeAccessFunctions(Expr, Subscripts, Sizes);
8646 if (Subscripts.empty())
8650 dbgs() << "succeeded to delinearize " << *Expr << "\n";
8651 dbgs() << "ArrayDecl[UnknownSize]";
8652 for (const SCEV *S : Sizes)
8653 dbgs() << "[" << *S << "]";
8655 dbgs() << "\nArrayRef";
8656 for (const SCEV *S : Subscripts)
8657 dbgs() << "[" << *S << "]";
8662 //===----------------------------------------------------------------------===//
8663 // SCEVCallbackVH Class Implementation
8664 //===----------------------------------------------------------------------===//
8666 void ScalarEvolution::SCEVCallbackVH::deleted() {
8667 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8668 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
8669 SE->ConstantEvolutionLoopExitValue.erase(PN);
8670 SE->ValueExprMap.erase(getValPtr());
8671 // this now dangles!
8674 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
8675 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8677 // Forget all the expressions associated with users of the old value,
8678 // so that future queries will recompute the expressions using the new
8680 Value *Old = getValPtr();
8681 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
8682 SmallPtrSet<User *, 8> Visited;
8683 while (!Worklist.empty()) {
8684 User *U = Worklist.pop_back_val();
8685 // Deleting the Old value will cause this to dangle. Postpone
8686 // that until everything else is done.
8689 if (!Visited.insert(U).second)
8691 if (PHINode *PN = dyn_cast<PHINode>(U))
8692 SE->ConstantEvolutionLoopExitValue.erase(PN);
8693 SE->ValueExprMap.erase(U);
8694 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
8696 // Delete the Old value.
8697 if (PHINode *PN = dyn_cast<PHINode>(Old))
8698 SE->ConstantEvolutionLoopExitValue.erase(PN);
8699 SE->ValueExprMap.erase(Old);
8700 // this now dangles!
8703 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
8704 : CallbackVH(V), SE(se) {}
8706 //===----------------------------------------------------------------------===//
8707 // ScalarEvolution Class Implementation
8708 //===----------------------------------------------------------------------===//
8710 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
8711 AssumptionCache &AC, DominatorTree &DT,
8713 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
8714 CouldNotCompute(new SCEVCouldNotCompute()),
8715 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
8716 ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
8717 FirstUnknown(nullptr) {}
8719 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
8720 : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
8721 CouldNotCompute(std::move(Arg.CouldNotCompute)),
8722 ValueExprMap(std::move(Arg.ValueExprMap)),
8723 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
8724 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
8725 ConstantEvolutionLoopExitValue(
8726 std::move(Arg.ConstantEvolutionLoopExitValue)),
8727 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
8728 LoopDispositions(std::move(Arg.LoopDispositions)),
8729 BlockDispositions(std::move(Arg.BlockDispositions)),
8730 UnsignedRanges(std::move(Arg.UnsignedRanges)),
8731 SignedRanges(std::move(Arg.SignedRanges)),
8732 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
8733 SCEVAllocator(std::move(Arg.SCEVAllocator)),
8734 FirstUnknown(Arg.FirstUnknown) {
8735 Arg.FirstUnknown = nullptr;
8738 ScalarEvolution::~ScalarEvolution() {
8739 // Iterate through all the SCEVUnknown instances and call their
8740 // destructors, so that they release their references to their values.
8741 for (SCEVUnknown *U = FirstUnknown; U;) {
8742 SCEVUnknown *Tmp = U;
8744 Tmp->~SCEVUnknown();
8746 FirstUnknown = nullptr;
8748 ValueExprMap.clear();
8750 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
8751 // that a loop had multiple computable exits.
8752 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8753 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
8758 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
8759 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
8760 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
8763 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8764 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8767 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8769 // Print all inner loops first
8770 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8771 PrintLoopInfo(OS, SE, *I);
8774 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8777 SmallVector<BasicBlock *, 8> ExitBlocks;
8778 L->getExitBlocks(ExitBlocks);
8779 if (ExitBlocks.size() != 1)
8780 OS << "<multiple exits> ";
8782 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8783 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8785 OS << "Unpredictable backedge-taken count. ";
8790 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8793 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8794 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8796 OS << "Unpredictable max backedge-taken count. ";
8802 void ScalarEvolution::print(raw_ostream &OS) const {
8803 // ScalarEvolution's implementation of the print method is to print
8804 // out SCEV values of all instructions that are interesting. Doing
8805 // this potentially causes it to create new SCEV objects though,
8806 // which technically conflicts with the const qualifier. This isn't
8807 // observable from outside the class though, so casting away the
8808 // const isn't dangerous.
8809 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8811 OS << "Classifying expressions for: ";
8812 F.printAsOperand(OS, /*PrintType=*/false);
8814 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
8815 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
8818 const SCEV *SV = SE.getSCEV(&*I);
8820 if (!isa<SCEVCouldNotCompute>(SV)) {
8822 SE.getUnsignedRange(SV).print(OS);
8824 SE.getSignedRange(SV).print(OS);
8827 const Loop *L = LI.getLoopFor((*I).getParent());
8829 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8833 if (!isa<SCEVCouldNotCompute>(AtUse)) {
8835 SE.getUnsignedRange(AtUse).print(OS);
8837 SE.getSignedRange(AtUse).print(OS);
8842 OS << "\t\t" "Exits: ";
8843 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8844 if (!SE.isLoopInvariant(ExitValue, L)) {
8845 OS << "<<Unknown>>";
8854 OS << "Determining loop execution counts for: ";
8855 F.printAsOperand(OS, /*PrintType=*/false);
8857 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
8858 PrintLoopInfo(OS, &SE, *I);
8861 ScalarEvolution::LoopDisposition
8862 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8863 auto &Values = LoopDispositions[S];
8864 for (auto &V : Values) {
8865 if (V.getPointer() == L)
8868 Values.emplace_back(L, LoopVariant);
8869 LoopDisposition D = computeLoopDisposition(S, L);
8870 auto &Values2 = LoopDispositions[S];
8871 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8872 if (V.getPointer() == L) {
8880 ScalarEvolution::LoopDisposition
8881 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8882 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8884 return LoopInvariant;
8888 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8889 case scAddRecExpr: {
8890 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8892 // If L is the addrec's loop, it's computable.
8893 if (AR->getLoop() == L)
8894 return LoopComputable;
8896 // Add recurrences are never invariant in the function-body (null loop).
8900 // This recurrence is variant w.r.t. L if L contains AR's loop.
8901 if (L->contains(AR->getLoop()))
8904 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8905 if (AR->getLoop()->contains(L))
8906 return LoopInvariant;
8908 // This recurrence is variant w.r.t. L if any of its operands
8910 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8912 if (!isLoopInvariant(*I, L))
8915 // Otherwise it's loop-invariant.
8916 return LoopInvariant;
8922 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8923 bool HasVarying = false;
8924 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8926 LoopDisposition D = getLoopDisposition(*I, L);
8927 if (D == LoopVariant)
8929 if (D == LoopComputable)
8932 return HasVarying ? LoopComputable : LoopInvariant;
8935 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8936 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8937 if (LD == LoopVariant)
8939 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8940 if (RD == LoopVariant)
8942 return (LD == LoopInvariant && RD == LoopInvariant) ?
8943 LoopInvariant : LoopComputable;
8946 // All non-instruction values are loop invariant. All instructions are loop
8947 // invariant if they are not contained in the specified loop.
8948 // Instructions are never considered invariant in the function body
8949 // (null loop) because they are defined within the "loop".
8950 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8951 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8952 return LoopInvariant;
8953 case scCouldNotCompute:
8954 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8956 llvm_unreachable("Unknown SCEV kind!");
8959 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8960 return getLoopDisposition(S, L) == LoopInvariant;
8963 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8964 return getLoopDisposition(S, L) == LoopComputable;
8967 ScalarEvolution::BlockDisposition
8968 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8969 auto &Values = BlockDispositions[S];
8970 for (auto &V : Values) {
8971 if (V.getPointer() == BB)
8974 Values.emplace_back(BB, DoesNotDominateBlock);
8975 BlockDisposition D = computeBlockDisposition(S, BB);
8976 auto &Values2 = BlockDispositions[S];
8977 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8978 if (V.getPointer() == BB) {
8986 ScalarEvolution::BlockDisposition
8987 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8988 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8990 return ProperlyDominatesBlock;
8994 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8995 case scAddRecExpr: {
8996 // This uses a "dominates" query instead of "properly dominates" query
8997 // to test for proper dominance too, because the instruction which
8998 // produces the addrec's value is a PHI, and a PHI effectively properly
8999 // dominates its entire containing block.
9000 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9001 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9002 return DoesNotDominateBlock;
9004 // FALL THROUGH into SCEVNAryExpr handling.
9009 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9011 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
9013 BlockDisposition D = getBlockDisposition(*I, BB);
9014 if (D == DoesNotDominateBlock)
9015 return DoesNotDominateBlock;
9016 if (D == DominatesBlock)
9019 return Proper ? ProperlyDominatesBlock : DominatesBlock;
9022 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9023 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9024 BlockDisposition LD = getBlockDisposition(LHS, BB);
9025 if (LD == DoesNotDominateBlock)
9026 return DoesNotDominateBlock;
9027 BlockDisposition RD = getBlockDisposition(RHS, BB);
9028 if (RD == DoesNotDominateBlock)
9029 return DoesNotDominateBlock;
9030 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9031 ProperlyDominatesBlock : DominatesBlock;
9034 if (Instruction *I =
9035 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9036 if (I->getParent() == BB)
9037 return DominatesBlock;
9038 if (DT.properlyDominates(I->getParent(), BB))
9039 return ProperlyDominatesBlock;
9040 return DoesNotDominateBlock;
9042 return ProperlyDominatesBlock;
9043 case scCouldNotCompute:
9044 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9046 llvm_unreachable("Unknown SCEV kind!");
9049 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9050 return getBlockDisposition(S, BB) >= DominatesBlock;
9053 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9054 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9058 // Search for a SCEV expression node within an expression tree.
9059 // Implements SCEVTraversal::Visitor.
9064 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
9066 bool follow(const SCEV *S) {
9067 IsFound |= (S == Node);
9070 bool isDone() const { return IsFound; }
9074 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9075 SCEVSearch Search(Op);
9076 visitAll(S, Search);
9077 return Search.IsFound;
9080 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9081 ValuesAtScopes.erase(S);
9082 LoopDispositions.erase(S);
9083 BlockDispositions.erase(S);
9084 UnsignedRanges.erase(S);
9085 SignedRanges.erase(S);
9087 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
9088 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
9089 BackedgeTakenInfo &BEInfo = I->second;
9090 if (BEInfo.hasOperand(S, this)) {
9092 BackedgeTakenCounts.erase(I++);
9099 typedef DenseMap<const Loop *, std::string> VerifyMap;
9101 /// replaceSubString - Replaces all occurrences of From in Str with To.
9102 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9104 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9105 Str.replace(Pos, From.size(), To.data(), To.size());
9110 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9112 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9113 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
9114 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
9116 std::string &S = Map[L];
9118 raw_string_ostream OS(S);
9119 SE.getBackedgeTakenCount(L)->print(OS);
9121 // false and 0 are semantically equivalent. This can happen in dead loops.
9122 replaceSubString(OS.str(), "false", "0");
9123 // Remove wrap flags, their use in SCEV is highly fragile.
9124 // FIXME: Remove this when SCEV gets smarter about them.
9125 replaceSubString(OS.str(), "<nw>", "");
9126 replaceSubString(OS.str(), "<nsw>", "");
9127 replaceSubString(OS.str(), "<nuw>", "");
9132 void ScalarEvolution::verify() const {
9133 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9135 // Gather stringified backedge taken counts for all loops using SCEV's caches.
9136 // FIXME: It would be much better to store actual values instead of strings,
9137 // but SCEV pointers will change if we drop the caches.
9138 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9139 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9140 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9142 // Gather stringified backedge taken counts for all loops using a fresh
9143 // ScalarEvolution object.
9144 ScalarEvolution SE2(F, TLI, AC, DT, LI);
9145 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9146 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9148 // Now compare whether they're the same with and without caches. This allows
9149 // verifying that no pass changed the cache.
9150 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
9151 "New loops suddenly appeared!");
9153 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
9154 OldE = BackedgeDumpsOld.end(),
9155 NewI = BackedgeDumpsNew.begin();
9156 OldI != OldE; ++OldI, ++NewI) {
9157 assert(OldI->first == NewI->first && "Loop order changed!");
9159 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
9161 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
9162 // means that a pass is buggy or SCEV has to learn a new pattern but is
9163 // usually not harmful.
9164 if (OldI->second != NewI->second &&
9165 OldI->second.find("undef") == std::string::npos &&
9166 NewI->second.find("undef") == std::string::npos &&
9167 OldI->second != "***COULDNOTCOMPUTE***" &&
9168 NewI->second != "***COULDNOTCOMPUTE***") {
9169 dbgs() << "SCEVValidator: SCEV for loop '"
9170 << OldI->first->getHeader()->getName()
9171 << "' changed from '" << OldI->second
9172 << "' to '" << NewI->second << "'!\n";
9177 // TODO: Verify more things.
9180 char ScalarEvolutionAnalysis::PassID;
9182 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
9183 AnalysisManager<Function> *AM) {
9184 return ScalarEvolution(F, AM->getResult<TargetLibraryAnalysis>(F),
9185 AM->getResult<AssumptionAnalysis>(F),
9186 AM->getResult<DominatorTreeAnalysis>(F),
9187 AM->getResult<LoopAnalysis>(F));
9191 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> *AM) {
9192 AM->getResult<ScalarEvolutionAnalysis>(F).print(OS);
9193 return PreservedAnalyses::all();
9196 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
9197 "Scalar Evolution Analysis", false, true)
9198 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
9199 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
9200 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
9201 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
9202 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
9203 "Scalar Evolution Analysis", false, true)
9204 char ScalarEvolutionWrapperPass::ID = 0;
9206 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
9207 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
9210 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
9211 SE.reset(new ScalarEvolution(
9212 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
9213 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
9214 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
9215 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
9219 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
9221 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
9225 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
9232 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
9233 AU.setPreservesAll();
9234 AU.addRequiredTransitive<AssumptionCacheTracker>();
9235 AU.addRequiredTransitive<LoopInfoWrapperPass>();
9236 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
9237 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();