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 // Checks if the SCEV S is available at BB. S is considered available at BB
3746 // if S can be materialized at BB without introducing a fault.
3747 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
3749 struct CheckAvailable {
3750 bool TraversalDone = false;
3751 bool Available = true;
3753 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
3754 BasicBlock *BB = nullptr;
3757 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
3758 : L(L), BB(BB), DT(DT) {}
3760 bool setUnavailable() {
3761 TraversalDone = true;
3766 bool follow(const SCEV *S) {
3767 switch (S->getSCEVType()) {
3768 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
3769 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
3770 // These expressions are available if their operand(s) is/are.
3773 case scAddRecExpr: {
3774 // We allow add recurrences that are on the loop BB is in, or some
3775 // outer loop. This guarantees availability because the value of the
3776 // add recurrence at BB is simply the "current" value of the induction
3777 // variable. We can relax this in the future; for instance an add
3778 // recurrence on a sibling dominating loop is also available at BB.
3779 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
3780 if (L && (ARLoop == L || ARLoop->contains(L)))
3783 return setUnavailable();
3787 // For SCEVUnknown, we check for simple dominance.
3788 const auto *SU = cast<SCEVUnknown>(S);
3789 Value *V = SU->getValue();
3791 if (isa<Argument>(V))
3794 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
3797 return setUnavailable();
3801 case scCouldNotCompute:
3802 // We do not try to smart about these at all.
3803 return setUnavailable();
3805 llvm_unreachable("switch should be fully covered!");
3808 bool isDone() { return TraversalDone; }
3811 CheckAvailable CA(L, BB, DT);
3812 SCEVTraversal<CheckAvailable> ST(CA);
3815 return CA.Available;
3818 // Try to match a control flow sequence that branches out at BI and merges back
3819 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
3821 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
3822 Value *&C, Value *&LHS, Value *&RHS) {
3823 C = BI->getCondition();
3825 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
3826 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
3828 if (!LeftEdge.isSingleEdge())
3831 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
3833 Use &LeftUse = Merge->getOperandUse(0);
3834 Use &RightUse = Merge->getOperandUse(1);
3836 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
3842 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
3851 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
3852 if (PN->getNumIncomingValues() == 2) {
3853 const Loop *L = LI.getLoopFor(PN->getParent());
3857 // br %cond, label %left, label %right
3863 // V = phi [ %x, %left ], [ %y, %right ]
3865 // as "select %cond, %x, %y"
3867 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
3868 assert(IDom && "At least the entry block should dominate PN");
3870 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
3871 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
3873 if (BI && BI->isConditional() &&
3874 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
3875 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
3876 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
3877 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
3883 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3884 if (const SCEV *S = createAddRecFromPHI(PN))
3887 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
3890 // If the PHI has a single incoming value, follow that value, unless the
3891 // PHI's incoming blocks are in a different loop, in which case doing so
3892 // risks breaking LCSSA form. Instcombine would normally zap these, but
3893 // it doesn't have DominatorTree information, so it may miss cases.
3894 if (Value *V = SimplifyInstruction(PN, F.getParent()->getDataLayout(), &TLI,
3896 if (LI.replacementPreservesLCSSAForm(PN, V))
3899 // If it's not a loop phi, we can't handle it yet.
3900 return getUnknown(PN);
3903 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
3907 // Handle "constant" branch or select. This can occur for instance when a
3908 // loop pass transforms an inner loop and moves on to process the outer loop.
3909 if (auto *CI = dyn_cast<ConstantInt>(Cond))
3910 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
3912 // Try to match some simple smax or umax patterns.
3913 auto *ICI = dyn_cast<ICmpInst>(Cond);
3915 return getUnknown(I);
3917 Value *LHS = ICI->getOperand(0);
3918 Value *RHS = ICI->getOperand(1);
3920 switch (ICI->getPredicate()) {
3921 case ICmpInst::ICMP_SLT:
3922 case ICmpInst::ICMP_SLE:
3923 std::swap(LHS, RHS);
3925 case ICmpInst::ICMP_SGT:
3926 case ICmpInst::ICMP_SGE:
3927 // a >s b ? a+x : b+x -> smax(a, b)+x
3928 // a >s b ? b+x : a+x -> smin(a, b)+x
3929 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
3930 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
3931 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
3932 const SCEV *LA = getSCEV(TrueVal);
3933 const SCEV *RA = getSCEV(FalseVal);
3934 const SCEV *LDiff = getMinusSCEV(LA, LS);
3935 const SCEV *RDiff = getMinusSCEV(RA, RS);
3937 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3938 LDiff = getMinusSCEV(LA, RS);
3939 RDiff = getMinusSCEV(RA, LS);
3941 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3944 case ICmpInst::ICMP_ULT:
3945 case ICmpInst::ICMP_ULE:
3946 std::swap(LHS, RHS);
3948 case ICmpInst::ICMP_UGT:
3949 case ICmpInst::ICMP_UGE:
3950 // a >u b ? a+x : b+x -> umax(a, b)+x
3951 // a >u b ? b+x : a+x -> umin(a, b)+x
3952 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
3953 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
3954 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
3955 const SCEV *LA = getSCEV(TrueVal);
3956 const SCEV *RA = getSCEV(FalseVal);
3957 const SCEV *LDiff = getMinusSCEV(LA, LS);
3958 const SCEV *RDiff = getMinusSCEV(RA, RS);
3960 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3961 LDiff = getMinusSCEV(LA, RS);
3962 RDiff = getMinusSCEV(RA, LS);
3964 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3967 case ICmpInst::ICMP_NE:
3968 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3969 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
3970 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
3971 const SCEV *One = getOne(I->getType());
3972 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
3973 const SCEV *LA = getSCEV(TrueVal);
3974 const SCEV *RA = getSCEV(FalseVal);
3975 const SCEV *LDiff = getMinusSCEV(LA, LS);
3976 const SCEV *RDiff = getMinusSCEV(RA, One);
3978 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3981 case ICmpInst::ICMP_EQ:
3982 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3983 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
3984 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
3985 const SCEV *One = getOne(I->getType());
3986 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
3987 const SCEV *LA = getSCEV(TrueVal);
3988 const SCEV *RA = getSCEV(FalseVal);
3989 const SCEV *LDiff = getMinusSCEV(LA, One);
3990 const SCEV *RDiff = getMinusSCEV(RA, LS);
3992 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3999 return getUnknown(I);
4002 /// createNodeForGEP - Expand GEP instructions into add and multiply
4003 /// operations. This allows them to be analyzed by regular SCEV code.
4005 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
4006 Value *Base = GEP->getOperand(0);
4007 // Don't attempt to analyze GEPs over unsized objects.
4008 if (!Base->getType()->getPointerElementType()->isSized())
4009 return getUnknown(GEP);
4011 SmallVector<const SCEV *, 4> IndexExprs;
4012 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4013 IndexExprs.push_back(getSCEV(*Index));
4014 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
4018 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
4019 /// guaranteed to end in (at every loop iteration). It is, at the same time,
4020 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
4021 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
4023 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4024 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4025 return C->getValue()->getValue().countTrailingZeros();
4027 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4028 return std::min(GetMinTrailingZeros(T->getOperand()),
4029 (uint32_t)getTypeSizeInBits(T->getType()));
4031 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4032 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4033 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4034 getTypeSizeInBits(E->getType()) : OpRes;
4037 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4038 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4039 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4040 getTypeSizeInBits(E->getType()) : OpRes;
4043 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4044 // The result is the min of all operands results.
4045 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4046 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4047 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4051 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4052 // The result is the sum of all operands results.
4053 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4054 uint32_t BitWidth = getTypeSizeInBits(M->getType());
4055 for (unsigned i = 1, e = M->getNumOperands();
4056 SumOpRes != BitWidth && i != e; ++i)
4057 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4062 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4063 // The result is the min of all operands results.
4064 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4065 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4066 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4070 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4071 // The result is the min of all operands results.
4072 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4073 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4074 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4078 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4079 // The result is the min of all operands results.
4080 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4081 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4082 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4086 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4087 // For a SCEVUnknown, ask ValueTracking.
4088 unsigned BitWidth = getTypeSizeInBits(U->getType());
4089 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4090 computeKnownBits(U->getValue(), Zeros, Ones, F.getParent()->getDataLayout(),
4091 0, &AC, nullptr, &DT);
4092 return Zeros.countTrailingOnes();
4099 /// GetRangeFromMetadata - Helper method to assign a range to V from
4100 /// metadata present in the IR.
4101 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4102 if (Instruction *I = dyn_cast<Instruction>(V)) {
4103 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
4104 ConstantRange TotalRange(
4105 cast<IntegerType>(I->getType())->getBitWidth(), false);
4107 unsigned NumRanges = MD->getNumOperands() / 2;
4108 assert(NumRanges >= 1);
4110 for (unsigned i = 0; i < NumRanges; ++i) {
4111 ConstantInt *Lower =
4112 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
4113 ConstantInt *Upper =
4114 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
4115 ConstantRange Range(Lower->getValue(), Upper->getValue());
4116 TotalRange = TotalRange.unionWith(Range);
4126 /// getRange - Determine the range for a particular SCEV. If SignHint is
4127 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4128 /// with a "cleaner" unsigned (resp. signed) representation.
4131 ScalarEvolution::getRange(const SCEV *S,
4132 ScalarEvolution::RangeSignHint SignHint) {
4133 DenseMap<const SCEV *, ConstantRange> &Cache =
4134 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4137 // See if we've computed this range already.
4138 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4139 if (I != Cache.end())
4142 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4143 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
4145 unsigned BitWidth = getTypeSizeInBits(S->getType());
4146 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4148 // If the value has known zeros, the maximum value will have those known zeros
4150 uint32_t TZ = GetMinTrailingZeros(S);
4152 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4153 ConservativeResult =
4154 ConstantRange(APInt::getMinValue(BitWidth),
4155 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4157 ConservativeResult = ConstantRange(
4158 APInt::getSignedMinValue(BitWidth),
4159 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4162 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4163 ConstantRange X = getRange(Add->getOperand(0), SignHint);
4164 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4165 X = X.add(getRange(Add->getOperand(i), SignHint));
4166 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4169 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4170 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4171 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4172 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4173 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4176 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4177 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4178 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4179 X = X.smax(getRange(SMax->getOperand(i), SignHint));
4180 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4183 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4184 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4185 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4186 X = X.umax(getRange(UMax->getOperand(i), SignHint));
4187 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4190 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4191 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4192 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4193 return setRange(UDiv, SignHint,
4194 ConservativeResult.intersectWith(X.udiv(Y)));
4197 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4198 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4199 return setRange(ZExt, SignHint,
4200 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4203 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4204 ConstantRange X = getRange(SExt->getOperand(), SignHint);
4205 return setRange(SExt, SignHint,
4206 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4209 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4210 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4211 return setRange(Trunc, SignHint,
4212 ConservativeResult.intersectWith(X.truncate(BitWidth)));
4215 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4216 // If there's no unsigned wrap, the value will never be less than its
4218 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
4219 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4220 if (!C->getValue()->isZero())
4221 ConservativeResult =
4222 ConservativeResult.intersectWith(
4223 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
4225 // If there's no signed wrap, and all the operands have the same sign or
4226 // zero, the value won't ever change sign.
4227 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
4228 bool AllNonNeg = true;
4229 bool AllNonPos = true;
4230 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4231 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4232 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4235 ConservativeResult = ConservativeResult.intersectWith(
4236 ConstantRange(APInt(BitWidth, 0),
4237 APInt::getSignedMinValue(BitWidth)));
4239 ConservativeResult = ConservativeResult.intersectWith(
4240 ConstantRange(APInt::getSignedMinValue(BitWidth),
4241 APInt(BitWidth, 1)));
4244 // TODO: non-affine addrec
4245 if (AddRec->isAffine()) {
4246 Type *Ty = AddRec->getType();
4247 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4248 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4249 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4251 // Check for overflow. This must be done with ConstantRange arithmetic
4252 // because we could be called from within the ScalarEvolution overflow
4255 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4256 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4257 ConstantRange ZExtMaxBECountRange =
4258 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4260 const SCEV *Start = AddRec->getStart();
4261 const SCEV *Step = AddRec->getStepRecurrence(*this);
4262 ConstantRange StepSRange = getSignedRange(Step);
4263 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4265 ConstantRange StartURange = getUnsignedRange(Start);
4266 ConstantRange EndURange =
4267 StartURange.add(MaxBECountRange.multiply(StepSRange));
4269 // Check for unsigned overflow.
4270 ConstantRange ZExtStartURange =
4271 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4272 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4273 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4275 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4276 EndURange.getUnsignedMin());
4277 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4278 EndURange.getUnsignedMax());
4279 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4281 ConservativeResult =
4282 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4285 ConstantRange StartSRange = getSignedRange(Start);
4286 ConstantRange EndSRange =
4287 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4289 // Check for signed overflow. This must be done with ConstantRange
4290 // arithmetic because we could be called from within the ScalarEvolution
4291 // overflow checking code.
4292 ConstantRange SExtStartSRange =
4293 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4294 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4295 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4297 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4298 EndSRange.getSignedMin());
4299 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4300 EndSRange.getSignedMax());
4301 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4303 ConservativeResult =
4304 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4309 return setRange(AddRec, SignHint, ConservativeResult);
4312 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4313 // Check if the IR explicitly contains !range metadata.
4314 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4315 if (MDRange.hasValue())
4316 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4318 // Split here to avoid paying the compile-time cost of calling both
4319 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4321 const DataLayout &DL = F.getParent()->getDataLayout();
4322 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4323 // For a SCEVUnknown, ask ValueTracking.
4324 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4325 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4326 if (Ones != ~Zeros + 1)
4327 ConservativeResult =
4328 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4330 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4331 "generalize as needed!");
4332 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4334 ConservativeResult = ConservativeResult.intersectWith(
4335 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4336 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4339 return setRange(U, SignHint, ConservativeResult);
4342 return setRange(S, SignHint, ConservativeResult);
4345 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4346 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4347 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4349 // Return early if there are no flags to propagate to the SCEV.
4350 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4351 if (BinOp->hasNoUnsignedWrap())
4352 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4353 if (BinOp->hasNoSignedWrap())
4354 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4355 if (Flags == SCEV::FlagAnyWrap) {
4356 return SCEV::FlagAnyWrap;
4359 // Here we check that BinOp is in the header of the innermost loop
4360 // containing BinOp, since we only deal with instructions in the loop
4361 // header. The actual loop we need to check later will come from an add
4362 // recurrence, but getting that requires computing the SCEV of the operands,
4363 // which can be expensive. This check we can do cheaply to rule out some
4365 Loop *innermostContainingLoop = LI.getLoopFor(BinOp->getParent());
4366 if (innermostContainingLoop == nullptr ||
4367 innermostContainingLoop->getHeader() != BinOp->getParent())
4368 return SCEV::FlagAnyWrap;
4370 // Only proceed if we can prove that BinOp does not yield poison.
4371 if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
4373 // At this point we know that if V is executed, then it does not wrap
4374 // according to at least one of NSW or NUW. If V is not executed, then we do
4375 // not know if the calculation that V represents would wrap. Multiple
4376 // instructions can map to the same SCEV. If we apply NSW or NUW from V to
4377 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4378 // derived from other instructions that map to the same SCEV. We cannot make
4379 // that guarantee for cases where V is not executed. So we need to find the
4380 // loop that V is considered in relation to and prove that V is executed for
4381 // every iteration of that loop. That implies that the value that V
4382 // calculates does not wrap anywhere in the loop, so then we can apply the
4383 // flags to the SCEV.
4385 // We check isLoopInvariant to disambiguate in case we are adding two
4386 // recurrences from different loops, so that we know which loop to prove
4387 // that V is executed in.
4388 for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
4389 const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
4390 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4391 const int OtherOpIndex = 1 - OpIndex;
4392 const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
4393 if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
4394 isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
4398 return SCEV::FlagAnyWrap;
4401 /// createSCEV - We know that there is no SCEV for the specified value. Analyze
4404 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4405 if (!isSCEVable(V->getType()))
4406 return getUnknown(V);
4408 unsigned Opcode = Instruction::UserOp1;
4409 if (Instruction *I = dyn_cast<Instruction>(V)) {
4410 Opcode = I->getOpcode();
4412 // Don't attempt to analyze instructions in blocks that aren't
4413 // reachable. Such instructions don't matter, and they aren't required
4414 // to obey basic rules for definitions dominating uses which this
4415 // analysis depends on.
4416 if (!DT.isReachableFromEntry(I->getParent()))
4417 return getUnknown(V);
4418 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4419 Opcode = CE->getOpcode();
4420 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4421 return getConstant(CI);
4422 else if (isa<ConstantPointerNull>(V))
4423 return getZero(V->getType());
4424 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4425 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4427 return getUnknown(V);
4429 Operator *U = cast<Operator>(V);
4431 case Instruction::Add: {
4432 // The simple thing to do would be to just call getSCEV on both operands
4433 // and call getAddExpr with the result. However if we're looking at a
4434 // bunch of things all added together, this can be quite inefficient,
4435 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4436 // Instead, gather up all the operands and make a single getAddExpr call.
4437 // LLVM IR canonical form means we need only traverse the left operands.
4438 SmallVector<const SCEV *, 4> AddOps;
4439 for (Value *Op = U;; Op = U->getOperand(0)) {
4440 U = dyn_cast<Operator>(Op);
4441 unsigned Opcode = U ? U->getOpcode() : 0;
4442 if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
4443 assert(Op != V && "V should be an add");
4444 AddOps.push_back(getSCEV(Op));
4448 if (auto *OpSCEV = getExistingSCEV(U)) {
4449 AddOps.push_back(OpSCEV);
4453 // If a NUW or NSW flag can be applied to the SCEV for this
4454 // addition, then compute the SCEV for this addition by itself
4455 // with a separate call to getAddExpr. We need to do that
4456 // instead of pushing the operands of the addition onto AddOps,
4457 // since the flags are only known to apply to this particular
4458 // addition - they may not apply to other additions that can be
4459 // formed with operands from AddOps.
4460 const SCEV *RHS = getSCEV(U->getOperand(1));
4461 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4462 if (Flags != SCEV::FlagAnyWrap) {
4463 const SCEV *LHS = getSCEV(U->getOperand(0));
4464 if (Opcode == Instruction::Sub)
4465 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4467 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4471 if (Opcode == Instruction::Sub)
4472 AddOps.push_back(getNegativeSCEV(RHS));
4474 AddOps.push_back(RHS);
4476 return getAddExpr(AddOps);
4479 case Instruction::Mul: {
4480 SmallVector<const SCEV *, 4> MulOps;
4481 for (Value *Op = U;; Op = U->getOperand(0)) {
4482 U = dyn_cast<Operator>(Op);
4483 if (!U || U->getOpcode() != Instruction::Mul) {
4484 assert(Op != V && "V should be a mul");
4485 MulOps.push_back(getSCEV(Op));
4489 if (auto *OpSCEV = getExistingSCEV(U)) {
4490 MulOps.push_back(OpSCEV);
4494 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4495 if (Flags != SCEV::FlagAnyWrap) {
4496 MulOps.push_back(getMulExpr(getSCEV(U->getOperand(0)),
4497 getSCEV(U->getOperand(1)), Flags));
4501 MulOps.push_back(getSCEV(U->getOperand(1)));
4503 return getMulExpr(MulOps);
4505 case Instruction::UDiv:
4506 return getUDivExpr(getSCEV(U->getOperand(0)),
4507 getSCEV(U->getOperand(1)));
4508 case Instruction::Sub:
4509 return getMinusSCEV(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)),
4510 getNoWrapFlagsFromUB(U));
4511 case Instruction::And:
4512 // For an expression like x&255 that merely masks off the high bits,
4513 // use zext(trunc(x)) as the SCEV expression.
4514 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4515 if (CI->isNullValue())
4516 return getSCEV(U->getOperand(1));
4517 if (CI->isAllOnesValue())
4518 return getSCEV(U->getOperand(0));
4519 const APInt &A = CI->getValue();
4521 // Instcombine's ShrinkDemandedConstant may strip bits out of
4522 // constants, obscuring what would otherwise be a low-bits mask.
4523 // Use computeKnownBits to compute what ShrinkDemandedConstant
4524 // knew about to reconstruct a low-bits mask value.
4525 unsigned LZ = A.countLeadingZeros();
4526 unsigned TZ = A.countTrailingZeros();
4527 unsigned BitWidth = A.getBitWidth();
4528 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4529 computeKnownBits(U->getOperand(0), KnownZero, KnownOne,
4530 F.getParent()->getDataLayout(), 0, &AC, nullptr, &DT);
4532 APInt EffectiveMask =
4533 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4534 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4535 const SCEV *MulCount = getConstant(
4536 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4540 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4541 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4548 case Instruction::Or:
4549 // If the RHS of the Or is a constant, we may have something like:
4550 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4551 // optimizations will transparently handle this case.
4553 // In order for this transformation to be safe, the LHS must be of the
4554 // form X*(2^n) and the Or constant must be less than 2^n.
4555 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4556 const SCEV *LHS = getSCEV(U->getOperand(0));
4557 const APInt &CIVal = CI->getValue();
4558 if (GetMinTrailingZeros(LHS) >=
4559 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4560 // Build a plain add SCEV.
4561 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4562 // If the LHS of the add was an addrec and it has no-wrap flags,
4563 // transfer the no-wrap flags, since an or won't introduce a wrap.
4564 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4565 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4566 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4567 OldAR->getNoWrapFlags());
4573 case Instruction::Xor:
4574 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4575 // If the RHS of the xor is a signbit, then this is just an add.
4576 // Instcombine turns add of signbit into xor as a strength reduction step.
4577 if (CI->getValue().isSignBit())
4578 return getAddExpr(getSCEV(U->getOperand(0)),
4579 getSCEV(U->getOperand(1)));
4581 // If the RHS of xor is -1, then this is a not operation.
4582 if (CI->isAllOnesValue())
4583 return getNotSCEV(getSCEV(U->getOperand(0)));
4585 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4586 // This is a variant of the check for xor with -1, and it handles
4587 // the case where instcombine has trimmed non-demanded bits out
4588 // of an xor with -1.
4589 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4590 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4591 if (BO->getOpcode() == Instruction::And &&
4592 LCI->getValue() == CI->getValue())
4593 if (const SCEVZeroExtendExpr *Z =
4594 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4595 Type *UTy = U->getType();
4596 const SCEV *Z0 = Z->getOperand();
4597 Type *Z0Ty = Z0->getType();
4598 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4600 // If C is a low-bits mask, the zero extend is serving to
4601 // mask off the high bits. Complement the operand and
4602 // re-apply the zext.
4603 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4604 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4606 // If C is a single bit, it may be in the sign-bit position
4607 // before the zero-extend. In this case, represent the xor
4608 // using an add, which is equivalent, and re-apply the zext.
4609 APInt Trunc = CI->getValue().trunc(Z0TySize);
4610 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4612 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4618 case Instruction::Shl:
4619 // Turn shift left of a constant amount into a multiply.
4620 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4621 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4623 // If the shift count is not less than the bitwidth, the result of
4624 // the shift is undefined. Don't try to analyze it, because the
4625 // resolution chosen here may differ from the resolution chosen in
4626 // other parts of the compiler.
4627 if (SA->getValue().uge(BitWidth))
4630 // It is currently not resolved how to interpret NSW for left
4631 // shift by BitWidth - 1, so we avoid applying flags in that
4632 // case. Remove this check (or this comment) once the situation
4634 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
4635 // and http://reviews.llvm.org/D8890 .
4636 auto Flags = SCEV::FlagAnyWrap;
4637 if (SA->getValue().ult(BitWidth - 1)) Flags = getNoWrapFlagsFromUB(U);
4639 Constant *X = ConstantInt::get(getContext(),
4640 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4641 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X), Flags);
4645 case Instruction::LShr:
4646 // Turn logical shift right of a constant into a unsigned divide.
4647 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4648 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4650 // If the shift count is not less than the bitwidth, the result of
4651 // the shift is undefined. Don't try to analyze it, because the
4652 // resolution chosen here may differ from the resolution chosen in
4653 // other parts of the compiler.
4654 if (SA->getValue().uge(BitWidth))
4657 Constant *X = ConstantInt::get(getContext(),
4658 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4659 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4663 case Instruction::AShr:
4664 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4665 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4666 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4667 if (L->getOpcode() == Instruction::Shl &&
4668 L->getOperand(1) == U->getOperand(1)) {
4669 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4671 // If the shift count is not less than the bitwidth, the result of
4672 // the shift is undefined. Don't try to analyze it, because the
4673 // resolution chosen here may differ from the resolution chosen in
4674 // other parts of the compiler.
4675 if (CI->getValue().uge(BitWidth))
4678 uint64_t Amt = BitWidth - CI->getZExtValue();
4679 if (Amt == BitWidth)
4680 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4682 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4683 IntegerType::get(getContext(),
4689 case Instruction::Trunc:
4690 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4692 case Instruction::ZExt:
4693 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4695 case Instruction::SExt:
4696 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4698 case Instruction::BitCast:
4699 // BitCasts are no-op casts so we just eliminate the cast.
4700 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4701 return getSCEV(U->getOperand(0));
4704 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4705 // lead to pointer expressions which cannot safely be expanded to GEPs,
4706 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4707 // simplifying integer expressions.
4709 case Instruction::GetElementPtr:
4710 return createNodeForGEP(cast<GEPOperator>(U));
4712 case Instruction::PHI:
4713 return createNodeForPHI(cast<PHINode>(U));
4715 case Instruction::Select:
4716 // U can also be a select constant expr, which let fall through. Since
4717 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
4718 // constant expressions cannot have instructions as operands, we'd have
4719 // returned getUnknown for a select constant expressions anyway.
4720 if (isa<Instruction>(U))
4721 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
4722 U->getOperand(1), U->getOperand(2));
4724 default: // We cannot analyze this expression.
4728 return getUnknown(V);
4733 //===----------------------------------------------------------------------===//
4734 // Iteration Count Computation Code
4737 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4738 if (BasicBlock *ExitingBB = L->getExitingBlock())
4739 return getSmallConstantTripCount(L, ExitingBB);
4741 // No trip count information for multiple exits.
4745 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4746 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4747 /// constant. Will also return 0 if the maximum trip count is very large (>=
4750 /// This "trip count" assumes that control exits via ExitingBlock. More
4751 /// precisely, it is the number of times that control may reach ExitingBlock
4752 /// before taking the branch. For loops with multiple exits, it may not be the
4753 /// number times that the loop header executes because the loop may exit
4754 /// prematurely via another branch.
4755 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4756 BasicBlock *ExitingBlock) {
4757 assert(ExitingBlock && "Must pass a non-null exiting block!");
4758 assert(L->isLoopExiting(ExitingBlock) &&
4759 "Exiting block must actually branch out of the loop!");
4760 const SCEVConstant *ExitCount =
4761 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4765 ConstantInt *ExitConst = ExitCount->getValue();
4767 // Guard against huge trip counts.
4768 if (ExitConst->getValue().getActiveBits() > 32)
4771 // In case of integer overflow, this returns 0, which is correct.
4772 return ((unsigned)ExitConst->getZExtValue()) + 1;
4775 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4776 if (BasicBlock *ExitingBB = L->getExitingBlock())
4777 return getSmallConstantTripMultiple(L, ExitingBB);
4779 // No trip multiple information for multiple exits.
4783 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4784 /// trip count of this loop as a normal unsigned value, if possible. This
4785 /// means that the actual trip count is always a multiple of the returned
4786 /// value (don't forget the trip count could very well be zero as well!).
4788 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4789 /// multiple of a constant (which is also the case if the trip count is simply
4790 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4791 /// if the trip count is very large (>= 2^32).
4793 /// As explained in the comments for getSmallConstantTripCount, this assumes
4794 /// that control exits the loop via ExitingBlock.
4796 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4797 BasicBlock *ExitingBlock) {
4798 assert(ExitingBlock && "Must pass a non-null exiting block!");
4799 assert(L->isLoopExiting(ExitingBlock) &&
4800 "Exiting block must actually branch out of the loop!");
4801 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4802 if (ExitCount == getCouldNotCompute())
4805 // Get the trip count from the BE count by adding 1.
4806 const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
4807 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4808 // to factor simple cases.
4809 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4810 TCMul = Mul->getOperand(0);
4812 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4816 ConstantInt *Result = MulC->getValue();
4818 // Guard against huge trip counts (this requires checking
4819 // for zero to handle the case where the trip count == -1 and the
4821 if (!Result || Result->getValue().getActiveBits() > 32 ||
4822 Result->getValue().getActiveBits() == 0)
4825 return (unsigned)Result->getZExtValue();
4828 // getExitCount - Get the expression for the number of loop iterations for which
4829 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4830 // SCEVCouldNotCompute.
4831 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4832 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4835 /// getBackedgeTakenCount - If the specified loop has a predictable
4836 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4837 /// object. The backedge-taken count is the number of times the loop header
4838 /// will be branched to from within the loop. This is one less than the
4839 /// trip count of the loop, since it doesn't count the first iteration,
4840 /// when the header is branched to from outside the loop.
4842 /// Note that it is not valid to call this method on a loop without a
4843 /// loop-invariant backedge-taken count (see
4844 /// hasLoopInvariantBackedgeTakenCount).
4846 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4847 return getBackedgeTakenInfo(L).getExact(this);
4850 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4851 /// return the least SCEV value that is known never to be less than the
4852 /// actual backedge taken count.
4853 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4854 return getBackedgeTakenInfo(L).getMax(this);
4857 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4858 /// onto the given Worklist.
4860 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4861 BasicBlock *Header = L->getHeader();
4863 // Push all Loop-header PHIs onto the Worklist stack.
4864 for (BasicBlock::iterator I = Header->begin();
4865 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4866 Worklist.push_back(PN);
4869 const ScalarEvolution::BackedgeTakenInfo &
4870 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4871 // Initially insert an invalid entry for this loop. If the insertion
4872 // succeeds, proceed to actually compute a backedge-taken count and
4873 // update the value. The temporary CouldNotCompute value tells SCEV
4874 // code elsewhere that it shouldn't attempt to request a new
4875 // backedge-taken count, which could result in infinite recursion.
4876 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4877 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4879 return Pair.first->second;
4881 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4882 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4883 // must be cleared in this scope.
4884 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4886 if (Result.getExact(this) != getCouldNotCompute()) {
4887 assert(isLoopInvariant(Result.getExact(this), L) &&
4888 isLoopInvariant(Result.getMax(this), L) &&
4889 "Computed backedge-taken count isn't loop invariant for loop!");
4890 ++NumTripCountsComputed;
4892 else if (Result.getMax(this) == getCouldNotCompute() &&
4893 isa<PHINode>(L->getHeader()->begin())) {
4894 // Only count loops that have phi nodes as not being computable.
4895 ++NumTripCountsNotComputed;
4898 // Now that we know more about the trip count for this loop, forget any
4899 // existing SCEV values for PHI nodes in this loop since they are only
4900 // conservative estimates made without the benefit of trip count
4901 // information. This is similar to the code in forgetLoop, except that
4902 // it handles SCEVUnknown PHI nodes specially.
4903 if (Result.hasAnyInfo()) {
4904 SmallVector<Instruction *, 16> Worklist;
4905 PushLoopPHIs(L, Worklist);
4907 SmallPtrSet<Instruction *, 8> Visited;
4908 while (!Worklist.empty()) {
4909 Instruction *I = Worklist.pop_back_val();
4910 if (!Visited.insert(I).second)
4913 ValueExprMapType::iterator It =
4914 ValueExprMap.find_as(static_cast<Value *>(I));
4915 if (It != ValueExprMap.end()) {
4916 const SCEV *Old = It->second;
4918 // SCEVUnknown for a PHI either means that it has an unrecognized
4919 // structure, or it's a PHI that's in the progress of being computed
4920 // by createNodeForPHI. In the former case, additional loop trip
4921 // count information isn't going to change anything. In the later
4922 // case, createNodeForPHI will perform the necessary updates on its
4923 // own when it gets to that point.
4924 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4925 forgetMemoizedResults(Old);
4926 ValueExprMap.erase(It);
4928 if (PHINode *PN = dyn_cast<PHINode>(I))
4929 ConstantEvolutionLoopExitValue.erase(PN);
4932 PushDefUseChildren(I, Worklist);
4936 // Re-lookup the insert position, since the call to
4937 // ComputeBackedgeTakenCount above could result in a
4938 // recusive call to getBackedgeTakenInfo (on a different
4939 // loop), which would invalidate the iterator computed
4941 return BackedgeTakenCounts.find(L)->second = Result;
4944 /// forgetLoop - This method should be called by the client when it has
4945 /// changed a loop in a way that may effect ScalarEvolution's ability to
4946 /// compute a trip count, or if the loop is deleted.
4947 void ScalarEvolution::forgetLoop(const Loop *L) {
4948 // Drop any stored trip count value.
4949 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4950 BackedgeTakenCounts.find(L);
4951 if (BTCPos != BackedgeTakenCounts.end()) {
4952 BTCPos->second.clear();
4953 BackedgeTakenCounts.erase(BTCPos);
4956 // Drop information about expressions based on loop-header PHIs.
4957 SmallVector<Instruction *, 16> Worklist;
4958 PushLoopPHIs(L, Worklist);
4960 SmallPtrSet<Instruction *, 8> Visited;
4961 while (!Worklist.empty()) {
4962 Instruction *I = Worklist.pop_back_val();
4963 if (!Visited.insert(I).second)
4966 ValueExprMapType::iterator It =
4967 ValueExprMap.find_as(static_cast<Value *>(I));
4968 if (It != ValueExprMap.end()) {
4969 forgetMemoizedResults(It->second);
4970 ValueExprMap.erase(It);
4971 if (PHINode *PN = dyn_cast<PHINode>(I))
4972 ConstantEvolutionLoopExitValue.erase(PN);
4975 PushDefUseChildren(I, Worklist);
4978 // Forget all contained loops too, to avoid dangling entries in the
4979 // ValuesAtScopes map.
4980 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4984 /// forgetValue - This method should be called by the client when it has
4985 /// changed a value in a way that may effect its value, or which may
4986 /// disconnect it from a def-use chain linking it to a loop.
4987 void ScalarEvolution::forgetValue(Value *V) {
4988 Instruction *I = dyn_cast<Instruction>(V);
4991 // Drop information about expressions based on loop-header PHIs.
4992 SmallVector<Instruction *, 16> Worklist;
4993 Worklist.push_back(I);
4995 SmallPtrSet<Instruction *, 8> Visited;
4996 while (!Worklist.empty()) {
4997 I = Worklist.pop_back_val();
4998 if (!Visited.insert(I).second)
5001 ValueExprMapType::iterator It =
5002 ValueExprMap.find_as(static_cast<Value *>(I));
5003 if (It != ValueExprMap.end()) {
5004 forgetMemoizedResults(It->second);
5005 ValueExprMap.erase(It);
5006 if (PHINode *PN = dyn_cast<PHINode>(I))
5007 ConstantEvolutionLoopExitValue.erase(PN);
5010 PushDefUseChildren(I, Worklist);
5014 /// getExact - Get the exact loop backedge taken count considering all loop
5015 /// exits. A computable result can only be returned for loops with a single
5016 /// exit. Returning the minimum taken count among all exits is incorrect
5017 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
5018 /// assumes that the limit of each loop test is never skipped. This is a valid
5019 /// assumption as long as the loop exits via that test. For precise results, it
5020 /// is the caller's responsibility to specify the relevant loop exit using
5021 /// getExact(ExitingBlock, SE).
5023 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
5024 // If any exits were not computable, the loop is not computable.
5025 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
5027 // We need exactly one computable exit.
5028 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
5029 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
5031 const SCEV *BECount = nullptr;
5032 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5033 ENT != nullptr; ENT = ENT->getNextExit()) {
5035 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5038 BECount = ENT->ExactNotTaken;
5039 else if (BECount != ENT->ExactNotTaken)
5040 return SE->getCouldNotCompute();
5042 assert(BECount && "Invalid not taken count for loop exit");
5046 /// getExact - Get the exact not taken count for this loop exit.
5048 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5049 ScalarEvolution *SE) const {
5050 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5051 ENT != nullptr; ENT = ENT->getNextExit()) {
5053 if (ENT->ExitingBlock == ExitingBlock)
5054 return ENT->ExactNotTaken;
5056 return SE->getCouldNotCompute();
5059 /// getMax - Get the max backedge taken count for the loop.
5061 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5062 return Max ? Max : SE->getCouldNotCompute();
5065 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5066 ScalarEvolution *SE) const {
5067 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
5070 if (!ExitNotTaken.ExitingBlock)
5073 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
5074 ENT != nullptr; ENT = ENT->getNextExit()) {
5076 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
5077 && SE->hasOperand(ENT->ExactNotTaken, S)) {
5084 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5085 /// computable exit into a persistent ExitNotTakenInfo array.
5086 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5087 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
5088 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
5091 ExitNotTaken.setIncomplete();
5093 unsigned NumExits = ExitCounts.size();
5094 if (NumExits == 0) return;
5096 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
5097 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
5098 if (NumExits == 1) return;
5100 // Handle the rare case of multiple computable exits.
5101 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
5103 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
5104 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
5105 PrevENT->setNextExit(ENT);
5106 ENT->ExitingBlock = ExitCounts[i].first;
5107 ENT->ExactNotTaken = ExitCounts[i].second;
5111 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
5112 void ScalarEvolution::BackedgeTakenInfo::clear() {
5113 ExitNotTaken.ExitingBlock = nullptr;
5114 ExitNotTaken.ExactNotTaken = nullptr;
5115 delete[] ExitNotTaken.getNextExit();
5118 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
5119 /// of the specified loop will execute.
5120 ScalarEvolution::BackedgeTakenInfo
5121 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
5122 SmallVector<BasicBlock *, 8> ExitingBlocks;
5123 L->getExitingBlocks(ExitingBlocks);
5125 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
5126 bool CouldComputeBECount = true;
5127 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5128 const SCEV *MustExitMaxBECount = nullptr;
5129 const SCEV *MayExitMaxBECount = nullptr;
5131 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5132 // and compute maxBECount.
5133 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5134 BasicBlock *ExitBB = ExitingBlocks[i];
5135 ExitLimit EL = ComputeExitLimit(L, ExitBB);
5137 // 1. For each exit that can be computed, add an entry to ExitCounts.
5138 // CouldComputeBECount is true only if all exits can be computed.
5139 if (EL.Exact == getCouldNotCompute())
5140 // We couldn't compute an exact value for this exit, so
5141 // we won't be able to compute an exact value for the loop.
5142 CouldComputeBECount = false;
5144 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
5146 // 2. Derive the loop's MaxBECount from each exit's max number of
5147 // non-exiting iterations. Partition the loop exits into two kinds:
5148 // LoopMustExits and LoopMayExits.
5150 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5151 // is a LoopMayExit. If any computable LoopMustExit is found, then
5152 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
5153 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
5154 // considered greater than any computable EL.Max.
5155 if (EL.Max != getCouldNotCompute() && Latch &&
5156 DT.dominates(ExitBB, Latch)) {
5157 if (!MustExitMaxBECount)
5158 MustExitMaxBECount = EL.Max;
5160 MustExitMaxBECount =
5161 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5163 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5164 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5165 MayExitMaxBECount = EL.Max;
5168 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5172 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5173 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5174 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5177 /// ComputeExitLimit - Compute the number of times the backedge of the specified
5178 /// loop will execute if it exits via the specified block.
5179 ScalarEvolution::ExitLimit
5180 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
5182 // Okay, we've chosen an exiting block. See what condition causes us to
5183 // exit at this block and remember the exit block and whether all other targets
5184 // lead to the loop header.
5185 bool MustExecuteLoopHeader = true;
5186 BasicBlock *Exit = nullptr;
5187 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5189 if (!L->contains(*SI)) {
5190 if (Exit) // Multiple exit successors.
5191 return getCouldNotCompute();
5193 } else if (*SI != L->getHeader()) {
5194 MustExecuteLoopHeader = false;
5197 // At this point, we know we have a conditional branch that determines whether
5198 // the loop is exited. However, we don't know if the branch is executed each
5199 // time through the loop. If not, then the execution count of the branch will
5200 // not be equal to the trip count of the loop.
5202 // Currently we check for this by checking to see if the Exit branch goes to
5203 // the loop header. If so, we know it will always execute the same number of
5204 // times as the loop. We also handle the case where the exit block *is* the
5205 // loop header. This is common for un-rotated loops.
5207 // If both of those tests fail, walk up the unique predecessor chain to the
5208 // header, stopping if there is an edge that doesn't exit the loop. If the
5209 // header is reached, the execution count of the branch will be equal to the
5210 // trip count of the loop.
5212 // More extensive analysis could be done to handle more cases here.
5214 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5215 // The simple checks failed, try climbing the unique predecessor chain
5216 // up to the header.
5218 for (BasicBlock *BB = ExitingBlock; BB; ) {
5219 BasicBlock *Pred = BB->getUniquePredecessor();
5221 return getCouldNotCompute();
5222 TerminatorInst *PredTerm = Pred->getTerminator();
5223 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5226 // If the predecessor has a successor that isn't BB and isn't
5227 // outside the loop, assume the worst.
5228 if (L->contains(PredSucc))
5229 return getCouldNotCompute();
5231 if (Pred == L->getHeader()) {
5238 return getCouldNotCompute();
5241 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5242 TerminatorInst *Term = ExitingBlock->getTerminator();
5243 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5244 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5245 // Proceed to the next level to examine the exit condition expression.
5246 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5247 BI->getSuccessor(1),
5248 /*ControlsExit=*/IsOnlyExit);
5251 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5252 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
5253 /*ControlsExit=*/IsOnlyExit);
5255 return getCouldNotCompute();
5258 /// ComputeExitLimitFromCond - Compute the number of times the
5259 /// backedge of the specified loop will execute if its exit condition
5260 /// were a conditional branch of ExitCond, TBB, and FBB.
5262 /// @param ControlsExit is true if ExitCond directly controls the exit
5263 /// branch. In this case, we can assume that the loop exits only if the
5264 /// condition is true and can infer that failing to meet the condition prior to
5265 /// integer wraparound results in undefined behavior.
5266 ScalarEvolution::ExitLimit
5267 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
5271 bool ControlsExit) {
5272 // Check if the controlling expression for this loop is an And or Or.
5273 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5274 if (BO->getOpcode() == Instruction::And) {
5275 // Recurse on the operands of the and.
5276 bool EitherMayExit = L->contains(TBB);
5277 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5278 ControlsExit && !EitherMayExit);
5279 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5280 ControlsExit && !EitherMayExit);
5281 const SCEV *BECount = getCouldNotCompute();
5282 const SCEV *MaxBECount = getCouldNotCompute();
5283 if (EitherMayExit) {
5284 // Both conditions must be true for the loop to continue executing.
5285 // Choose the less conservative count.
5286 if (EL0.Exact == getCouldNotCompute() ||
5287 EL1.Exact == getCouldNotCompute())
5288 BECount = getCouldNotCompute();
5290 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5291 if (EL0.Max == getCouldNotCompute())
5292 MaxBECount = EL1.Max;
5293 else if (EL1.Max == getCouldNotCompute())
5294 MaxBECount = EL0.Max;
5296 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5298 // Both conditions must be true at the same time for the loop to exit.
5299 // For now, be conservative.
5300 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5301 if (EL0.Max == EL1.Max)
5302 MaxBECount = EL0.Max;
5303 if (EL0.Exact == EL1.Exact)
5304 BECount = EL0.Exact;
5307 return ExitLimit(BECount, MaxBECount);
5309 if (BO->getOpcode() == Instruction::Or) {
5310 // Recurse on the operands of the or.
5311 bool EitherMayExit = L->contains(FBB);
5312 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5313 ControlsExit && !EitherMayExit);
5314 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5315 ControlsExit && !EitherMayExit);
5316 const SCEV *BECount = getCouldNotCompute();
5317 const SCEV *MaxBECount = getCouldNotCompute();
5318 if (EitherMayExit) {
5319 // Both conditions must be false for the loop to continue executing.
5320 // Choose the less conservative count.
5321 if (EL0.Exact == getCouldNotCompute() ||
5322 EL1.Exact == getCouldNotCompute())
5323 BECount = getCouldNotCompute();
5325 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5326 if (EL0.Max == getCouldNotCompute())
5327 MaxBECount = EL1.Max;
5328 else if (EL1.Max == getCouldNotCompute())
5329 MaxBECount = EL0.Max;
5331 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5333 // Both conditions must be false at the same time for the loop to exit.
5334 // For now, be conservative.
5335 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5336 if (EL0.Max == EL1.Max)
5337 MaxBECount = EL0.Max;
5338 if (EL0.Exact == EL1.Exact)
5339 BECount = EL0.Exact;
5342 return ExitLimit(BECount, MaxBECount);
5346 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5347 // Proceed to the next level to examine the icmp.
5348 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5349 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5351 // Check for a constant condition. These are normally stripped out by
5352 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5353 // preserve the CFG and is temporarily leaving constant conditions
5355 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5356 if (L->contains(FBB) == !CI->getZExtValue())
5357 // The backedge is always taken.
5358 return getCouldNotCompute();
5360 // The backedge is never taken.
5361 return getZero(CI->getType());
5364 // If it's not an integer or pointer comparison then compute it the hard way.
5365 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5368 /// ComputeExitLimitFromICmp - Compute the number of times the
5369 /// backedge of the specified loop will execute if its exit condition
5370 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5371 ScalarEvolution::ExitLimit
5372 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5376 bool ControlsExit) {
5378 // If the condition was exit on true, convert the condition to exit on false
5379 ICmpInst::Predicate Cond;
5380 if (!L->contains(FBB))
5381 Cond = ExitCond->getPredicate();
5383 Cond = ExitCond->getInversePredicate();
5385 // Handle common loops like: for (X = "string"; *X; ++X)
5386 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5387 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5389 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5390 if (ItCnt.hasAnyInfo())
5394 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5395 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5397 // Try to evaluate any dependencies out of the loop.
5398 LHS = getSCEVAtScope(LHS, L);
5399 RHS = getSCEVAtScope(RHS, L);
5401 // At this point, we would like to compute how many iterations of the
5402 // loop the predicate will return true for these inputs.
5403 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5404 // If there is a loop-invariant, force it into the RHS.
5405 std::swap(LHS, RHS);
5406 Cond = ICmpInst::getSwappedPredicate(Cond);
5409 // Simplify the operands before analyzing them.
5410 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5412 // If we have a comparison of a chrec against a constant, try to use value
5413 // ranges to answer this query.
5414 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5415 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5416 if (AddRec->getLoop() == L) {
5417 // Form the constant range.
5418 ConstantRange CompRange(
5419 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5421 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5422 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5426 case ICmpInst::ICMP_NE: { // while (X != Y)
5427 // Convert to: while (X-Y != 0)
5428 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5429 if (EL.hasAnyInfo()) return EL;
5432 case ICmpInst::ICMP_EQ: { // while (X == Y)
5433 // Convert to: while (X-Y == 0)
5434 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5435 if (EL.hasAnyInfo()) return EL;
5438 case ICmpInst::ICMP_SLT:
5439 case ICmpInst::ICMP_ULT: { // while (X < Y)
5440 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5441 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5442 if (EL.hasAnyInfo()) return EL;
5445 case ICmpInst::ICMP_SGT:
5446 case ICmpInst::ICMP_UGT: { // while (X > Y)
5447 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5448 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5449 if (EL.hasAnyInfo()) return EL;
5454 dbgs() << "ComputeBackedgeTakenCount ";
5455 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5456 dbgs() << "[unsigned] ";
5457 dbgs() << *LHS << " "
5458 << Instruction::getOpcodeName(Instruction::ICmp)
5459 << " " << *RHS << "\n";
5463 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5466 ScalarEvolution::ExitLimit
5467 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5469 BasicBlock *ExitingBlock,
5470 bool ControlsExit) {
5471 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5473 // Give up if the exit is the default dest of a switch.
5474 if (Switch->getDefaultDest() == ExitingBlock)
5475 return getCouldNotCompute();
5477 assert(L->contains(Switch->getDefaultDest()) &&
5478 "Default case must not exit the loop!");
5479 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5480 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5482 // while (X != Y) --> while (X-Y != 0)
5483 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5484 if (EL.hasAnyInfo())
5487 return getCouldNotCompute();
5490 static ConstantInt *
5491 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5492 ScalarEvolution &SE) {
5493 const SCEV *InVal = SE.getConstant(C);
5494 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5495 assert(isa<SCEVConstant>(Val) &&
5496 "Evaluation of SCEV at constant didn't fold correctly?");
5497 return cast<SCEVConstant>(Val)->getValue();
5500 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5501 /// 'icmp op load X, cst', try to see if we can compute the backedge
5502 /// execution count.
5503 ScalarEvolution::ExitLimit
5504 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5508 ICmpInst::Predicate predicate) {
5510 if (LI->isVolatile()) return getCouldNotCompute();
5512 // Check to see if the loaded pointer is a getelementptr of a global.
5513 // TODO: Use SCEV instead of manually grubbing with GEPs.
5514 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5515 if (!GEP) return getCouldNotCompute();
5517 // Make sure that it is really a constant global we are gepping, with an
5518 // initializer, and make sure the first IDX is really 0.
5519 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5520 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5521 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5522 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5523 return getCouldNotCompute();
5525 // Okay, we allow one non-constant index into the GEP instruction.
5526 Value *VarIdx = nullptr;
5527 std::vector<Constant*> Indexes;
5528 unsigned VarIdxNum = 0;
5529 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5530 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5531 Indexes.push_back(CI);
5532 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5533 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5534 VarIdx = GEP->getOperand(i);
5536 Indexes.push_back(nullptr);
5539 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5541 return getCouldNotCompute();
5543 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5544 // Check to see if X is a loop variant variable value now.
5545 const SCEV *Idx = getSCEV(VarIdx);
5546 Idx = getSCEVAtScope(Idx, L);
5548 // We can only recognize very limited forms of loop index expressions, in
5549 // particular, only affine AddRec's like {C1,+,C2}.
5550 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5551 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5552 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5553 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5554 return getCouldNotCompute();
5556 unsigned MaxSteps = MaxBruteForceIterations;
5557 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5558 ConstantInt *ItCst = ConstantInt::get(
5559 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5560 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5562 // Form the GEP offset.
5563 Indexes[VarIdxNum] = Val;
5565 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5567 if (!Result) break; // Cannot compute!
5569 // Evaluate the condition for this iteration.
5570 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5571 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5572 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5574 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5575 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5578 ++NumArrayLenItCounts;
5579 return getConstant(ItCst); // Found terminating iteration!
5582 return getCouldNotCompute();
5586 /// CanConstantFold - Return true if we can constant fold an instruction of the
5587 /// specified type, assuming that all operands were constants.
5588 static bool CanConstantFold(const Instruction *I) {
5589 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5590 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5594 if (const CallInst *CI = dyn_cast<CallInst>(I))
5595 if (const Function *F = CI->getCalledFunction())
5596 return canConstantFoldCallTo(F);
5600 /// Determine whether this instruction can constant evolve within this loop
5601 /// assuming its operands can all constant evolve.
5602 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5603 // An instruction outside of the loop can't be derived from a loop PHI.
5604 if (!L->contains(I)) return false;
5606 if (isa<PHINode>(I)) {
5607 // We don't currently keep track of the control flow needed to evaluate
5608 // PHIs, so we cannot handle PHIs inside of loops.
5609 return L->getHeader() == I->getParent();
5612 // If we won't be able to constant fold this expression even if the operands
5613 // are constants, bail early.
5614 return CanConstantFold(I);
5617 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5618 /// recursing through each instruction operand until reaching a loop header phi.
5620 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5621 DenseMap<Instruction *, PHINode *> &PHIMap) {
5623 // Otherwise, we can evaluate this instruction if all of its operands are
5624 // constant or derived from a PHI node themselves.
5625 PHINode *PHI = nullptr;
5626 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5627 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5629 if (isa<Constant>(*OpI)) continue;
5631 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5632 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5634 PHINode *P = dyn_cast<PHINode>(OpInst);
5636 // If this operand is already visited, reuse the prior result.
5637 // We may have P != PHI if this is the deepest point at which the
5638 // inconsistent paths meet.
5639 P = PHIMap.lookup(OpInst);
5641 // Recurse and memoize the results, whether a phi is found or not.
5642 // This recursive call invalidates pointers into PHIMap.
5643 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5647 return nullptr; // Not evolving from PHI
5648 if (PHI && PHI != P)
5649 return nullptr; // Evolving from multiple different PHIs.
5652 // This is a expression evolving from a constant PHI!
5656 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5657 /// in the loop that V is derived from. We allow arbitrary operations along the
5658 /// way, but the operands of an operation must either be constants or a value
5659 /// derived from a constant PHI. If this expression does not fit with these
5660 /// constraints, return null.
5661 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5662 Instruction *I = dyn_cast<Instruction>(V);
5663 if (!I || !canConstantEvolve(I, L)) return nullptr;
5665 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5669 // Record non-constant instructions contained by the loop.
5670 DenseMap<Instruction *, PHINode *> PHIMap;
5671 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5674 /// EvaluateExpression - Given an expression that passes the
5675 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5676 /// in the loop has the value PHIVal. If we can't fold this expression for some
5677 /// reason, return null.
5678 static Constant *EvaluateExpression(Value *V, const Loop *L,
5679 DenseMap<Instruction *, Constant *> &Vals,
5680 const DataLayout &DL,
5681 const TargetLibraryInfo *TLI) {
5682 // Convenient constant check, but redundant for recursive calls.
5683 if (Constant *C = dyn_cast<Constant>(V)) return C;
5684 Instruction *I = dyn_cast<Instruction>(V);
5685 if (!I) return nullptr;
5687 if (Constant *C = Vals.lookup(I)) return C;
5689 // An instruction inside the loop depends on a value outside the loop that we
5690 // weren't given a mapping for, or a value such as a call inside the loop.
5691 if (!canConstantEvolve(I, L)) return nullptr;
5693 // An unmapped PHI can be due to a branch or another loop inside this loop,
5694 // or due to this not being the initial iteration through a loop where we
5695 // couldn't compute the evolution of this particular PHI last time.
5696 if (isa<PHINode>(I)) return nullptr;
5698 std::vector<Constant*> Operands(I->getNumOperands());
5700 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5701 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5703 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5704 if (!Operands[i]) return nullptr;
5707 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5709 if (!C) return nullptr;
5713 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5714 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5715 Operands[1], DL, TLI);
5716 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5717 if (!LI->isVolatile())
5718 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5720 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5724 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5725 /// in the header of its containing loop, we know the loop executes a
5726 /// constant number of times, and the PHI node is just a recurrence
5727 /// involving constants, fold it.
5729 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5732 auto I = ConstantEvolutionLoopExitValue.find(PN);
5733 if (I != ConstantEvolutionLoopExitValue.end())
5736 if (BEs.ugt(MaxBruteForceIterations))
5737 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5739 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5741 DenseMap<Instruction *, Constant *> CurrentIterVals;
5742 BasicBlock *Header = L->getHeader();
5743 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5745 BasicBlock *Latch = L->getLoopLatch();
5749 // Since the loop has one latch, the PHI node must have two entries. One
5750 // entry must be a constant (coming in from outside of the loop), and the
5751 // second must be derived from the same PHI.
5753 BasicBlock *NonLatch = Latch == PN->getIncomingBlock(0)
5754 ? PN->getIncomingBlock(1)
5755 : PN->getIncomingBlock(0);
5757 assert(PN->getNumIncomingValues() == 2 && "Follows from having one latch!");
5759 // Note: not all PHI nodes in the same block have to have their incoming
5760 // values in the same order, so we use the basic block to look up the incoming
5761 // value, not an index.
5763 for (auto &I : *Header) {
5764 PHINode *PHI = dyn_cast<PHINode>(&I);
5767 dyn_cast<Constant>(PHI->getIncomingValueForBlock(NonLatch));
5768 if (!StartCST) continue;
5769 CurrentIterVals[PHI] = StartCST;
5771 if (!CurrentIterVals.count(PN))
5772 return RetVal = nullptr;
5774 Value *BEValue = PN->getIncomingValueForBlock(Latch);
5776 // Execute the loop symbolically to determine the exit value.
5777 if (BEs.getActiveBits() >= 32)
5778 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5780 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5781 unsigned IterationNum = 0;
5782 const DataLayout &DL = F.getParent()->getDataLayout();
5783 for (; ; ++IterationNum) {
5784 if (IterationNum == NumIterations)
5785 return RetVal = CurrentIterVals[PN]; // Got exit value!
5787 // Compute the value of the PHIs for the next iteration.
5788 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5789 DenseMap<Instruction *, Constant *> NextIterVals;
5791 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5793 return nullptr; // Couldn't evaluate!
5794 NextIterVals[PN] = NextPHI;
5796 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5798 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5799 // cease to be able to evaluate one of them or if they stop evolving,
5800 // because that doesn't necessarily prevent us from computing PN.
5801 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5802 for (const auto &I : CurrentIterVals) {
5803 PHINode *PHI = dyn_cast<PHINode>(I.first);
5804 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5805 PHIsToCompute.emplace_back(PHI, I.second);
5807 // We use two distinct loops because EvaluateExpression may invalidate any
5808 // iterators into CurrentIterVals.
5809 for (const auto &I : PHIsToCompute) {
5810 PHINode *PHI = I.first;
5811 Constant *&NextPHI = NextIterVals[PHI];
5812 if (!NextPHI) { // Not already computed.
5813 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
5814 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5816 if (NextPHI != I.second)
5817 StoppedEvolving = false;
5820 // If all entries in CurrentIterVals == NextIterVals then we can stop
5821 // iterating, the loop can't continue to change.
5822 if (StoppedEvolving)
5823 return RetVal = CurrentIterVals[PN];
5825 CurrentIterVals.swap(NextIterVals);
5829 /// ComputeExitCountExhaustively - If the loop is known to execute a
5830 /// constant number of times (the condition evolves only from constants),
5831 /// try to evaluate a few iterations of the loop until we get the exit
5832 /// condition gets a value of ExitWhen (true or false). If we cannot
5833 /// evaluate the trip count of the loop, return getCouldNotCompute().
5834 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5837 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5838 if (!PN) return getCouldNotCompute();
5840 // If the loop is canonicalized, the PHI will have exactly two entries.
5841 // That's the only form we support here.
5842 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5844 DenseMap<Instruction *, Constant *> CurrentIterVals;
5845 BasicBlock *Header = L->getHeader();
5846 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5848 BasicBlock *Latch = L->getLoopLatch();
5849 assert(Latch && "Should follow from NumIncomingValues == 2!");
5851 // NonLatch is the preheader, or something equivalent.
5852 BasicBlock *NonLatch = Latch == PN->getIncomingBlock(0)
5853 ? PN->getIncomingBlock(1)
5854 : PN->getIncomingBlock(0);
5856 // Note: not all PHI nodes in the same block have to have their incoming
5857 // values in the same order, so we use the basic block to look up the incoming
5858 // value, not an index.
5860 for (auto &I : *Header) {
5861 PHINode *PHI = dyn_cast<PHINode>(&I);
5865 dyn_cast<Constant>(PHI->getIncomingValueForBlock(NonLatch));
5866 if (!StartCST) continue;
5867 CurrentIterVals[PHI] = StartCST;
5869 if (!CurrentIterVals.count(PN))
5870 return getCouldNotCompute();
5872 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5873 // the loop symbolically to determine when the condition gets a value of
5875 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5876 const DataLayout &DL = F.getParent()->getDataLayout();
5877 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5878 auto *CondVal = dyn_cast_or_null<ConstantInt>(
5879 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
5881 // Couldn't symbolically evaluate.
5882 if (!CondVal) return getCouldNotCompute();
5884 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5885 ++NumBruteForceTripCountsComputed;
5886 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5889 // Update all the PHI nodes for the next iteration.
5890 DenseMap<Instruction *, Constant *> NextIterVals;
5892 // Create a list of which PHIs we need to compute. We want to do this before
5893 // calling EvaluateExpression on them because that may invalidate iterators
5894 // into CurrentIterVals.
5895 SmallVector<PHINode *, 8> PHIsToCompute;
5896 for (const auto &I : CurrentIterVals) {
5897 PHINode *PHI = dyn_cast<PHINode>(I.first);
5898 if (!PHI || PHI->getParent() != Header) continue;
5899 PHIsToCompute.push_back(PHI);
5901 for (PHINode *PHI : PHIsToCompute) {
5902 Constant *&NextPHI = NextIterVals[PHI];
5903 if (NextPHI) continue; // Already computed!
5905 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
5906 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
5908 CurrentIterVals.swap(NextIterVals);
5911 // Too many iterations were needed to evaluate.
5912 return getCouldNotCompute();
5915 /// getSCEVAtScope - Return a SCEV expression for the specified value
5916 /// at the specified scope in the program. The L value specifies a loop
5917 /// nest to evaluate the expression at, where null is the top-level or a
5918 /// specified loop is immediately inside of the loop.
5920 /// This method can be used to compute the exit value for a variable defined
5921 /// in a loop by querying what the value will hold in the parent loop.
5923 /// In the case that a relevant loop exit value cannot be computed, the
5924 /// original value V is returned.
5925 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5926 // Check to see if we've folded this expression at this loop before.
5927 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5928 for (unsigned u = 0; u < Values.size(); u++) {
5929 if (Values[u].first == L)
5930 return Values[u].second ? Values[u].second : V;
5932 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5933 // Otherwise compute it.
5934 const SCEV *C = computeSCEVAtScope(V, L);
5935 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5936 for (unsigned u = Values2.size(); u > 0; u--) {
5937 if (Values2[u - 1].first == L) {
5938 Values2[u - 1].second = C;
5945 /// This builds up a Constant using the ConstantExpr interface. That way, we
5946 /// will return Constants for objects which aren't represented by a
5947 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5948 /// Returns NULL if the SCEV isn't representable as a Constant.
5949 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5950 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5951 case scCouldNotCompute:
5955 return cast<SCEVConstant>(V)->getValue();
5957 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5958 case scSignExtend: {
5959 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5960 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5961 return ConstantExpr::getSExt(CastOp, SS->getType());
5964 case scZeroExtend: {
5965 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5966 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5967 return ConstantExpr::getZExt(CastOp, SZ->getType());
5971 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5972 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5973 return ConstantExpr::getTrunc(CastOp, ST->getType());
5977 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5978 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5979 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5980 unsigned AS = PTy->getAddressSpace();
5981 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5982 C = ConstantExpr::getBitCast(C, DestPtrTy);
5984 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5985 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5986 if (!C2) return nullptr;
5989 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5990 unsigned AS = C2->getType()->getPointerAddressSpace();
5992 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5993 // The offsets have been converted to bytes. We can add bytes to an
5994 // i8* by GEP with the byte count in the first index.
5995 C = ConstantExpr::getBitCast(C, DestPtrTy);
5998 // Don't bother trying to sum two pointers. We probably can't
5999 // statically compute a load that results from it anyway.
6000 if (C2->getType()->isPointerTy())
6003 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6004 if (PTy->getElementType()->isStructTy())
6005 C2 = ConstantExpr::getIntegerCast(
6006 C2, Type::getInt32Ty(C->getContext()), true);
6007 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
6009 C = ConstantExpr::getAdd(C, C2);
6016 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
6017 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
6018 // Don't bother with pointers at all.
6019 if (C->getType()->isPointerTy()) return nullptr;
6020 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
6021 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
6022 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
6023 C = ConstantExpr::getMul(C, C2);
6030 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6031 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6032 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6033 if (LHS->getType() == RHS->getType())
6034 return ConstantExpr::getUDiv(LHS, RHS);
6039 break; // TODO: smax, umax.
6044 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6045 if (isa<SCEVConstant>(V)) return V;
6047 // If this instruction is evolved from a constant-evolving PHI, compute the
6048 // exit value from the loop without using SCEVs.
6049 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6050 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6051 const Loop *LI = this->LI[I->getParent()];
6052 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
6053 if (PHINode *PN = dyn_cast<PHINode>(I))
6054 if (PN->getParent() == LI->getHeader()) {
6055 // Okay, there is no closed form solution for the PHI node. Check
6056 // to see if the loop that contains it has a known backedge-taken
6057 // count. If so, we may be able to force computation of the exit
6059 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6060 if (const SCEVConstant *BTCC =
6061 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6062 // Okay, we know how many times the containing loop executes. If
6063 // this is a constant evolving PHI node, get the final value at
6064 // the specified iteration number.
6065 Constant *RV = getConstantEvolutionLoopExitValue(PN,
6066 BTCC->getValue()->getValue(),
6068 if (RV) return getSCEV(RV);
6072 // Okay, this is an expression that we cannot symbolically evaluate
6073 // into a SCEV. Check to see if it's possible to symbolically evaluate
6074 // the arguments into constants, and if so, try to constant propagate the
6075 // result. This is particularly useful for computing loop exit values.
6076 if (CanConstantFold(I)) {
6077 SmallVector<Constant *, 4> Operands;
6078 bool MadeImprovement = false;
6079 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
6080 Value *Op = I->getOperand(i);
6081 if (Constant *C = dyn_cast<Constant>(Op)) {
6082 Operands.push_back(C);
6086 // If any of the operands is non-constant and if they are
6087 // non-integer and non-pointer, don't even try to analyze them
6088 // with scev techniques.
6089 if (!isSCEVable(Op->getType()))
6092 const SCEV *OrigV = getSCEV(Op);
6093 const SCEV *OpV = getSCEVAtScope(OrigV, L);
6094 MadeImprovement |= OrigV != OpV;
6096 Constant *C = BuildConstantFromSCEV(OpV);
6098 if (C->getType() != Op->getType())
6099 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6103 Operands.push_back(C);
6106 // Check to see if getSCEVAtScope actually made an improvement.
6107 if (MadeImprovement) {
6108 Constant *C = nullptr;
6109 const DataLayout &DL = F.getParent()->getDataLayout();
6110 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6111 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6112 Operands[1], DL, &TLI);
6113 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6114 if (!LI->isVolatile())
6115 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
6117 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
6125 // This is some other type of SCEVUnknown, just return it.
6129 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6130 // Avoid performing the look-up in the common case where the specified
6131 // expression has no loop-variant portions.
6132 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6133 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6134 if (OpAtScope != Comm->getOperand(i)) {
6135 // Okay, at least one of these operands is loop variant but might be
6136 // foldable. Build a new instance of the folded commutative expression.
6137 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6138 Comm->op_begin()+i);
6139 NewOps.push_back(OpAtScope);
6141 for (++i; i != e; ++i) {
6142 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6143 NewOps.push_back(OpAtScope);
6145 if (isa<SCEVAddExpr>(Comm))
6146 return getAddExpr(NewOps);
6147 if (isa<SCEVMulExpr>(Comm))
6148 return getMulExpr(NewOps);
6149 if (isa<SCEVSMaxExpr>(Comm))
6150 return getSMaxExpr(NewOps);
6151 if (isa<SCEVUMaxExpr>(Comm))
6152 return getUMaxExpr(NewOps);
6153 llvm_unreachable("Unknown commutative SCEV type!");
6156 // If we got here, all operands are loop invariant.
6160 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6161 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6162 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6163 if (LHS == Div->getLHS() && RHS == Div->getRHS())
6164 return Div; // must be loop invariant
6165 return getUDivExpr(LHS, RHS);
6168 // If this is a loop recurrence for a loop that does not contain L, then we
6169 // are dealing with the final value computed by the loop.
6170 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6171 // First, attempt to evaluate each operand.
6172 // Avoid performing the look-up in the common case where the specified
6173 // expression has no loop-variant portions.
6174 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6175 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6176 if (OpAtScope == AddRec->getOperand(i))
6179 // Okay, at least one of these operands is loop variant but might be
6180 // foldable. Build a new instance of the folded commutative expression.
6181 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6182 AddRec->op_begin()+i);
6183 NewOps.push_back(OpAtScope);
6184 for (++i; i != e; ++i)
6185 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6187 const SCEV *FoldedRec =
6188 getAddRecExpr(NewOps, AddRec->getLoop(),
6189 AddRec->getNoWrapFlags(SCEV::FlagNW));
6190 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6191 // The addrec may be folded to a nonrecurrence, for example, if the
6192 // induction variable is multiplied by zero after constant folding. Go
6193 // ahead and return the folded value.
6199 // If the scope is outside the addrec's loop, evaluate it by using the
6200 // loop exit value of the addrec.
6201 if (!AddRec->getLoop()->contains(L)) {
6202 // To evaluate this recurrence, we need to know how many times the AddRec
6203 // loop iterates. Compute this now.
6204 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6205 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6207 // Then, evaluate the AddRec.
6208 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6214 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6215 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6216 if (Op == Cast->getOperand())
6217 return Cast; // must be loop invariant
6218 return getZeroExtendExpr(Op, Cast->getType());
6221 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6222 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6223 if (Op == Cast->getOperand())
6224 return Cast; // must be loop invariant
6225 return getSignExtendExpr(Op, Cast->getType());
6228 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6229 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6230 if (Op == Cast->getOperand())
6231 return Cast; // must be loop invariant
6232 return getTruncateExpr(Op, Cast->getType());
6235 llvm_unreachable("Unknown SCEV type!");
6238 /// getSCEVAtScope - This is a convenience function which does
6239 /// getSCEVAtScope(getSCEV(V), L).
6240 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6241 return getSCEVAtScope(getSCEV(V), L);
6244 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6245 /// following equation:
6247 /// A * X = B (mod N)
6249 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6250 /// A and B isn't important.
6252 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6253 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6254 ScalarEvolution &SE) {
6255 uint32_t BW = A.getBitWidth();
6256 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6257 assert(A != 0 && "A must be non-zero.");
6261 // The gcd of A and N may have only one prime factor: 2. The number of
6262 // trailing zeros in A is its multiplicity
6263 uint32_t Mult2 = A.countTrailingZeros();
6266 // 2. Check if B is divisible by D.
6268 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6269 // is not less than multiplicity of this prime factor for D.
6270 if (B.countTrailingZeros() < Mult2)
6271 return SE.getCouldNotCompute();
6273 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6276 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6277 // bit width during computations.
6278 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6279 APInt Mod(BW + 1, 0);
6280 Mod.setBit(BW - Mult2); // Mod = N / D
6281 APInt I = AD.multiplicativeInverse(Mod);
6283 // 4. Compute the minimum unsigned root of the equation:
6284 // I * (B / D) mod (N / D)
6285 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6287 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6289 return SE.getConstant(Result.trunc(BW));
6292 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6293 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6294 /// might be the same) or two SCEVCouldNotCompute objects.
6296 static std::pair<const SCEV *,const SCEV *>
6297 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6298 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6299 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6300 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6301 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6303 // We currently can only solve this if the coefficients are constants.
6304 if (!LC || !MC || !NC) {
6305 const SCEV *CNC = SE.getCouldNotCompute();
6306 return std::make_pair(CNC, CNC);
6309 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6310 const APInt &L = LC->getValue()->getValue();
6311 const APInt &M = MC->getValue()->getValue();
6312 const APInt &N = NC->getValue()->getValue();
6313 APInt Two(BitWidth, 2);
6314 APInt Four(BitWidth, 4);
6317 using namespace APIntOps;
6319 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6320 // The B coefficient is M-N/2
6324 // The A coefficient is N/2
6325 APInt A(N.sdiv(Two));
6327 // Compute the B^2-4ac term.
6330 SqrtTerm -= Four * (A * C);
6332 if (SqrtTerm.isNegative()) {
6333 // The loop is provably infinite.
6334 const SCEV *CNC = SE.getCouldNotCompute();
6335 return std::make_pair(CNC, CNC);
6338 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6339 // integer value or else APInt::sqrt() will assert.
6340 APInt SqrtVal(SqrtTerm.sqrt());
6342 // Compute the two solutions for the quadratic formula.
6343 // The divisions must be performed as signed divisions.
6346 if (TwoA.isMinValue()) {
6347 const SCEV *CNC = SE.getCouldNotCompute();
6348 return std::make_pair(CNC, CNC);
6351 LLVMContext &Context = SE.getContext();
6353 ConstantInt *Solution1 =
6354 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6355 ConstantInt *Solution2 =
6356 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6358 return std::make_pair(SE.getConstant(Solution1),
6359 SE.getConstant(Solution2));
6360 } // end APIntOps namespace
6363 /// HowFarToZero - Return the number of times a backedge comparing the specified
6364 /// value to zero will execute. If not computable, return CouldNotCompute.
6366 /// This is only used for loops with a "x != y" exit test. The exit condition is
6367 /// now expressed as a single expression, V = x-y. So the exit test is
6368 /// effectively V != 0. We know and take advantage of the fact that this
6369 /// expression only being used in a comparison by zero context.
6370 ScalarEvolution::ExitLimit
6371 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6372 // If the value is a constant
6373 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6374 // If the value is already zero, the branch will execute zero times.
6375 if (C->getValue()->isZero()) return C;
6376 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6379 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6380 if (!AddRec || AddRec->getLoop() != L)
6381 return getCouldNotCompute();
6383 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6384 // the quadratic equation to solve it.
6385 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6386 std::pair<const SCEV *,const SCEV *> Roots =
6387 SolveQuadraticEquation(AddRec, *this);
6388 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6389 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6392 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6393 << " sol#2: " << *R2 << "\n";
6395 // Pick the smallest positive root value.
6396 if (ConstantInt *CB =
6397 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6400 if (!CB->getZExtValue())
6401 std::swap(R1, R2); // R1 is the minimum root now.
6403 // We can only use this value if the chrec ends up with an exact zero
6404 // value at this index. When solving for "X*X != 5", for example, we
6405 // should not accept a root of 2.
6406 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6408 return R1; // We found a quadratic root!
6411 return getCouldNotCompute();
6414 // Otherwise we can only handle this if it is affine.
6415 if (!AddRec->isAffine())
6416 return getCouldNotCompute();
6418 // If this is an affine expression, the execution count of this branch is
6419 // the minimum unsigned root of the following equation:
6421 // Start + Step*N = 0 (mod 2^BW)
6425 // Step*N = -Start (mod 2^BW)
6427 // where BW is the common bit width of Start and Step.
6429 // Get the initial value for the loop.
6430 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6431 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6433 // For now we handle only constant steps.
6435 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6436 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6437 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6438 // We have not yet seen any such cases.
6439 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6440 if (!StepC || StepC->getValue()->equalsInt(0))
6441 return getCouldNotCompute();
6443 // For positive steps (counting up until unsigned overflow):
6444 // N = -Start/Step (as unsigned)
6445 // For negative steps (counting down to zero):
6447 // First compute the unsigned distance from zero in the direction of Step.
6448 bool CountDown = StepC->getValue()->getValue().isNegative();
6449 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6451 // Handle unitary steps, which cannot wraparound.
6452 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6453 // N = Distance (as unsigned)
6454 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6455 ConstantRange CR = getUnsignedRange(Start);
6456 const SCEV *MaxBECount;
6457 if (!CountDown && CR.getUnsignedMin().isMinValue())
6458 // When counting up, the worst starting value is 1, not 0.
6459 MaxBECount = CR.getUnsignedMax().isMinValue()
6460 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6461 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6463 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6464 : -CR.getUnsignedMin());
6465 return ExitLimit(Distance, MaxBECount);
6468 // As a special case, handle the instance where Step is a positive power of
6469 // two. In this case, determining whether Step divides Distance evenly can be
6470 // done by counting and comparing the number of trailing zeros of Step and
6473 const APInt &StepV = StepC->getValue()->getValue();
6474 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6475 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6476 // case is not handled as this code is guarded by !CountDown.
6477 if (StepV.isPowerOf2() &&
6478 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
6479 // Here we've constrained the equation to be of the form
6481 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
6483 // where we're operating on a W bit wide integer domain and k is
6484 // non-negative. The smallest unsigned solution for X is the trip count.
6486 // (0) is equivalent to:
6488 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
6489 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
6490 // <=> 2^k * Distance' - X = L * 2^(W - N)
6491 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
6493 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
6496 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
6498 // E.g. say we're solving
6500 // 2 * Val = 2 * X (in i8) ... (3)
6502 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
6504 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
6505 // necessarily the smallest unsigned value of X that satisfies (3).
6506 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
6507 // is i8 1, not i8 -127
6509 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
6511 // Since SCEV does not have a URem node, we construct one using a truncate
6512 // and a zero extend.
6514 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
6515 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
6516 auto *WideTy = Distance->getType();
6518 return getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
6522 // If the condition controls loop exit (the loop exits only if the expression
6523 // is true) and the addition is no-wrap we can use unsigned divide to
6524 // compute the backedge count. In this case, the step may not divide the
6525 // distance, but we don't care because if the condition is "missed" the loop
6526 // will have undefined behavior due to wrapping.
6527 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6529 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6530 return ExitLimit(Exact, Exact);
6533 // Then, try to solve the above equation provided that Start is constant.
6534 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6535 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6536 -StartC->getValue()->getValue(),
6538 return getCouldNotCompute();
6541 /// HowFarToNonZero - Return the number of times a backedge checking the
6542 /// specified value for nonzero will execute. If not computable, return
6544 ScalarEvolution::ExitLimit
6545 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6546 // Loops that look like: while (X == 0) are very strange indeed. We don't
6547 // handle them yet except for the trivial case. This could be expanded in the
6548 // future as needed.
6550 // If the value is a constant, check to see if it is known to be non-zero
6551 // already. If so, the backedge will execute zero times.
6552 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6553 if (!C->getValue()->isNullValue())
6554 return getZero(C->getType());
6555 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6558 // We could implement others, but I really doubt anyone writes loops like
6559 // this, and if they did, they would already be constant folded.
6560 return getCouldNotCompute();
6563 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6564 /// (which may not be an immediate predecessor) which has exactly one
6565 /// successor from which BB is reachable, or null if no such block is
6568 std::pair<BasicBlock *, BasicBlock *>
6569 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6570 // If the block has a unique predecessor, then there is no path from the
6571 // predecessor to the block that does not go through the direct edge
6572 // from the predecessor to the block.
6573 if (BasicBlock *Pred = BB->getSinglePredecessor())
6574 return std::make_pair(Pred, BB);
6576 // A loop's header is defined to be a block that dominates the loop.
6577 // If the header has a unique predecessor outside the loop, it must be
6578 // a block that has exactly one successor that can reach the loop.
6579 if (Loop *L = LI.getLoopFor(BB))
6580 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6582 return std::pair<BasicBlock *, BasicBlock *>();
6585 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6586 /// testing whether two expressions are equal, however for the purposes of
6587 /// looking for a condition guarding a loop, it can be useful to be a little
6588 /// more general, since a front-end may have replicated the controlling
6591 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6592 // Quick check to see if they are the same SCEV.
6593 if (A == B) return true;
6595 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
6596 // Not all instructions that are "identical" compute the same value. For
6597 // instance, two distinct alloca instructions allocating the same type are
6598 // identical and do not read memory; but compute distinct values.
6599 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
6602 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6603 // two different instructions with the same value. Check for this case.
6604 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6605 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6606 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6607 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6608 if (ComputesEqualValues(AI, BI))
6611 // Otherwise assume they may have a different value.
6615 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6616 /// predicate Pred. Return true iff any changes were made.
6618 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6619 const SCEV *&LHS, const SCEV *&RHS,
6621 bool Changed = false;
6623 // If we hit the max recursion limit bail out.
6627 // Canonicalize a constant to the right side.
6628 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6629 // Check for both operands constant.
6630 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6631 if (ConstantExpr::getICmp(Pred,
6633 RHSC->getValue())->isNullValue())
6634 goto trivially_false;
6636 goto trivially_true;
6638 // Otherwise swap the operands to put the constant on the right.
6639 std::swap(LHS, RHS);
6640 Pred = ICmpInst::getSwappedPredicate(Pred);
6644 // If we're comparing an addrec with a value which is loop-invariant in the
6645 // addrec's loop, put the addrec on the left. Also make a dominance check,
6646 // as both operands could be addrecs loop-invariant in each other's loop.
6647 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6648 const Loop *L = AR->getLoop();
6649 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6650 std::swap(LHS, RHS);
6651 Pred = ICmpInst::getSwappedPredicate(Pred);
6656 // If there's a constant operand, canonicalize comparisons with boundary
6657 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6658 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6659 const APInt &RA = RC->getValue()->getValue();
6661 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6662 case ICmpInst::ICMP_EQ:
6663 case ICmpInst::ICMP_NE:
6664 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6666 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6667 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6668 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6669 ME->getOperand(0)->isAllOnesValue()) {
6670 RHS = AE->getOperand(1);
6671 LHS = ME->getOperand(1);
6675 case ICmpInst::ICMP_UGE:
6676 if ((RA - 1).isMinValue()) {
6677 Pred = ICmpInst::ICMP_NE;
6678 RHS = getConstant(RA - 1);
6682 if (RA.isMaxValue()) {
6683 Pred = ICmpInst::ICMP_EQ;
6687 if (RA.isMinValue()) goto trivially_true;
6689 Pred = ICmpInst::ICMP_UGT;
6690 RHS = getConstant(RA - 1);
6693 case ICmpInst::ICMP_ULE:
6694 if ((RA + 1).isMaxValue()) {
6695 Pred = ICmpInst::ICMP_NE;
6696 RHS = getConstant(RA + 1);
6700 if (RA.isMinValue()) {
6701 Pred = ICmpInst::ICMP_EQ;
6705 if (RA.isMaxValue()) goto trivially_true;
6707 Pred = ICmpInst::ICMP_ULT;
6708 RHS = getConstant(RA + 1);
6711 case ICmpInst::ICMP_SGE:
6712 if ((RA - 1).isMinSignedValue()) {
6713 Pred = ICmpInst::ICMP_NE;
6714 RHS = getConstant(RA - 1);
6718 if (RA.isMaxSignedValue()) {
6719 Pred = ICmpInst::ICMP_EQ;
6723 if (RA.isMinSignedValue()) goto trivially_true;
6725 Pred = ICmpInst::ICMP_SGT;
6726 RHS = getConstant(RA - 1);
6729 case ICmpInst::ICMP_SLE:
6730 if ((RA + 1).isMaxSignedValue()) {
6731 Pred = ICmpInst::ICMP_NE;
6732 RHS = getConstant(RA + 1);
6736 if (RA.isMinSignedValue()) {
6737 Pred = ICmpInst::ICMP_EQ;
6741 if (RA.isMaxSignedValue()) goto trivially_true;
6743 Pred = ICmpInst::ICMP_SLT;
6744 RHS = getConstant(RA + 1);
6747 case ICmpInst::ICMP_UGT:
6748 if (RA.isMinValue()) {
6749 Pred = ICmpInst::ICMP_NE;
6753 if ((RA + 1).isMaxValue()) {
6754 Pred = ICmpInst::ICMP_EQ;
6755 RHS = getConstant(RA + 1);
6759 if (RA.isMaxValue()) goto trivially_false;
6761 case ICmpInst::ICMP_ULT:
6762 if (RA.isMaxValue()) {
6763 Pred = ICmpInst::ICMP_NE;
6767 if ((RA - 1).isMinValue()) {
6768 Pred = ICmpInst::ICMP_EQ;
6769 RHS = getConstant(RA - 1);
6773 if (RA.isMinValue()) goto trivially_false;
6775 case ICmpInst::ICMP_SGT:
6776 if (RA.isMinSignedValue()) {
6777 Pred = ICmpInst::ICMP_NE;
6781 if ((RA + 1).isMaxSignedValue()) {
6782 Pred = ICmpInst::ICMP_EQ;
6783 RHS = getConstant(RA + 1);
6787 if (RA.isMaxSignedValue()) goto trivially_false;
6789 case ICmpInst::ICMP_SLT:
6790 if (RA.isMaxSignedValue()) {
6791 Pred = ICmpInst::ICMP_NE;
6795 if ((RA - 1).isMinSignedValue()) {
6796 Pred = ICmpInst::ICMP_EQ;
6797 RHS = getConstant(RA - 1);
6801 if (RA.isMinSignedValue()) goto trivially_false;
6806 // Check for obvious equality.
6807 if (HasSameValue(LHS, RHS)) {
6808 if (ICmpInst::isTrueWhenEqual(Pred))
6809 goto trivially_true;
6810 if (ICmpInst::isFalseWhenEqual(Pred))
6811 goto trivially_false;
6814 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6815 // adding or subtracting 1 from one of the operands.
6817 case ICmpInst::ICMP_SLE:
6818 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6819 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6821 Pred = ICmpInst::ICMP_SLT;
6823 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6824 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6826 Pred = ICmpInst::ICMP_SLT;
6830 case ICmpInst::ICMP_SGE:
6831 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6832 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6834 Pred = ICmpInst::ICMP_SGT;
6836 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6837 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6839 Pred = ICmpInst::ICMP_SGT;
6843 case ICmpInst::ICMP_ULE:
6844 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6845 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6847 Pred = ICmpInst::ICMP_ULT;
6849 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6850 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6852 Pred = ICmpInst::ICMP_ULT;
6856 case ICmpInst::ICMP_UGE:
6857 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6858 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6860 Pred = ICmpInst::ICMP_UGT;
6862 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6863 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6865 Pred = ICmpInst::ICMP_UGT;
6873 // TODO: More simplifications are possible here.
6875 // Recursively simplify until we either hit a recursion limit or nothing
6878 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6884 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6885 Pred = ICmpInst::ICMP_EQ;
6890 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6891 Pred = ICmpInst::ICMP_NE;
6895 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6896 return getSignedRange(S).getSignedMax().isNegative();
6899 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6900 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6903 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6904 return !getSignedRange(S).getSignedMin().isNegative();
6907 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6908 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6911 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6912 return isKnownNegative(S) || isKnownPositive(S);
6915 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6916 const SCEV *LHS, const SCEV *RHS) {
6917 // Canonicalize the inputs first.
6918 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6920 // If LHS or RHS is an addrec, check to see if the condition is true in
6921 // every iteration of the loop.
6922 // If LHS and RHS are both addrec, both conditions must be true in
6923 // every iteration of the loop.
6924 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6925 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6926 bool LeftGuarded = false;
6927 bool RightGuarded = false;
6929 const Loop *L = LAR->getLoop();
6930 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6931 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6932 if (!RAR) return true;
6937 const Loop *L = RAR->getLoop();
6938 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6939 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6940 if (!LAR) return true;
6941 RightGuarded = true;
6944 if (LeftGuarded && RightGuarded)
6947 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
6950 // Otherwise see what can be done with known constant ranges.
6951 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6954 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
6955 ICmpInst::Predicate Pred,
6957 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
6960 // Verify an invariant: inverting the predicate should turn a monotonically
6961 // increasing change to a monotonically decreasing one, and vice versa.
6962 bool IncreasingSwapped;
6963 bool ResultSwapped = isMonotonicPredicateImpl(
6964 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
6966 assert(Result == ResultSwapped && "should be able to analyze both!");
6968 assert(Increasing == !IncreasingSwapped &&
6969 "monotonicity should flip as we flip the predicate");
6975 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
6976 ICmpInst::Predicate Pred,
6979 // A zero step value for LHS means the induction variable is essentially a
6980 // loop invariant value. We don't really depend on the predicate actually
6981 // flipping from false to true (for increasing predicates, and the other way
6982 // around for decreasing predicates), all we care about is that *if* the
6983 // predicate changes then it only changes from false to true.
6985 // A zero step value in itself is not very useful, but there may be places
6986 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
6987 // as general as possible.
6991 return false; // Conservative answer
6993 case ICmpInst::ICMP_UGT:
6994 case ICmpInst::ICMP_UGE:
6995 case ICmpInst::ICMP_ULT:
6996 case ICmpInst::ICMP_ULE:
6997 if (!LHS->getNoWrapFlags(SCEV::FlagNUW))
7000 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
7003 case ICmpInst::ICMP_SGT:
7004 case ICmpInst::ICMP_SGE:
7005 case ICmpInst::ICMP_SLT:
7006 case ICmpInst::ICMP_SLE: {
7007 if (!LHS->getNoWrapFlags(SCEV::FlagNSW))
7010 const SCEV *Step = LHS->getStepRecurrence(*this);
7012 if (isKnownNonNegative(Step)) {
7013 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
7017 if (isKnownNonPositive(Step)) {
7018 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7027 llvm_unreachable("switch has default clause!");
7030 bool ScalarEvolution::isLoopInvariantPredicate(
7031 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7032 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7033 const SCEV *&InvariantRHS) {
7035 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7036 if (!isLoopInvariant(RHS, L)) {
7037 if (!isLoopInvariant(LHS, L))
7040 std::swap(LHS, RHS);
7041 Pred = ICmpInst::getSwappedPredicate(Pred);
7044 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7045 if (!ArLHS || ArLHS->getLoop() != L)
7049 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7052 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7053 // true as the loop iterates, and the backedge is control dependent on
7054 // "ArLHS `Pred` RHS" == true then we can reason as follows:
7056 // * if the predicate was false in the first iteration then the predicate
7057 // is never evaluated again, since the loop exits without taking the
7059 // * if the predicate was true in the first iteration then it will
7060 // continue to be true for all future iterations since it is
7061 // monotonically increasing.
7063 // For both the above possibilities, we can replace the loop varying
7064 // predicate with its value on the first iteration of the loop (which is
7067 // A similar reasoning applies for a monotonically decreasing predicate, by
7068 // replacing true with false and false with true in the above two bullets.
7070 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7072 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7075 InvariantPred = Pred;
7076 InvariantLHS = ArLHS->getStart();
7082 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
7083 const SCEV *LHS, const SCEV *RHS) {
7084 if (HasSameValue(LHS, RHS))
7085 return ICmpInst::isTrueWhenEqual(Pred);
7087 // This code is split out from isKnownPredicate because it is called from
7088 // within isLoopEntryGuardedByCond.
7091 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7092 case ICmpInst::ICMP_SGT:
7093 std::swap(LHS, RHS);
7094 case ICmpInst::ICMP_SLT: {
7095 ConstantRange LHSRange = getSignedRange(LHS);
7096 ConstantRange RHSRange = getSignedRange(RHS);
7097 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
7099 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
7103 case ICmpInst::ICMP_SGE:
7104 std::swap(LHS, RHS);
7105 case ICmpInst::ICMP_SLE: {
7106 ConstantRange LHSRange = getSignedRange(LHS);
7107 ConstantRange RHSRange = getSignedRange(RHS);
7108 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
7110 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
7114 case ICmpInst::ICMP_UGT:
7115 std::swap(LHS, RHS);
7116 case ICmpInst::ICMP_ULT: {
7117 ConstantRange LHSRange = getUnsignedRange(LHS);
7118 ConstantRange RHSRange = getUnsignedRange(RHS);
7119 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
7121 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
7125 case ICmpInst::ICMP_UGE:
7126 std::swap(LHS, RHS);
7127 case ICmpInst::ICMP_ULE: {
7128 ConstantRange LHSRange = getUnsignedRange(LHS);
7129 ConstantRange RHSRange = getUnsignedRange(RHS);
7130 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
7132 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
7136 case ICmpInst::ICMP_NE: {
7137 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
7139 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
7142 const SCEV *Diff = getMinusSCEV(LHS, RHS);
7143 if (isKnownNonZero(Diff))
7147 case ICmpInst::ICMP_EQ:
7148 // The check at the top of the function catches the case where
7149 // the values are known to be equal.
7155 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7158 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
7161 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7162 // the stack can result in exponential time complexity.
7163 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7165 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7167 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7168 // isKnownPredicate. isKnownPredicate is more powerful, but also more
7169 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7170 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
7171 // use isKnownPredicate later if needed.
7172 if (isKnownNonNegative(RHS) &&
7173 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7174 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS))
7180 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7181 /// protected by a conditional between LHS and RHS. This is used to
7182 /// to eliminate casts.
7184 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7185 ICmpInst::Predicate Pred,
7186 const SCEV *LHS, const SCEV *RHS) {
7187 // Interpret a null as meaning no loop, where there is obviously no guard
7188 // (interprocedural conditions notwithstanding).
7189 if (!L) return true;
7191 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7193 BasicBlock *Latch = L->getLoopLatch();
7197 BranchInst *LoopContinuePredicate =
7198 dyn_cast<BranchInst>(Latch->getTerminator());
7199 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7200 isImpliedCond(Pred, LHS, RHS,
7201 LoopContinuePredicate->getCondition(),
7202 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7205 // We don't want more than one activation of the following loops on the stack
7206 // -- that can lead to O(n!) time complexity.
7207 if (WalkingBEDominatingConds)
7210 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7212 // See if we can exploit a trip count to prove the predicate.
7213 const auto &BETakenInfo = getBackedgeTakenInfo(L);
7214 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7215 if (LatchBECount != getCouldNotCompute()) {
7216 // We know that Latch branches back to the loop header exactly
7217 // LatchBECount times. This means the backdege condition at Latch is
7218 // equivalent to "{0,+,1} u< LatchBECount".
7219 Type *Ty = LatchBECount->getType();
7220 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7221 const SCEV *LoopCounter =
7222 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7223 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7228 // Check conditions due to any @llvm.assume intrinsics.
7229 for (auto &AssumeVH : AC.assumptions()) {
7232 auto *CI = cast<CallInst>(AssumeVH);
7233 if (!DT.dominates(CI, Latch->getTerminator()))
7236 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7240 // If the loop is not reachable from the entry block, we risk running into an
7241 // infinite loop as we walk up into the dom tree. These loops do not matter
7242 // anyway, so we just return a conservative answer when we see them.
7243 if (!DT.isReachableFromEntry(L->getHeader()))
7246 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7247 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7249 assert(DTN && "should reach the loop header before reaching the root!");
7251 BasicBlock *BB = DTN->getBlock();
7252 BasicBlock *PBB = BB->getSinglePredecessor();
7256 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7257 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7260 Value *Condition = ContinuePredicate->getCondition();
7262 // If we have an edge `E` within the loop body that dominates the only
7263 // latch, the condition guarding `E` also guards the backedge. This
7264 // reasoning works only for loops with a single latch.
7266 BasicBlockEdge DominatingEdge(PBB, BB);
7267 if (DominatingEdge.isSingleEdge()) {
7268 // We're constructively (and conservatively) enumerating edges within the
7269 // loop body that dominate the latch. The dominator tree better agree
7271 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7273 if (isImpliedCond(Pred, LHS, RHS, Condition,
7274 BB != ContinuePredicate->getSuccessor(0)))
7282 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7283 /// by a conditional between LHS and RHS. This is used to help avoid max
7284 /// expressions in loop trip counts, and to eliminate casts.
7286 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7287 ICmpInst::Predicate Pred,
7288 const SCEV *LHS, const SCEV *RHS) {
7289 // Interpret a null as meaning no loop, where there is obviously no guard
7290 // (interprocedural conditions notwithstanding).
7291 if (!L) return false;
7293 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7295 // Starting at the loop predecessor, climb up the predecessor chain, as long
7296 // as there are predecessors that can be found that have unique successors
7297 // leading to the original header.
7298 for (std::pair<BasicBlock *, BasicBlock *>
7299 Pair(L->getLoopPredecessor(), L->getHeader());
7301 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7303 BranchInst *LoopEntryPredicate =
7304 dyn_cast<BranchInst>(Pair.first->getTerminator());
7305 if (!LoopEntryPredicate ||
7306 LoopEntryPredicate->isUnconditional())
7309 if (isImpliedCond(Pred, LHS, RHS,
7310 LoopEntryPredicate->getCondition(),
7311 LoopEntryPredicate->getSuccessor(0) != Pair.second))
7315 // Check conditions due to any @llvm.assume intrinsics.
7316 for (auto &AssumeVH : AC.assumptions()) {
7319 auto *CI = cast<CallInst>(AssumeVH);
7320 if (!DT.dominates(CI, L->getHeader()))
7323 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7330 /// RAII wrapper to prevent recursive application of isImpliedCond.
7331 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7332 /// currently evaluating isImpliedCond.
7333 struct MarkPendingLoopPredicate {
7335 DenseSet<Value*> &LoopPreds;
7338 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7339 : Cond(C), LoopPreds(LP) {
7340 Pending = !LoopPreds.insert(Cond).second;
7342 ~MarkPendingLoopPredicate() {
7344 LoopPreds.erase(Cond);
7348 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7349 /// and RHS is true whenever the given Cond value evaluates to true.
7350 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7351 const SCEV *LHS, const SCEV *RHS,
7352 Value *FoundCondValue,
7354 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7358 // Recursively handle And and Or conditions.
7359 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7360 if (BO->getOpcode() == Instruction::And) {
7362 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7363 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7364 } else if (BO->getOpcode() == Instruction::Or) {
7366 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7367 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7371 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
7372 if (!ICI) return false;
7374 // Now that we found a conditional branch that dominates the loop or controls
7375 // the loop latch. Check to see if it is the comparison we are looking for.
7376 ICmpInst::Predicate FoundPred;
7378 FoundPred = ICI->getInversePredicate();
7380 FoundPred = ICI->getPredicate();
7382 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
7383 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
7385 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
7388 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
7390 ICmpInst::Predicate FoundPred,
7391 const SCEV *FoundLHS,
7392 const SCEV *FoundRHS) {
7393 // Balance the types.
7394 if (getTypeSizeInBits(LHS->getType()) <
7395 getTypeSizeInBits(FoundLHS->getType())) {
7396 if (CmpInst::isSigned(Pred)) {
7397 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
7398 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
7400 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
7401 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
7403 } else if (getTypeSizeInBits(LHS->getType()) >
7404 getTypeSizeInBits(FoundLHS->getType())) {
7405 if (CmpInst::isSigned(FoundPred)) {
7406 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
7407 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
7409 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
7410 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
7414 // Canonicalize the query to match the way instcombine will have
7415 // canonicalized the comparison.
7416 if (SimplifyICmpOperands(Pred, LHS, RHS))
7418 return CmpInst::isTrueWhenEqual(Pred);
7419 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
7420 if (FoundLHS == FoundRHS)
7421 return CmpInst::isFalseWhenEqual(FoundPred);
7423 // Check to see if we can make the LHS or RHS match.
7424 if (LHS == FoundRHS || RHS == FoundLHS) {
7425 if (isa<SCEVConstant>(RHS)) {
7426 std::swap(FoundLHS, FoundRHS);
7427 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
7429 std::swap(LHS, RHS);
7430 Pred = ICmpInst::getSwappedPredicate(Pred);
7434 // Check whether the found predicate is the same as the desired predicate.
7435 if (FoundPred == Pred)
7436 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7438 // Check whether swapping the found predicate makes it the same as the
7439 // desired predicate.
7440 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
7441 if (isa<SCEVConstant>(RHS))
7442 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
7444 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
7445 RHS, LHS, FoundLHS, FoundRHS);
7448 // Check if we can make progress by sharpening ranges.
7449 if (FoundPred == ICmpInst::ICMP_NE &&
7450 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
7452 const SCEVConstant *C = nullptr;
7453 const SCEV *V = nullptr;
7455 if (isa<SCEVConstant>(FoundLHS)) {
7456 C = cast<SCEVConstant>(FoundLHS);
7459 C = cast<SCEVConstant>(FoundRHS);
7463 // The guarding predicate tells us that C != V. If the known range
7464 // of V is [C, t), we can sharpen the range to [C + 1, t). The
7465 // range we consider has to correspond to same signedness as the
7466 // predicate we're interested in folding.
7468 APInt Min = ICmpInst::isSigned(Pred) ?
7469 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7471 if (Min == C->getValue()->getValue()) {
7472 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7473 // This is true even if (Min + 1) wraps around -- in case of
7474 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7476 APInt SharperMin = Min + 1;
7479 case ICmpInst::ICMP_SGE:
7480 case ICmpInst::ICMP_UGE:
7481 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7483 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7484 getConstant(SharperMin)))
7487 case ICmpInst::ICMP_SGT:
7488 case ICmpInst::ICMP_UGT:
7489 // We know from the range information that (V `Pred` Min ||
7490 // V == Min). We know from the guarding condition that !(V
7491 // == Min). This gives us
7493 // V `Pred` Min || V == Min && !(V == Min)
7496 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7498 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7508 // Check whether the actual condition is beyond sufficient.
7509 if (FoundPred == ICmpInst::ICMP_EQ)
7510 if (ICmpInst::isTrueWhenEqual(Pred))
7511 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7513 if (Pred == ICmpInst::ICMP_NE)
7514 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7515 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7518 // Otherwise assume the worst.
7522 // Return true if More == (Less + C), where C is a constant.
7523 static bool IsConstDiff(ScalarEvolution &SE, const SCEV *Less, const SCEV *More,
7525 // We avoid subtracting expressions here because this function is usually
7526 // fairly deep in the call stack (i.e. is called many times).
7528 auto SplitBinaryAdd = [](const SCEV *Expr, const SCEV *&L, const SCEV *&R) {
7529 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
7530 if (!AE || AE->getNumOperands() != 2)
7533 L = AE->getOperand(0);
7534 R = AE->getOperand(1);
7538 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
7539 const auto *LAR = cast<SCEVAddRecExpr>(Less);
7540 const auto *MAR = cast<SCEVAddRecExpr>(More);
7542 if (LAR->getLoop() != MAR->getLoop())
7545 // We look at affine expressions only; not for correctness but to keep
7546 // getStepRecurrence cheap.
7547 if (!LAR->isAffine() || !MAR->isAffine())
7550 if (LAR->getStepRecurrence(SE) != MAR->getStepRecurrence(SE))
7553 Less = LAR->getStart();
7554 More = MAR->getStart();
7559 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
7560 const auto &M = cast<SCEVConstant>(More)->getValue()->getValue();
7561 const auto &L = cast<SCEVConstant>(Less)->getValue()->getValue();
7567 if (SplitBinaryAdd(Less, L, R))
7568 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7570 C = -(LC->getValue()->getValue());
7574 if (SplitBinaryAdd(More, L, R))
7575 if (const auto *LC = dyn_cast<SCEVConstant>(L))
7577 C = LC->getValue()->getValue();
7584 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
7585 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
7586 const SCEV *FoundLHS, const SCEV *FoundRHS) {
7587 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
7590 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7594 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
7595 if (!AddRecFoundLHS)
7598 // We'd like to let SCEV reason about control dependencies, so we constrain
7599 // both the inequalities to be about add recurrences on the same loop. This
7600 // way we can use isLoopEntryGuardedByCond later.
7602 const Loop *L = AddRecFoundLHS->getLoop();
7603 if (L != AddRecLHS->getLoop())
7606 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
7608 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
7611 // Informal proof for (2), assuming (1) [*]:
7613 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
7617 // FoundLHS s< FoundRHS s< INT_MIN - C
7618 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
7619 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
7620 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
7621 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
7622 // <=> FoundLHS + C s< FoundRHS + C
7624 // [*]: (1) can be proved by ruling out overflow.
7626 // [**]: This can be proved by analyzing all the four possibilities:
7627 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
7628 // (A s>= 0, B s>= 0).
7631 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
7632 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
7633 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
7634 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
7635 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
7639 if (!IsConstDiff(*this, FoundLHS, LHS, LDiff) ||
7640 !IsConstDiff(*this, FoundRHS, RHS, RDiff) ||
7647 APInt FoundRHSLimit;
7649 if (Pred == CmpInst::ICMP_ULT) {
7650 FoundRHSLimit = -RDiff;
7652 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
7653 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - RDiff;
7656 // Try to prove (1) or (2), as needed.
7657 return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
7658 getConstant(FoundRHSLimit));
7661 /// isImpliedCondOperands - Test whether the condition described by Pred,
7662 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7663 /// and FoundRHS is true.
7664 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7665 const SCEV *LHS, const SCEV *RHS,
7666 const SCEV *FoundLHS,
7667 const SCEV *FoundRHS) {
7668 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7671 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
7674 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7675 FoundLHS, FoundRHS) ||
7676 // ~x < ~y --> x > y
7677 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7678 getNotSCEV(FoundRHS),
7679 getNotSCEV(FoundLHS));
7683 /// If Expr computes ~A, return A else return nullptr
7684 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7685 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7686 if (!Add || Add->getNumOperands() != 2) return nullptr;
7688 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
7689 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
7692 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7693 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
7695 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
7696 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
7699 return AddRHS->getOperand(1);
7703 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7704 template<typename MaxExprType>
7705 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7706 const SCEV *Candidate) {
7707 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7708 if (!MaxExpr) return false;
7710 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7711 return It != MaxExpr->op_end();
7715 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7716 template<typename MaxExprType>
7717 static bool IsMinConsistingOf(ScalarEvolution &SE,
7718 const SCEV *MaybeMinExpr,
7719 const SCEV *Candidate) {
7720 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7724 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7727 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
7728 ICmpInst::Predicate Pred,
7729 const SCEV *LHS, const SCEV *RHS) {
7731 // If both sides are affine addrecs for the same loop, with equal
7732 // steps, and we know the recurrences don't wrap, then we only
7733 // need to check the predicate on the starting values.
7735 if (!ICmpInst::isRelational(Pred))
7738 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7741 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7744 if (LAR->getLoop() != RAR->getLoop())
7746 if (!LAR->isAffine() || !RAR->isAffine())
7749 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
7752 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
7753 SCEV::FlagNSW : SCEV::FlagNUW;
7754 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
7757 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
7760 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7762 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7763 ICmpInst::Predicate Pred,
7764 const SCEV *LHS, const SCEV *RHS) {
7769 case ICmpInst::ICMP_SGE:
7770 std::swap(LHS, RHS);
7772 case ICmpInst::ICMP_SLE:
7775 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7777 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7779 case ICmpInst::ICMP_UGE:
7780 std::swap(LHS, RHS);
7782 case ICmpInst::ICMP_ULE:
7785 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7787 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7790 llvm_unreachable("covered switch fell through?!");
7793 /// isImpliedCondOperandsHelper - Test whether the condition described by
7794 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7795 /// FoundLHS, and FoundRHS is true.
7797 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7798 const SCEV *LHS, const SCEV *RHS,
7799 const SCEV *FoundLHS,
7800 const SCEV *FoundRHS) {
7801 auto IsKnownPredicateFull =
7802 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7803 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7804 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
7805 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS);
7809 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7810 case ICmpInst::ICMP_EQ:
7811 case ICmpInst::ICMP_NE:
7812 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7815 case ICmpInst::ICMP_SLT:
7816 case ICmpInst::ICMP_SLE:
7817 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7818 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7821 case ICmpInst::ICMP_SGT:
7822 case ICmpInst::ICMP_SGE:
7823 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7824 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7827 case ICmpInst::ICMP_ULT:
7828 case ICmpInst::ICMP_ULE:
7829 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7830 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7833 case ICmpInst::ICMP_UGT:
7834 case ICmpInst::ICMP_UGE:
7835 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7836 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7844 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
7845 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
7846 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
7849 const SCEV *FoundLHS,
7850 const SCEV *FoundRHS) {
7851 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
7852 // The restriction on `FoundRHS` be lifted easily -- it exists only to
7853 // reduce the compile time impact of this optimization.
7856 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
7857 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
7858 !isa<SCEVConstant>(AddLHS->getOperand(0)))
7861 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
7863 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
7864 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
7865 ConstantRange FoundLHSRange =
7866 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
7868 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
7871 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
7872 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
7874 // We can also compute the range of values for `LHS` that satisfy the
7875 // consequent, "`LHS` `Pred` `RHS`":
7876 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
7877 ConstantRange SatisfyingLHSRange =
7878 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
7880 // The antecedent implies the consequent if every value of `LHS` that
7881 // satisfies the antecedent also satisfies the consequent.
7882 return SatisfyingLHSRange.contains(LHSRange);
7885 // Verify if an linear IV with positive stride can overflow when in a
7886 // less-than comparison, knowing the invariant term of the comparison, the
7887 // stride and the knowledge of NSW/NUW flags on the recurrence.
7888 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7889 bool IsSigned, bool NoWrap) {
7890 if (NoWrap) return false;
7892 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7893 const SCEV *One = getOne(Stride->getType());
7896 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7897 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7898 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7901 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7902 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7905 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7906 APInt MaxValue = APInt::getMaxValue(BitWidth);
7907 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7910 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7911 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7914 // Verify if an linear IV with negative stride can overflow when in a
7915 // greater-than comparison, knowing the invariant term of the comparison,
7916 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7917 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7918 bool IsSigned, bool NoWrap) {
7919 if (NoWrap) return false;
7921 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7922 const SCEV *One = getOne(Stride->getType());
7925 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7926 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7927 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7930 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7931 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7934 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7935 APInt MinValue = APInt::getMinValue(BitWidth);
7936 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7939 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7940 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7943 // Compute the backedge taken count knowing the interval difference, the
7944 // stride and presence of the equality in the comparison.
7945 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7947 const SCEV *One = getOne(Step->getType());
7948 Delta = Equality ? getAddExpr(Delta, Step)
7949 : getAddExpr(Delta, getMinusSCEV(Step, One));
7950 return getUDivExpr(Delta, Step);
7953 /// HowManyLessThans - Return the number of times a backedge containing the
7954 /// specified less-than comparison will execute. If not computable, return
7955 /// CouldNotCompute.
7957 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7958 /// the branch (loops exits only if condition is true). In this case, we can use
7959 /// NoWrapFlags to skip overflow checks.
7960 ScalarEvolution::ExitLimit
7961 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7962 const Loop *L, bool IsSigned,
7963 bool ControlsExit) {
7964 // We handle only IV < Invariant
7965 if (!isLoopInvariant(RHS, L))
7966 return getCouldNotCompute();
7968 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7970 // Avoid weird loops
7971 if (!IV || IV->getLoop() != L || !IV->isAffine())
7972 return getCouldNotCompute();
7974 bool NoWrap = ControlsExit &&
7975 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7977 const SCEV *Stride = IV->getStepRecurrence(*this);
7979 // Avoid negative or zero stride values
7980 if (!isKnownPositive(Stride))
7981 return getCouldNotCompute();
7983 // Avoid proven overflow cases: this will ensure that the backedge taken count
7984 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7985 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7986 // behaviors like the case of C language.
7987 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7988 return getCouldNotCompute();
7990 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7991 : ICmpInst::ICMP_ULT;
7992 const SCEV *Start = IV->getStart();
7993 const SCEV *End = RHS;
7994 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7995 const SCEV *Diff = getMinusSCEV(RHS, Start);
7996 // If we have NoWrap set, then we can assume that the increment won't
7997 // overflow, in which case if RHS - Start is a constant, we don't need to
7998 // do a max operation since we can just figure it out statically
7999 if (NoWrap && isa<SCEVConstant>(Diff)) {
8000 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
8004 End = IsSigned ? getSMaxExpr(RHS, Start)
8005 : getUMaxExpr(RHS, Start);
8008 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
8010 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
8011 : getUnsignedRange(Start).getUnsignedMin();
8013 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8014 : getUnsignedRange(Stride).getUnsignedMin();
8016 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8017 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
8018 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
8020 // Although End can be a MAX expression we estimate MaxEnd considering only
8021 // the case End = RHS. This is safe because in the other case (End - Start)
8022 // is zero, leading to a zero maximum backedge taken count.
8024 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8025 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8027 const SCEV *MaxBECount;
8028 if (isa<SCEVConstant>(BECount))
8029 MaxBECount = BECount;
8031 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8032 getConstant(MinStride), false);
8034 if (isa<SCEVCouldNotCompute>(MaxBECount))
8035 MaxBECount = BECount;
8037 return ExitLimit(BECount, MaxBECount);
8040 ScalarEvolution::ExitLimit
8041 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8042 const Loop *L, bool IsSigned,
8043 bool ControlsExit) {
8044 // We handle only IV > Invariant
8045 if (!isLoopInvariant(RHS, L))
8046 return getCouldNotCompute();
8048 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8050 // Avoid weird loops
8051 if (!IV || IV->getLoop() != L || !IV->isAffine())
8052 return getCouldNotCompute();
8054 bool NoWrap = ControlsExit &&
8055 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8057 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8059 // Avoid negative or zero stride values
8060 if (!isKnownPositive(Stride))
8061 return getCouldNotCompute();
8063 // Avoid proven overflow cases: this will ensure that the backedge taken count
8064 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8065 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8066 // behaviors like the case of C language.
8067 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8068 return getCouldNotCompute();
8070 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8071 : ICmpInst::ICMP_UGT;
8073 const SCEV *Start = IV->getStart();
8074 const SCEV *End = RHS;
8075 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
8076 const SCEV *Diff = getMinusSCEV(RHS, Start);
8077 // If we have NoWrap set, then we can assume that the increment won't
8078 // overflow, in which case if RHS - Start is a constant, we don't need to
8079 // do a max operation since we can just figure it out statically
8080 if (NoWrap && isa<SCEVConstant>(Diff)) {
8081 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
8082 if (!D.isNegative())
8085 End = IsSigned ? getSMinExpr(RHS, Start)
8086 : getUMinExpr(RHS, Start);
8089 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8091 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8092 : getUnsignedRange(Start).getUnsignedMax();
8094 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8095 : getUnsignedRange(Stride).getUnsignedMin();
8097 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8098 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8099 : APInt::getMinValue(BitWidth) + (MinStride - 1);
8101 // Although End can be a MIN expression we estimate MinEnd considering only
8102 // the case End = RHS. This is safe because in the other case (Start - End)
8103 // is zero, leading to a zero maximum backedge taken count.
8105 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8106 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8109 const SCEV *MaxBECount = getCouldNotCompute();
8110 if (isa<SCEVConstant>(BECount))
8111 MaxBECount = BECount;
8113 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8114 getConstant(MinStride), false);
8116 if (isa<SCEVCouldNotCompute>(MaxBECount))
8117 MaxBECount = BECount;
8119 return ExitLimit(BECount, MaxBECount);
8122 /// getNumIterationsInRange - Return the number of iterations of this loop that
8123 /// produce values in the specified constant range. Another way of looking at
8124 /// this is that it returns the first iteration number where the value is not in
8125 /// the condition, thus computing the exit count. If the iteration count can't
8126 /// be computed, an instance of SCEVCouldNotCompute is returned.
8127 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
8128 ScalarEvolution &SE) const {
8129 if (Range.isFullSet()) // Infinite loop.
8130 return SE.getCouldNotCompute();
8132 // If the start is a non-zero constant, shift the range to simplify things.
8133 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8134 if (!SC->getValue()->isZero()) {
8135 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8136 Operands[0] = SE.getZero(SC->getType());
8137 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8138 getNoWrapFlags(FlagNW));
8139 if (const SCEVAddRecExpr *ShiftedAddRec =
8140 dyn_cast<SCEVAddRecExpr>(Shifted))
8141 return ShiftedAddRec->getNumIterationsInRange(
8142 Range.subtract(SC->getValue()->getValue()), SE);
8143 // This is strange and shouldn't happen.
8144 return SE.getCouldNotCompute();
8147 // The only time we can solve this is when we have all constant indices.
8148 // Otherwise, we cannot determine the overflow conditions.
8149 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
8150 if (!isa<SCEVConstant>(getOperand(i)))
8151 return SE.getCouldNotCompute();
8154 // Okay at this point we know that all elements of the chrec are constants and
8155 // that the start element is zero.
8157 // First check to see if the range contains zero. If not, the first
8159 unsigned BitWidth = SE.getTypeSizeInBits(getType());
8160 if (!Range.contains(APInt(BitWidth, 0)))
8161 return SE.getZero(getType());
8164 // If this is an affine expression then we have this situation:
8165 // Solve {0,+,A} in Range === Ax in Range
8167 // We know that zero is in the range. If A is positive then we know that
8168 // the upper value of the range must be the first possible exit value.
8169 // If A is negative then the lower of the range is the last possible loop
8170 // value. Also note that we already checked for a full range.
8171 APInt One(BitWidth,1);
8172 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
8173 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8175 // The exit value should be (End+A)/A.
8176 APInt ExitVal = (End + A).udiv(A);
8177 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8179 // Evaluate at the exit value. If we really did fall out of the valid
8180 // range, then we computed our trip count, otherwise wrap around or other
8181 // things must have happened.
8182 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8183 if (Range.contains(Val->getValue()))
8184 return SE.getCouldNotCompute(); // Something strange happened
8186 // Ensure that the previous value is in the range. This is a sanity check.
8187 assert(Range.contains(
8188 EvaluateConstantChrecAtConstant(this,
8189 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8190 "Linear scev computation is off in a bad way!");
8191 return SE.getConstant(ExitValue);
8192 } else if (isQuadratic()) {
8193 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8194 // quadratic equation to solve it. To do this, we must frame our problem in
8195 // terms of figuring out when zero is crossed, instead of when
8196 // Range.getUpper() is crossed.
8197 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8198 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8199 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
8200 // getNoWrapFlags(FlagNW)
8203 // Next, solve the constructed addrec
8204 std::pair<const SCEV *,const SCEV *> Roots =
8205 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
8206 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
8207 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
8209 // Pick the smallest positive root value.
8210 if (ConstantInt *CB =
8211 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
8212 R1->getValue(), R2->getValue()))) {
8213 if (!CB->getZExtValue())
8214 std::swap(R1, R2); // R1 is the minimum root now.
8216 // Make sure the root is not off by one. The returned iteration should
8217 // not be in the range, but the previous one should be. When solving
8218 // for "X*X < 5", for example, we should not return a root of 2.
8219 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
8222 if (Range.contains(R1Val->getValue())) {
8223 // The next iteration must be out of the range...
8224 ConstantInt *NextVal =
8225 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
8227 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8228 if (!Range.contains(R1Val->getValue()))
8229 return SE.getConstant(NextVal);
8230 return SE.getCouldNotCompute(); // Something strange happened
8233 // If R1 was not in the range, then it is a good return value. Make
8234 // sure that R1-1 WAS in the range though, just in case.
8235 ConstantInt *NextVal =
8236 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
8237 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8238 if (Range.contains(R1Val->getValue()))
8240 return SE.getCouldNotCompute(); // Something strange happened
8245 return SE.getCouldNotCompute();
8251 FindUndefs() : Found(false) {}
8253 bool follow(const SCEV *S) {
8254 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
8255 if (isa<UndefValue>(C->getValue()))
8257 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
8258 if (isa<UndefValue>(C->getValue()))
8262 // Keep looking if we haven't found it yet.
8265 bool isDone() const {
8266 // Stop recursion if we have found an undef.
8272 // Return true when S contains at least an undef value.
8274 containsUndefs(const SCEV *S) {
8276 SCEVTraversal<FindUndefs> ST(F);
8283 // Collect all steps of SCEV expressions.
8284 struct SCEVCollectStrides {
8285 ScalarEvolution &SE;
8286 SmallVectorImpl<const SCEV *> &Strides;
8288 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
8289 : SE(SE), Strides(S) {}
8291 bool follow(const SCEV *S) {
8292 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
8293 Strides.push_back(AR->getStepRecurrence(SE));
8296 bool isDone() const { return false; }
8299 // Collect all SCEVUnknown and SCEVMulExpr expressions.
8300 struct SCEVCollectTerms {
8301 SmallVectorImpl<const SCEV *> &Terms;
8303 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
8306 bool follow(const SCEV *S) {
8307 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
8308 if (!containsUndefs(S))
8311 // Stop recursion: once we collected a term, do not walk its operands.
8318 bool isDone() const { return false; }
8322 /// Find parametric terms in this SCEVAddRecExpr.
8323 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
8324 SmallVectorImpl<const SCEV *> &Terms) {
8325 SmallVector<const SCEV *, 4> Strides;
8326 SCEVCollectStrides StrideCollector(*this, Strides);
8327 visitAll(Expr, StrideCollector);
8330 dbgs() << "Strides:\n";
8331 for (const SCEV *S : Strides)
8332 dbgs() << *S << "\n";
8335 for (const SCEV *S : Strides) {
8336 SCEVCollectTerms TermCollector(Terms);
8337 visitAll(S, TermCollector);
8341 dbgs() << "Terms:\n";
8342 for (const SCEV *T : Terms)
8343 dbgs() << *T << "\n";
8347 static bool findArrayDimensionsRec(ScalarEvolution &SE,
8348 SmallVectorImpl<const SCEV *> &Terms,
8349 SmallVectorImpl<const SCEV *> &Sizes) {
8350 int Last = Terms.size() - 1;
8351 const SCEV *Step = Terms[Last];
8353 // End of recursion.
8355 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
8356 SmallVector<const SCEV *, 2> Qs;
8357 for (const SCEV *Op : M->operands())
8358 if (!isa<SCEVConstant>(Op))
8361 Step = SE.getMulExpr(Qs);
8364 Sizes.push_back(Step);
8368 for (const SCEV *&Term : Terms) {
8369 // Normalize the terms before the next call to findArrayDimensionsRec.
8371 SCEVDivision::divide(SE, Term, Step, &Q, &R);
8373 // Bail out when GCD does not evenly divide one of the terms.
8380 // Remove all SCEVConstants.
8381 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
8382 return isa<SCEVConstant>(E);
8386 if (Terms.size() > 0)
8387 if (!findArrayDimensionsRec(SE, Terms, Sizes))
8390 Sizes.push_back(Step);
8395 struct FindParameter {
8396 bool FoundParameter;
8397 FindParameter() : FoundParameter(false) {}
8399 bool follow(const SCEV *S) {
8400 if (isa<SCEVUnknown>(S)) {
8401 FoundParameter = true;
8402 // Stop recursion: we found a parameter.
8408 bool isDone() const {
8409 // Stop recursion if we have found a parameter.
8410 return FoundParameter;
8415 // Returns true when S contains at least a SCEVUnknown parameter.
8417 containsParameters(const SCEV *S) {
8419 SCEVTraversal<FindParameter> ST(F);
8422 return F.FoundParameter;
8425 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
8427 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
8428 for (const SCEV *T : Terms)
8429 if (containsParameters(T))
8434 // Return the number of product terms in S.
8435 static inline int numberOfTerms(const SCEV *S) {
8436 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
8437 return Expr->getNumOperands();
8441 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
8442 if (isa<SCEVConstant>(T))
8445 if (isa<SCEVUnknown>(T))
8448 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
8449 SmallVector<const SCEV *, 2> Factors;
8450 for (const SCEV *Op : M->operands())
8451 if (!isa<SCEVConstant>(Op))
8452 Factors.push_back(Op);
8454 return SE.getMulExpr(Factors);
8460 /// Return the size of an element read or written by Inst.
8461 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
8463 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
8464 Ty = Store->getValueOperand()->getType();
8465 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
8466 Ty = Load->getType();
8470 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
8471 return getSizeOfExpr(ETy, Ty);
8474 /// Second step of delinearization: compute the array dimensions Sizes from the
8475 /// set of Terms extracted from the memory access function of this SCEVAddRec.
8476 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
8477 SmallVectorImpl<const SCEV *> &Sizes,
8478 const SCEV *ElementSize) const {
8480 if (Terms.size() < 1 || !ElementSize)
8483 // Early return when Terms do not contain parameters: we do not delinearize
8484 // non parametric SCEVs.
8485 if (!containsParameters(Terms))
8489 dbgs() << "Terms:\n";
8490 for (const SCEV *T : Terms)
8491 dbgs() << *T << "\n";
8494 // Remove duplicates.
8495 std::sort(Terms.begin(), Terms.end());
8496 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
8498 // Put larger terms first.
8499 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
8500 return numberOfTerms(LHS) > numberOfTerms(RHS);
8503 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8505 // Divide all terms by the element size.
8506 for (const SCEV *&Term : Terms) {
8508 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
8512 SmallVector<const SCEV *, 4> NewTerms;
8514 // Remove constant factors.
8515 for (const SCEV *T : Terms)
8516 if (const SCEV *NewT = removeConstantFactors(SE, T))
8517 NewTerms.push_back(NewT);
8520 dbgs() << "Terms after sorting:\n";
8521 for (const SCEV *T : NewTerms)
8522 dbgs() << *T << "\n";
8525 if (NewTerms.empty() ||
8526 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
8531 // The last element to be pushed into Sizes is the size of an element.
8532 Sizes.push_back(ElementSize);
8535 dbgs() << "Sizes:\n";
8536 for (const SCEV *S : Sizes)
8537 dbgs() << *S << "\n";
8541 /// Third step of delinearization: compute the access functions for the
8542 /// Subscripts based on the dimensions in Sizes.
8543 void ScalarEvolution::computeAccessFunctions(
8544 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
8545 SmallVectorImpl<const SCEV *> &Sizes) {
8547 // Early exit in case this SCEV is not an affine multivariate function.
8551 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
8552 if (!AR->isAffine())
8555 const SCEV *Res = Expr;
8556 int Last = Sizes.size() - 1;
8557 for (int i = Last; i >= 0; i--) {
8559 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
8562 dbgs() << "Res: " << *Res << "\n";
8563 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
8564 dbgs() << "Res divided by Sizes[i]:\n";
8565 dbgs() << "Quotient: " << *Q << "\n";
8566 dbgs() << "Remainder: " << *R << "\n";
8571 // Do not record the last subscript corresponding to the size of elements in
8575 // Bail out if the remainder is too complex.
8576 if (isa<SCEVAddRecExpr>(R)) {
8585 // Record the access function for the current subscript.
8586 Subscripts.push_back(R);
8589 // Also push in last position the remainder of the last division: it will be
8590 // the access function of the innermost dimension.
8591 Subscripts.push_back(Res);
8593 std::reverse(Subscripts.begin(), Subscripts.end());
8596 dbgs() << "Subscripts:\n";
8597 for (const SCEV *S : Subscripts)
8598 dbgs() << *S << "\n";
8602 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
8603 /// sizes of an array access. Returns the remainder of the delinearization that
8604 /// is the offset start of the array. The SCEV->delinearize algorithm computes
8605 /// the multiples of SCEV coefficients: that is a pattern matching of sub
8606 /// expressions in the stride and base of a SCEV corresponding to the
8607 /// computation of a GCD (greatest common divisor) of base and stride. When
8608 /// SCEV->delinearize fails, it returns the SCEV unchanged.
8610 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
8612 /// void foo(long n, long m, long o, double A[n][m][o]) {
8614 /// for (long i = 0; i < n; i++)
8615 /// for (long j = 0; j < m; j++)
8616 /// for (long k = 0; k < o; k++)
8617 /// A[i][j][k] = 1.0;
8620 /// the delinearization input is the following AddRec SCEV:
8622 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
8624 /// From this SCEV, we are able to say that the base offset of the access is %A
8625 /// because it appears as an offset that does not divide any of the strides in
8628 /// CHECK: Base offset: %A
8630 /// and then SCEV->delinearize determines the size of some of the dimensions of
8631 /// the array as these are the multiples by which the strides are happening:
8633 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
8635 /// Note that the outermost dimension remains of UnknownSize because there are
8636 /// no strides that would help identifying the size of the last dimension: when
8637 /// the array has been statically allocated, one could compute the size of that
8638 /// dimension by dividing the overall size of the array by the size of the known
8639 /// dimensions: %m * %o * 8.
8641 /// Finally delinearize provides the access functions for the array reference
8642 /// that does correspond to A[i][j][k] of the above C testcase:
8644 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
8646 /// The testcases are checking the output of a function pass:
8647 /// DelinearizationPass that walks through all loads and stores of a function
8648 /// asking for the SCEV of the memory access with respect to all enclosing
8649 /// loops, calling SCEV->delinearize on that and printing the results.
8651 void ScalarEvolution::delinearize(const SCEV *Expr,
8652 SmallVectorImpl<const SCEV *> &Subscripts,
8653 SmallVectorImpl<const SCEV *> &Sizes,
8654 const SCEV *ElementSize) {
8655 // First step: collect parametric terms.
8656 SmallVector<const SCEV *, 4> Terms;
8657 collectParametricTerms(Expr, Terms);
8662 // Second step: find subscript sizes.
8663 findArrayDimensions(Terms, Sizes, ElementSize);
8668 // Third step: compute the access functions for each subscript.
8669 computeAccessFunctions(Expr, Subscripts, Sizes);
8671 if (Subscripts.empty())
8675 dbgs() << "succeeded to delinearize " << *Expr << "\n";
8676 dbgs() << "ArrayDecl[UnknownSize]";
8677 for (const SCEV *S : Sizes)
8678 dbgs() << "[" << *S << "]";
8680 dbgs() << "\nArrayRef";
8681 for (const SCEV *S : Subscripts)
8682 dbgs() << "[" << *S << "]";
8687 //===----------------------------------------------------------------------===//
8688 // SCEVCallbackVH Class Implementation
8689 //===----------------------------------------------------------------------===//
8691 void ScalarEvolution::SCEVCallbackVH::deleted() {
8692 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8693 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
8694 SE->ConstantEvolutionLoopExitValue.erase(PN);
8695 SE->ValueExprMap.erase(getValPtr());
8696 // this now dangles!
8699 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
8700 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8702 // Forget all the expressions associated with users of the old value,
8703 // so that future queries will recompute the expressions using the new
8705 Value *Old = getValPtr();
8706 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
8707 SmallPtrSet<User *, 8> Visited;
8708 while (!Worklist.empty()) {
8709 User *U = Worklist.pop_back_val();
8710 // Deleting the Old value will cause this to dangle. Postpone
8711 // that until everything else is done.
8714 if (!Visited.insert(U).second)
8716 if (PHINode *PN = dyn_cast<PHINode>(U))
8717 SE->ConstantEvolutionLoopExitValue.erase(PN);
8718 SE->ValueExprMap.erase(U);
8719 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
8721 // Delete the Old value.
8722 if (PHINode *PN = dyn_cast<PHINode>(Old))
8723 SE->ConstantEvolutionLoopExitValue.erase(PN);
8724 SE->ValueExprMap.erase(Old);
8725 // this now dangles!
8728 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
8729 : CallbackVH(V), SE(se) {}
8731 //===----------------------------------------------------------------------===//
8732 // ScalarEvolution Class Implementation
8733 //===----------------------------------------------------------------------===//
8735 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
8736 AssumptionCache &AC, DominatorTree &DT,
8738 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
8739 CouldNotCompute(new SCEVCouldNotCompute()),
8740 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
8741 ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
8742 FirstUnknown(nullptr) {}
8744 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
8745 : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
8746 CouldNotCompute(std::move(Arg.CouldNotCompute)),
8747 ValueExprMap(std::move(Arg.ValueExprMap)),
8748 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
8749 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
8750 ConstantEvolutionLoopExitValue(
8751 std::move(Arg.ConstantEvolutionLoopExitValue)),
8752 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
8753 LoopDispositions(std::move(Arg.LoopDispositions)),
8754 BlockDispositions(std::move(Arg.BlockDispositions)),
8755 UnsignedRanges(std::move(Arg.UnsignedRanges)),
8756 SignedRanges(std::move(Arg.SignedRanges)),
8757 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
8758 SCEVAllocator(std::move(Arg.SCEVAllocator)),
8759 FirstUnknown(Arg.FirstUnknown) {
8760 Arg.FirstUnknown = nullptr;
8763 ScalarEvolution::~ScalarEvolution() {
8764 // Iterate through all the SCEVUnknown instances and call their
8765 // destructors, so that they release their references to their values.
8766 for (SCEVUnknown *U = FirstUnknown; U;) {
8767 SCEVUnknown *Tmp = U;
8769 Tmp->~SCEVUnknown();
8771 FirstUnknown = nullptr;
8773 ValueExprMap.clear();
8775 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
8776 // that a loop had multiple computable exits.
8777 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8778 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
8783 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
8784 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
8785 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
8788 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8789 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8792 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8794 // Print all inner loops first
8795 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8796 PrintLoopInfo(OS, SE, *I);
8799 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8802 SmallVector<BasicBlock *, 8> ExitBlocks;
8803 L->getExitBlocks(ExitBlocks);
8804 if (ExitBlocks.size() != 1)
8805 OS << "<multiple exits> ";
8807 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8808 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8810 OS << "Unpredictable backedge-taken count. ";
8815 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8818 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8819 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8821 OS << "Unpredictable max backedge-taken count. ";
8827 void ScalarEvolution::print(raw_ostream &OS) const {
8828 // ScalarEvolution's implementation of the print method is to print
8829 // out SCEV values of all instructions that are interesting. Doing
8830 // this potentially causes it to create new SCEV objects though,
8831 // which technically conflicts with the const qualifier. This isn't
8832 // observable from outside the class though, so casting away the
8833 // const isn't dangerous.
8834 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8836 OS << "Classifying expressions for: ";
8837 F.printAsOperand(OS, /*PrintType=*/false);
8839 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
8840 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
8843 const SCEV *SV = SE.getSCEV(&*I);
8845 if (!isa<SCEVCouldNotCompute>(SV)) {
8847 SE.getUnsignedRange(SV).print(OS);
8849 SE.getSignedRange(SV).print(OS);
8852 const Loop *L = LI.getLoopFor((*I).getParent());
8854 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8858 if (!isa<SCEVCouldNotCompute>(AtUse)) {
8860 SE.getUnsignedRange(AtUse).print(OS);
8862 SE.getSignedRange(AtUse).print(OS);
8867 OS << "\t\t" "Exits: ";
8868 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8869 if (!SE.isLoopInvariant(ExitValue, L)) {
8870 OS << "<<Unknown>>";
8879 OS << "Determining loop execution counts for: ";
8880 F.printAsOperand(OS, /*PrintType=*/false);
8882 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
8883 PrintLoopInfo(OS, &SE, *I);
8886 ScalarEvolution::LoopDisposition
8887 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8888 auto &Values = LoopDispositions[S];
8889 for (auto &V : Values) {
8890 if (V.getPointer() == L)
8893 Values.emplace_back(L, LoopVariant);
8894 LoopDisposition D = computeLoopDisposition(S, L);
8895 auto &Values2 = LoopDispositions[S];
8896 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8897 if (V.getPointer() == L) {
8905 ScalarEvolution::LoopDisposition
8906 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8907 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8909 return LoopInvariant;
8913 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8914 case scAddRecExpr: {
8915 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8917 // If L is the addrec's loop, it's computable.
8918 if (AR->getLoop() == L)
8919 return LoopComputable;
8921 // Add recurrences are never invariant in the function-body (null loop).
8925 // This recurrence is variant w.r.t. L if L contains AR's loop.
8926 if (L->contains(AR->getLoop()))
8929 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8930 if (AR->getLoop()->contains(L))
8931 return LoopInvariant;
8933 // This recurrence is variant w.r.t. L if any of its operands
8935 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8937 if (!isLoopInvariant(*I, L))
8940 // Otherwise it's loop-invariant.
8941 return LoopInvariant;
8947 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8948 bool HasVarying = false;
8949 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8951 LoopDisposition D = getLoopDisposition(*I, L);
8952 if (D == LoopVariant)
8954 if (D == LoopComputable)
8957 return HasVarying ? LoopComputable : LoopInvariant;
8960 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8961 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8962 if (LD == LoopVariant)
8964 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8965 if (RD == LoopVariant)
8967 return (LD == LoopInvariant && RD == LoopInvariant) ?
8968 LoopInvariant : LoopComputable;
8971 // All non-instruction values are loop invariant. All instructions are loop
8972 // invariant if they are not contained in the specified loop.
8973 // Instructions are never considered invariant in the function body
8974 // (null loop) because they are defined within the "loop".
8975 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8976 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8977 return LoopInvariant;
8978 case scCouldNotCompute:
8979 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8981 llvm_unreachable("Unknown SCEV kind!");
8984 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8985 return getLoopDisposition(S, L) == LoopInvariant;
8988 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8989 return getLoopDisposition(S, L) == LoopComputable;
8992 ScalarEvolution::BlockDisposition
8993 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8994 auto &Values = BlockDispositions[S];
8995 for (auto &V : Values) {
8996 if (V.getPointer() == BB)
8999 Values.emplace_back(BB, DoesNotDominateBlock);
9000 BlockDisposition D = computeBlockDisposition(S, BB);
9001 auto &Values2 = BlockDispositions[S];
9002 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9003 if (V.getPointer() == BB) {
9011 ScalarEvolution::BlockDisposition
9012 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9013 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9015 return ProperlyDominatesBlock;
9019 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
9020 case scAddRecExpr: {
9021 // This uses a "dominates" query instead of "properly dominates" query
9022 // to test for proper dominance too, because the instruction which
9023 // produces the addrec's value is a PHI, and a PHI effectively properly
9024 // dominates its entire containing block.
9025 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9026 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9027 return DoesNotDominateBlock;
9029 // FALL THROUGH into SCEVNAryExpr handling.
9034 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9036 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
9038 BlockDisposition D = getBlockDisposition(*I, BB);
9039 if (D == DoesNotDominateBlock)
9040 return DoesNotDominateBlock;
9041 if (D == DominatesBlock)
9044 return Proper ? ProperlyDominatesBlock : DominatesBlock;
9047 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9048 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9049 BlockDisposition LD = getBlockDisposition(LHS, BB);
9050 if (LD == DoesNotDominateBlock)
9051 return DoesNotDominateBlock;
9052 BlockDisposition RD = getBlockDisposition(RHS, BB);
9053 if (RD == DoesNotDominateBlock)
9054 return DoesNotDominateBlock;
9055 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9056 ProperlyDominatesBlock : DominatesBlock;
9059 if (Instruction *I =
9060 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9061 if (I->getParent() == BB)
9062 return DominatesBlock;
9063 if (DT.properlyDominates(I->getParent(), BB))
9064 return ProperlyDominatesBlock;
9065 return DoesNotDominateBlock;
9067 return ProperlyDominatesBlock;
9068 case scCouldNotCompute:
9069 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9071 llvm_unreachable("Unknown SCEV kind!");
9074 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9075 return getBlockDisposition(S, BB) >= DominatesBlock;
9078 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9079 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9083 // Search for a SCEV expression node within an expression tree.
9084 // Implements SCEVTraversal::Visitor.
9089 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
9091 bool follow(const SCEV *S) {
9092 IsFound |= (S == Node);
9095 bool isDone() const { return IsFound; }
9099 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9100 SCEVSearch Search(Op);
9101 visitAll(S, Search);
9102 return Search.IsFound;
9105 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9106 ValuesAtScopes.erase(S);
9107 LoopDispositions.erase(S);
9108 BlockDispositions.erase(S);
9109 UnsignedRanges.erase(S);
9110 SignedRanges.erase(S);
9112 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
9113 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
9114 BackedgeTakenInfo &BEInfo = I->second;
9115 if (BEInfo.hasOperand(S, this)) {
9117 BackedgeTakenCounts.erase(I++);
9124 typedef DenseMap<const Loop *, std::string> VerifyMap;
9126 /// replaceSubString - Replaces all occurrences of From in Str with To.
9127 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9129 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9130 Str.replace(Pos, From.size(), To.data(), To.size());
9135 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9137 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9138 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
9139 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
9141 std::string &S = Map[L];
9143 raw_string_ostream OS(S);
9144 SE.getBackedgeTakenCount(L)->print(OS);
9146 // false and 0 are semantically equivalent. This can happen in dead loops.
9147 replaceSubString(OS.str(), "false", "0");
9148 // Remove wrap flags, their use in SCEV is highly fragile.
9149 // FIXME: Remove this when SCEV gets smarter about them.
9150 replaceSubString(OS.str(), "<nw>", "");
9151 replaceSubString(OS.str(), "<nsw>", "");
9152 replaceSubString(OS.str(), "<nuw>", "");
9157 void ScalarEvolution::verify() const {
9158 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9160 // Gather stringified backedge taken counts for all loops using SCEV's caches.
9161 // FIXME: It would be much better to store actual values instead of strings,
9162 // but SCEV pointers will change if we drop the caches.
9163 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9164 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9165 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9167 // Gather stringified backedge taken counts for all loops using a fresh
9168 // ScalarEvolution object.
9169 ScalarEvolution SE2(F, TLI, AC, DT, LI);
9170 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9171 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9173 // Now compare whether they're the same with and without caches. This allows
9174 // verifying that no pass changed the cache.
9175 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
9176 "New loops suddenly appeared!");
9178 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
9179 OldE = BackedgeDumpsOld.end(),
9180 NewI = BackedgeDumpsNew.begin();
9181 OldI != OldE; ++OldI, ++NewI) {
9182 assert(OldI->first == NewI->first && "Loop order changed!");
9184 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
9186 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
9187 // means that a pass is buggy or SCEV has to learn a new pattern but is
9188 // usually not harmful.
9189 if (OldI->second != NewI->second &&
9190 OldI->second.find("undef") == std::string::npos &&
9191 NewI->second.find("undef") == std::string::npos &&
9192 OldI->second != "***COULDNOTCOMPUTE***" &&
9193 NewI->second != "***COULDNOTCOMPUTE***") {
9194 dbgs() << "SCEVValidator: SCEV for loop '"
9195 << OldI->first->getHeader()->getName()
9196 << "' changed from '" << OldI->second
9197 << "' to '" << NewI->second << "'!\n";
9202 // TODO: Verify more things.
9205 char ScalarEvolutionAnalysis::PassID;
9207 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
9208 AnalysisManager<Function> *AM) {
9209 return ScalarEvolution(F, AM->getResult<TargetLibraryAnalysis>(F),
9210 AM->getResult<AssumptionAnalysis>(F),
9211 AM->getResult<DominatorTreeAnalysis>(F),
9212 AM->getResult<LoopAnalysis>(F));
9216 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> *AM) {
9217 AM->getResult<ScalarEvolutionAnalysis>(F).print(OS);
9218 return PreservedAnalyses::all();
9221 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
9222 "Scalar Evolution Analysis", false, true)
9223 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
9224 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
9225 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
9226 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
9227 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
9228 "Scalar Evolution Analysis", false, true)
9229 char ScalarEvolutionWrapperPass::ID = 0;
9231 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
9232 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
9235 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
9236 SE.reset(new ScalarEvolution(
9237 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
9238 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
9239 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
9240 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
9244 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
9246 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
9250 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
9257 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
9258 AU.setPreservesAll();
9259 AU.addRequiredTransitive<AssumptionCacheTracker>();
9260 AU.addRequiredTransitive<LoopInfoWrapperPass>();
9261 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
9262 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();