1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
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/STLExtras.h"
63 #include "llvm/ADT/SmallPtrSet.h"
64 #include "llvm/ADT/Statistic.h"
65 #include "llvm/Analysis/ConstantFolding.h"
66 #include "llvm/Analysis/InstructionSimplify.h"
67 #include "llvm/Analysis/LoopInfo.h"
68 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
69 #include "llvm/Analysis/ValueTracking.h"
70 #include "llvm/IR/ConstantRange.h"
71 #include "llvm/IR/Constants.h"
72 #include "llvm/IR/DataLayout.h"
73 #include "llvm/IR/DerivedTypes.h"
74 #include "llvm/IR/Dominators.h"
75 #include "llvm/IR/GetElementPtrTypeIterator.h"
76 #include "llvm/IR/GlobalAlias.h"
77 #include "llvm/IR/GlobalVariable.h"
78 #include "llvm/IR/InstIterator.h"
79 #include "llvm/IR/Instructions.h"
80 #include "llvm/IR/LLVMContext.h"
81 #include "llvm/IR/Operator.h"
82 #include "llvm/Support/CommandLine.h"
83 #include "llvm/Support/Debug.h"
84 #include "llvm/Support/ErrorHandling.h"
85 #include "llvm/Support/MathExtras.h"
86 #include "llvm/Support/raw_ostream.h"
87 #include "llvm/Target/TargetLibraryInfo.h"
91 #define DEBUG_TYPE "scalar-evolution"
93 STATISTIC(NumArrayLenItCounts,
94 "Number of trip counts computed with array length");
95 STATISTIC(NumTripCountsComputed,
96 "Number of loops with predictable loop counts");
97 STATISTIC(NumTripCountsNotComputed,
98 "Number of loops without predictable loop counts");
99 STATISTIC(NumBruteForceTripCountsComputed,
100 "Number of loops with trip counts computed by force");
102 static cl::opt<unsigned>
103 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
104 cl::desc("Maximum number of iterations SCEV will "
105 "symbolically execute a constant "
109 // FIXME: Enable this with XDEBUG when the test suite is clean.
111 VerifySCEV("verify-scev",
112 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
114 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
115 "Scalar Evolution Analysis", false, true)
116 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
117 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
118 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
119 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
120 "Scalar Evolution Analysis", false, true)
121 char ScalarEvolution::ID = 0;
123 //===----------------------------------------------------------------------===//
124 // SCEV class definitions
125 //===----------------------------------------------------------------------===//
127 //===----------------------------------------------------------------------===//
128 // Implementation of the SCEV class.
131 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
132 void SCEV::dump() const {
138 void SCEV::print(raw_ostream &OS) const {
139 switch (static_cast<SCEVTypes>(getSCEVType())) {
141 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
144 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
145 const SCEV *Op = Trunc->getOperand();
146 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
147 << *Trunc->getType() << ")";
151 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
152 const SCEV *Op = ZExt->getOperand();
153 OS << "(zext " << *Op->getType() << " " << *Op << " to "
154 << *ZExt->getType() << ")";
158 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
159 const SCEV *Op = SExt->getOperand();
160 OS << "(sext " << *Op->getType() << " " << *Op << " to "
161 << *SExt->getType() << ")";
165 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
166 OS << "{" << *AR->getOperand(0);
167 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
168 OS << ",+," << *AR->getOperand(i);
170 if (AR->getNoWrapFlags(FlagNUW))
172 if (AR->getNoWrapFlags(FlagNSW))
174 if (AR->getNoWrapFlags(FlagNW) &&
175 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
177 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
185 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
186 const char *OpStr = nullptr;
187 switch (NAry->getSCEVType()) {
188 case scAddExpr: OpStr = " + "; break;
189 case scMulExpr: OpStr = " * "; break;
190 case scUMaxExpr: OpStr = " umax "; break;
191 case scSMaxExpr: OpStr = " smax "; break;
194 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
197 if (std::next(I) != E)
201 switch (NAry->getSCEVType()) {
204 if (NAry->getNoWrapFlags(FlagNUW))
206 if (NAry->getNoWrapFlags(FlagNSW))
212 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
213 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
217 const SCEVUnknown *U = cast<SCEVUnknown>(this);
219 if (U->isSizeOf(AllocTy)) {
220 OS << "sizeof(" << *AllocTy << ")";
223 if (U->isAlignOf(AllocTy)) {
224 OS << "alignof(" << *AllocTy << ")";
230 if (U->isOffsetOf(CTy, FieldNo)) {
231 OS << "offsetof(" << *CTy << ", ";
232 FieldNo->printAsOperand(OS, false);
237 // Otherwise just print it normally.
238 U->getValue()->printAsOperand(OS, false);
241 case scCouldNotCompute:
242 OS << "***COULDNOTCOMPUTE***";
245 llvm_unreachable("Unknown SCEV kind!");
248 Type *SCEV::getType() const {
249 switch (static_cast<SCEVTypes>(getSCEVType())) {
251 return cast<SCEVConstant>(this)->getType();
255 return cast<SCEVCastExpr>(this)->getType();
260 return cast<SCEVNAryExpr>(this)->getType();
262 return cast<SCEVAddExpr>(this)->getType();
264 return cast<SCEVUDivExpr>(this)->getType();
266 return cast<SCEVUnknown>(this)->getType();
267 case scCouldNotCompute:
268 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
270 llvm_unreachable("Unknown SCEV kind!");
273 bool SCEV::isZero() const {
274 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
275 return SC->getValue()->isZero();
279 bool SCEV::isOne() const {
280 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
281 return SC->getValue()->isOne();
285 bool SCEV::isAllOnesValue() const {
286 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
287 return SC->getValue()->isAllOnesValue();
291 /// isNonConstantNegative - Return true if the specified scev is negated, but
293 bool SCEV::isNonConstantNegative() const {
294 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
295 if (!Mul) return false;
297 // If there is a constant factor, it will be first.
298 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
299 if (!SC) return false;
301 // Return true if the value is negative, this matches things like (-42 * V).
302 return SC->getValue()->getValue().isNegative();
305 SCEVCouldNotCompute::SCEVCouldNotCompute() :
306 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
308 bool SCEVCouldNotCompute::classof(const SCEV *S) {
309 return S->getSCEVType() == scCouldNotCompute;
312 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
314 ID.AddInteger(scConstant);
317 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
318 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
319 UniqueSCEVs.InsertNode(S, IP);
323 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
324 return getConstant(ConstantInt::get(getContext(), Val));
328 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
329 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
330 return getConstant(ConstantInt::get(ITy, V, isSigned));
333 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
334 unsigned SCEVTy, const SCEV *op, Type *ty)
335 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
337 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
338 const SCEV *op, Type *ty)
339 : SCEVCastExpr(ID, scTruncate, op, ty) {
340 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
341 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
342 "Cannot truncate non-integer value!");
345 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
346 const SCEV *op, Type *ty)
347 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
348 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
349 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
350 "Cannot zero extend non-integer value!");
353 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
354 const SCEV *op, Type *ty)
355 : SCEVCastExpr(ID, scSignExtend, op, ty) {
356 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
357 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
358 "Cannot sign extend non-integer value!");
361 void SCEVUnknown::deleted() {
362 // Clear this SCEVUnknown from various maps.
363 SE->forgetMemoizedResults(this);
365 // Remove this SCEVUnknown from the uniquing map.
366 SE->UniqueSCEVs.RemoveNode(this);
368 // Release the value.
372 void SCEVUnknown::allUsesReplacedWith(Value *New) {
373 // Clear this SCEVUnknown from various maps.
374 SE->forgetMemoizedResults(this);
376 // Remove this SCEVUnknown from the uniquing map.
377 SE->UniqueSCEVs.RemoveNode(this);
379 // Update this SCEVUnknown to point to the new value. This is needed
380 // because there may still be outstanding SCEVs which still point to
385 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
386 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
387 if (VCE->getOpcode() == Instruction::PtrToInt)
388 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
389 if (CE->getOpcode() == Instruction::GetElementPtr &&
390 CE->getOperand(0)->isNullValue() &&
391 CE->getNumOperands() == 2)
392 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
394 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
402 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
403 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
404 if (VCE->getOpcode() == Instruction::PtrToInt)
405 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
406 if (CE->getOpcode() == Instruction::GetElementPtr &&
407 CE->getOperand(0)->isNullValue()) {
409 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
410 if (StructType *STy = dyn_cast<StructType>(Ty))
411 if (!STy->isPacked() &&
412 CE->getNumOperands() == 3 &&
413 CE->getOperand(1)->isNullValue()) {
414 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
416 STy->getNumElements() == 2 &&
417 STy->getElementType(0)->isIntegerTy(1)) {
418 AllocTy = STy->getElementType(1);
427 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
428 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
429 if (VCE->getOpcode() == Instruction::PtrToInt)
430 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
431 if (CE->getOpcode() == Instruction::GetElementPtr &&
432 CE->getNumOperands() == 3 &&
433 CE->getOperand(0)->isNullValue() &&
434 CE->getOperand(1)->isNullValue()) {
436 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
437 // Ignore vector types here so that ScalarEvolutionExpander doesn't
438 // emit getelementptrs that index into vectors.
439 if (Ty->isStructTy() || Ty->isArrayTy()) {
441 FieldNo = CE->getOperand(2);
449 //===----------------------------------------------------------------------===//
451 //===----------------------------------------------------------------------===//
454 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
455 /// than the complexity of the RHS. This comparator is used to canonicalize
457 class SCEVComplexityCompare {
458 const LoopInfo *const LI;
460 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
462 // Return true or false if LHS is less than, or at least RHS, respectively.
463 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
464 return compare(LHS, RHS) < 0;
467 // Return negative, zero, or positive, if LHS is less than, equal to, or
468 // greater than RHS, respectively. A three-way result allows recursive
469 // comparisons to be more efficient.
470 int compare(const SCEV *LHS, const SCEV *RHS) const {
471 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
475 // Primarily, sort the SCEVs by their getSCEVType().
476 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
478 return (int)LType - (int)RType;
480 // Aside from the getSCEVType() ordering, the particular ordering
481 // isn't very important except that it's beneficial to be consistent,
482 // so that (a + b) and (b + a) don't end up as different expressions.
483 switch (static_cast<SCEVTypes>(LType)) {
485 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
486 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
488 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
489 // not as complete as it could be.
490 const Value *LV = LU->getValue(), *RV = RU->getValue();
492 // Order pointer values after integer values. This helps SCEVExpander
494 bool LIsPointer = LV->getType()->isPointerTy(),
495 RIsPointer = RV->getType()->isPointerTy();
496 if (LIsPointer != RIsPointer)
497 return (int)LIsPointer - (int)RIsPointer;
499 // Compare getValueID values.
500 unsigned LID = LV->getValueID(),
501 RID = RV->getValueID();
503 return (int)LID - (int)RID;
505 // Sort arguments by their position.
506 if (const Argument *LA = dyn_cast<Argument>(LV)) {
507 const Argument *RA = cast<Argument>(RV);
508 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
509 return (int)LArgNo - (int)RArgNo;
512 // For instructions, compare their loop depth, and their operand
513 // count. This is pretty loose.
514 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
515 const Instruction *RInst = cast<Instruction>(RV);
517 // Compare loop depths.
518 const BasicBlock *LParent = LInst->getParent(),
519 *RParent = RInst->getParent();
520 if (LParent != RParent) {
521 unsigned LDepth = LI->getLoopDepth(LParent),
522 RDepth = LI->getLoopDepth(RParent);
523 if (LDepth != RDepth)
524 return (int)LDepth - (int)RDepth;
527 // Compare the number of operands.
528 unsigned LNumOps = LInst->getNumOperands(),
529 RNumOps = RInst->getNumOperands();
530 return (int)LNumOps - (int)RNumOps;
537 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
538 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
540 // Compare constant values.
541 const APInt &LA = LC->getValue()->getValue();
542 const APInt &RA = RC->getValue()->getValue();
543 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
544 if (LBitWidth != RBitWidth)
545 return (int)LBitWidth - (int)RBitWidth;
546 return LA.ult(RA) ? -1 : 1;
550 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
551 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
553 // Compare addrec loop depths.
554 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
555 if (LLoop != RLoop) {
556 unsigned LDepth = LLoop->getLoopDepth(),
557 RDepth = RLoop->getLoopDepth();
558 if (LDepth != RDepth)
559 return (int)LDepth - (int)RDepth;
562 // Addrec complexity grows with operand count.
563 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
564 if (LNumOps != RNumOps)
565 return (int)LNumOps - (int)RNumOps;
567 // Lexicographically compare.
568 for (unsigned i = 0; i != LNumOps; ++i) {
569 long X = compare(LA->getOperand(i), RA->getOperand(i));
581 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
582 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
584 // Lexicographically compare n-ary expressions.
585 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
586 if (LNumOps != RNumOps)
587 return (int)LNumOps - (int)RNumOps;
589 for (unsigned i = 0; i != LNumOps; ++i) {
592 long X = compare(LC->getOperand(i), RC->getOperand(i));
596 return (int)LNumOps - (int)RNumOps;
600 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
601 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
603 // Lexicographically compare udiv expressions.
604 long X = compare(LC->getLHS(), RC->getLHS());
607 return compare(LC->getRHS(), RC->getRHS());
613 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
614 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
616 // Compare cast expressions by operand.
617 return compare(LC->getOperand(), RC->getOperand());
620 case scCouldNotCompute:
621 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
623 llvm_unreachable("Unknown SCEV kind!");
628 /// GroupByComplexity - Given a list of SCEV objects, order them by their
629 /// complexity, and group objects of the same complexity together by value.
630 /// When this routine is finished, we know that any duplicates in the vector are
631 /// consecutive and that complexity is monotonically increasing.
633 /// Note that we go take special precautions to ensure that we get deterministic
634 /// results from this routine. In other words, we don't want the results of
635 /// this to depend on where the addresses of various SCEV objects happened to
638 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
640 if (Ops.size() < 2) return; // Noop
641 if (Ops.size() == 2) {
642 // This is the common case, which also happens to be trivially simple.
644 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
645 if (SCEVComplexityCompare(LI)(RHS, LHS))
650 // Do the rough sort by complexity.
651 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
653 // Now that we are sorted by complexity, group elements of the same
654 // complexity. Note that this is, at worst, N^2, but the vector is likely to
655 // be extremely short in practice. Note that we take this approach because we
656 // do not want to depend on the addresses of the objects we are grouping.
657 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
658 const SCEV *S = Ops[i];
659 unsigned Complexity = S->getSCEVType();
661 // If there are any objects of the same complexity and same value as this
663 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
664 if (Ops[j] == S) { // Found a duplicate.
665 // Move it to immediately after i'th element.
666 std::swap(Ops[i+1], Ops[j]);
667 ++i; // no need to rescan it.
668 if (i == e-2) return; // Done!
676 //===----------------------------------------------------------------------===//
677 // Simple SCEV method implementations
678 //===----------------------------------------------------------------------===//
680 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
682 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
685 // Handle the simplest case efficiently.
687 return SE.getTruncateOrZeroExtend(It, ResultTy);
689 // We are using the following formula for BC(It, K):
691 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
693 // Suppose, W is the bitwidth of the return value. We must be prepared for
694 // overflow. Hence, we must assure that the result of our computation is
695 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
696 // safe in modular arithmetic.
698 // However, this code doesn't use exactly that formula; the formula it uses
699 // is something like the following, where T is the number of factors of 2 in
700 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
703 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
705 // This formula is trivially equivalent to the previous formula. However,
706 // this formula can be implemented much more efficiently. The trick is that
707 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
708 // arithmetic. To do exact division in modular arithmetic, all we have
709 // to do is multiply by the inverse. Therefore, this step can be done at
712 // The next issue is how to safely do the division by 2^T. The way this
713 // is done is by doing the multiplication step at a width of at least W + T
714 // bits. This way, the bottom W+T bits of the product are accurate. Then,
715 // when we perform the division by 2^T (which is equivalent to a right shift
716 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
717 // truncated out after the division by 2^T.
719 // In comparison to just directly using the first formula, this technique
720 // is much more efficient; using the first formula requires W * K bits,
721 // but this formula less than W + K bits. Also, the first formula requires
722 // a division step, whereas this formula only requires multiplies and shifts.
724 // It doesn't matter whether the subtraction step is done in the calculation
725 // width or the input iteration count's width; if the subtraction overflows,
726 // the result must be zero anyway. We prefer here to do it in the width of
727 // the induction variable because it helps a lot for certain cases; CodeGen
728 // isn't smart enough to ignore the overflow, which leads to much less
729 // efficient code if the width of the subtraction is wider than the native
732 // (It's possible to not widen at all by pulling out factors of 2 before
733 // the multiplication; for example, K=2 can be calculated as
734 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
735 // extra arithmetic, so it's not an obvious win, and it gets
736 // much more complicated for K > 3.)
738 // Protection from insane SCEVs; this bound is conservative,
739 // but it probably doesn't matter.
741 return SE.getCouldNotCompute();
743 unsigned W = SE.getTypeSizeInBits(ResultTy);
745 // Calculate K! / 2^T and T; we divide out the factors of two before
746 // multiplying for calculating K! / 2^T to avoid overflow.
747 // Other overflow doesn't matter because we only care about the bottom
748 // W bits of the result.
749 APInt OddFactorial(W, 1);
751 for (unsigned i = 3; i <= K; ++i) {
753 unsigned TwoFactors = Mult.countTrailingZeros();
755 Mult = Mult.lshr(TwoFactors);
756 OddFactorial *= Mult;
759 // We need at least W + T bits for the multiplication step
760 unsigned CalculationBits = W + T;
762 // Calculate 2^T, at width T+W.
763 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
765 // Calculate the multiplicative inverse of K! / 2^T;
766 // this multiplication factor will perform the exact division by
768 APInt Mod = APInt::getSignedMinValue(W+1);
769 APInt MultiplyFactor = OddFactorial.zext(W+1);
770 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
771 MultiplyFactor = MultiplyFactor.trunc(W);
773 // Calculate the product, at width T+W
774 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
776 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
777 for (unsigned i = 1; i != K; ++i) {
778 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
779 Dividend = SE.getMulExpr(Dividend,
780 SE.getTruncateOrZeroExtend(S, CalculationTy));
784 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
786 // Truncate the result, and divide by K! / 2^T.
788 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
789 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
792 /// evaluateAtIteration - Return the value of this chain of recurrences at
793 /// the specified iteration number. We can evaluate this recurrence by
794 /// multiplying each element in the chain by the binomial coefficient
795 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
797 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
799 /// where BC(It, k) stands for binomial coefficient.
801 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
802 ScalarEvolution &SE) const {
803 const SCEV *Result = getStart();
804 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
805 // The computation is correct in the face of overflow provided that the
806 // multiplication is performed _after_ the evaluation of the binomial
808 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
809 if (isa<SCEVCouldNotCompute>(Coeff))
812 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
817 //===----------------------------------------------------------------------===//
818 // SCEV Expression folder implementations
819 //===----------------------------------------------------------------------===//
821 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
823 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
824 "This is not a truncating conversion!");
825 assert(isSCEVable(Ty) &&
826 "This is not a conversion to a SCEVable type!");
827 Ty = getEffectiveSCEVType(Ty);
830 ID.AddInteger(scTruncate);
834 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
836 // Fold if the operand is constant.
837 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
839 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
841 // trunc(trunc(x)) --> trunc(x)
842 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
843 return getTruncateExpr(ST->getOperand(), Ty);
845 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
846 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
847 return getTruncateOrSignExtend(SS->getOperand(), Ty);
849 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
850 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
851 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
853 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
854 // eliminate all the truncates.
855 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
856 SmallVector<const SCEV *, 4> Operands;
857 bool hasTrunc = false;
858 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
859 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
860 hasTrunc = isa<SCEVTruncateExpr>(S);
861 Operands.push_back(S);
864 return getAddExpr(Operands);
865 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
868 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
869 // eliminate all the truncates.
870 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
871 SmallVector<const SCEV *, 4> Operands;
872 bool hasTrunc = false;
873 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
874 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
875 hasTrunc = isa<SCEVTruncateExpr>(S);
876 Operands.push_back(S);
879 return getMulExpr(Operands);
880 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
883 // If the input value is a chrec scev, truncate the chrec's operands.
884 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
885 SmallVector<const SCEV *, 4> Operands;
886 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
887 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
888 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
891 // The cast wasn't folded; create an explicit cast node. We can reuse
892 // the existing insert position since if we get here, we won't have
893 // made any changes which would invalidate it.
894 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
896 UniqueSCEVs.InsertNode(S, IP);
900 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
902 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
903 "This is not an extending conversion!");
904 assert(isSCEVable(Ty) &&
905 "This is not a conversion to a SCEVable type!");
906 Ty = getEffectiveSCEVType(Ty);
908 // Fold if the operand is constant.
909 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
911 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
913 // zext(zext(x)) --> zext(x)
914 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
915 return getZeroExtendExpr(SZ->getOperand(), Ty);
917 // Before doing any expensive analysis, check to see if we've already
918 // computed a SCEV for this Op and Ty.
920 ID.AddInteger(scZeroExtend);
924 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
926 // zext(trunc(x)) --> zext(x) or x or trunc(x)
927 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
928 // It's possible the bits taken off by the truncate were all zero bits. If
929 // so, we should be able to simplify this further.
930 const SCEV *X = ST->getOperand();
931 ConstantRange CR = getUnsignedRange(X);
932 unsigned TruncBits = getTypeSizeInBits(ST->getType());
933 unsigned NewBits = getTypeSizeInBits(Ty);
934 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
935 CR.zextOrTrunc(NewBits)))
936 return getTruncateOrZeroExtend(X, Ty);
939 // If the input value is a chrec scev, and we can prove that the value
940 // did not overflow the old, smaller, value, we can zero extend all of the
941 // operands (often constants). This allows analysis of something like
942 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
943 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
944 if (AR->isAffine()) {
945 const SCEV *Start = AR->getStart();
946 const SCEV *Step = AR->getStepRecurrence(*this);
947 unsigned BitWidth = getTypeSizeInBits(AR->getType());
948 const Loop *L = AR->getLoop();
950 // If we have special knowledge that this addrec won't overflow,
951 // we don't need to do any further analysis.
952 if (AR->getNoWrapFlags(SCEV::FlagNUW))
953 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
954 getZeroExtendExpr(Step, Ty),
955 L, AR->getNoWrapFlags());
957 // Check whether the backedge-taken count is SCEVCouldNotCompute.
958 // Note that this serves two purposes: It filters out loops that are
959 // simply not analyzable, and it covers the case where this code is
960 // being called from within backedge-taken count analysis, such that
961 // attempting to ask for the backedge-taken count would likely result
962 // in infinite recursion. In the later case, the analysis code will
963 // cope with a conservative value, and it will take care to purge
964 // that value once it has finished.
965 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
966 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
967 // Manually compute the final value for AR, checking for
970 // Check whether the backedge-taken count can be losslessly casted to
971 // the addrec's type. The count is always unsigned.
972 const SCEV *CastedMaxBECount =
973 getTruncateOrZeroExtend(MaxBECount, Start->getType());
974 const SCEV *RecastedMaxBECount =
975 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
976 if (MaxBECount == RecastedMaxBECount) {
977 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
978 // Check whether Start+Step*MaxBECount has no unsigned overflow.
979 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
980 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
981 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
982 const SCEV *WideMaxBECount =
983 getZeroExtendExpr(CastedMaxBECount, WideTy);
984 const SCEV *OperandExtendedAdd =
985 getAddExpr(WideStart,
986 getMulExpr(WideMaxBECount,
987 getZeroExtendExpr(Step, WideTy)));
988 if (ZAdd == OperandExtendedAdd) {
989 // Cache knowledge of AR NUW, which is propagated to this AddRec.
990 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
991 // Return the expression with the addrec on the outside.
992 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
993 getZeroExtendExpr(Step, Ty),
994 L, AR->getNoWrapFlags());
996 // Similar to above, only this time treat the step value as signed.
997 // This covers loops that count down.
999 getAddExpr(WideStart,
1000 getMulExpr(WideMaxBECount,
1001 getSignExtendExpr(Step, WideTy)));
1002 if (ZAdd == OperandExtendedAdd) {
1003 // Cache knowledge of AR NW, which is propagated to this AddRec.
1004 // Negative step causes unsigned wrap, but it still can't self-wrap.
1005 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1006 // Return the expression with the addrec on the outside.
1007 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1008 getSignExtendExpr(Step, Ty),
1009 L, AR->getNoWrapFlags());
1013 // If the backedge is guarded by a comparison with the pre-inc value
1014 // the addrec is safe. Also, if the entry is guarded by a comparison
1015 // with the start value and the backedge is guarded by a comparison
1016 // with the post-inc value, the addrec is safe.
1017 if (isKnownPositive(Step)) {
1018 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1019 getUnsignedRange(Step).getUnsignedMax());
1020 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1021 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1022 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1023 AR->getPostIncExpr(*this), N))) {
1024 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1025 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1026 // Return the expression with the addrec on the outside.
1027 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1028 getZeroExtendExpr(Step, Ty),
1029 L, AR->getNoWrapFlags());
1031 } else if (isKnownNegative(Step)) {
1032 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1033 getSignedRange(Step).getSignedMin());
1034 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1035 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1036 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1037 AR->getPostIncExpr(*this), N))) {
1038 // Cache knowledge of AR NW, which is propagated to this AddRec.
1039 // Negative step causes unsigned wrap, but it still can't self-wrap.
1040 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1041 // Return the expression with the addrec on the outside.
1042 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1043 getSignExtendExpr(Step, Ty),
1044 L, AR->getNoWrapFlags());
1050 // The cast wasn't folded; create an explicit cast node.
1051 // Recompute the insert position, as it may have been invalidated.
1052 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1053 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1055 UniqueSCEVs.InsertNode(S, IP);
1059 // Get the limit of a recurrence such that incrementing by Step cannot cause
1060 // signed overflow as long as the value of the recurrence within the loop does
1061 // not exceed this limit before incrementing.
1062 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1063 ICmpInst::Predicate *Pred,
1064 ScalarEvolution *SE) {
1065 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1066 if (SE->isKnownPositive(Step)) {
1067 *Pred = ICmpInst::ICMP_SLT;
1068 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1069 SE->getSignedRange(Step).getSignedMax());
1071 if (SE->isKnownNegative(Step)) {
1072 *Pred = ICmpInst::ICMP_SGT;
1073 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1074 SE->getSignedRange(Step).getSignedMin());
1079 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1080 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1081 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1082 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1083 // result, the expression "Step + sext(PreIncAR)" is congruent with
1084 // "sext(PostIncAR)"
1085 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1087 ScalarEvolution *SE) {
1088 const Loop *L = AR->getLoop();
1089 const SCEV *Start = AR->getStart();
1090 const SCEV *Step = AR->getStepRecurrence(*SE);
1092 // Check for a simple looking step prior to loop entry.
1093 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1097 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1098 // subtraction is expensive. For this purpose, perform a quick and dirty
1099 // difference, by checking for Step in the operand list.
1100 SmallVector<const SCEV *, 4> DiffOps;
1101 for (const SCEV *Op : SA->operands())
1103 DiffOps.push_back(Op);
1105 if (DiffOps.size() == SA->getNumOperands())
1108 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1109 // same three conditions that getSignExtendedExpr checks.
1111 // 1. NSW flags on the step increment.
1112 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1113 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1114 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1116 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1119 // 2. Direct overflow check on the step operation's expression.
1120 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1121 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1122 const SCEV *OperandExtendedStart =
1123 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1124 SE->getSignExtendExpr(Step, WideTy));
1125 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1126 // Cache knowledge of PreAR NSW.
1128 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1129 // FIXME: this optimization needs a unit test
1130 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1134 // 3. Loop precondition.
1135 ICmpInst::Predicate Pred;
1136 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1138 if (OverflowLimit &&
1139 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1145 // Get the normalized sign-extended expression for this AddRec's Start.
1146 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1148 ScalarEvolution *SE) {
1149 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1151 return SE->getSignExtendExpr(AR->getStart(), Ty);
1153 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1154 SE->getSignExtendExpr(PreStart, Ty));
1157 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1159 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1160 "This is not an extending conversion!");
1161 assert(isSCEVable(Ty) &&
1162 "This is not a conversion to a SCEVable type!");
1163 Ty = getEffectiveSCEVType(Ty);
1165 // Fold if the operand is constant.
1166 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1168 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1170 // sext(sext(x)) --> sext(x)
1171 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1172 return getSignExtendExpr(SS->getOperand(), Ty);
1174 // sext(zext(x)) --> zext(x)
1175 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1176 return getZeroExtendExpr(SZ->getOperand(), Ty);
1178 // Before doing any expensive analysis, check to see if we've already
1179 // computed a SCEV for this Op and Ty.
1180 FoldingSetNodeID ID;
1181 ID.AddInteger(scSignExtend);
1185 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1187 // If the input value is provably positive, build a zext instead.
1188 if (isKnownNonNegative(Op))
1189 return getZeroExtendExpr(Op, Ty);
1191 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1192 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1193 // It's possible the bits taken off by the truncate were all sign bits. If
1194 // so, we should be able to simplify this further.
1195 const SCEV *X = ST->getOperand();
1196 ConstantRange CR = getSignedRange(X);
1197 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1198 unsigned NewBits = getTypeSizeInBits(Ty);
1199 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1200 CR.sextOrTrunc(NewBits)))
1201 return getTruncateOrSignExtend(X, Ty);
1204 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1205 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1206 if (SA->getNumOperands() == 2) {
1207 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1208 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1210 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1211 const APInt &C1 = SC1->getValue()->getValue();
1212 const APInt &C2 = SC2->getValue()->getValue();
1213 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1214 C2.ugt(C1) && C2.isPowerOf2())
1215 return getAddExpr(getSignExtendExpr(SC1, Ty),
1216 getSignExtendExpr(SMul, Ty));
1221 // If the input value is a chrec scev, and we can prove that the value
1222 // did not overflow the old, smaller, value, we can sign extend all of the
1223 // operands (often constants). This allows analysis of something like
1224 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1225 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1226 if (AR->isAffine()) {
1227 const SCEV *Start = AR->getStart();
1228 const SCEV *Step = AR->getStepRecurrence(*this);
1229 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1230 const Loop *L = AR->getLoop();
1232 // If we have special knowledge that this addrec won't overflow,
1233 // we don't need to do any further analysis.
1234 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1235 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1236 getSignExtendExpr(Step, Ty),
1239 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1240 // Note that this serves two purposes: It filters out loops that are
1241 // simply not analyzable, and it covers the case where this code is
1242 // being called from within backedge-taken count analysis, such that
1243 // attempting to ask for the backedge-taken count would likely result
1244 // in infinite recursion. In the later case, the analysis code will
1245 // cope with a conservative value, and it will take care to purge
1246 // that value once it has finished.
1247 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1248 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1249 // Manually compute the final value for AR, checking for
1252 // Check whether the backedge-taken count can be losslessly casted to
1253 // the addrec's type. The count is always unsigned.
1254 const SCEV *CastedMaxBECount =
1255 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1256 const SCEV *RecastedMaxBECount =
1257 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1258 if (MaxBECount == RecastedMaxBECount) {
1259 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1260 // Check whether Start+Step*MaxBECount has no signed overflow.
1261 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1262 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1263 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1264 const SCEV *WideMaxBECount =
1265 getZeroExtendExpr(CastedMaxBECount, WideTy);
1266 const SCEV *OperandExtendedAdd =
1267 getAddExpr(WideStart,
1268 getMulExpr(WideMaxBECount,
1269 getSignExtendExpr(Step, WideTy)));
1270 if (SAdd == OperandExtendedAdd) {
1271 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1272 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1273 // Return the expression with the addrec on the outside.
1274 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1275 getSignExtendExpr(Step, Ty),
1276 L, AR->getNoWrapFlags());
1278 // Similar to above, only this time treat the step value as unsigned.
1279 // This covers loops that count up with an unsigned step.
1280 OperandExtendedAdd =
1281 getAddExpr(WideStart,
1282 getMulExpr(WideMaxBECount,
1283 getZeroExtendExpr(Step, WideTy)));
1284 if (SAdd == OperandExtendedAdd) {
1285 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1286 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1287 // Return the expression with the addrec on the outside.
1288 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1289 getZeroExtendExpr(Step, Ty),
1290 L, AR->getNoWrapFlags());
1294 // If the backedge is guarded by a comparison with the pre-inc value
1295 // the addrec is safe. Also, if the entry is guarded by a comparison
1296 // with the start value and the backedge is guarded by a comparison
1297 // with the post-inc value, the addrec is safe.
1298 ICmpInst::Predicate Pred;
1299 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1300 if (OverflowLimit &&
1301 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1302 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1303 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1305 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1306 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1307 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1308 getSignExtendExpr(Step, Ty),
1309 L, AR->getNoWrapFlags());
1312 // If Start and Step are constants, check if we can apply this
1314 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1315 auto SC1 = dyn_cast<SCEVConstant>(Start);
1316 auto SC2 = dyn_cast<SCEVConstant>(Step);
1318 const APInt &C1 = SC1->getValue()->getValue();
1319 const APInt &C2 = SC2->getValue()->getValue();
1320 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1322 Start = getSignExtendExpr(Start, Ty);
1323 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1324 L, AR->getNoWrapFlags());
1325 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1330 // The cast wasn't folded; create an explicit cast node.
1331 // Recompute the insert position, as it may have been invalidated.
1332 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1333 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1335 UniqueSCEVs.InsertNode(S, IP);
1339 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1340 /// unspecified bits out to the given type.
1342 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1344 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1345 "This is not an extending conversion!");
1346 assert(isSCEVable(Ty) &&
1347 "This is not a conversion to a SCEVable type!");
1348 Ty = getEffectiveSCEVType(Ty);
1350 // Sign-extend negative constants.
1351 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1352 if (SC->getValue()->getValue().isNegative())
1353 return getSignExtendExpr(Op, Ty);
1355 // Peel off a truncate cast.
1356 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1357 const SCEV *NewOp = T->getOperand();
1358 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1359 return getAnyExtendExpr(NewOp, Ty);
1360 return getTruncateOrNoop(NewOp, Ty);
1363 // Next try a zext cast. If the cast is folded, use it.
1364 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1365 if (!isa<SCEVZeroExtendExpr>(ZExt))
1368 // Next try a sext cast. If the cast is folded, use it.
1369 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1370 if (!isa<SCEVSignExtendExpr>(SExt))
1373 // Force the cast to be folded into the operands of an addrec.
1374 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1375 SmallVector<const SCEV *, 4> Ops;
1376 for (const SCEV *Op : AR->operands())
1377 Ops.push_back(getAnyExtendExpr(Op, Ty));
1378 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1381 // If the expression is obviously signed, use the sext cast value.
1382 if (isa<SCEVSMaxExpr>(Op))
1385 // Absent any other information, use the zext cast value.
1389 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1390 /// a list of operands to be added under the given scale, update the given
1391 /// map. This is a helper function for getAddRecExpr. As an example of
1392 /// what it does, given a sequence of operands that would form an add
1393 /// expression like this:
1395 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1397 /// where A and B are constants, update the map with these values:
1399 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1401 /// and add 13 + A*B*29 to AccumulatedConstant.
1402 /// This will allow getAddRecExpr to produce this:
1404 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1406 /// This form often exposes folding opportunities that are hidden in
1407 /// the original operand list.
1409 /// Return true iff it appears that any interesting folding opportunities
1410 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1411 /// the common case where no interesting opportunities are present, and
1412 /// is also used as a check to avoid infinite recursion.
1415 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1416 SmallVectorImpl<const SCEV *> &NewOps,
1417 APInt &AccumulatedConstant,
1418 const SCEV *const *Ops, size_t NumOperands,
1420 ScalarEvolution &SE) {
1421 bool Interesting = false;
1423 // Iterate over the add operands. They are sorted, with constants first.
1425 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1427 // Pull a buried constant out to the outside.
1428 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1430 AccumulatedConstant += Scale * C->getValue()->getValue();
1433 // Next comes everything else. We're especially interested in multiplies
1434 // here, but they're in the middle, so just visit the rest with one loop.
1435 for (; i != NumOperands; ++i) {
1436 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1437 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1439 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1440 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1441 // A multiplication of a constant with another add; recurse.
1442 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1444 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1445 Add->op_begin(), Add->getNumOperands(),
1448 // A multiplication of a constant with some other value. Update
1450 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1451 const SCEV *Key = SE.getMulExpr(MulOps);
1452 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1453 M.insert(std::make_pair(Key, NewScale));
1455 NewOps.push_back(Pair.first->first);
1457 Pair.first->second += NewScale;
1458 // The map already had an entry for this value, which may indicate
1459 // a folding opportunity.
1464 // An ordinary operand. Update the map.
1465 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1466 M.insert(std::make_pair(Ops[i], Scale));
1468 NewOps.push_back(Pair.first->first);
1470 Pair.first->second += Scale;
1471 // The map already had an entry for this value, which may indicate
1472 // a folding opportunity.
1482 struct APIntCompare {
1483 bool operator()(const APInt &LHS, const APInt &RHS) const {
1484 return LHS.ult(RHS);
1489 /// getAddExpr - Get a canonical add expression, or something simpler if
1491 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1492 SCEV::NoWrapFlags Flags) {
1493 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1494 "only nuw or nsw allowed");
1495 assert(!Ops.empty() && "Cannot get empty add!");
1496 if (Ops.size() == 1) return Ops[0];
1498 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1499 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1500 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1501 "SCEVAddExpr operand types don't match!");
1504 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1506 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1507 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1508 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1510 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1511 E = Ops.end(); I != E; ++I)
1512 if (!isKnownNonNegative(*I)) {
1516 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1519 // Sort by complexity, this groups all similar expression types together.
1520 GroupByComplexity(Ops, LI);
1522 // If there are any constants, fold them together.
1524 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1526 assert(Idx < Ops.size());
1527 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1528 // We found two constants, fold them together!
1529 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1530 RHSC->getValue()->getValue());
1531 if (Ops.size() == 2) return Ops[0];
1532 Ops.erase(Ops.begin()+1); // Erase the folded element
1533 LHSC = cast<SCEVConstant>(Ops[0]);
1536 // If we are left with a constant zero being added, strip it off.
1537 if (LHSC->getValue()->isZero()) {
1538 Ops.erase(Ops.begin());
1542 if (Ops.size() == 1) return Ops[0];
1545 // Okay, check to see if the same value occurs in the operand list more than
1546 // once. If so, merge them together into an multiply expression. Since we
1547 // sorted the list, these values are required to be adjacent.
1548 Type *Ty = Ops[0]->getType();
1549 bool FoundMatch = false;
1550 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1551 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1552 // Scan ahead to count how many equal operands there are.
1554 while (i+Count != e && Ops[i+Count] == Ops[i])
1556 // Merge the values into a multiply.
1557 const SCEV *Scale = getConstant(Ty, Count);
1558 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1559 if (Ops.size() == Count)
1562 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1563 --i; e -= Count - 1;
1567 return getAddExpr(Ops, Flags);
1569 // Check for truncates. If all the operands are truncated from the same
1570 // type, see if factoring out the truncate would permit the result to be
1571 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1572 // if the contents of the resulting outer trunc fold to something simple.
1573 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1574 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1575 Type *DstType = Trunc->getType();
1576 Type *SrcType = Trunc->getOperand()->getType();
1577 SmallVector<const SCEV *, 8> LargeOps;
1579 // Check all the operands to see if they can be represented in the
1580 // source type of the truncate.
1581 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1582 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1583 if (T->getOperand()->getType() != SrcType) {
1587 LargeOps.push_back(T->getOperand());
1588 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1589 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1590 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1591 SmallVector<const SCEV *, 8> LargeMulOps;
1592 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1593 if (const SCEVTruncateExpr *T =
1594 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1595 if (T->getOperand()->getType() != SrcType) {
1599 LargeMulOps.push_back(T->getOperand());
1600 } else if (const SCEVConstant *C =
1601 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1602 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1609 LargeOps.push_back(getMulExpr(LargeMulOps));
1616 // Evaluate the expression in the larger type.
1617 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1618 // If it folds to something simple, use it. Otherwise, don't.
1619 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1620 return getTruncateExpr(Fold, DstType);
1624 // Skip past any other cast SCEVs.
1625 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1628 // If there are add operands they would be next.
1629 if (Idx < Ops.size()) {
1630 bool DeletedAdd = false;
1631 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1632 // If we have an add, expand the add operands onto the end of the operands
1634 Ops.erase(Ops.begin()+Idx);
1635 Ops.append(Add->op_begin(), Add->op_end());
1639 // If we deleted at least one add, we added operands to the end of the list,
1640 // and they are not necessarily sorted. Recurse to resort and resimplify
1641 // any operands we just acquired.
1643 return getAddExpr(Ops);
1646 // Skip over the add expression until we get to a multiply.
1647 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1650 // Check to see if there are any folding opportunities present with
1651 // operands multiplied by constant values.
1652 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1653 uint64_t BitWidth = getTypeSizeInBits(Ty);
1654 DenseMap<const SCEV *, APInt> M;
1655 SmallVector<const SCEV *, 8> NewOps;
1656 APInt AccumulatedConstant(BitWidth, 0);
1657 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1658 Ops.data(), Ops.size(),
1659 APInt(BitWidth, 1), *this)) {
1660 // Some interesting folding opportunity is present, so its worthwhile to
1661 // re-generate the operands list. Group the operands by constant scale,
1662 // to avoid multiplying by the same constant scale multiple times.
1663 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1664 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1665 E = NewOps.end(); I != E; ++I)
1666 MulOpLists[M.find(*I)->second].push_back(*I);
1667 // Re-generate the operands list.
1669 if (AccumulatedConstant != 0)
1670 Ops.push_back(getConstant(AccumulatedConstant));
1671 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1672 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1674 Ops.push_back(getMulExpr(getConstant(I->first),
1675 getAddExpr(I->second)));
1677 return getConstant(Ty, 0);
1678 if (Ops.size() == 1)
1680 return getAddExpr(Ops);
1684 // If we are adding something to a multiply expression, make sure the
1685 // something is not already an operand of the multiply. If so, merge it into
1687 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1688 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1689 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1690 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1691 if (isa<SCEVConstant>(MulOpSCEV))
1693 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1694 if (MulOpSCEV == Ops[AddOp]) {
1695 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1696 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1697 if (Mul->getNumOperands() != 2) {
1698 // If the multiply has more than two operands, we must get the
1700 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1701 Mul->op_begin()+MulOp);
1702 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1703 InnerMul = getMulExpr(MulOps);
1705 const SCEV *One = getConstant(Ty, 1);
1706 const SCEV *AddOne = getAddExpr(One, InnerMul);
1707 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1708 if (Ops.size() == 2) return OuterMul;
1710 Ops.erase(Ops.begin()+AddOp);
1711 Ops.erase(Ops.begin()+Idx-1);
1713 Ops.erase(Ops.begin()+Idx);
1714 Ops.erase(Ops.begin()+AddOp-1);
1716 Ops.push_back(OuterMul);
1717 return getAddExpr(Ops);
1720 // Check this multiply against other multiplies being added together.
1721 for (unsigned OtherMulIdx = Idx+1;
1722 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1724 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1725 // If MulOp occurs in OtherMul, we can fold the two multiplies
1727 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1728 OMulOp != e; ++OMulOp)
1729 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1730 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1731 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1732 if (Mul->getNumOperands() != 2) {
1733 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1734 Mul->op_begin()+MulOp);
1735 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1736 InnerMul1 = getMulExpr(MulOps);
1738 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1739 if (OtherMul->getNumOperands() != 2) {
1740 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1741 OtherMul->op_begin()+OMulOp);
1742 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1743 InnerMul2 = getMulExpr(MulOps);
1745 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1746 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1747 if (Ops.size() == 2) return OuterMul;
1748 Ops.erase(Ops.begin()+Idx);
1749 Ops.erase(Ops.begin()+OtherMulIdx-1);
1750 Ops.push_back(OuterMul);
1751 return getAddExpr(Ops);
1757 // If there are any add recurrences in the operands list, see if any other
1758 // added values are loop invariant. If so, we can fold them into the
1760 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1763 // Scan over all recurrences, trying to fold loop invariants into them.
1764 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1765 // Scan all of the other operands to this add and add them to the vector if
1766 // they are loop invariant w.r.t. the recurrence.
1767 SmallVector<const SCEV *, 8> LIOps;
1768 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1769 const Loop *AddRecLoop = AddRec->getLoop();
1770 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1771 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1772 LIOps.push_back(Ops[i]);
1773 Ops.erase(Ops.begin()+i);
1777 // If we found some loop invariants, fold them into the recurrence.
1778 if (!LIOps.empty()) {
1779 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1780 LIOps.push_back(AddRec->getStart());
1782 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1784 AddRecOps[0] = getAddExpr(LIOps);
1786 // Build the new addrec. Propagate the NUW and NSW flags if both the
1787 // outer add and the inner addrec are guaranteed to have no overflow.
1788 // Always propagate NW.
1789 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1790 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1792 // If all of the other operands were loop invariant, we are done.
1793 if (Ops.size() == 1) return NewRec;
1795 // Otherwise, add the folded AddRec by the non-invariant parts.
1796 for (unsigned i = 0;; ++i)
1797 if (Ops[i] == AddRec) {
1801 return getAddExpr(Ops);
1804 // Okay, if there weren't any loop invariants to be folded, check to see if
1805 // there are multiple AddRec's with the same loop induction variable being
1806 // added together. If so, we can fold them.
1807 for (unsigned OtherIdx = Idx+1;
1808 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1810 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1811 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1812 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1814 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1816 if (const SCEVAddRecExpr *OtherAddRec =
1817 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1818 if (OtherAddRec->getLoop() == AddRecLoop) {
1819 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1821 if (i >= AddRecOps.size()) {
1822 AddRecOps.append(OtherAddRec->op_begin()+i,
1823 OtherAddRec->op_end());
1826 AddRecOps[i] = getAddExpr(AddRecOps[i],
1827 OtherAddRec->getOperand(i));
1829 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1831 // Step size has changed, so we cannot guarantee no self-wraparound.
1832 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1833 return getAddExpr(Ops);
1836 // Otherwise couldn't fold anything into this recurrence. Move onto the
1840 // Okay, it looks like we really DO need an add expr. Check to see if we
1841 // already have one, otherwise create a new one.
1842 FoldingSetNodeID ID;
1843 ID.AddInteger(scAddExpr);
1844 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1845 ID.AddPointer(Ops[i]);
1848 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1850 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1851 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1852 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1854 UniqueSCEVs.InsertNode(S, IP);
1856 S->setNoWrapFlags(Flags);
1860 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1862 if (j > 1 && k / j != i) Overflow = true;
1866 /// Compute the result of "n choose k", the binomial coefficient. If an
1867 /// intermediate computation overflows, Overflow will be set and the return will
1868 /// be garbage. Overflow is not cleared on absence of overflow.
1869 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1870 // We use the multiplicative formula:
1871 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1872 // At each iteration, we take the n-th term of the numeral and divide by the
1873 // (k-n)th term of the denominator. This division will always produce an
1874 // integral result, and helps reduce the chance of overflow in the
1875 // intermediate computations. However, we can still overflow even when the
1876 // final result would fit.
1878 if (n == 0 || n == k) return 1;
1879 if (k > n) return 0;
1885 for (uint64_t i = 1; i <= k; ++i) {
1886 r = umul_ov(r, n-(i-1), Overflow);
1892 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1894 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1895 SCEV::NoWrapFlags Flags) {
1896 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1897 "only nuw or nsw allowed");
1898 assert(!Ops.empty() && "Cannot get empty mul!");
1899 if (Ops.size() == 1) return Ops[0];
1901 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1902 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1903 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1904 "SCEVMulExpr operand types don't match!");
1907 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1909 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1910 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1911 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1913 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1914 E = Ops.end(); I != E; ++I)
1915 if (!isKnownNonNegative(*I)) {
1919 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1922 // Sort by complexity, this groups all similar expression types together.
1923 GroupByComplexity(Ops, LI);
1925 // If there are any constants, fold them together.
1927 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1929 // C1*(C2+V) -> C1*C2 + C1*V
1930 if (Ops.size() == 2)
1931 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1932 if (Add->getNumOperands() == 2 &&
1933 isa<SCEVConstant>(Add->getOperand(0)))
1934 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1935 getMulExpr(LHSC, Add->getOperand(1)));
1938 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1939 // We found two constants, fold them together!
1940 ConstantInt *Fold = ConstantInt::get(getContext(),
1941 LHSC->getValue()->getValue() *
1942 RHSC->getValue()->getValue());
1943 Ops[0] = getConstant(Fold);
1944 Ops.erase(Ops.begin()+1); // Erase the folded element
1945 if (Ops.size() == 1) return Ops[0];
1946 LHSC = cast<SCEVConstant>(Ops[0]);
1949 // If we are left with a constant one being multiplied, strip it off.
1950 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1951 Ops.erase(Ops.begin());
1953 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1954 // If we have a multiply of zero, it will always be zero.
1956 } else if (Ops[0]->isAllOnesValue()) {
1957 // If we have a mul by -1 of an add, try distributing the -1 among the
1959 if (Ops.size() == 2) {
1960 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1961 SmallVector<const SCEV *, 4> NewOps;
1962 bool AnyFolded = false;
1963 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1964 E = Add->op_end(); I != E; ++I) {
1965 const SCEV *Mul = getMulExpr(Ops[0], *I);
1966 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1967 NewOps.push_back(Mul);
1970 return getAddExpr(NewOps);
1972 else if (const SCEVAddRecExpr *
1973 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1974 // Negation preserves a recurrence's no self-wrap property.
1975 SmallVector<const SCEV *, 4> Operands;
1976 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1977 E = AddRec->op_end(); I != E; ++I) {
1978 Operands.push_back(getMulExpr(Ops[0], *I));
1980 return getAddRecExpr(Operands, AddRec->getLoop(),
1981 AddRec->getNoWrapFlags(SCEV::FlagNW));
1986 if (Ops.size() == 1)
1990 // Skip over the add expression until we get to a multiply.
1991 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1994 // If there are mul operands inline them all into this expression.
1995 if (Idx < Ops.size()) {
1996 bool DeletedMul = false;
1997 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1998 // If we have an mul, expand the mul operands onto the end of the operands
2000 Ops.erase(Ops.begin()+Idx);
2001 Ops.append(Mul->op_begin(), Mul->op_end());
2005 // If we deleted at least one mul, we added operands to the end of the list,
2006 // and they are not necessarily sorted. Recurse to resort and resimplify
2007 // any operands we just acquired.
2009 return getMulExpr(Ops);
2012 // If there are any add recurrences in the operands list, see if any other
2013 // added values are loop invariant. If so, we can fold them into the
2015 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2018 // Scan over all recurrences, trying to fold loop invariants into them.
2019 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2020 // Scan all of the other operands to this mul and add them to the vector if
2021 // they are loop invariant w.r.t. the recurrence.
2022 SmallVector<const SCEV *, 8> LIOps;
2023 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2024 const Loop *AddRecLoop = AddRec->getLoop();
2025 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2026 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2027 LIOps.push_back(Ops[i]);
2028 Ops.erase(Ops.begin()+i);
2032 // If we found some loop invariants, fold them into the recurrence.
2033 if (!LIOps.empty()) {
2034 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2035 SmallVector<const SCEV *, 4> NewOps;
2036 NewOps.reserve(AddRec->getNumOperands());
2037 const SCEV *Scale = getMulExpr(LIOps);
2038 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2039 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2041 // Build the new addrec. Propagate the NUW and NSW flags if both the
2042 // outer mul and the inner addrec are guaranteed to have no overflow.
2044 // No self-wrap cannot be guaranteed after changing the step size, but
2045 // will be inferred if either NUW or NSW is true.
2046 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2047 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2049 // If all of the other operands were loop invariant, we are done.
2050 if (Ops.size() == 1) return NewRec;
2052 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2053 for (unsigned i = 0;; ++i)
2054 if (Ops[i] == AddRec) {
2058 return getMulExpr(Ops);
2061 // Okay, if there weren't any loop invariants to be folded, check to see if
2062 // there are multiple AddRec's with the same loop induction variable being
2063 // multiplied together. If so, we can fold them.
2064 for (unsigned OtherIdx = Idx+1;
2065 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2067 if (AddRecLoop != cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop())
2070 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2071 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2072 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2073 // ]]],+,...up to x=2n}.
2074 // Note that the arguments to choose() are always integers with values
2075 // known at compile time, never SCEV objects.
2077 // The implementation avoids pointless extra computations when the two
2078 // addrec's are of different length (mathematically, it's equivalent to
2079 // an infinite stream of zeros on the right).
2080 bool OpsModified = false;
2081 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2083 const SCEVAddRecExpr *OtherAddRec =
2084 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2085 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2088 bool Overflow = false;
2089 Type *Ty = AddRec->getType();
2090 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2091 SmallVector<const SCEV*, 7> AddRecOps;
2092 for (int x = 0, xe = AddRec->getNumOperands() +
2093 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2094 const SCEV *Term = getConstant(Ty, 0);
2095 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2096 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2097 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2098 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2099 z < ze && !Overflow; ++z) {
2100 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2102 if (LargerThan64Bits)
2103 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2105 Coeff = Coeff1*Coeff2;
2106 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2107 const SCEV *Term1 = AddRec->getOperand(y-z);
2108 const SCEV *Term2 = OtherAddRec->getOperand(z);
2109 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2112 AddRecOps.push_back(Term);
2115 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2117 if (Ops.size() == 2) return NewAddRec;
2118 Ops[Idx] = NewAddRec;
2119 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2121 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2127 return getMulExpr(Ops);
2130 // Otherwise couldn't fold anything into this recurrence. Move onto the
2134 // Okay, it looks like we really DO need an mul expr. Check to see if we
2135 // already have one, otherwise create a new one.
2136 FoldingSetNodeID ID;
2137 ID.AddInteger(scMulExpr);
2138 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2139 ID.AddPointer(Ops[i]);
2142 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2144 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2145 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2146 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2148 UniqueSCEVs.InsertNode(S, IP);
2150 S->setNoWrapFlags(Flags);
2154 /// getUDivExpr - Get a canonical unsigned division expression, or something
2155 /// simpler if possible.
2156 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2158 assert(getEffectiveSCEVType(LHS->getType()) ==
2159 getEffectiveSCEVType(RHS->getType()) &&
2160 "SCEVUDivExpr operand types don't match!");
2162 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2163 if (RHSC->getValue()->equalsInt(1))
2164 return LHS; // X udiv 1 --> x
2165 // If the denominator is zero, the result of the udiv is undefined. Don't
2166 // try to analyze it, because the resolution chosen here may differ from
2167 // the resolution chosen in other parts of the compiler.
2168 if (!RHSC->getValue()->isZero()) {
2169 // Determine if the division can be folded into the operands of
2171 // TODO: Generalize this to non-constants by using known-bits information.
2172 Type *Ty = LHS->getType();
2173 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2174 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2175 // For non-power-of-two values, effectively round the value up to the
2176 // nearest power of two.
2177 if (!RHSC->getValue()->getValue().isPowerOf2())
2179 IntegerType *ExtTy =
2180 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2181 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2182 if (const SCEVConstant *Step =
2183 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2184 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2185 const APInt &StepInt = Step->getValue()->getValue();
2186 const APInt &DivInt = RHSC->getValue()->getValue();
2187 if (!StepInt.urem(DivInt) &&
2188 getZeroExtendExpr(AR, ExtTy) ==
2189 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2190 getZeroExtendExpr(Step, ExtTy),
2191 AR->getLoop(), SCEV::FlagAnyWrap)) {
2192 SmallVector<const SCEV *, 4> Operands;
2193 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2194 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2195 return getAddRecExpr(Operands, AR->getLoop(),
2198 /// Get a canonical UDivExpr for a recurrence.
2199 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2200 // We can currently only fold X%N if X is constant.
2201 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2202 if (StartC && !DivInt.urem(StepInt) &&
2203 getZeroExtendExpr(AR, ExtTy) ==
2204 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2205 getZeroExtendExpr(Step, ExtTy),
2206 AR->getLoop(), SCEV::FlagAnyWrap)) {
2207 const APInt &StartInt = StartC->getValue()->getValue();
2208 const APInt &StartRem = StartInt.urem(StepInt);
2210 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2211 AR->getLoop(), SCEV::FlagNW);
2214 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2215 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2216 SmallVector<const SCEV *, 4> Operands;
2217 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2218 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2219 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2220 // Find an operand that's safely divisible.
2221 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2222 const SCEV *Op = M->getOperand(i);
2223 const SCEV *Div = getUDivExpr(Op, RHSC);
2224 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2225 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2228 return getMulExpr(Operands);
2232 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2233 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2234 SmallVector<const SCEV *, 4> Operands;
2235 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2236 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2237 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2239 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2240 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2241 if (isa<SCEVUDivExpr>(Op) ||
2242 getMulExpr(Op, RHS) != A->getOperand(i))
2244 Operands.push_back(Op);
2246 if (Operands.size() == A->getNumOperands())
2247 return getAddExpr(Operands);
2251 // Fold if both operands are constant.
2252 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2253 Constant *LHSCV = LHSC->getValue();
2254 Constant *RHSCV = RHSC->getValue();
2255 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2261 FoldingSetNodeID ID;
2262 ID.AddInteger(scUDivExpr);
2266 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2267 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2269 UniqueSCEVs.InsertNode(S, IP);
2273 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2274 APInt A = C1->getValue()->getValue().abs();
2275 APInt B = C2->getValue()->getValue().abs();
2276 uint32_t ABW = A.getBitWidth();
2277 uint32_t BBW = B.getBitWidth();
2284 return APIntOps::GreatestCommonDivisor(A, B);
2287 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2288 /// something simpler if possible. There is no representation for an exact udiv
2289 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2290 /// We can't do this when it's not exact because the udiv may be clearing bits.
2291 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2293 // TODO: we could try to find factors in all sorts of things, but for now we
2294 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2295 // end of this file for inspiration.
2297 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2299 return getUDivExpr(LHS, RHS);
2301 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2302 // If the mulexpr multiplies by a constant, then that constant must be the
2303 // first element of the mulexpr.
2304 if (const SCEVConstant *LHSCst =
2305 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2306 if (LHSCst == RHSCst) {
2307 SmallVector<const SCEV *, 2> Operands;
2308 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2309 return getMulExpr(Operands);
2312 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2313 // that there's a factor provided by one of the other terms. We need to
2315 APInt Factor = gcd(LHSCst, RHSCst);
2316 if (!Factor.isIntN(1)) {
2317 LHSCst = cast<SCEVConstant>(
2318 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2319 RHSCst = cast<SCEVConstant>(
2320 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2321 SmallVector<const SCEV *, 2> Operands;
2322 Operands.push_back(LHSCst);
2323 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2324 LHS = getMulExpr(Operands);
2326 Mul = dyn_cast<SCEVMulExpr>(LHS);
2328 return getUDivExactExpr(LHS, RHS);
2333 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2334 if (Mul->getOperand(i) == RHS) {
2335 SmallVector<const SCEV *, 2> Operands;
2336 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2337 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2338 return getMulExpr(Operands);
2342 return getUDivExpr(LHS, RHS);
2345 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2346 /// Simplify the expression as much as possible.
2347 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2349 SCEV::NoWrapFlags Flags) {
2350 SmallVector<const SCEV *, 4> Operands;
2351 Operands.push_back(Start);
2352 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2353 if (StepChrec->getLoop() == L) {
2354 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2355 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2358 Operands.push_back(Step);
2359 return getAddRecExpr(Operands, L, Flags);
2362 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2363 /// Simplify the expression as much as possible.
2365 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2366 const Loop *L, SCEV::NoWrapFlags Flags) {
2367 if (Operands.size() == 1) return Operands[0];
2369 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2370 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2371 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2372 "SCEVAddRecExpr operand types don't match!");
2373 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2374 assert(isLoopInvariant(Operands[i], L) &&
2375 "SCEVAddRecExpr operand is not loop-invariant!");
2378 if (Operands.back()->isZero()) {
2379 Operands.pop_back();
2380 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2383 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2384 // use that information to infer NUW and NSW flags. However, computing a
2385 // BE count requires calling getAddRecExpr, so we may not yet have a
2386 // meaningful BE count at this point (and if we don't, we'd be stuck
2387 // with a SCEVCouldNotCompute as the cached BE count).
2389 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2391 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2392 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2393 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2395 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2396 E = Operands.end(); I != E; ++I)
2397 if (!isKnownNonNegative(*I)) {
2401 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2404 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2405 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2406 const Loop *NestedLoop = NestedAR->getLoop();
2407 if (L->contains(NestedLoop) ?
2408 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2409 (!NestedLoop->contains(L) &&
2410 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2411 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2412 NestedAR->op_end());
2413 Operands[0] = NestedAR->getStart();
2414 // AddRecs require their operands be loop-invariant with respect to their
2415 // loops. Don't perform this transformation if it would break this
2417 bool AllInvariant = true;
2418 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2419 if (!isLoopInvariant(Operands[i], L)) {
2420 AllInvariant = false;
2424 // Create a recurrence for the outer loop with the same step size.
2426 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2427 // inner recurrence has the same property.
2428 SCEV::NoWrapFlags OuterFlags =
2429 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2431 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2432 AllInvariant = true;
2433 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2434 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2435 AllInvariant = false;
2439 // Ok, both add recurrences are valid after the transformation.
2441 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2442 // the outer recurrence has the same property.
2443 SCEV::NoWrapFlags InnerFlags =
2444 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2445 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2448 // Reset Operands to its original state.
2449 Operands[0] = NestedAR;
2453 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2454 // already have one, otherwise create a new one.
2455 FoldingSetNodeID ID;
2456 ID.AddInteger(scAddRecExpr);
2457 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2458 ID.AddPointer(Operands[i]);
2462 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2464 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2465 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2466 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2467 O, Operands.size(), L);
2468 UniqueSCEVs.InsertNode(S, IP);
2470 S->setNoWrapFlags(Flags);
2474 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2476 SmallVector<const SCEV *, 2> Ops;
2479 return getSMaxExpr(Ops);
2483 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2484 assert(!Ops.empty() && "Cannot get empty smax!");
2485 if (Ops.size() == 1) return Ops[0];
2487 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2488 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2489 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2490 "SCEVSMaxExpr operand types don't match!");
2493 // Sort by complexity, this groups all similar expression types together.
2494 GroupByComplexity(Ops, LI);
2496 // If there are any constants, fold them together.
2498 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2500 assert(Idx < Ops.size());
2501 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2502 // We found two constants, fold them together!
2503 ConstantInt *Fold = ConstantInt::get(getContext(),
2504 APIntOps::smax(LHSC->getValue()->getValue(),
2505 RHSC->getValue()->getValue()));
2506 Ops[0] = getConstant(Fold);
2507 Ops.erase(Ops.begin()+1); // Erase the folded element
2508 if (Ops.size() == 1) return Ops[0];
2509 LHSC = cast<SCEVConstant>(Ops[0]);
2512 // If we are left with a constant minimum-int, strip it off.
2513 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2514 Ops.erase(Ops.begin());
2516 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2517 // If we have an smax with a constant maximum-int, it will always be
2522 if (Ops.size() == 1) return Ops[0];
2525 // Find the first SMax
2526 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2529 // Check to see if one of the operands is an SMax. If so, expand its operands
2530 // onto our operand list, and recurse to simplify.
2531 if (Idx < Ops.size()) {
2532 bool DeletedSMax = false;
2533 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2534 Ops.erase(Ops.begin()+Idx);
2535 Ops.append(SMax->op_begin(), SMax->op_end());
2540 return getSMaxExpr(Ops);
2543 // Okay, check to see if the same value occurs in the operand list twice. If
2544 // so, delete one. Since we sorted the list, these values are required to
2546 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2547 // X smax Y smax Y --> X smax Y
2548 // X smax Y --> X, if X is always greater than Y
2549 if (Ops[i] == Ops[i+1] ||
2550 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2551 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2553 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2554 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2558 if (Ops.size() == 1) return Ops[0];
2560 assert(!Ops.empty() && "Reduced smax down to nothing!");
2562 // Okay, it looks like we really DO need an smax expr. Check to see if we
2563 // already have one, otherwise create a new one.
2564 FoldingSetNodeID ID;
2565 ID.AddInteger(scSMaxExpr);
2566 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2567 ID.AddPointer(Ops[i]);
2569 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2570 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2571 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2572 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2574 UniqueSCEVs.InsertNode(S, IP);
2578 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2580 SmallVector<const SCEV *, 2> Ops;
2583 return getUMaxExpr(Ops);
2587 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2588 assert(!Ops.empty() && "Cannot get empty umax!");
2589 if (Ops.size() == 1) return Ops[0];
2591 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2592 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2593 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2594 "SCEVUMaxExpr operand types don't match!");
2597 // Sort by complexity, this groups all similar expression types together.
2598 GroupByComplexity(Ops, LI);
2600 // If there are any constants, fold them together.
2602 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2604 assert(Idx < Ops.size());
2605 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2606 // We found two constants, fold them together!
2607 ConstantInt *Fold = ConstantInt::get(getContext(),
2608 APIntOps::umax(LHSC->getValue()->getValue(),
2609 RHSC->getValue()->getValue()));
2610 Ops[0] = getConstant(Fold);
2611 Ops.erase(Ops.begin()+1); // Erase the folded element
2612 if (Ops.size() == 1) return Ops[0];
2613 LHSC = cast<SCEVConstant>(Ops[0]);
2616 // If we are left with a constant minimum-int, strip it off.
2617 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2618 Ops.erase(Ops.begin());
2620 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2621 // If we have an umax with a constant maximum-int, it will always be
2626 if (Ops.size() == 1) return Ops[0];
2629 // Find the first UMax
2630 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2633 // Check to see if one of the operands is a UMax. If so, expand its operands
2634 // onto our operand list, and recurse to simplify.
2635 if (Idx < Ops.size()) {
2636 bool DeletedUMax = false;
2637 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2638 Ops.erase(Ops.begin()+Idx);
2639 Ops.append(UMax->op_begin(), UMax->op_end());
2644 return getUMaxExpr(Ops);
2647 // Okay, check to see if the same value occurs in the operand list twice. If
2648 // so, delete one. Since we sorted the list, these values are required to
2650 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2651 // X umax Y umax Y --> X umax Y
2652 // X umax Y --> X, if X is always greater than Y
2653 if (Ops[i] == Ops[i+1] ||
2654 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2655 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2657 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2658 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2662 if (Ops.size() == 1) return Ops[0];
2664 assert(!Ops.empty() && "Reduced umax down to nothing!");
2666 // Okay, it looks like we really DO need a umax expr. Check to see if we
2667 // already have one, otherwise create a new one.
2668 FoldingSetNodeID ID;
2669 ID.AddInteger(scUMaxExpr);
2670 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2671 ID.AddPointer(Ops[i]);
2673 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2674 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2675 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2676 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2678 UniqueSCEVs.InsertNode(S, IP);
2682 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2684 // ~smax(~x, ~y) == smin(x, y).
2685 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2688 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2690 // ~umax(~x, ~y) == umin(x, y)
2691 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2694 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2695 // If we have DataLayout, we can bypass creating a target-independent
2696 // constant expression and then folding it back into a ConstantInt.
2697 // This is just a compile-time optimization.
2699 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
2701 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2702 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2703 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2705 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2706 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2707 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2710 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2713 // If we have DataLayout, we can bypass creating a target-independent
2714 // constant expression and then folding it back into a ConstantInt.
2715 // This is just a compile-time optimization.
2717 return getConstant(IntTy,
2718 DL->getStructLayout(STy)->getElementOffset(FieldNo));
2721 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2722 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2723 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2726 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2727 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2730 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2731 // Don't attempt to do anything other than create a SCEVUnknown object
2732 // here. createSCEV only calls getUnknown after checking for all other
2733 // interesting possibilities, and any other code that calls getUnknown
2734 // is doing so in order to hide a value from SCEV canonicalization.
2736 FoldingSetNodeID ID;
2737 ID.AddInteger(scUnknown);
2740 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2741 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2742 "Stale SCEVUnknown in uniquing map!");
2745 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2747 FirstUnknown = cast<SCEVUnknown>(S);
2748 UniqueSCEVs.InsertNode(S, IP);
2752 //===----------------------------------------------------------------------===//
2753 // Basic SCEV Analysis and PHI Idiom Recognition Code
2756 /// isSCEVable - Test if values of the given type are analyzable within
2757 /// the SCEV framework. This primarily includes integer types, and it
2758 /// can optionally include pointer types if the ScalarEvolution class
2759 /// has access to target-specific information.
2760 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2761 // Integers and pointers are always SCEVable.
2762 return Ty->isIntegerTy() || Ty->isPointerTy();
2765 /// getTypeSizeInBits - Return the size in bits of the specified type,
2766 /// for which isSCEVable must return true.
2767 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2768 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2770 // If we have a DataLayout, use it!
2772 return DL->getTypeSizeInBits(Ty);
2774 // Integer types have fixed sizes.
2775 if (Ty->isIntegerTy())
2776 return Ty->getPrimitiveSizeInBits();
2778 // The only other support type is pointer. Without DataLayout, conservatively
2779 // assume pointers are 64-bit.
2780 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2784 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2785 /// the given type and which represents how SCEV will treat the given
2786 /// type, for which isSCEVable must return true. For pointer types,
2787 /// this is the pointer-sized integer type.
2788 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2789 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2791 if (Ty->isIntegerTy()) {
2795 // The only other support type is pointer.
2796 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2799 return DL->getIntPtrType(Ty);
2801 // Without DataLayout, conservatively assume pointers are 64-bit.
2802 return Type::getInt64Ty(getContext());
2805 const SCEV *ScalarEvolution::getCouldNotCompute() {
2806 return &CouldNotCompute;
2810 // Helper class working with SCEVTraversal to figure out if a SCEV contains
2811 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
2812 // is set iff if find such SCEVUnknown.
2814 struct FindInvalidSCEVUnknown {
2816 FindInvalidSCEVUnknown() { FindOne = false; }
2817 bool follow(const SCEV *S) {
2818 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
2822 if (!cast<SCEVUnknown>(S)->getValue())
2829 bool isDone() const { return FindOne; }
2833 bool ScalarEvolution::checkValidity(const SCEV *S) const {
2834 FindInvalidSCEVUnknown F;
2835 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
2841 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2842 /// expression and create a new one.
2843 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2844 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2846 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
2847 if (I != ValueExprMap.end()) {
2848 const SCEV *S = I->second;
2849 if (checkValidity(S))
2852 ValueExprMap.erase(I);
2854 const SCEV *S = createSCEV(V);
2856 // The process of creating a SCEV for V may have caused other SCEVs
2857 // to have been created, so it's necessary to insert the new entry
2858 // from scratch, rather than trying to remember the insert position
2860 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2864 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2866 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2867 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2869 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2871 Type *Ty = V->getType();
2872 Ty = getEffectiveSCEVType(Ty);
2873 return getMulExpr(V,
2874 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2877 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2878 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2879 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2881 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2883 Type *Ty = V->getType();
2884 Ty = getEffectiveSCEVType(Ty);
2885 const SCEV *AllOnes =
2886 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2887 return getMinusSCEV(AllOnes, V);
2890 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2891 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2892 SCEV::NoWrapFlags Flags) {
2893 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2895 // Fast path: X - X --> 0.
2897 return getConstant(LHS->getType(), 0);
2900 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2903 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2904 /// input value to the specified type. If the type must be extended, it is zero
2907 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2908 Type *SrcTy = V->getType();
2909 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2910 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2911 "Cannot truncate or zero extend with non-integer arguments!");
2912 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2913 return V; // No conversion
2914 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2915 return getTruncateExpr(V, Ty);
2916 return getZeroExtendExpr(V, Ty);
2919 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2920 /// input value to the specified type. If the type must be extended, it is sign
2923 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2925 Type *SrcTy = V->getType();
2926 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2927 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2928 "Cannot truncate or zero extend with non-integer arguments!");
2929 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2930 return V; // No conversion
2931 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2932 return getTruncateExpr(V, Ty);
2933 return getSignExtendExpr(V, Ty);
2936 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2937 /// input value to the specified type. If the type must be extended, it is zero
2938 /// extended. The conversion must not be narrowing.
2940 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2941 Type *SrcTy = V->getType();
2942 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2943 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2944 "Cannot noop or zero extend with non-integer arguments!");
2945 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2946 "getNoopOrZeroExtend cannot truncate!");
2947 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2948 return V; // No conversion
2949 return getZeroExtendExpr(V, Ty);
2952 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2953 /// input value to the specified type. If the type must be extended, it is sign
2954 /// extended. The conversion must not be narrowing.
2956 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2957 Type *SrcTy = V->getType();
2958 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2959 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2960 "Cannot noop or sign extend with non-integer arguments!");
2961 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2962 "getNoopOrSignExtend cannot truncate!");
2963 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2964 return V; // No conversion
2965 return getSignExtendExpr(V, Ty);
2968 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2969 /// the input value to the specified type. If the type must be extended,
2970 /// it is extended with unspecified bits. The conversion must not be
2973 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2974 Type *SrcTy = V->getType();
2975 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2976 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2977 "Cannot noop or any extend with non-integer arguments!");
2978 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2979 "getNoopOrAnyExtend cannot truncate!");
2980 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2981 return V; // No conversion
2982 return getAnyExtendExpr(V, Ty);
2985 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2986 /// input value to the specified type. The conversion must not be widening.
2988 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2989 Type *SrcTy = V->getType();
2990 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2991 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2992 "Cannot truncate or noop with non-integer arguments!");
2993 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2994 "getTruncateOrNoop cannot extend!");
2995 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2996 return V; // No conversion
2997 return getTruncateExpr(V, Ty);
3000 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3001 /// the types using zero-extension, and then perform a umax operation
3003 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3005 const SCEV *PromotedLHS = LHS;
3006 const SCEV *PromotedRHS = RHS;
3008 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3009 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3011 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3013 return getUMaxExpr(PromotedLHS, PromotedRHS);
3016 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3017 /// the types using zero-extension, and then perform a umin operation
3019 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3021 const SCEV *PromotedLHS = LHS;
3022 const SCEV *PromotedRHS = RHS;
3024 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3025 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3027 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3029 return getUMinExpr(PromotedLHS, PromotedRHS);
3032 /// getPointerBase - Transitively follow the chain of pointer-type operands
3033 /// until reaching a SCEV that does not have a single pointer operand. This
3034 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3035 /// but corner cases do exist.
3036 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3037 // A pointer operand may evaluate to a nonpointer expression, such as null.
3038 if (!V->getType()->isPointerTy())
3041 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3042 return getPointerBase(Cast->getOperand());
3044 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3045 const SCEV *PtrOp = nullptr;
3046 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3048 if ((*I)->getType()->isPointerTy()) {
3049 // Cannot find the base of an expression with multiple pointer operands.
3057 return getPointerBase(PtrOp);
3062 /// PushDefUseChildren - Push users of the given Instruction
3063 /// onto the given Worklist.
3065 PushDefUseChildren(Instruction *I,
3066 SmallVectorImpl<Instruction *> &Worklist) {
3067 // Push the def-use children onto the Worklist stack.
3068 for (User *U : I->users())
3069 Worklist.push_back(cast<Instruction>(U));
3072 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3073 /// instructions that depend on the given instruction and removes them from
3074 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3077 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3078 SmallVector<Instruction *, 16> Worklist;
3079 PushDefUseChildren(PN, Worklist);
3081 SmallPtrSet<Instruction *, 8> Visited;
3083 while (!Worklist.empty()) {
3084 Instruction *I = Worklist.pop_back_val();
3085 if (!Visited.insert(I)) continue;
3087 ValueExprMapType::iterator It =
3088 ValueExprMap.find_as(static_cast<Value *>(I));
3089 if (It != ValueExprMap.end()) {
3090 const SCEV *Old = It->second;
3092 // Short-circuit the def-use traversal if the symbolic name
3093 // ceases to appear in expressions.
3094 if (Old != SymName && !hasOperand(Old, SymName))
3097 // SCEVUnknown for a PHI either means that it has an unrecognized
3098 // structure, it's a PHI that's in the progress of being computed
3099 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3100 // additional loop trip count information isn't going to change anything.
3101 // In the second case, createNodeForPHI will perform the necessary
3102 // updates on its own when it gets to that point. In the third, we do
3103 // want to forget the SCEVUnknown.
3104 if (!isa<PHINode>(I) ||
3105 !isa<SCEVUnknown>(Old) ||
3106 (I != PN && Old == SymName)) {
3107 forgetMemoizedResults(Old);
3108 ValueExprMap.erase(It);
3112 PushDefUseChildren(I, Worklist);
3116 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3117 /// a loop header, making it a potential recurrence, or it doesn't.
3119 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3120 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3121 if (L->getHeader() == PN->getParent()) {
3122 // The loop may have multiple entrances or multiple exits; we can analyze
3123 // this phi as an addrec if it has a unique entry value and a unique
3125 Value *BEValueV = nullptr, *StartValueV = nullptr;
3126 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3127 Value *V = PN->getIncomingValue(i);
3128 if (L->contains(PN->getIncomingBlock(i))) {
3131 } else if (BEValueV != V) {
3135 } else if (!StartValueV) {
3137 } else if (StartValueV != V) {
3138 StartValueV = nullptr;
3142 if (BEValueV && StartValueV) {
3143 // While we are analyzing this PHI node, handle its value symbolically.
3144 const SCEV *SymbolicName = getUnknown(PN);
3145 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3146 "PHI node already processed?");
3147 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3149 // Using this symbolic name for the PHI, analyze the value coming around
3151 const SCEV *BEValue = getSCEV(BEValueV);
3153 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3154 // has a special value for the first iteration of the loop.
3156 // If the value coming around the backedge is an add with the symbolic
3157 // value we just inserted, then we found a simple induction variable!
3158 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3159 // If there is a single occurrence of the symbolic value, replace it
3160 // with a recurrence.
3161 unsigned FoundIndex = Add->getNumOperands();
3162 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3163 if (Add->getOperand(i) == SymbolicName)
3164 if (FoundIndex == e) {
3169 if (FoundIndex != Add->getNumOperands()) {
3170 // Create an add with everything but the specified operand.
3171 SmallVector<const SCEV *, 8> Ops;
3172 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3173 if (i != FoundIndex)
3174 Ops.push_back(Add->getOperand(i));
3175 const SCEV *Accum = getAddExpr(Ops);
3177 // This is not a valid addrec if the step amount is varying each
3178 // loop iteration, but is not itself an addrec in this loop.
3179 if (isLoopInvariant(Accum, L) ||
3180 (isa<SCEVAddRecExpr>(Accum) &&
3181 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3182 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3184 // If the increment doesn't overflow, then neither the addrec nor
3185 // the post-increment will overflow.
3186 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3187 if (OBO->hasNoUnsignedWrap())
3188 Flags = setFlags(Flags, SCEV::FlagNUW);
3189 if (OBO->hasNoSignedWrap())
3190 Flags = setFlags(Flags, SCEV::FlagNSW);
3191 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3192 // If the increment is an inbounds GEP, then we know the address
3193 // space cannot be wrapped around. We cannot make any guarantee
3194 // about signed or unsigned overflow because pointers are
3195 // unsigned but we may have a negative index from the base
3196 // pointer. We can guarantee that no unsigned wrap occurs if the
3197 // indices form a positive value.
3198 if (GEP->isInBounds()) {
3199 Flags = setFlags(Flags, SCEV::FlagNW);
3201 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3202 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3203 Flags = setFlags(Flags, SCEV::FlagNUW);
3205 } else if (const SubOperator *OBO =
3206 dyn_cast<SubOperator>(BEValueV)) {
3207 if (OBO->hasNoUnsignedWrap())
3208 Flags = setFlags(Flags, SCEV::FlagNUW);
3209 if (OBO->hasNoSignedWrap())
3210 Flags = setFlags(Flags, SCEV::FlagNSW);
3213 const SCEV *StartVal = getSCEV(StartValueV);
3214 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3216 // Since the no-wrap flags are on the increment, they apply to the
3217 // post-incremented value as well.
3218 if (isLoopInvariant(Accum, L))
3219 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3222 // Okay, for the entire analysis of this edge we assumed the PHI
3223 // to be symbolic. We now need to go back and purge all of the
3224 // entries for the scalars that use the symbolic expression.
3225 ForgetSymbolicName(PN, SymbolicName);
3226 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3230 } else if (const SCEVAddRecExpr *AddRec =
3231 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3232 // Otherwise, this could be a loop like this:
3233 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3234 // In this case, j = {1,+,1} and BEValue is j.
3235 // Because the other in-value of i (0) fits the evolution of BEValue
3236 // i really is an addrec evolution.
3237 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3238 const SCEV *StartVal = getSCEV(StartValueV);
3240 // If StartVal = j.start - j.stride, we can use StartVal as the
3241 // initial step of the addrec evolution.
3242 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3243 AddRec->getOperand(1))) {
3244 // FIXME: For constant StartVal, we should be able to infer
3246 const SCEV *PHISCEV =
3247 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3250 // Okay, for the entire analysis of this edge we assumed the PHI
3251 // to be symbolic. We now need to go back and purge all of the
3252 // entries for the scalars that use the symbolic expression.
3253 ForgetSymbolicName(PN, SymbolicName);
3254 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3262 // If the PHI has a single incoming value, follow that value, unless the
3263 // PHI's incoming blocks are in a different loop, in which case doing so
3264 // risks breaking LCSSA form. Instcombine would normally zap these, but
3265 // it doesn't have DominatorTree information, so it may miss cases.
3266 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT))
3267 if (LI->replacementPreservesLCSSAForm(PN, V))
3270 // If it's not a loop phi, we can't handle it yet.
3271 return getUnknown(PN);
3274 /// createNodeForGEP - Expand GEP instructions into add and multiply
3275 /// operations. This allows them to be analyzed by regular SCEV code.
3277 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3278 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3279 Value *Base = GEP->getOperand(0);
3280 // Don't attempt to analyze GEPs over unsized objects.
3281 if (!Base->getType()->getPointerElementType()->isSized())
3282 return getUnknown(GEP);
3284 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3285 // Add expression, because the Instruction may be guarded by control flow
3286 // and the no-overflow bits may not be valid for the expression in any
3288 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3290 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3291 gep_type_iterator GTI = gep_type_begin(GEP);
3292 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3296 // Compute the (potentially symbolic) offset in bytes for this index.
3297 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3298 // For a struct, add the member offset.
3299 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3300 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3302 // Add the field offset to the running total offset.
3303 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3305 // For an array, add the element offset, explicitly scaled.
3306 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3307 const SCEV *IndexS = getSCEV(Index);
3308 // Getelementptr indices are signed.
3309 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3311 // Multiply the index by the element size to compute the element offset.
3312 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3314 // Add the element offset to the running total offset.
3315 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3319 // Get the SCEV for the GEP base.
3320 const SCEV *BaseS = getSCEV(Base);
3322 // Add the total offset from all the GEP indices to the base.
3323 return getAddExpr(BaseS, TotalOffset, Wrap);
3326 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3327 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3328 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3329 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3331 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3332 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3333 return C->getValue()->getValue().countTrailingZeros();
3335 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3336 return std::min(GetMinTrailingZeros(T->getOperand()),
3337 (uint32_t)getTypeSizeInBits(T->getType()));
3339 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3340 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3341 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3342 getTypeSizeInBits(E->getType()) : OpRes;
3345 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3346 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3347 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3348 getTypeSizeInBits(E->getType()) : OpRes;
3351 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3352 // The result is the min of all operands results.
3353 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3354 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3355 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3359 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3360 // The result is the sum of all operands results.
3361 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3362 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3363 for (unsigned i = 1, e = M->getNumOperands();
3364 SumOpRes != BitWidth && i != e; ++i)
3365 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3370 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3371 // The result is the min of all operands results.
3372 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3373 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3374 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3378 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3379 // The result is the min of all operands results.
3380 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3381 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3382 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3386 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3387 // The result is the min of all operands results.
3388 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3389 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3390 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3394 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3395 // For a SCEVUnknown, ask ValueTracking.
3396 unsigned BitWidth = getTypeSizeInBits(U->getType());
3397 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3398 computeKnownBits(U->getValue(), Zeros, Ones);
3399 return Zeros.countTrailingOnes();
3406 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3409 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3410 // See if we've computed this range already.
3411 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3412 if (I != UnsignedRanges.end())
3415 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3416 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3418 unsigned BitWidth = getTypeSizeInBits(S->getType());
3419 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3421 // If the value has known zeros, the maximum unsigned value will have those
3422 // known zeros as well.
3423 uint32_t TZ = GetMinTrailingZeros(S);
3425 ConservativeResult =
3426 ConstantRange(APInt::getMinValue(BitWidth),
3427 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3429 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3430 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3431 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3432 X = X.add(getUnsignedRange(Add->getOperand(i)));
3433 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3436 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3437 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3438 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3439 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3440 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3443 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3444 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3445 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3446 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3447 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3450 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3451 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3452 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3453 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3454 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3457 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3458 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3459 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3460 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3463 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3464 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3465 return setUnsignedRange(ZExt,
3466 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3469 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3470 ConstantRange X = getUnsignedRange(SExt->getOperand());
3471 return setUnsignedRange(SExt,
3472 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3475 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3476 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3477 return setUnsignedRange(Trunc,
3478 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3481 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3482 // If there's no unsigned wrap, the value will never be less than its
3484 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3485 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3486 if (!C->getValue()->isZero())
3487 ConservativeResult =
3488 ConservativeResult.intersectWith(
3489 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3491 // TODO: non-affine addrec
3492 if (AddRec->isAffine()) {
3493 Type *Ty = AddRec->getType();
3494 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3495 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3496 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3497 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3499 const SCEV *Start = AddRec->getStart();
3500 const SCEV *Step = AddRec->getStepRecurrence(*this);
3502 ConstantRange StartRange = getUnsignedRange(Start);
3503 ConstantRange StepRange = getSignedRange(Step);
3504 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3505 ConstantRange EndRange =
3506 StartRange.add(MaxBECountRange.multiply(StepRange));
3508 // Check for overflow. This must be done with ConstantRange arithmetic
3509 // because we could be called from within the ScalarEvolution overflow
3511 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3512 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3513 ConstantRange ExtMaxBECountRange =
3514 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3515 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3516 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3518 return setUnsignedRange(AddRec, ConservativeResult);
3520 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3521 EndRange.getUnsignedMin());
3522 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3523 EndRange.getUnsignedMax());
3524 if (Min.isMinValue() && Max.isMaxValue())
3525 return setUnsignedRange(AddRec, ConservativeResult);
3526 return setUnsignedRange(AddRec,
3527 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3531 return setUnsignedRange(AddRec, ConservativeResult);
3534 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3535 // For a SCEVUnknown, ask ValueTracking.
3536 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3537 computeKnownBits(U->getValue(), Zeros, Ones, DL);
3538 if (Ones == ~Zeros + 1)
3539 return setUnsignedRange(U, ConservativeResult);
3540 return setUnsignedRange(U,
3541 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3544 return setUnsignedRange(S, ConservativeResult);
3547 /// getSignedRange - Determine the signed range for a particular SCEV.
3550 ScalarEvolution::getSignedRange(const SCEV *S) {
3551 // See if we've computed this range already.
3552 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3553 if (I != SignedRanges.end())
3556 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3557 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3559 unsigned BitWidth = getTypeSizeInBits(S->getType());
3560 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3562 // If the value has known zeros, the maximum signed value will have those
3563 // known zeros as well.
3564 uint32_t TZ = GetMinTrailingZeros(S);
3566 ConservativeResult =
3567 ConstantRange(APInt::getSignedMinValue(BitWidth),
3568 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3570 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3571 ConstantRange X = getSignedRange(Add->getOperand(0));
3572 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3573 X = X.add(getSignedRange(Add->getOperand(i)));
3574 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3577 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3578 ConstantRange X = getSignedRange(Mul->getOperand(0));
3579 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3580 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3581 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3584 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3585 ConstantRange X = getSignedRange(SMax->getOperand(0));
3586 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3587 X = X.smax(getSignedRange(SMax->getOperand(i)));
3588 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3591 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3592 ConstantRange X = getSignedRange(UMax->getOperand(0));
3593 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3594 X = X.umax(getSignedRange(UMax->getOperand(i)));
3595 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3598 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3599 ConstantRange X = getSignedRange(UDiv->getLHS());
3600 ConstantRange Y = getSignedRange(UDiv->getRHS());
3601 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3604 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3605 ConstantRange X = getSignedRange(ZExt->getOperand());
3606 return setSignedRange(ZExt,
3607 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3610 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3611 ConstantRange X = getSignedRange(SExt->getOperand());
3612 return setSignedRange(SExt,
3613 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3616 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3617 ConstantRange X = getSignedRange(Trunc->getOperand());
3618 return setSignedRange(Trunc,
3619 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3622 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3623 // If there's no signed wrap, and all the operands have the same sign or
3624 // zero, the value won't ever change sign.
3625 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3626 bool AllNonNeg = true;
3627 bool AllNonPos = true;
3628 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3629 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3630 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3633 ConservativeResult = ConservativeResult.intersectWith(
3634 ConstantRange(APInt(BitWidth, 0),
3635 APInt::getSignedMinValue(BitWidth)));
3637 ConservativeResult = ConservativeResult.intersectWith(
3638 ConstantRange(APInt::getSignedMinValue(BitWidth),
3639 APInt(BitWidth, 1)));
3642 // TODO: non-affine addrec
3643 if (AddRec->isAffine()) {
3644 Type *Ty = AddRec->getType();
3645 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3646 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3647 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3648 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3650 const SCEV *Start = AddRec->getStart();
3651 const SCEV *Step = AddRec->getStepRecurrence(*this);
3653 ConstantRange StartRange = getSignedRange(Start);
3654 ConstantRange StepRange = getSignedRange(Step);
3655 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3656 ConstantRange EndRange =
3657 StartRange.add(MaxBECountRange.multiply(StepRange));
3659 // Check for overflow. This must be done with ConstantRange arithmetic
3660 // because we could be called from within the ScalarEvolution overflow
3662 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3663 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3664 ConstantRange ExtMaxBECountRange =
3665 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3666 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3667 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3669 return setSignedRange(AddRec, ConservativeResult);
3671 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3672 EndRange.getSignedMin());
3673 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3674 EndRange.getSignedMax());
3675 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3676 return setSignedRange(AddRec, ConservativeResult);
3677 return setSignedRange(AddRec,
3678 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3682 return setSignedRange(AddRec, ConservativeResult);
3685 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3686 // For a SCEVUnknown, ask ValueTracking.
3687 if (!U->getValue()->getType()->isIntegerTy() && !DL)
3688 return setSignedRange(U, ConservativeResult);
3689 unsigned NS = ComputeNumSignBits(U->getValue(), DL);
3691 return setSignedRange(U, ConservativeResult);
3692 return setSignedRange(U, ConservativeResult.intersectWith(
3693 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3694 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3697 return setSignedRange(S, ConservativeResult);
3700 /// createSCEV - We know that there is no SCEV for the specified value.
3701 /// Analyze the expression.
3703 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3704 if (!isSCEVable(V->getType()))
3705 return getUnknown(V);
3707 unsigned Opcode = Instruction::UserOp1;
3708 if (Instruction *I = dyn_cast<Instruction>(V)) {
3709 Opcode = I->getOpcode();
3711 // Don't attempt to analyze instructions in blocks that aren't
3712 // reachable. Such instructions don't matter, and they aren't required
3713 // to obey basic rules for definitions dominating uses which this
3714 // analysis depends on.
3715 if (!DT->isReachableFromEntry(I->getParent()))
3716 return getUnknown(V);
3717 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3718 Opcode = CE->getOpcode();
3719 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3720 return getConstant(CI);
3721 else if (isa<ConstantPointerNull>(V))
3722 return getConstant(V->getType(), 0);
3723 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3724 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3726 return getUnknown(V);
3728 Operator *U = cast<Operator>(V);
3730 case Instruction::Add: {
3731 // The simple thing to do would be to just call getSCEV on both operands
3732 // and call getAddExpr with the result. However if we're looking at a
3733 // bunch of things all added together, this can be quite inefficient,
3734 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3735 // Instead, gather up all the operands and make a single getAddExpr call.
3736 // LLVM IR canonical form means we need only traverse the left operands.
3738 // Don't apply this instruction's NSW or NUW flags to the new
3739 // expression. The instruction may be guarded by control flow that the
3740 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3741 // mapped to the same SCEV expression, and it would be incorrect to transfer
3742 // NSW/NUW semantics to those operations.
3743 SmallVector<const SCEV *, 4> AddOps;
3744 AddOps.push_back(getSCEV(U->getOperand(1)));
3745 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3746 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3747 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3749 U = cast<Operator>(Op);
3750 const SCEV *Op1 = getSCEV(U->getOperand(1));
3751 if (Opcode == Instruction::Sub)
3752 AddOps.push_back(getNegativeSCEV(Op1));
3754 AddOps.push_back(Op1);
3756 AddOps.push_back(getSCEV(U->getOperand(0)));
3757 return getAddExpr(AddOps);
3759 case Instruction::Mul: {
3760 // Don't transfer NSW/NUW for the same reason as AddExpr.
3761 SmallVector<const SCEV *, 4> MulOps;
3762 MulOps.push_back(getSCEV(U->getOperand(1)));
3763 for (Value *Op = U->getOperand(0);
3764 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3765 Op = U->getOperand(0)) {
3766 U = cast<Operator>(Op);
3767 MulOps.push_back(getSCEV(U->getOperand(1)));
3769 MulOps.push_back(getSCEV(U->getOperand(0)));
3770 return getMulExpr(MulOps);
3772 case Instruction::UDiv:
3773 return getUDivExpr(getSCEV(U->getOperand(0)),
3774 getSCEV(U->getOperand(1)));
3775 case Instruction::Sub:
3776 return getMinusSCEV(getSCEV(U->getOperand(0)),
3777 getSCEV(U->getOperand(1)));
3778 case Instruction::And:
3779 // For an expression like x&255 that merely masks off the high bits,
3780 // use zext(trunc(x)) as the SCEV expression.
3781 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3782 if (CI->isNullValue())
3783 return getSCEV(U->getOperand(1));
3784 if (CI->isAllOnesValue())
3785 return getSCEV(U->getOperand(0));
3786 const APInt &A = CI->getValue();
3788 // Instcombine's ShrinkDemandedConstant may strip bits out of
3789 // constants, obscuring what would otherwise be a low-bits mask.
3790 // Use computeKnownBits to compute what ShrinkDemandedConstant
3791 // knew about to reconstruct a low-bits mask value.
3792 unsigned LZ = A.countLeadingZeros();
3793 unsigned TZ = A.countTrailingZeros();
3794 unsigned BitWidth = A.getBitWidth();
3795 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3796 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL);
3798 APInt EffectiveMask =
3799 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
3800 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
3801 const SCEV *MulCount = getConstant(
3802 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
3806 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
3807 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
3814 case Instruction::Or:
3815 // If the RHS of the Or is a constant, we may have something like:
3816 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3817 // optimizations will transparently handle this case.
3819 // In order for this transformation to be safe, the LHS must be of the
3820 // form X*(2^n) and the Or constant must be less than 2^n.
3821 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3822 const SCEV *LHS = getSCEV(U->getOperand(0));
3823 const APInt &CIVal = CI->getValue();
3824 if (GetMinTrailingZeros(LHS) >=
3825 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3826 // Build a plain add SCEV.
3827 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3828 // If the LHS of the add was an addrec and it has no-wrap flags,
3829 // transfer the no-wrap flags, since an or won't introduce a wrap.
3830 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3831 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3832 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3833 OldAR->getNoWrapFlags());
3839 case Instruction::Xor:
3840 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3841 // If the RHS of the xor is a signbit, then this is just an add.
3842 // Instcombine turns add of signbit into xor as a strength reduction step.
3843 if (CI->getValue().isSignBit())
3844 return getAddExpr(getSCEV(U->getOperand(0)),
3845 getSCEV(U->getOperand(1)));
3847 // If the RHS of xor is -1, then this is a not operation.
3848 if (CI->isAllOnesValue())
3849 return getNotSCEV(getSCEV(U->getOperand(0)));
3851 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3852 // This is a variant of the check for xor with -1, and it handles
3853 // the case where instcombine has trimmed non-demanded bits out
3854 // of an xor with -1.
3855 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3856 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3857 if (BO->getOpcode() == Instruction::And &&
3858 LCI->getValue() == CI->getValue())
3859 if (const SCEVZeroExtendExpr *Z =
3860 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3861 Type *UTy = U->getType();
3862 const SCEV *Z0 = Z->getOperand();
3863 Type *Z0Ty = Z0->getType();
3864 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3866 // If C is a low-bits mask, the zero extend is serving to
3867 // mask off the high bits. Complement the operand and
3868 // re-apply the zext.
3869 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3870 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3872 // If C is a single bit, it may be in the sign-bit position
3873 // before the zero-extend. In this case, represent the xor
3874 // using an add, which is equivalent, and re-apply the zext.
3875 APInt Trunc = CI->getValue().trunc(Z0TySize);
3876 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3878 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3884 case Instruction::Shl:
3885 // Turn shift left of a constant amount into a multiply.
3886 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3887 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3889 // If the shift count is not less than the bitwidth, the result of
3890 // the shift is undefined. Don't try to analyze it, because the
3891 // resolution chosen here may differ from the resolution chosen in
3892 // other parts of the compiler.
3893 if (SA->getValue().uge(BitWidth))
3896 Constant *X = ConstantInt::get(getContext(),
3897 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3898 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3902 case Instruction::LShr:
3903 // Turn logical shift right of a constant into a unsigned divide.
3904 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3905 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3907 // If the shift count is not less than the bitwidth, the result of
3908 // the shift is undefined. Don't try to analyze it, because the
3909 // resolution chosen here may differ from the resolution chosen in
3910 // other parts of the compiler.
3911 if (SA->getValue().uge(BitWidth))
3914 Constant *X = ConstantInt::get(getContext(),
3915 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3916 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3920 case Instruction::AShr:
3921 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3922 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3923 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3924 if (L->getOpcode() == Instruction::Shl &&
3925 L->getOperand(1) == U->getOperand(1)) {
3926 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3928 // If the shift count is not less than the bitwidth, the result of
3929 // the shift is undefined. Don't try to analyze it, because the
3930 // resolution chosen here may differ from the resolution chosen in
3931 // other parts of the compiler.
3932 if (CI->getValue().uge(BitWidth))
3935 uint64_t Amt = BitWidth - CI->getZExtValue();
3936 if (Amt == BitWidth)
3937 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3939 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3940 IntegerType::get(getContext(),
3946 case Instruction::Trunc:
3947 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3949 case Instruction::ZExt:
3950 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3952 case Instruction::SExt:
3953 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3955 case Instruction::BitCast:
3956 // BitCasts are no-op casts so we just eliminate the cast.
3957 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3958 return getSCEV(U->getOperand(0));
3961 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3962 // lead to pointer expressions which cannot safely be expanded to GEPs,
3963 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3964 // simplifying integer expressions.
3966 case Instruction::GetElementPtr:
3967 return createNodeForGEP(cast<GEPOperator>(U));
3969 case Instruction::PHI:
3970 return createNodeForPHI(cast<PHINode>(U));
3972 case Instruction::Select:
3973 // This could be a smax or umax that was lowered earlier.
3974 // Try to recover it.
3975 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3976 Value *LHS = ICI->getOperand(0);
3977 Value *RHS = ICI->getOperand(1);
3978 switch (ICI->getPredicate()) {
3979 case ICmpInst::ICMP_SLT:
3980 case ICmpInst::ICMP_SLE:
3981 std::swap(LHS, RHS);
3983 case ICmpInst::ICMP_SGT:
3984 case ICmpInst::ICMP_SGE:
3985 // a >s b ? a+x : b+x -> smax(a, b)+x
3986 // a >s b ? b+x : a+x -> smin(a, b)+x
3987 if (LHS->getType() == U->getType()) {
3988 const SCEV *LS = getSCEV(LHS);
3989 const SCEV *RS = getSCEV(RHS);
3990 const SCEV *LA = getSCEV(U->getOperand(1));
3991 const SCEV *RA = getSCEV(U->getOperand(2));
3992 const SCEV *LDiff = getMinusSCEV(LA, LS);
3993 const SCEV *RDiff = getMinusSCEV(RA, RS);
3995 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3996 LDiff = getMinusSCEV(LA, RS);
3997 RDiff = getMinusSCEV(RA, LS);
3999 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4002 case ICmpInst::ICMP_ULT:
4003 case ICmpInst::ICMP_ULE:
4004 std::swap(LHS, RHS);
4006 case ICmpInst::ICMP_UGT:
4007 case ICmpInst::ICMP_UGE:
4008 // a >u b ? a+x : b+x -> umax(a, b)+x
4009 // a >u b ? b+x : a+x -> umin(a, b)+x
4010 if (LHS->getType() == U->getType()) {
4011 const SCEV *LS = getSCEV(LHS);
4012 const SCEV *RS = getSCEV(RHS);
4013 const SCEV *LA = getSCEV(U->getOperand(1));
4014 const SCEV *RA = getSCEV(U->getOperand(2));
4015 const SCEV *LDiff = getMinusSCEV(LA, LS);
4016 const SCEV *RDiff = getMinusSCEV(RA, RS);
4018 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4019 LDiff = getMinusSCEV(LA, RS);
4020 RDiff = getMinusSCEV(RA, LS);
4022 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4025 case ICmpInst::ICMP_NE:
4026 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4027 if (LHS->getType() == U->getType() &&
4028 isa<ConstantInt>(RHS) &&
4029 cast<ConstantInt>(RHS)->isZero()) {
4030 const SCEV *One = getConstant(LHS->getType(), 1);
4031 const SCEV *LS = getSCEV(LHS);
4032 const SCEV *LA = getSCEV(U->getOperand(1));
4033 const SCEV *RA = getSCEV(U->getOperand(2));
4034 const SCEV *LDiff = getMinusSCEV(LA, LS);
4035 const SCEV *RDiff = getMinusSCEV(RA, One);
4037 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4040 case ICmpInst::ICMP_EQ:
4041 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4042 if (LHS->getType() == U->getType() &&
4043 isa<ConstantInt>(RHS) &&
4044 cast<ConstantInt>(RHS)->isZero()) {
4045 const SCEV *One = getConstant(LHS->getType(), 1);
4046 const SCEV *LS = getSCEV(LHS);
4047 const SCEV *LA = getSCEV(U->getOperand(1));
4048 const SCEV *RA = getSCEV(U->getOperand(2));
4049 const SCEV *LDiff = getMinusSCEV(LA, One);
4050 const SCEV *RDiff = getMinusSCEV(RA, LS);
4052 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4060 default: // We cannot analyze this expression.
4064 return getUnknown(V);
4069 //===----------------------------------------------------------------------===//
4070 // Iteration Count Computation Code
4073 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4074 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4075 /// constant. Will also return 0 if the maximum trip count is very large (>=
4078 /// This "trip count" assumes that control exits via ExitingBlock. More
4079 /// precisely, it is the number of times that control may reach ExitingBlock
4080 /// before taking the branch. For loops with multiple exits, it may not be the
4081 /// number times that the loop header executes because the loop may exit
4082 /// prematurely via another branch.
4084 /// FIXME: We conservatively call getBackedgeTakenCount(L) instead of
4085 /// getExitCount(L, ExitingBlock) to compute a safe trip count considering all
4086 /// loop exits. getExitCount() may return an exact count for this branch
4087 /// assuming no-signed-wrap. The number of well-defined iterations may actually
4088 /// be higher than this trip count if this exit test is skipped and the loop
4089 /// exits via a different branch. Ideally, getExitCount() would know whether it
4090 /// depends on a NSW assumption, and we would only fall back to a conservative
4091 /// trip count in that case.
4092 unsigned ScalarEvolution::
4093 getSmallConstantTripCount(Loop *L, BasicBlock * /*ExitingBlock*/) {
4094 const SCEVConstant *ExitCount =
4095 dyn_cast<SCEVConstant>(getBackedgeTakenCount(L));
4099 ConstantInt *ExitConst = ExitCount->getValue();
4101 // Guard against huge trip counts.
4102 if (ExitConst->getValue().getActiveBits() > 32)
4105 // In case of integer overflow, this returns 0, which is correct.
4106 return ((unsigned)ExitConst->getZExtValue()) + 1;
4109 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4110 /// trip count of this loop as a normal unsigned value, if possible. This
4111 /// means that the actual trip count is always a multiple of the returned
4112 /// value (don't forget the trip count could very well be zero as well!).
4114 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4115 /// multiple of a constant (which is also the case if the trip count is simply
4116 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4117 /// if the trip count is very large (>= 2^32).
4119 /// As explained in the comments for getSmallConstantTripCount, this assumes
4120 /// that control exits the loop via ExitingBlock.
4121 unsigned ScalarEvolution::
4122 getSmallConstantTripMultiple(Loop *L, BasicBlock * /*ExitingBlock*/) {
4123 const SCEV *ExitCount = getBackedgeTakenCount(L);
4124 if (ExitCount == getCouldNotCompute())
4127 // Get the trip count from the BE count by adding 1.
4128 const SCEV *TCMul = getAddExpr(ExitCount,
4129 getConstant(ExitCount->getType(), 1));
4130 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4131 // to factor simple cases.
4132 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4133 TCMul = Mul->getOperand(0);
4135 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4139 ConstantInt *Result = MulC->getValue();
4141 // Guard against huge trip counts (this requires checking
4142 // for zero to handle the case where the trip count == -1 and the
4144 if (!Result || Result->getValue().getActiveBits() > 32 ||
4145 Result->getValue().getActiveBits() == 0)
4148 return (unsigned)Result->getZExtValue();
4151 // getExitCount - Get the expression for the number of loop iterations for which
4152 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4153 // SCEVCouldNotCompute.
4154 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4155 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4158 /// getBackedgeTakenCount - If the specified loop has a predictable
4159 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4160 /// object. The backedge-taken count is the number of times the loop header
4161 /// will be branched to from within the loop. This is one less than the
4162 /// trip count of the loop, since it doesn't count the first iteration,
4163 /// when the header is branched to from outside the loop.
4165 /// Note that it is not valid to call this method on a loop without a
4166 /// loop-invariant backedge-taken count (see
4167 /// hasLoopInvariantBackedgeTakenCount).
4169 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4170 return getBackedgeTakenInfo(L).getExact(this);
4173 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4174 /// return the least SCEV value that is known never to be less than the
4175 /// actual backedge taken count.
4176 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4177 return getBackedgeTakenInfo(L).getMax(this);
4180 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4181 /// onto the given Worklist.
4183 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4184 BasicBlock *Header = L->getHeader();
4186 // Push all Loop-header PHIs onto the Worklist stack.
4187 for (BasicBlock::iterator I = Header->begin();
4188 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4189 Worklist.push_back(PN);
4192 const ScalarEvolution::BackedgeTakenInfo &
4193 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4194 // Initially insert an invalid entry for this loop. If the insertion
4195 // succeeds, proceed to actually compute a backedge-taken count and
4196 // update the value. The temporary CouldNotCompute value tells SCEV
4197 // code elsewhere that it shouldn't attempt to request a new
4198 // backedge-taken count, which could result in infinite recursion.
4199 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4200 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4202 return Pair.first->second;
4204 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4205 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4206 // must be cleared in this scope.
4207 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4209 if (Result.getExact(this) != getCouldNotCompute()) {
4210 assert(isLoopInvariant(Result.getExact(this), L) &&
4211 isLoopInvariant(Result.getMax(this), L) &&
4212 "Computed backedge-taken count isn't loop invariant for loop!");
4213 ++NumTripCountsComputed;
4215 else if (Result.getMax(this) == getCouldNotCompute() &&
4216 isa<PHINode>(L->getHeader()->begin())) {
4217 // Only count loops that have phi nodes as not being computable.
4218 ++NumTripCountsNotComputed;
4221 // Now that we know more about the trip count for this loop, forget any
4222 // existing SCEV values for PHI nodes in this loop since they are only
4223 // conservative estimates made without the benefit of trip count
4224 // information. This is similar to the code in forgetLoop, except that
4225 // it handles SCEVUnknown PHI nodes specially.
4226 if (Result.hasAnyInfo()) {
4227 SmallVector<Instruction *, 16> Worklist;
4228 PushLoopPHIs(L, Worklist);
4230 SmallPtrSet<Instruction *, 8> Visited;
4231 while (!Worklist.empty()) {
4232 Instruction *I = Worklist.pop_back_val();
4233 if (!Visited.insert(I)) continue;
4235 ValueExprMapType::iterator It =
4236 ValueExprMap.find_as(static_cast<Value *>(I));
4237 if (It != ValueExprMap.end()) {
4238 const SCEV *Old = It->second;
4240 // SCEVUnknown for a PHI either means that it has an unrecognized
4241 // structure, or it's a PHI that's in the progress of being computed
4242 // by createNodeForPHI. In the former case, additional loop trip
4243 // count information isn't going to change anything. In the later
4244 // case, createNodeForPHI will perform the necessary updates on its
4245 // own when it gets to that point.
4246 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4247 forgetMemoizedResults(Old);
4248 ValueExprMap.erase(It);
4250 if (PHINode *PN = dyn_cast<PHINode>(I))
4251 ConstantEvolutionLoopExitValue.erase(PN);
4254 PushDefUseChildren(I, Worklist);
4258 // Re-lookup the insert position, since the call to
4259 // ComputeBackedgeTakenCount above could result in a
4260 // recusive call to getBackedgeTakenInfo (on a different
4261 // loop), which would invalidate the iterator computed
4263 return BackedgeTakenCounts.find(L)->second = Result;
4266 /// forgetLoop - This method should be called by the client when it has
4267 /// changed a loop in a way that may effect ScalarEvolution's ability to
4268 /// compute a trip count, or if the loop is deleted.
4269 void ScalarEvolution::forgetLoop(const Loop *L) {
4270 // Drop any stored trip count value.
4271 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4272 BackedgeTakenCounts.find(L);
4273 if (BTCPos != BackedgeTakenCounts.end()) {
4274 BTCPos->second.clear();
4275 BackedgeTakenCounts.erase(BTCPos);
4278 // Drop information about expressions based on loop-header PHIs.
4279 SmallVector<Instruction *, 16> Worklist;
4280 PushLoopPHIs(L, Worklist);
4282 SmallPtrSet<Instruction *, 8> Visited;
4283 while (!Worklist.empty()) {
4284 Instruction *I = Worklist.pop_back_val();
4285 if (!Visited.insert(I)) continue;
4287 ValueExprMapType::iterator It =
4288 ValueExprMap.find_as(static_cast<Value *>(I));
4289 if (It != ValueExprMap.end()) {
4290 forgetMemoizedResults(It->second);
4291 ValueExprMap.erase(It);
4292 if (PHINode *PN = dyn_cast<PHINode>(I))
4293 ConstantEvolutionLoopExitValue.erase(PN);
4296 PushDefUseChildren(I, Worklist);
4299 // Forget all contained loops too, to avoid dangling entries in the
4300 // ValuesAtScopes map.
4301 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4305 /// forgetValue - This method should be called by the client when it has
4306 /// changed a value in a way that may effect its value, or which may
4307 /// disconnect it from a def-use chain linking it to a loop.
4308 void ScalarEvolution::forgetValue(Value *V) {
4309 Instruction *I = dyn_cast<Instruction>(V);
4312 // Drop information about expressions based on loop-header PHIs.
4313 SmallVector<Instruction *, 16> Worklist;
4314 Worklist.push_back(I);
4316 SmallPtrSet<Instruction *, 8> Visited;
4317 while (!Worklist.empty()) {
4318 I = Worklist.pop_back_val();
4319 if (!Visited.insert(I)) continue;
4321 ValueExprMapType::iterator It =
4322 ValueExprMap.find_as(static_cast<Value *>(I));
4323 if (It != ValueExprMap.end()) {
4324 forgetMemoizedResults(It->second);
4325 ValueExprMap.erase(It);
4326 if (PHINode *PN = dyn_cast<PHINode>(I))
4327 ConstantEvolutionLoopExitValue.erase(PN);
4330 PushDefUseChildren(I, Worklist);
4334 /// getExact - Get the exact loop backedge taken count considering all loop
4335 /// exits. A computable result can only be return for loops with a single exit.
4336 /// Returning the minimum taken count among all exits is incorrect because one
4337 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4338 /// the limit of each loop test is never skipped. This is a valid assumption as
4339 /// long as the loop exits via that test. For precise results, it is the
4340 /// caller's responsibility to specify the relevant loop exit using
4341 /// getExact(ExitingBlock, SE).
4343 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4344 // If any exits were not computable, the loop is not computable.
4345 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4347 // We need exactly one computable exit.
4348 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4349 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4351 const SCEV *BECount = nullptr;
4352 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4353 ENT != nullptr; ENT = ENT->getNextExit()) {
4355 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4358 BECount = ENT->ExactNotTaken;
4359 else if (BECount != ENT->ExactNotTaken)
4360 return SE->getCouldNotCompute();
4362 assert(BECount && "Invalid not taken count for loop exit");
4366 /// getExact - Get the exact not taken count for this loop exit.
4368 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4369 ScalarEvolution *SE) const {
4370 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4371 ENT != nullptr; ENT = ENT->getNextExit()) {
4373 if (ENT->ExitingBlock == ExitingBlock)
4374 return ENT->ExactNotTaken;
4376 return SE->getCouldNotCompute();
4379 /// getMax - Get the max backedge taken count for the loop.
4381 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4382 return Max ? Max : SE->getCouldNotCompute();
4385 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4386 ScalarEvolution *SE) const {
4387 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4390 if (!ExitNotTaken.ExitingBlock)
4393 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4394 ENT != nullptr; ENT = ENT->getNextExit()) {
4396 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4397 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4404 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4405 /// computable exit into a persistent ExitNotTakenInfo array.
4406 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4407 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4408 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4411 ExitNotTaken.setIncomplete();
4413 unsigned NumExits = ExitCounts.size();
4414 if (NumExits == 0) return;
4416 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4417 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4418 if (NumExits == 1) return;
4420 // Handle the rare case of multiple computable exits.
4421 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4423 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4424 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4425 PrevENT->setNextExit(ENT);
4426 ENT->ExitingBlock = ExitCounts[i].first;
4427 ENT->ExactNotTaken = ExitCounts[i].second;
4431 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4432 void ScalarEvolution::BackedgeTakenInfo::clear() {
4433 ExitNotTaken.ExitingBlock = nullptr;
4434 ExitNotTaken.ExactNotTaken = nullptr;
4435 delete[] ExitNotTaken.getNextExit();
4438 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4439 /// of the specified loop will execute.
4440 ScalarEvolution::BackedgeTakenInfo
4441 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4442 SmallVector<BasicBlock *, 8> ExitingBlocks;
4443 L->getExitingBlocks(ExitingBlocks);
4445 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4446 bool CouldComputeBECount = true;
4447 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4448 const SCEV *MustExitMaxBECount = nullptr;
4449 const SCEV *MayExitMaxBECount = nullptr;
4451 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4452 // and compute maxBECount.
4453 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4454 BasicBlock *ExitBB = ExitingBlocks[i];
4455 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4457 // 1. For each exit that can be computed, add an entry to ExitCounts.
4458 // CouldComputeBECount is true only if all exits can be computed.
4459 if (EL.Exact == getCouldNotCompute())
4460 // We couldn't compute an exact value for this exit, so
4461 // we won't be able to compute an exact value for the loop.
4462 CouldComputeBECount = false;
4464 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4466 // 2. Derive the loop's MaxBECount from each exit's max number of
4467 // non-exiting iterations. Partition the loop exits into two kinds:
4468 // LoopMustExits and LoopMayExits.
4470 // A LoopMustExit meets two requirements:
4472 // (a) Its ExitLimit.MustExit flag must be set which indicates that the exit
4473 // test condition cannot be skipped (the tested variable has unit stride or
4474 // the test is less-than or greater-than, rather than a strict inequality).
4476 // (b) It must dominate the loop latch, hence must be tested on every loop
4479 // If any computable LoopMustExit is found, then MaxBECount is the minimum
4480 // EL.Max of computable LoopMustExits. Otherwise, MaxBECount is
4481 // conservatively the maximum EL.Max, where CouldNotCompute is considered
4482 // greater than any computable EL.Max.
4483 if (EL.MustExit && EL.Max != getCouldNotCompute() && Latch &&
4484 DT->dominates(ExitBB, Latch)) {
4485 if (!MustExitMaxBECount)
4486 MustExitMaxBECount = EL.Max;
4488 MustExitMaxBECount =
4489 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4491 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4492 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4493 MayExitMaxBECount = EL.Max;
4496 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4500 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4501 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4502 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4505 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4506 /// loop will execute if it exits via the specified block.
4507 ScalarEvolution::ExitLimit
4508 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4510 // Okay, we've chosen an exiting block. See what condition causes us to
4511 // exit at this block and remember the exit block and whether all other targets
4512 // lead to the loop header.
4513 bool MustExecuteLoopHeader = true;
4514 BasicBlock *Exit = nullptr;
4515 for (BasicBlock *Succ : successors(ExitingBlock))
4516 if (!L->contains(Succ)) {
4517 if (Exit) // Multiple exit successors.
4518 return getCouldNotCompute();
4520 } else if (Succ != L->getHeader()) {
4521 MustExecuteLoopHeader = false;
4524 // At this point, we know we have a conditional branch that determines whether
4525 // the loop is exited. However, we don't know if the branch is executed each
4526 // time through the loop. If not, then the execution count of the branch will
4527 // not be equal to the trip count of the loop.
4529 // Currently we check for this by checking to see if the Exit branch goes to
4530 // the loop header. If so, we know it will always execute the same number of
4531 // times as the loop. We also handle the case where the exit block *is* the
4532 // loop header. This is common for un-rotated loops.
4534 // If both of those tests fail, walk up the unique predecessor chain to the
4535 // header, stopping if there is an edge that doesn't exit the loop. If the
4536 // header is reached, the execution count of the branch will be equal to the
4537 // trip count of the loop.
4539 // More extensive analysis could be done to handle more cases here.
4541 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4542 // The simple checks failed, try climbing the unique predecessor chain
4543 // up to the header.
4545 for (BasicBlock *BB = ExitingBlock; BB; ) {
4546 BasicBlock *Pred = BB->getUniquePredecessor();
4548 return getCouldNotCompute();
4549 TerminatorInst *PredTerm = Pred->getTerminator();
4550 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4551 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4554 // If the predecessor has a successor that isn't BB and isn't
4555 // outside the loop, assume the worst.
4556 if (L->contains(PredSucc))
4557 return getCouldNotCompute();
4559 if (Pred == L->getHeader()) {
4566 return getCouldNotCompute();
4569 TerminatorInst *Term = ExitingBlock->getTerminator();
4570 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4571 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4572 // Proceed to the next level to examine the exit condition expression.
4573 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4574 BI->getSuccessor(1),
4575 /*IsSubExpr=*/false);
4578 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4579 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4580 /*IsSubExpr=*/false);
4582 return getCouldNotCompute();
4585 /// ComputeExitLimitFromCond - Compute the number of times the
4586 /// backedge of the specified loop will execute if its exit condition
4587 /// were a conditional branch of ExitCond, TBB, and FBB.
4589 /// @param IsSubExpr is true if ExitCond does not directly control the exit
4590 /// branch. In this case, we cannot assume that the loop only exits when the
4591 /// condition is true and cannot infer that failing to meet the condition prior
4592 /// to integer wraparound results in undefined behavior.
4593 ScalarEvolution::ExitLimit
4594 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4599 // Check if the controlling expression for this loop is an And or Or.
4600 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4601 if (BO->getOpcode() == Instruction::And) {
4602 // Recurse on the operands of the and.
4603 bool EitherMayExit = L->contains(TBB);
4604 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4605 IsSubExpr || EitherMayExit);
4606 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4607 IsSubExpr || EitherMayExit);
4608 const SCEV *BECount = getCouldNotCompute();
4609 const SCEV *MaxBECount = getCouldNotCompute();
4610 bool MustExit = false;
4611 if (EitherMayExit) {
4612 // Both conditions must be true for the loop to continue executing.
4613 // Choose the less conservative count.
4614 if (EL0.Exact == getCouldNotCompute() ||
4615 EL1.Exact == getCouldNotCompute())
4616 BECount = getCouldNotCompute();
4618 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4619 if (EL0.Max == getCouldNotCompute())
4620 MaxBECount = EL1.Max;
4621 else if (EL1.Max == getCouldNotCompute())
4622 MaxBECount = EL0.Max;
4624 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4625 MustExit = EL0.MustExit || EL1.MustExit;
4627 // Both conditions must be true at the same time for the loop to exit.
4628 // For now, be conservative.
4629 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4630 if (EL0.Max == EL1.Max)
4631 MaxBECount = EL0.Max;
4632 if (EL0.Exact == EL1.Exact)
4633 BECount = EL0.Exact;
4634 MustExit = EL0.MustExit && EL1.MustExit;
4637 return ExitLimit(BECount, MaxBECount, MustExit);
4639 if (BO->getOpcode() == Instruction::Or) {
4640 // Recurse on the operands of the or.
4641 bool EitherMayExit = L->contains(FBB);
4642 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4643 IsSubExpr || EitherMayExit);
4644 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4645 IsSubExpr || EitherMayExit);
4646 const SCEV *BECount = getCouldNotCompute();
4647 const SCEV *MaxBECount = getCouldNotCompute();
4648 bool MustExit = false;
4649 if (EitherMayExit) {
4650 // Both conditions must be false for the loop to continue executing.
4651 // Choose the less conservative count.
4652 if (EL0.Exact == getCouldNotCompute() ||
4653 EL1.Exact == getCouldNotCompute())
4654 BECount = getCouldNotCompute();
4656 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4657 if (EL0.Max == getCouldNotCompute())
4658 MaxBECount = EL1.Max;
4659 else if (EL1.Max == getCouldNotCompute())
4660 MaxBECount = EL0.Max;
4662 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4663 MustExit = EL0.MustExit || EL1.MustExit;
4665 // Both conditions must be false at the same time for the loop to exit.
4666 // For now, be conservative.
4667 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4668 if (EL0.Max == EL1.Max)
4669 MaxBECount = EL0.Max;
4670 if (EL0.Exact == EL1.Exact)
4671 BECount = EL0.Exact;
4672 MustExit = EL0.MustExit && EL1.MustExit;
4675 return ExitLimit(BECount, MaxBECount, MustExit);
4679 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4680 // Proceed to the next level to examine the icmp.
4681 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4682 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, IsSubExpr);
4684 // Check for a constant condition. These are normally stripped out by
4685 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4686 // preserve the CFG and is temporarily leaving constant conditions
4688 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4689 if (L->contains(FBB) == !CI->getZExtValue())
4690 // The backedge is always taken.
4691 return getCouldNotCompute();
4693 // The backedge is never taken.
4694 return getConstant(CI->getType(), 0);
4697 // If it's not an integer or pointer comparison then compute it the hard way.
4698 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4701 /// ComputeExitLimitFromICmp - Compute the number of times the
4702 /// backedge of the specified loop will execute if its exit condition
4703 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4704 ScalarEvolution::ExitLimit
4705 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4711 // If the condition was exit on true, convert the condition to exit on false
4712 ICmpInst::Predicate Cond;
4713 if (!L->contains(FBB))
4714 Cond = ExitCond->getPredicate();
4716 Cond = ExitCond->getInversePredicate();
4718 // Handle common loops like: for (X = "string"; *X; ++X)
4719 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4720 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4722 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4723 if (ItCnt.hasAnyInfo())
4727 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4728 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4730 // Try to evaluate any dependencies out of the loop.
4731 LHS = getSCEVAtScope(LHS, L);
4732 RHS = getSCEVAtScope(RHS, L);
4734 // At this point, we would like to compute how many iterations of the
4735 // loop the predicate will return true for these inputs.
4736 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4737 // If there is a loop-invariant, force it into the RHS.
4738 std::swap(LHS, RHS);
4739 Cond = ICmpInst::getSwappedPredicate(Cond);
4742 // Simplify the operands before analyzing them.
4743 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4745 // If we have a comparison of a chrec against a constant, try to use value
4746 // ranges to answer this query.
4747 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4748 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4749 if (AddRec->getLoop() == L) {
4750 // Form the constant range.
4751 ConstantRange CompRange(
4752 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4754 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4755 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4759 case ICmpInst::ICMP_NE: { // while (X != Y)
4760 // Convert to: while (X-Y != 0)
4761 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4762 if (EL.hasAnyInfo()) return EL;
4765 case ICmpInst::ICMP_EQ: { // while (X == Y)
4766 // Convert to: while (X-Y == 0)
4767 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4768 if (EL.hasAnyInfo()) return EL;
4771 case ICmpInst::ICMP_SLT:
4772 case ICmpInst::ICMP_ULT: { // while (X < Y)
4773 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
4774 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, IsSubExpr);
4775 if (EL.hasAnyInfo()) return EL;
4778 case ICmpInst::ICMP_SGT:
4779 case ICmpInst::ICMP_UGT: { // while (X > Y)
4780 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
4781 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, IsSubExpr);
4782 if (EL.hasAnyInfo()) return EL;
4787 dbgs() << "ComputeBackedgeTakenCount ";
4788 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4789 dbgs() << "[unsigned] ";
4790 dbgs() << *LHS << " "
4791 << Instruction::getOpcodeName(Instruction::ICmp)
4792 << " " << *RHS << "\n";
4796 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4799 ScalarEvolution::ExitLimit
4800 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
4802 BasicBlock *ExitingBlock,
4804 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
4806 // Give up if the exit is the default dest of a switch.
4807 if (Switch->getDefaultDest() == ExitingBlock)
4808 return getCouldNotCompute();
4810 assert(L->contains(Switch->getDefaultDest()) &&
4811 "Default case must not exit the loop!");
4812 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
4813 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
4815 // while (X != Y) --> while (X-Y != 0)
4816 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4817 if (EL.hasAnyInfo())
4820 return getCouldNotCompute();
4823 static ConstantInt *
4824 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4825 ScalarEvolution &SE) {
4826 const SCEV *InVal = SE.getConstant(C);
4827 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4828 assert(isa<SCEVConstant>(Val) &&
4829 "Evaluation of SCEV at constant didn't fold correctly?");
4830 return cast<SCEVConstant>(Val)->getValue();
4833 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4834 /// 'icmp op load X, cst', try to see if we can compute the backedge
4835 /// execution count.
4836 ScalarEvolution::ExitLimit
4837 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4841 ICmpInst::Predicate predicate) {
4843 if (LI->isVolatile()) return getCouldNotCompute();
4845 // Check to see if the loaded pointer is a getelementptr of a global.
4846 // TODO: Use SCEV instead of manually grubbing with GEPs.
4847 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4848 if (!GEP) return getCouldNotCompute();
4850 // Make sure that it is really a constant global we are gepping, with an
4851 // initializer, and make sure the first IDX is really 0.
4852 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4853 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4854 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4855 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4856 return getCouldNotCompute();
4858 // Okay, we allow one non-constant index into the GEP instruction.
4859 Value *VarIdx = nullptr;
4860 std::vector<Constant*> Indexes;
4861 unsigned VarIdxNum = 0;
4862 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4863 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4864 Indexes.push_back(CI);
4865 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4866 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4867 VarIdx = GEP->getOperand(i);
4869 Indexes.push_back(nullptr);
4872 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4874 return getCouldNotCompute();
4876 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4877 // Check to see if X is a loop variant variable value now.
4878 const SCEV *Idx = getSCEV(VarIdx);
4879 Idx = getSCEVAtScope(Idx, L);
4881 // We can only recognize very limited forms of loop index expressions, in
4882 // particular, only affine AddRec's like {C1,+,C2}.
4883 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4884 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4885 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4886 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4887 return getCouldNotCompute();
4889 unsigned MaxSteps = MaxBruteForceIterations;
4890 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4891 ConstantInt *ItCst = ConstantInt::get(
4892 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4893 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4895 // Form the GEP offset.
4896 Indexes[VarIdxNum] = Val;
4898 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4900 if (!Result) break; // Cannot compute!
4902 // Evaluate the condition for this iteration.
4903 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4904 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4905 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4907 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4908 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4911 ++NumArrayLenItCounts;
4912 return getConstant(ItCst); // Found terminating iteration!
4915 return getCouldNotCompute();
4919 /// CanConstantFold - Return true if we can constant fold an instruction of the
4920 /// specified type, assuming that all operands were constants.
4921 static bool CanConstantFold(const Instruction *I) {
4922 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4923 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4927 if (const CallInst *CI = dyn_cast<CallInst>(I))
4928 if (const Function *F = CI->getCalledFunction())
4929 return canConstantFoldCallTo(F);
4933 /// Determine whether this instruction can constant evolve within this loop
4934 /// assuming its operands can all constant evolve.
4935 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4936 // An instruction outside of the loop can't be derived from a loop PHI.
4937 if (!L->contains(I)) return false;
4939 if (isa<PHINode>(I)) {
4940 if (L->getHeader() == I->getParent())
4943 // We don't currently keep track of the control flow needed to evaluate
4944 // PHIs, so we cannot handle PHIs inside of loops.
4948 // If we won't be able to constant fold this expression even if the operands
4949 // are constants, bail early.
4950 return CanConstantFold(I);
4953 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4954 /// recursing through each instruction operand until reaching a loop header phi.
4956 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4957 DenseMap<Instruction *, PHINode *> &PHIMap) {
4959 // Otherwise, we can evaluate this instruction if all of its operands are
4960 // constant or derived from a PHI node themselves.
4961 PHINode *PHI = nullptr;
4962 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4963 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4965 if (isa<Constant>(*OpI)) continue;
4967 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4968 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
4970 PHINode *P = dyn_cast<PHINode>(OpInst);
4972 // If this operand is already visited, reuse the prior result.
4973 // We may have P != PHI if this is the deepest point at which the
4974 // inconsistent paths meet.
4975 P = PHIMap.lookup(OpInst);
4977 // Recurse and memoize the results, whether a phi is found or not.
4978 // This recursive call invalidates pointers into PHIMap.
4979 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4983 return nullptr; // Not evolving from PHI
4984 if (PHI && PHI != P)
4985 return nullptr; // Evolving from multiple different PHIs.
4988 // This is a expression evolving from a constant PHI!
4992 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4993 /// in the loop that V is derived from. We allow arbitrary operations along the
4994 /// way, but the operands of an operation must either be constants or a value
4995 /// derived from a constant PHI. If this expression does not fit with these
4996 /// constraints, return null.
4997 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4998 Instruction *I = dyn_cast<Instruction>(V);
4999 if (!I || !canConstantEvolve(I, L)) return nullptr;
5001 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5005 // Record non-constant instructions contained by the loop.
5006 DenseMap<Instruction *, PHINode *> PHIMap;
5007 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5010 /// EvaluateExpression - Given an expression that passes the
5011 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5012 /// in the loop has the value PHIVal. If we can't fold this expression for some
5013 /// reason, return null.
5014 static Constant *EvaluateExpression(Value *V, const Loop *L,
5015 DenseMap<Instruction *, Constant *> &Vals,
5016 const DataLayout *DL,
5017 const TargetLibraryInfo *TLI) {
5018 // Convenient constant check, but redundant for recursive calls.
5019 if (Constant *C = dyn_cast<Constant>(V)) return C;
5020 Instruction *I = dyn_cast<Instruction>(V);
5021 if (!I) return nullptr;
5023 if (Constant *C = Vals.lookup(I)) return C;
5025 // An instruction inside the loop depends on a value outside the loop that we
5026 // weren't given a mapping for, or a value such as a call inside the loop.
5027 if (!canConstantEvolve(I, L)) return nullptr;
5029 // An unmapped PHI can be due to a branch or another loop inside this loop,
5030 // or due to this not being the initial iteration through a loop where we
5031 // couldn't compute the evolution of this particular PHI last time.
5032 if (isa<PHINode>(I)) return nullptr;
5034 std::vector<Constant*> Operands(I->getNumOperands());
5036 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5037 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5039 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5040 if (!Operands[i]) return nullptr;
5043 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5045 if (!C) return nullptr;
5049 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5050 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5051 Operands[1], DL, TLI);
5052 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5053 if (!LI->isVolatile())
5054 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5056 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5060 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5061 /// in the header of its containing loop, we know the loop executes a
5062 /// constant number of times, and the PHI node is just a recurrence
5063 /// involving constants, fold it.
5065 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5068 DenseMap<PHINode*, Constant*>::const_iterator I =
5069 ConstantEvolutionLoopExitValue.find(PN);
5070 if (I != ConstantEvolutionLoopExitValue.end())
5073 if (BEs.ugt(MaxBruteForceIterations))
5074 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5076 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5078 DenseMap<Instruction *, Constant *> CurrentIterVals;
5079 BasicBlock *Header = L->getHeader();
5080 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5082 // Since the loop is canonicalized, the PHI node must have two entries. One
5083 // entry must be a constant (coming in from outside of the loop), and the
5084 // second must be derived from the same PHI.
5085 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5086 PHINode *PHI = nullptr;
5087 for (BasicBlock::iterator I = Header->begin();
5088 (PHI = dyn_cast<PHINode>(I)); ++I) {
5089 Constant *StartCST =
5090 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5091 if (!StartCST) continue;
5092 CurrentIterVals[PHI] = StartCST;
5094 if (!CurrentIterVals.count(PN))
5095 return RetVal = nullptr;
5097 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5099 // Execute the loop symbolically to determine the exit value.
5100 if (BEs.getActiveBits() >= 32)
5101 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5103 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5104 unsigned IterationNum = 0;
5105 for (; ; ++IterationNum) {
5106 if (IterationNum == NumIterations)
5107 return RetVal = CurrentIterVals[PN]; // Got exit value!
5109 // Compute the value of the PHIs for the next iteration.
5110 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5111 DenseMap<Instruction *, Constant *> NextIterVals;
5112 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5115 return nullptr; // Couldn't evaluate!
5116 NextIterVals[PN] = NextPHI;
5118 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5120 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5121 // cease to be able to evaluate one of them or if they stop evolving,
5122 // because that doesn't necessarily prevent us from computing PN.
5123 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5124 for (DenseMap<Instruction *, Constant *>::const_iterator
5125 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5126 PHINode *PHI = dyn_cast<PHINode>(I->first);
5127 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5128 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5130 // We use two distinct loops because EvaluateExpression may invalidate any
5131 // iterators into CurrentIterVals.
5132 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5133 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5134 PHINode *PHI = I->first;
5135 Constant *&NextPHI = NextIterVals[PHI];
5136 if (!NextPHI) { // Not already computed.
5137 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5138 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5140 if (NextPHI != I->second)
5141 StoppedEvolving = false;
5144 // If all entries in CurrentIterVals == NextIterVals then we can stop
5145 // iterating, the loop can't continue to change.
5146 if (StoppedEvolving)
5147 return RetVal = CurrentIterVals[PN];
5149 CurrentIterVals.swap(NextIterVals);
5153 /// ComputeExitCountExhaustively - If the loop is known to execute a
5154 /// constant number of times (the condition evolves only from constants),
5155 /// try to evaluate a few iterations of the loop until we get the exit
5156 /// condition gets a value of ExitWhen (true or false). If we cannot
5157 /// evaluate the trip count of the loop, return getCouldNotCompute().
5158 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5161 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5162 if (!PN) return getCouldNotCompute();
5164 // If the loop is canonicalized, the PHI will have exactly two entries.
5165 // That's the only form we support here.
5166 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5168 DenseMap<Instruction *, Constant *> CurrentIterVals;
5169 BasicBlock *Header = L->getHeader();
5170 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5172 // One entry must be a constant (coming in from outside of the loop), and the
5173 // second must be derived from the same PHI.
5174 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5175 PHINode *PHI = nullptr;
5176 for (BasicBlock::iterator I = Header->begin();
5177 (PHI = dyn_cast<PHINode>(I)); ++I) {
5178 Constant *StartCST =
5179 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5180 if (!StartCST) continue;
5181 CurrentIterVals[PHI] = StartCST;
5183 if (!CurrentIterVals.count(PN))
5184 return getCouldNotCompute();
5186 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5187 // the loop symbolically to determine when the condition gets a value of
5190 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5191 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5192 ConstantInt *CondVal =
5193 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5196 // Couldn't symbolically evaluate.
5197 if (!CondVal) return getCouldNotCompute();
5199 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5200 ++NumBruteForceTripCountsComputed;
5201 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5204 // Update all the PHI nodes for the next iteration.
5205 DenseMap<Instruction *, Constant *> NextIterVals;
5207 // Create a list of which PHIs we need to compute. We want to do this before
5208 // calling EvaluateExpression on them because that may invalidate iterators
5209 // into CurrentIterVals.
5210 SmallVector<PHINode *, 8> PHIsToCompute;
5211 for (DenseMap<Instruction *, Constant *>::const_iterator
5212 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5213 PHINode *PHI = dyn_cast<PHINode>(I->first);
5214 if (!PHI || PHI->getParent() != Header) continue;
5215 PHIsToCompute.push_back(PHI);
5217 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5218 E = PHIsToCompute.end(); I != E; ++I) {
5220 Constant *&NextPHI = NextIterVals[PHI];
5221 if (NextPHI) continue; // Already computed!
5223 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5224 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5226 CurrentIterVals.swap(NextIterVals);
5229 // Too many iterations were needed to evaluate.
5230 return getCouldNotCompute();
5233 /// getSCEVAtScope - Return a SCEV expression for the specified value
5234 /// at the specified scope in the program. The L value specifies a loop
5235 /// nest to evaluate the expression at, where null is the top-level or a
5236 /// specified loop is immediately inside of the loop.
5238 /// This method can be used to compute the exit value for a variable defined
5239 /// in a loop by querying what the value will hold in the parent loop.
5241 /// In the case that a relevant loop exit value cannot be computed, the
5242 /// original value V is returned.
5243 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5244 // Check to see if we've folded this expression at this loop before.
5245 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5246 for (unsigned u = 0; u < Values.size(); u++) {
5247 if (Values[u].first == L)
5248 return Values[u].second ? Values[u].second : V;
5250 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5251 // Otherwise compute it.
5252 const SCEV *C = computeSCEVAtScope(V, L);
5253 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5254 for (unsigned u = Values2.size(); u > 0; u--) {
5255 if (Values2[u - 1].first == L) {
5256 Values2[u - 1].second = C;
5263 /// This builds up a Constant using the ConstantExpr interface. That way, we
5264 /// will return Constants for objects which aren't represented by a
5265 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5266 /// Returns NULL if the SCEV isn't representable as a Constant.
5267 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5268 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5269 case scCouldNotCompute:
5273 return cast<SCEVConstant>(V)->getValue();
5275 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5276 case scSignExtend: {
5277 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5278 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5279 return ConstantExpr::getSExt(CastOp, SS->getType());
5282 case scZeroExtend: {
5283 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5284 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5285 return ConstantExpr::getZExt(CastOp, SZ->getType());
5289 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5290 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5291 return ConstantExpr::getTrunc(CastOp, ST->getType());
5295 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5296 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5297 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5298 unsigned AS = PTy->getAddressSpace();
5299 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5300 C = ConstantExpr::getBitCast(C, DestPtrTy);
5302 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5303 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5304 if (!C2) return nullptr;
5307 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5308 unsigned AS = C2->getType()->getPointerAddressSpace();
5310 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5311 // The offsets have been converted to bytes. We can add bytes to an
5312 // i8* by GEP with the byte count in the first index.
5313 C = ConstantExpr::getBitCast(C, DestPtrTy);
5316 // Don't bother trying to sum two pointers. We probably can't
5317 // statically compute a load that results from it anyway.
5318 if (C2->getType()->isPointerTy())
5321 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5322 if (PTy->getElementType()->isStructTy())
5323 C2 = ConstantExpr::getIntegerCast(
5324 C2, Type::getInt32Ty(C->getContext()), true);
5325 C = ConstantExpr::getGetElementPtr(C, C2);
5327 C = ConstantExpr::getAdd(C, C2);
5334 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5335 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5336 // Don't bother with pointers at all.
5337 if (C->getType()->isPointerTy()) return nullptr;
5338 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5339 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5340 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5341 C = ConstantExpr::getMul(C, C2);
5348 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5349 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5350 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5351 if (LHS->getType() == RHS->getType())
5352 return ConstantExpr::getUDiv(LHS, RHS);
5357 break; // TODO: smax, umax.
5362 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5363 if (isa<SCEVConstant>(V)) return V;
5365 // If this instruction is evolved from a constant-evolving PHI, compute the
5366 // exit value from the loop without using SCEVs.
5367 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5368 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5369 const Loop *LI = (*this->LI)[I->getParent()];
5370 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5371 if (PHINode *PN = dyn_cast<PHINode>(I))
5372 if (PN->getParent() == LI->getHeader()) {
5373 // Okay, there is no closed form solution for the PHI node. Check
5374 // to see if the loop that contains it has a known backedge-taken
5375 // count. If so, we may be able to force computation of the exit
5377 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5378 if (const SCEVConstant *BTCC =
5379 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5380 // Okay, we know how many times the containing loop executes. If
5381 // this is a constant evolving PHI node, get the final value at
5382 // the specified iteration number.
5383 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5384 BTCC->getValue()->getValue(),
5386 if (RV) return getSCEV(RV);
5390 // Okay, this is an expression that we cannot symbolically evaluate
5391 // into a SCEV. Check to see if it's possible to symbolically evaluate
5392 // the arguments into constants, and if so, try to constant propagate the
5393 // result. This is particularly useful for computing loop exit values.
5394 if (CanConstantFold(I)) {
5395 SmallVector<Constant *, 4> Operands;
5396 bool MadeImprovement = false;
5397 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5398 Value *Op = I->getOperand(i);
5399 if (Constant *C = dyn_cast<Constant>(Op)) {
5400 Operands.push_back(C);
5404 // If any of the operands is non-constant and if they are
5405 // non-integer and non-pointer, don't even try to analyze them
5406 // with scev techniques.
5407 if (!isSCEVable(Op->getType()))
5410 const SCEV *OrigV = getSCEV(Op);
5411 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5412 MadeImprovement |= OrigV != OpV;
5414 Constant *C = BuildConstantFromSCEV(OpV);
5416 if (C->getType() != Op->getType())
5417 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5421 Operands.push_back(C);
5424 // Check to see if getSCEVAtScope actually made an improvement.
5425 if (MadeImprovement) {
5426 Constant *C = nullptr;
5427 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5428 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5429 Operands[0], Operands[1], DL,
5431 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5432 if (!LI->isVolatile())
5433 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5435 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5443 // This is some other type of SCEVUnknown, just return it.
5447 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5448 // Avoid performing the look-up in the common case where the specified
5449 // expression has no loop-variant portions.
5450 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5451 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5452 if (OpAtScope != Comm->getOperand(i)) {
5453 // Okay, at least one of these operands is loop variant but might be
5454 // foldable. Build a new instance of the folded commutative expression.
5455 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5456 Comm->op_begin()+i);
5457 NewOps.push_back(OpAtScope);
5459 for (++i; i != e; ++i) {
5460 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5461 NewOps.push_back(OpAtScope);
5463 if (isa<SCEVAddExpr>(Comm))
5464 return getAddExpr(NewOps);
5465 if (isa<SCEVMulExpr>(Comm))
5466 return getMulExpr(NewOps);
5467 if (isa<SCEVSMaxExpr>(Comm))
5468 return getSMaxExpr(NewOps);
5469 if (isa<SCEVUMaxExpr>(Comm))
5470 return getUMaxExpr(NewOps);
5471 llvm_unreachable("Unknown commutative SCEV type!");
5474 // If we got here, all operands are loop invariant.
5478 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5479 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5480 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5481 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5482 return Div; // must be loop invariant
5483 return getUDivExpr(LHS, RHS);
5486 // If this is a loop recurrence for a loop that does not contain L, then we
5487 // are dealing with the final value computed by the loop.
5488 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5489 // First, attempt to evaluate each operand.
5490 // Avoid performing the look-up in the common case where the specified
5491 // expression has no loop-variant portions.
5492 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5493 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5494 if (OpAtScope == AddRec->getOperand(i))
5497 // Okay, at least one of these operands is loop variant but might be
5498 // foldable. Build a new instance of the folded commutative expression.
5499 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5500 AddRec->op_begin()+i);
5501 NewOps.push_back(OpAtScope);
5502 for (++i; i != e; ++i)
5503 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5505 const SCEV *FoldedRec =
5506 getAddRecExpr(NewOps, AddRec->getLoop(),
5507 AddRec->getNoWrapFlags(SCEV::FlagNW));
5508 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5509 // The addrec may be folded to a nonrecurrence, for example, if the
5510 // induction variable is multiplied by zero after constant folding. Go
5511 // ahead and return the folded value.
5517 // If the scope is outside the addrec's loop, evaluate it by using the
5518 // loop exit value of the addrec.
5519 if (!AddRec->getLoop()->contains(L)) {
5520 // To evaluate this recurrence, we need to know how many times the AddRec
5521 // loop iterates. Compute this now.
5522 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5523 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5525 // Then, evaluate the AddRec.
5526 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5532 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5533 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5534 if (Op == Cast->getOperand())
5535 return Cast; // must be loop invariant
5536 return getZeroExtendExpr(Op, Cast->getType());
5539 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5540 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5541 if (Op == Cast->getOperand())
5542 return Cast; // must be loop invariant
5543 return getSignExtendExpr(Op, Cast->getType());
5546 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5547 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5548 if (Op == Cast->getOperand())
5549 return Cast; // must be loop invariant
5550 return getTruncateExpr(Op, Cast->getType());
5553 llvm_unreachable("Unknown SCEV type!");
5556 /// getSCEVAtScope - This is a convenience function which does
5557 /// getSCEVAtScope(getSCEV(V), L).
5558 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5559 return getSCEVAtScope(getSCEV(V), L);
5562 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5563 /// following equation:
5565 /// A * X = B (mod N)
5567 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5568 /// A and B isn't important.
5570 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5571 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5572 ScalarEvolution &SE) {
5573 uint32_t BW = A.getBitWidth();
5574 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5575 assert(A != 0 && "A must be non-zero.");
5579 // The gcd of A and N may have only one prime factor: 2. The number of
5580 // trailing zeros in A is its multiplicity
5581 uint32_t Mult2 = A.countTrailingZeros();
5584 // 2. Check if B is divisible by D.
5586 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5587 // is not less than multiplicity of this prime factor for D.
5588 if (B.countTrailingZeros() < Mult2)
5589 return SE.getCouldNotCompute();
5591 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5594 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5595 // bit width during computations.
5596 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5597 APInt Mod(BW + 1, 0);
5598 Mod.setBit(BW - Mult2); // Mod = N / D
5599 APInt I = AD.multiplicativeInverse(Mod);
5601 // 4. Compute the minimum unsigned root of the equation:
5602 // I * (B / D) mod (N / D)
5603 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5605 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5607 return SE.getConstant(Result.trunc(BW));
5610 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5611 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5612 /// might be the same) or two SCEVCouldNotCompute objects.
5614 static std::pair<const SCEV *,const SCEV *>
5615 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5616 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5617 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5618 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5619 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5621 // We currently can only solve this if the coefficients are constants.
5622 if (!LC || !MC || !NC) {
5623 const SCEV *CNC = SE.getCouldNotCompute();
5624 return std::make_pair(CNC, CNC);
5627 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5628 const APInt &L = LC->getValue()->getValue();
5629 const APInt &M = MC->getValue()->getValue();
5630 const APInt &N = NC->getValue()->getValue();
5631 APInt Two(BitWidth, 2);
5632 APInt Four(BitWidth, 4);
5635 using namespace APIntOps;
5637 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5638 // The B coefficient is M-N/2
5642 // The A coefficient is N/2
5643 APInt A(N.sdiv(Two));
5645 // Compute the B^2-4ac term.
5648 SqrtTerm -= Four * (A * C);
5650 if (SqrtTerm.isNegative()) {
5651 // The loop is provably infinite.
5652 const SCEV *CNC = SE.getCouldNotCompute();
5653 return std::make_pair(CNC, CNC);
5656 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5657 // integer value or else APInt::sqrt() will assert.
5658 APInt SqrtVal(SqrtTerm.sqrt());
5660 // Compute the two solutions for the quadratic formula.
5661 // The divisions must be performed as signed divisions.
5664 if (TwoA.isMinValue()) {
5665 const SCEV *CNC = SE.getCouldNotCompute();
5666 return std::make_pair(CNC, CNC);
5669 LLVMContext &Context = SE.getContext();
5671 ConstantInt *Solution1 =
5672 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5673 ConstantInt *Solution2 =
5674 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5676 return std::make_pair(SE.getConstant(Solution1),
5677 SE.getConstant(Solution2));
5678 } // end APIntOps namespace
5681 /// HowFarToZero - Return the number of times a backedge comparing the specified
5682 /// value to zero will execute. If not computable, return CouldNotCompute.
5684 /// This is only used for loops with a "x != y" exit test. The exit condition is
5685 /// now expressed as a single expression, V = x-y. So the exit test is
5686 /// effectively V != 0. We know and take advantage of the fact that this
5687 /// expression only being used in a comparison by zero context.
5688 ScalarEvolution::ExitLimit
5689 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
5690 // If the value is a constant
5691 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5692 // If the value is already zero, the branch will execute zero times.
5693 if (C->getValue()->isZero()) return C;
5694 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5697 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5698 if (!AddRec || AddRec->getLoop() != L)
5699 return getCouldNotCompute();
5701 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5702 // the quadratic equation to solve it.
5703 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5704 std::pair<const SCEV *,const SCEV *> Roots =
5705 SolveQuadraticEquation(AddRec, *this);
5706 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5707 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5710 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5711 << " sol#2: " << *R2 << "\n";
5713 // Pick the smallest positive root value.
5714 if (ConstantInt *CB =
5715 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5718 if (CB->getZExtValue() == false)
5719 std::swap(R1, R2); // R1 is the minimum root now.
5721 // We can only use this value if the chrec ends up with an exact zero
5722 // value at this index. When solving for "X*X != 5", for example, we
5723 // should not accept a root of 2.
5724 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5726 return R1; // We found a quadratic root!
5729 return getCouldNotCompute();
5732 // Otherwise we can only handle this if it is affine.
5733 if (!AddRec->isAffine())
5734 return getCouldNotCompute();
5736 // If this is an affine expression, the execution count of this branch is
5737 // the minimum unsigned root of the following equation:
5739 // Start + Step*N = 0 (mod 2^BW)
5743 // Step*N = -Start (mod 2^BW)
5745 // where BW is the common bit width of Start and Step.
5747 // Get the initial value for the loop.
5748 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5749 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5751 // For now we handle only constant steps.
5753 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5754 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5755 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5756 // We have not yet seen any such cases.
5757 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5758 if (!StepC || StepC->getValue()->equalsInt(0))
5759 return getCouldNotCompute();
5761 // For positive steps (counting up until unsigned overflow):
5762 // N = -Start/Step (as unsigned)
5763 // For negative steps (counting down to zero):
5765 // First compute the unsigned distance from zero in the direction of Step.
5766 bool CountDown = StepC->getValue()->getValue().isNegative();
5767 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5769 // Handle unitary steps, which cannot wraparound.
5770 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5771 // N = Distance (as unsigned)
5772 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5773 ConstantRange CR = getUnsignedRange(Start);
5774 const SCEV *MaxBECount;
5775 if (!CountDown && CR.getUnsignedMin().isMinValue())
5776 // When counting up, the worst starting value is 1, not 0.
5777 MaxBECount = CR.getUnsignedMax().isMinValue()
5778 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5779 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5781 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5782 : -CR.getUnsignedMin());
5783 return ExitLimit(Distance, MaxBECount, /*MustExit=*/true);
5786 // If the recurrence is known not to wraparound, unsigned divide computes the
5787 // back edge count. (Ideally we would have an "isexact" bit for udiv). We know
5788 // that the value will either become zero (and thus the loop terminates), that
5789 // the loop will terminate through some other exit condition first, or that
5790 // the loop has undefined behavior. This means we can't "miss" the exit
5791 // value, even with nonunit stride, and exit later via the same branch. Note
5792 // that we can skip this exit if loop later exits via a different
5793 // branch. Hence MustExit=false.
5795 // This is only valid for expressions that directly compute the loop exit. It
5796 // is invalid for subexpressions in which the loop may exit through this
5797 // branch even if this subexpression is false. In that case, the trip count
5798 // computed by this udiv could be smaller than the number of well-defined
5800 if (!IsSubExpr && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5802 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5803 return ExitLimit(Exact, Exact, /*MustExit=*/false);
5806 // If Step is a power of two that evenly divides Start we know that the loop
5807 // will always terminate. Start may not be a constant so we just have the
5808 // number of trailing zeros available. This is safe even in presence of
5809 // overflow as the recurrence will overflow to exactly 0.
5810 const APInt &StepV = StepC->getValue()->getValue();
5811 if (StepV.isPowerOf2() &&
5812 GetMinTrailingZeros(getNegativeSCEV(Start)) >= StepV.countTrailingZeros())
5813 return getUDivExactExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5815 // Then, try to solve the above equation provided that Start is constant.
5816 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5817 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5818 -StartC->getValue()->getValue(),
5820 return getCouldNotCompute();
5823 /// HowFarToNonZero - Return the number of times a backedge checking the
5824 /// specified value for nonzero will execute. If not computable, return
5826 ScalarEvolution::ExitLimit
5827 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5828 // Loops that look like: while (X == 0) are very strange indeed. We don't
5829 // handle them yet except for the trivial case. This could be expanded in the
5830 // future as needed.
5832 // If the value is a constant, check to see if it is known to be non-zero
5833 // already. If so, the backedge will execute zero times.
5834 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5835 if (!C->getValue()->isNullValue())
5836 return getConstant(C->getType(), 0);
5837 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5840 // We could implement others, but I really doubt anyone writes loops like
5841 // this, and if they did, they would already be constant folded.
5842 return getCouldNotCompute();
5845 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5846 /// (which may not be an immediate predecessor) which has exactly one
5847 /// successor from which BB is reachable, or null if no such block is
5850 std::pair<BasicBlock *, BasicBlock *>
5851 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5852 // If the block has a unique predecessor, then there is no path from the
5853 // predecessor to the block that does not go through the direct edge
5854 // from the predecessor to the block.
5855 if (BasicBlock *Pred = BB->getSinglePredecessor())
5856 return std::make_pair(Pred, BB);
5858 // A loop's header is defined to be a block that dominates the loop.
5859 // If the header has a unique predecessor outside the loop, it must be
5860 // a block that has exactly one successor that can reach the loop.
5861 if (Loop *L = LI->getLoopFor(BB))
5862 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5864 return std::pair<BasicBlock *, BasicBlock *>();
5867 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5868 /// testing whether two expressions are equal, however for the purposes of
5869 /// looking for a condition guarding a loop, it can be useful to be a little
5870 /// more general, since a front-end may have replicated the controlling
5873 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5874 // Quick check to see if they are the same SCEV.
5875 if (A == B) return true;
5877 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5878 // two different instructions with the same value. Check for this case.
5879 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5880 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5881 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5882 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5883 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5886 // Otherwise assume they may have a different value.
5890 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5891 /// predicate Pred. Return true iff any changes were made.
5893 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5894 const SCEV *&LHS, const SCEV *&RHS,
5896 bool Changed = false;
5898 // If we hit the max recursion limit bail out.
5902 // Canonicalize a constant to the right side.
5903 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5904 // Check for both operands constant.
5905 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5906 if (ConstantExpr::getICmp(Pred,
5908 RHSC->getValue())->isNullValue())
5909 goto trivially_false;
5911 goto trivially_true;
5913 // Otherwise swap the operands to put the constant on the right.
5914 std::swap(LHS, RHS);
5915 Pred = ICmpInst::getSwappedPredicate(Pred);
5919 // If we're comparing an addrec with a value which is loop-invariant in the
5920 // addrec's loop, put the addrec on the left. Also make a dominance check,
5921 // as both operands could be addrecs loop-invariant in each other's loop.
5922 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5923 const Loop *L = AR->getLoop();
5924 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5925 std::swap(LHS, RHS);
5926 Pred = ICmpInst::getSwappedPredicate(Pred);
5931 // If there's a constant operand, canonicalize comparisons with boundary
5932 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5933 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5934 const APInt &RA = RC->getValue()->getValue();
5936 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5937 case ICmpInst::ICMP_EQ:
5938 case ICmpInst::ICMP_NE:
5939 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5941 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5942 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5943 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5944 ME->getOperand(0)->isAllOnesValue()) {
5945 RHS = AE->getOperand(1);
5946 LHS = ME->getOperand(1);
5950 case ICmpInst::ICMP_UGE:
5951 if ((RA - 1).isMinValue()) {
5952 Pred = ICmpInst::ICMP_NE;
5953 RHS = getConstant(RA - 1);
5957 if (RA.isMaxValue()) {
5958 Pred = ICmpInst::ICMP_EQ;
5962 if (RA.isMinValue()) goto trivially_true;
5964 Pred = ICmpInst::ICMP_UGT;
5965 RHS = getConstant(RA - 1);
5968 case ICmpInst::ICMP_ULE:
5969 if ((RA + 1).isMaxValue()) {
5970 Pred = ICmpInst::ICMP_NE;
5971 RHS = getConstant(RA + 1);
5975 if (RA.isMinValue()) {
5976 Pred = ICmpInst::ICMP_EQ;
5980 if (RA.isMaxValue()) goto trivially_true;
5982 Pred = ICmpInst::ICMP_ULT;
5983 RHS = getConstant(RA + 1);
5986 case ICmpInst::ICMP_SGE:
5987 if ((RA - 1).isMinSignedValue()) {
5988 Pred = ICmpInst::ICMP_NE;
5989 RHS = getConstant(RA - 1);
5993 if (RA.isMaxSignedValue()) {
5994 Pred = ICmpInst::ICMP_EQ;
5998 if (RA.isMinSignedValue()) goto trivially_true;
6000 Pred = ICmpInst::ICMP_SGT;
6001 RHS = getConstant(RA - 1);
6004 case ICmpInst::ICMP_SLE:
6005 if ((RA + 1).isMaxSignedValue()) {
6006 Pred = ICmpInst::ICMP_NE;
6007 RHS = getConstant(RA + 1);
6011 if (RA.isMinSignedValue()) {
6012 Pred = ICmpInst::ICMP_EQ;
6016 if (RA.isMaxSignedValue()) goto trivially_true;
6018 Pred = ICmpInst::ICMP_SLT;
6019 RHS = getConstant(RA + 1);
6022 case ICmpInst::ICMP_UGT:
6023 if (RA.isMinValue()) {
6024 Pred = ICmpInst::ICMP_NE;
6028 if ((RA + 1).isMaxValue()) {
6029 Pred = ICmpInst::ICMP_EQ;
6030 RHS = getConstant(RA + 1);
6034 if (RA.isMaxValue()) goto trivially_false;
6036 case ICmpInst::ICMP_ULT:
6037 if (RA.isMaxValue()) {
6038 Pred = ICmpInst::ICMP_NE;
6042 if ((RA - 1).isMinValue()) {
6043 Pred = ICmpInst::ICMP_EQ;
6044 RHS = getConstant(RA - 1);
6048 if (RA.isMinValue()) goto trivially_false;
6050 case ICmpInst::ICMP_SGT:
6051 if (RA.isMinSignedValue()) {
6052 Pred = ICmpInst::ICMP_NE;
6056 if ((RA + 1).isMaxSignedValue()) {
6057 Pred = ICmpInst::ICMP_EQ;
6058 RHS = getConstant(RA + 1);
6062 if (RA.isMaxSignedValue()) goto trivially_false;
6064 case ICmpInst::ICMP_SLT:
6065 if (RA.isMaxSignedValue()) {
6066 Pred = ICmpInst::ICMP_NE;
6070 if ((RA - 1).isMinSignedValue()) {
6071 Pred = ICmpInst::ICMP_EQ;
6072 RHS = getConstant(RA - 1);
6076 if (RA.isMinSignedValue()) goto trivially_false;
6081 // Check for obvious equality.
6082 if (HasSameValue(LHS, RHS)) {
6083 if (ICmpInst::isTrueWhenEqual(Pred))
6084 goto trivially_true;
6085 if (ICmpInst::isFalseWhenEqual(Pred))
6086 goto trivially_false;
6089 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6090 // adding or subtracting 1 from one of the operands.
6092 case ICmpInst::ICMP_SLE:
6093 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6094 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6096 Pred = ICmpInst::ICMP_SLT;
6098 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6099 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6101 Pred = ICmpInst::ICMP_SLT;
6105 case ICmpInst::ICMP_SGE:
6106 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6107 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6109 Pred = ICmpInst::ICMP_SGT;
6111 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6112 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6114 Pred = ICmpInst::ICMP_SGT;
6118 case ICmpInst::ICMP_ULE:
6119 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6120 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6122 Pred = ICmpInst::ICMP_ULT;
6124 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6125 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6127 Pred = ICmpInst::ICMP_ULT;
6131 case ICmpInst::ICMP_UGE:
6132 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6133 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6135 Pred = ICmpInst::ICMP_UGT;
6137 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6138 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6140 Pred = ICmpInst::ICMP_UGT;
6148 // TODO: More simplifications are possible here.
6150 // Recursively simplify until we either hit a recursion limit or nothing
6153 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6159 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6160 Pred = ICmpInst::ICMP_EQ;
6165 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6166 Pred = ICmpInst::ICMP_NE;
6170 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6171 return getSignedRange(S).getSignedMax().isNegative();
6174 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6175 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6178 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6179 return !getSignedRange(S).getSignedMin().isNegative();
6182 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6183 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6186 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6187 return isKnownNegative(S) || isKnownPositive(S);
6190 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6191 const SCEV *LHS, const SCEV *RHS) {
6192 // Canonicalize the inputs first.
6193 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6195 // If LHS or RHS is an addrec, check to see if the condition is true in
6196 // every iteration of the loop.
6197 // If LHS and RHS are both addrec, both conditions must be true in
6198 // every iteration of the loop.
6199 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6200 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6201 bool LeftGuarded = false;
6202 bool RightGuarded = false;
6204 const Loop *L = LAR->getLoop();
6205 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6206 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6207 if (!RAR) return true;
6212 const Loop *L = RAR->getLoop();
6213 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6214 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6215 if (!LAR) return true;
6216 RightGuarded = true;
6219 if (LeftGuarded && RightGuarded)
6222 // Otherwise see what can be done with known constant ranges.
6223 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6227 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6228 const SCEV *LHS, const SCEV *RHS) {
6229 if (HasSameValue(LHS, RHS))
6230 return ICmpInst::isTrueWhenEqual(Pred);
6232 // This code is split out from isKnownPredicate because it is called from
6233 // within isLoopEntryGuardedByCond.
6236 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6237 case ICmpInst::ICMP_SGT:
6238 std::swap(LHS, RHS);
6239 case ICmpInst::ICMP_SLT: {
6240 ConstantRange LHSRange = getSignedRange(LHS);
6241 ConstantRange RHSRange = getSignedRange(RHS);
6242 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6244 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6248 case ICmpInst::ICMP_SGE:
6249 std::swap(LHS, RHS);
6250 case ICmpInst::ICMP_SLE: {
6251 ConstantRange LHSRange = getSignedRange(LHS);
6252 ConstantRange RHSRange = getSignedRange(RHS);
6253 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6255 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6259 case ICmpInst::ICMP_UGT:
6260 std::swap(LHS, RHS);
6261 case ICmpInst::ICMP_ULT: {
6262 ConstantRange LHSRange = getUnsignedRange(LHS);
6263 ConstantRange RHSRange = getUnsignedRange(RHS);
6264 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6266 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6270 case ICmpInst::ICMP_UGE:
6271 std::swap(LHS, RHS);
6272 case ICmpInst::ICMP_ULE: {
6273 ConstantRange LHSRange = getUnsignedRange(LHS);
6274 ConstantRange RHSRange = getUnsignedRange(RHS);
6275 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6277 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6281 case ICmpInst::ICMP_NE: {
6282 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6284 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6287 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6288 if (isKnownNonZero(Diff))
6292 case ICmpInst::ICMP_EQ:
6293 // The check at the top of the function catches the case where
6294 // the values are known to be equal.
6300 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6301 /// protected by a conditional between LHS and RHS. This is used to
6302 /// to eliminate casts.
6304 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6305 ICmpInst::Predicate Pred,
6306 const SCEV *LHS, const SCEV *RHS) {
6307 // Interpret a null as meaning no loop, where there is obviously no guard
6308 // (interprocedural conditions notwithstanding).
6309 if (!L) return true;
6311 BasicBlock *Latch = L->getLoopLatch();
6315 BranchInst *LoopContinuePredicate =
6316 dyn_cast<BranchInst>(Latch->getTerminator());
6317 if (!LoopContinuePredicate ||
6318 LoopContinuePredicate->isUnconditional())
6321 return isImpliedCond(Pred, LHS, RHS,
6322 LoopContinuePredicate->getCondition(),
6323 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6326 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6327 /// by a conditional between LHS and RHS. This is used to help avoid max
6328 /// expressions in loop trip counts, and to eliminate casts.
6330 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6331 ICmpInst::Predicate Pred,
6332 const SCEV *LHS, const SCEV *RHS) {
6333 // Interpret a null as meaning no loop, where there is obviously no guard
6334 // (interprocedural conditions notwithstanding).
6335 if (!L) return false;
6337 // Starting at the loop predecessor, climb up the predecessor chain, as long
6338 // as there are predecessors that can be found that have unique successors
6339 // leading to the original header.
6340 for (std::pair<BasicBlock *, BasicBlock *>
6341 Pair(L->getLoopPredecessor(), L->getHeader());
6343 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6345 BranchInst *LoopEntryPredicate =
6346 dyn_cast<BranchInst>(Pair.first->getTerminator());
6347 if (!LoopEntryPredicate ||
6348 LoopEntryPredicate->isUnconditional())
6351 if (isImpliedCond(Pred, LHS, RHS,
6352 LoopEntryPredicate->getCondition(),
6353 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6360 /// RAII wrapper to prevent recursive application of isImpliedCond.
6361 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6362 /// currently evaluating isImpliedCond.
6363 struct MarkPendingLoopPredicate {
6365 DenseSet<Value*> &LoopPreds;
6368 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6369 : Cond(C), LoopPreds(LP) {
6370 Pending = !LoopPreds.insert(Cond).second;
6372 ~MarkPendingLoopPredicate() {
6374 LoopPreds.erase(Cond);
6378 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6379 /// and RHS is true whenever the given Cond value evaluates to true.
6380 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6381 const SCEV *LHS, const SCEV *RHS,
6382 Value *FoundCondValue,
6384 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6388 // Recursively handle And and Or conditions.
6389 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6390 if (BO->getOpcode() == Instruction::And) {
6392 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6393 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6394 } else if (BO->getOpcode() == Instruction::Or) {
6396 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6397 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6401 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6402 if (!ICI) return false;
6404 // Bail if the ICmp's operands' types are wider than the needed type
6405 // before attempting to call getSCEV on them. This avoids infinite
6406 // recursion, since the analysis of widening casts can require loop
6407 // exit condition information for overflow checking, which would
6409 if (getTypeSizeInBits(LHS->getType()) <
6410 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6413 // Now that we found a conditional branch that dominates the loop or controls
6414 // the loop latch. Check to see if it is the comparison we are looking for.
6415 ICmpInst::Predicate FoundPred;
6417 FoundPred = ICI->getInversePredicate();
6419 FoundPred = ICI->getPredicate();
6421 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6422 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6424 // Balance the types. The case where FoundLHS' type is wider than
6425 // LHS' type is checked for above.
6426 if (getTypeSizeInBits(LHS->getType()) >
6427 getTypeSizeInBits(FoundLHS->getType())) {
6428 if (CmpInst::isSigned(FoundPred)) {
6429 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6430 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6432 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6433 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6437 // Canonicalize the query to match the way instcombine will have
6438 // canonicalized the comparison.
6439 if (SimplifyICmpOperands(Pred, LHS, RHS))
6441 return CmpInst::isTrueWhenEqual(Pred);
6442 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6443 if (FoundLHS == FoundRHS)
6444 return CmpInst::isFalseWhenEqual(FoundPred);
6446 // Check to see if we can make the LHS or RHS match.
6447 if (LHS == FoundRHS || RHS == FoundLHS) {
6448 if (isa<SCEVConstant>(RHS)) {
6449 std::swap(FoundLHS, FoundRHS);
6450 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6452 std::swap(LHS, RHS);
6453 Pred = ICmpInst::getSwappedPredicate(Pred);
6457 // Check whether the found predicate is the same as the desired predicate.
6458 if (FoundPred == Pred)
6459 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6461 // Check whether swapping the found predicate makes it the same as the
6462 // desired predicate.
6463 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6464 if (isa<SCEVConstant>(RHS))
6465 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6467 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6468 RHS, LHS, FoundLHS, FoundRHS);
6471 // Check whether the actual condition is beyond sufficient.
6472 if (FoundPred == ICmpInst::ICMP_EQ)
6473 if (ICmpInst::isTrueWhenEqual(Pred))
6474 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6476 if (Pred == ICmpInst::ICMP_NE)
6477 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6478 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6481 // Otherwise assume the worst.
6485 /// isImpliedCondOperands - Test whether the condition described by Pred,
6486 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6487 /// and FoundRHS is true.
6488 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6489 const SCEV *LHS, const SCEV *RHS,
6490 const SCEV *FoundLHS,
6491 const SCEV *FoundRHS) {
6492 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6493 FoundLHS, FoundRHS) ||
6494 // ~x < ~y --> x > y
6495 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6496 getNotSCEV(FoundRHS),
6497 getNotSCEV(FoundLHS));
6500 /// isImpliedCondOperandsHelper - Test whether the condition described by
6501 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6502 /// FoundLHS, and FoundRHS is true.
6504 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6505 const SCEV *LHS, const SCEV *RHS,
6506 const SCEV *FoundLHS,
6507 const SCEV *FoundRHS) {
6509 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6510 case ICmpInst::ICMP_EQ:
6511 case ICmpInst::ICMP_NE:
6512 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6515 case ICmpInst::ICMP_SLT:
6516 case ICmpInst::ICMP_SLE:
6517 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6518 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6521 case ICmpInst::ICMP_SGT:
6522 case ICmpInst::ICMP_SGE:
6523 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6524 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6527 case ICmpInst::ICMP_ULT:
6528 case ICmpInst::ICMP_ULE:
6529 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6530 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6533 case ICmpInst::ICMP_UGT:
6534 case ICmpInst::ICMP_UGE:
6535 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6536 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6544 // Verify if an linear IV with positive stride can overflow when in a
6545 // less-than comparison, knowing the invariant term of the comparison, the
6546 // stride and the knowledge of NSW/NUW flags on the recurrence.
6547 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
6548 bool IsSigned, bool NoWrap) {
6549 if (NoWrap) return false;
6551 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6552 const SCEV *One = getConstant(Stride->getType(), 1);
6555 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
6556 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
6557 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6560 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
6561 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
6564 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
6565 APInt MaxValue = APInt::getMaxValue(BitWidth);
6566 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6569 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
6570 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
6573 // Verify if an linear IV with negative stride can overflow when in a
6574 // greater-than comparison, knowing the invariant term of the comparison,
6575 // the stride and the knowledge of NSW/NUW flags on the recurrence.
6576 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
6577 bool IsSigned, bool NoWrap) {
6578 if (NoWrap) return false;
6580 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6581 const SCEV *One = getConstant(Stride->getType(), 1);
6584 APInt MinRHS = getSignedRange(RHS).getSignedMin();
6585 APInt MinValue = APInt::getSignedMinValue(BitWidth);
6586 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6589 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
6590 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
6593 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
6594 APInt MinValue = APInt::getMinValue(BitWidth);
6595 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6598 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
6599 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
6602 // Compute the backedge taken count knowing the interval difference, the
6603 // stride and presence of the equality in the comparison.
6604 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
6606 const SCEV *One = getConstant(Step->getType(), 1);
6607 Delta = Equality ? getAddExpr(Delta, Step)
6608 : getAddExpr(Delta, getMinusSCEV(Step, One));
6609 return getUDivExpr(Delta, Step);
6612 /// HowManyLessThans - Return the number of times a backedge containing the
6613 /// specified less-than comparison will execute. If not computable, return
6614 /// CouldNotCompute.
6616 /// @param IsSubExpr is true when the LHS < RHS condition does not directly
6617 /// control the branch. In this case, we can only compute an iteration count for
6618 /// a subexpression that cannot overflow before evaluating true.
6619 ScalarEvolution::ExitLimit
6620 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6621 const Loop *L, bool IsSigned,
6623 // We handle only IV < Invariant
6624 if (!isLoopInvariant(RHS, L))
6625 return getCouldNotCompute();
6627 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6629 // Avoid weird loops
6630 if (!IV || IV->getLoop() != L || !IV->isAffine())
6631 return getCouldNotCompute();
6633 bool NoWrap = !IsSubExpr &&
6634 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6636 const SCEV *Stride = IV->getStepRecurrence(*this);
6638 // Avoid negative or zero stride values
6639 if (!isKnownPositive(Stride))
6640 return getCouldNotCompute();
6642 // Avoid proven overflow cases: this will ensure that the backedge taken count
6643 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6644 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6645 // behaviors like the case of C language.
6646 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
6647 return getCouldNotCompute();
6649 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
6650 : ICmpInst::ICMP_ULT;
6651 const SCEV *Start = IV->getStart();
6652 const SCEV *End = RHS;
6653 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
6654 End = IsSigned ? getSMaxExpr(RHS, Start)
6655 : getUMaxExpr(RHS, Start);
6657 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
6659 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
6660 : getUnsignedRange(Start).getUnsignedMin();
6662 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6663 : getUnsignedRange(Stride).getUnsignedMin();
6665 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6666 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
6667 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
6669 // Although End can be a MAX expression we estimate MaxEnd considering only
6670 // the case End = RHS. This is safe because in the other case (End - Start)
6671 // is zero, leading to a zero maximum backedge taken count.
6673 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
6674 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
6676 const SCEV *MaxBECount;
6677 if (isa<SCEVConstant>(BECount))
6678 MaxBECount = BECount;
6680 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
6681 getConstant(MinStride), false);
6683 if (isa<SCEVCouldNotCompute>(MaxBECount))
6684 MaxBECount = BECount;
6686 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6689 ScalarEvolution::ExitLimit
6690 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
6691 const Loop *L, bool IsSigned,
6693 // We handle only IV > Invariant
6694 if (!isLoopInvariant(RHS, L))
6695 return getCouldNotCompute();
6697 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6699 // Avoid weird loops
6700 if (!IV || IV->getLoop() != L || !IV->isAffine())
6701 return getCouldNotCompute();
6703 bool NoWrap = !IsSubExpr &&
6704 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6706 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
6708 // Avoid negative or zero stride values
6709 if (!isKnownPositive(Stride))
6710 return getCouldNotCompute();
6712 // Avoid proven overflow cases: this will ensure that the backedge taken count
6713 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6714 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6715 // behaviors like the case of C language.
6716 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
6717 return getCouldNotCompute();
6719 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
6720 : ICmpInst::ICMP_UGT;
6722 const SCEV *Start = IV->getStart();
6723 const SCEV *End = RHS;
6724 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
6725 End = IsSigned ? getSMinExpr(RHS, Start)
6726 : getUMinExpr(RHS, Start);
6728 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
6730 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
6731 : getUnsignedRange(Start).getUnsignedMax();
6733 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6734 : getUnsignedRange(Stride).getUnsignedMin();
6736 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6737 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
6738 : APInt::getMinValue(BitWidth) + (MinStride - 1);
6740 // Although End can be a MIN expression we estimate MinEnd considering only
6741 // the case End = RHS. This is safe because in the other case (Start - End)
6742 // is zero, leading to a zero maximum backedge taken count.
6744 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
6745 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
6748 const SCEV *MaxBECount = getCouldNotCompute();
6749 if (isa<SCEVConstant>(BECount))
6750 MaxBECount = BECount;
6752 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
6753 getConstant(MinStride), false);
6755 if (isa<SCEVCouldNotCompute>(MaxBECount))
6756 MaxBECount = BECount;
6758 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6761 /// getNumIterationsInRange - Return the number of iterations of this loop that
6762 /// produce values in the specified constant range. Another way of looking at
6763 /// this is that it returns the first iteration number where the value is not in
6764 /// the condition, thus computing the exit count. If the iteration count can't
6765 /// be computed, an instance of SCEVCouldNotCompute is returned.
6766 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6767 ScalarEvolution &SE) const {
6768 if (Range.isFullSet()) // Infinite loop.
6769 return SE.getCouldNotCompute();
6771 // If the start is a non-zero constant, shift the range to simplify things.
6772 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6773 if (!SC->getValue()->isZero()) {
6774 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6775 Operands[0] = SE.getConstant(SC->getType(), 0);
6776 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6777 getNoWrapFlags(FlagNW));
6778 if (const SCEVAddRecExpr *ShiftedAddRec =
6779 dyn_cast<SCEVAddRecExpr>(Shifted))
6780 return ShiftedAddRec->getNumIterationsInRange(
6781 Range.subtract(SC->getValue()->getValue()), SE);
6782 // This is strange and shouldn't happen.
6783 return SE.getCouldNotCompute();
6786 // The only time we can solve this is when we have all constant indices.
6787 // Otherwise, we cannot determine the overflow conditions.
6788 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6789 if (!isa<SCEVConstant>(getOperand(i)))
6790 return SE.getCouldNotCompute();
6793 // Okay at this point we know that all elements of the chrec are constants and
6794 // that the start element is zero.
6796 // First check to see if the range contains zero. If not, the first
6798 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6799 if (!Range.contains(APInt(BitWidth, 0)))
6800 return SE.getConstant(getType(), 0);
6803 // If this is an affine expression then we have this situation:
6804 // Solve {0,+,A} in Range === Ax in Range
6806 // We know that zero is in the range. If A is positive then we know that
6807 // the upper value of the range must be the first possible exit value.
6808 // If A is negative then the lower of the range is the last possible loop
6809 // value. Also note that we already checked for a full range.
6810 APInt One(BitWidth,1);
6811 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6812 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6814 // The exit value should be (End+A)/A.
6815 APInt ExitVal = (End + A).udiv(A);
6816 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6818 // Evaluate at the exit value. If we really did fall out of the valid
6819 // range, then we computed our trip count, otherwise wrap around or other
6820 // things must have happened.
6821 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6822 if (Range.contains(Val->getValue()))
6823 return SE.getCouldNotCompute(); // Something strange happened
6825 // Ensure that the previous value is in the range. This is a sanity check.
6826 assert(Range.contains(
6827 EvaluateConstantChrecAtConstant(this,
6828 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6829 "Linear scev computation is off in a bad way!");
6830 return SE.getConstant(ExitValue);
6831 } else if (isQuadratic()) {
6832 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6833 // quadratic equation to solve it. To do this, we must frame our problem in
6834 // terms of figuring out when zero is crossed, instead of when
6835 // Range.getUpper() is crossed.
6836 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6837 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6838 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6839 // getNoWrapFlags(FlagNW)
6842 // Next, solve the constructed addrec
6843 std::pair<const SCEV *,const SCEV *> Roots =
6844 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6845 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6846 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6848 // Pick the smallest positive root value.
6849 if (ConstantInt *CB =
6850 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6851 R1->getValue(), R2->getValue()))) {
6852 if (CB->getZExtValue() == false)
6853 std::swap(R1, R2); // R1 is the minimum root now.
6855 // Make sure the root is not off by one. The returned iteration should
6856 // not be in the range, but the previous one should be. When solving
6857 // for "X*X < 5", for example, we should not return a root of 2.
6858 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6861 if (Range.contains(R1Val->getValue())) {
6862 // The next iteration must be out of the range...
6863 ConstantInt *NextVal =
6864 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6866 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6867 if (!Range.contains(R1Val->getValue()))
6868 return SE.getConstant(NextVal);
6869 return SE.getCouldNotCompute(); // Something strange happened
6872 // If R1 was not in the range, then it is a good return value. Make
6873 // sure that R1-1 WAS in the range though, just in case.
6874 ConstantInt *NextVal =
6875 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6876 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6877 if (Range.contains(R1Val->getValue()))
6879 return SE.getCouldNotCompute(); // Something strange happened
6884 return SE.getCouldNotCompute();
6890 FindUndefs() : Found(false) {}
6892 bool follow(const SCEV *S) {
6893 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
6894 if (isa<UndefValue>(C->getValue()))
6896 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
6897 if (isa<UndefValue>(C->getValue()))
6901 // Keep looking if we haven't found it yet.
6904 bool isDone() const {
6905 // Stop recursion if we have found an undef.
6911 // Return true when S contains at least an undef value.
6913 containsUndefs(const SCEV *S) {
6915 SCEVTraversal<FindUndefs> ST(F);
6922 // Collect all steps of SCEV expressions.
6923 struct SCEVCollectStrides {
6924 ScalarEvolution &SE;
6925 SmallVectorImpl<const SCEV *> &Strides;
6927 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
6928 : SE(SE), Strides(S) {}
6930 bool follow(const SCEV *S) {
6931 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
6932 Strides.push_back(AR->getStepRecurrence(SE));
6935 bool isDone() const { return false; }
6938 // Collect all SCEVUnknown and SCEVMulExpr expressions.
6939 struct SCEVCollectTerms {
6940 SmallVectorImpl<const SCEV *> &Terms;
6942 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
6945 bool follow(const SCEV *S) {
6946 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
6947 if (!containsUndefs(S))
6950 // Stop recursion: once we collected a term, do not walk its operands.
6957 bool isDone() const { return false; }
6961 /// Find parametric terms in this SCEVAddRecExpr.
6962 void SCEVAddRecExpr::collectParametricTerms(
6963 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
6964 SmallVector<const SCEV *, 4> Strides;
6965 SCEVCollectStrides StrideCollector(SE, Strides);
6966 visitAll(this, StrideCollector);
6969 dbgs() << "Strides:\n";
6970 for (const SCEV *S : Strides)
6971 dbgs() << *S << "\n";
6974 for (const SCEV *S : Strides) {
6975 SCEVCollectTerms TermCollector(Terms);
6976 visitAll(S, TermCollector);
6980 dbgs() << "Terms:\n";
6981 for (const SCEV *T : Terms)
6982 dbgs() << *T << "\n";
6986 static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
6987 APInt A = C1->getValue()->getValue();
6988 APInt B = C2->getValue()->getValue();
6989 uint32_t ABW = A.getBitWidth();
6990 uint32_t BBW = B.getBitWidth();
6997 return APIntOps::srem(A, B);
7000 static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
7001 APInt A = C1->getValue()->getValue();
7002 APInt B = C2->getValue()->getValue();
7003 uint32_t ABW = A.getBitWidth();
7004 uint32_t BBW = B.getBitWidth();
7011 return APIntOps::sdiv(A, B);
7015 struct FindSCEVSize {
7017 FindSCEVSize() : Size(0) {}
7019 bool follow(const SCEV *S) {
7021 // Keep looking at all operands of S.
7024 bool isDone() const {
7030 // Returns the size of the SCEV S.
7031 static inline int sizeOfSCEV(const SCEV *S) {
7033 SCEVTraversal<FindSCEVSize> ST(F);
7040 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
7042 // Computes the Quotient and Remainder of the division of Numerator by
7044 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
7045 const SCEV *Denominator, const SCEV **Quotient,
7046 const SCEV **Remainder) {
7047 assert(Numerator && Denominator && "Uninitialized SCEV");
7049 SCEVDivision D(SE, Numerator, Denominator);
7051 // Check for the trivial case here to avoid having to check for it in the
7052 // rest of the code.
7053 if (Numerator == Denominator) {
7055 *Remainder = D.Zero;
7059 if (Numerator->isZero()) {
7061 *Remainder = D.Zero;
7065 // Split the Denominator when it is a product.
7066 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
7068 *Quotient = Numerator;
7069 for (const SCEV *Op : T->operands()) {
7070 divide(SE, *Quotient, Op, &Q, &R);
7073 // Bail out when the Numerator is not divisible by one of the terms of
7077 *Remainder = Numerator;
7081 *Remainder = D.Zero;
7086 *Quotient = D.Quotient;
7087 *Remainder = D.Remainder;
7090 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator, const SCEV *Denominator)
7091 : SE(S), Denominator(Denominator) {
7092 Zero = SE.getConstant(Denominator->getType(), 0);
7093 One = SE.getConstant(Denominator->getType(), 1);
7095 // By default, we don't know how to divide Expr by Denominator.
7096 // Providing the default here simplifies the rest of the code.
7098 Remainder = Numerator;
7101 // Except in the trivial case described above, we do not know how to divide
7102 // Expr by Denominator for the following functions with empty implementation.
7103 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
7104 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
7105 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
7106 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
7107 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
7108 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
7109 void visitUnknown(const SCEVUnknown *Numerator) {}
7110 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
7112 void visitConstant(const SCEVConstant *Numerator) {
7113 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
7114 Quotient = SE.getConstant(sdiv(Numerator, D));
7115 Remainder = SE.getConstant(srem(Numerator, D));
7120 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
7121 const SCEV *StartQ, *StartR, *StepQ, *StepR;
7122 assert(Numerator->isAffine() && "Numerator should be affine");
7123 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
7124 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
7125 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
7126 Numerator->getNoWrapFlags());
7127 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
7128 Numerator->getNoWrapFlags());
7131 void visitAddExpr(const SCEVAddExpr *Numerator) {
7132 SmallVector<const SCEV *, 2> Qs, Rs;
7133 Type *Ty = Denominator->getType();
7135 for (const SCEV *Op : Numerator->operands()) {
7137 divide(SE, Op, Denominator, &Q, &R);
7139 // Bail out if types do not match.
7140 if (Ty != Q->getType() || Ty != R->getType()) {
7142 Remainder = Numerator;
7150 if (Qs.size() == 1) {
7156 Quotient = SE.getAddExpr(Qs);
7157 Remainder = SE.getAddExpr(Rs);
7160 void visitMulExpr(const SCEVMulExpr *Numerator) {
7161 SmallVector<const SCEV *, 2> Qs;
7162 Type *Ty = Denominator->getType();
7164 bool FoundDenominatorTerm = false;
7165 for (const SCEV *Op : Numerator->operands()) {
7166 // Bail out if types do not match.
7167 if (Ty != Op->getType()) {
7169 Remainder = Numerator;
7173 if (FoundDenominatorTerm) {
7178 // Check whether Denominator divides one of the product operands.
7180 divide(SE, Op, Denominator, &Q, &R);
7186 // Bail out if types do not match.
7187 if (Ty != Q->getType()) {
7189 Remainder = Numerator;
7193 FoundDenominatorTerm = true;
7197 if (FoundDenominatorTerm) {
7202 Quotient = SE.getMulExpr(Qs);
7206 if (!isa<SCEVUnknown>(Denominator)) {
7208 Remainder = Numerator;
7212 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
7213 ValueToValueMap RewriteMap;
7214 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
7215 cast<SCEVConstant>(Zero)->getValue();
7216 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
7218 if (Remainder->isZero()) {
7219 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
7220 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
7221 cast<SCEVConstant>(One)->getValue();
7223 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
7227 // Quotient is (Numerator - Remainder) divided by Denominator.
7229 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
7230 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
7231 // This SCEV does not seem to simplify: fail the division here.
7233 Remainder = Numerator;
7236 divide(SE, Diff, Denominator, &Q, &R);
7238 "(Numerator - Remainder) should evenly divide Denominator");
7243 ScalarEvolution &SE;
7244 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
7248 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7249 SmallVectorImpl<const SCEV *> &Terms,
7250 SmallVectorImpl<const SCEV *> &Sizes) {
7251 int Last = Terms.size() - 1;
7252 const SCEV *Step = Terms[Last];
7254 // End of recursion.
7256 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7257 SmallVector<const SCEV *, 2> Qs;
7258 for (const SCEV *Op : M->operands())
7259 if (!isa<SCEVConstant>(Op))
7262 Step = SE.getMulExpr(Qs);
7265 Sizes.push_back(Step);
7269 for (const SCEV *&Term : Terms) {
7270 // Normalize the terms before the next call to findArrayDimensionsRec.
7272 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7274 // Bail out when GCD does not evenly divide one of the terms.
7281 // Remove all SCEVConstants.
7282 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7283 return isa<SCEVConstant>(E);
7287 if (Terms.size() > 0)
7288 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7291 Sizes.push_back(Step);
7296 struct FindParameter {
7297 bool FoundParameter;
7298 FindParameter() : FoundParameter(false) {}
7300 bool follow(const SCEV *S) {
7301 if (isa<SCEVUnknown>(S)) {
7302 FoundParameter = true;
7303 // Stop recursion: we found a parameter.
7309 bool isDone() const {
7310 // Stop recursion if we have found a parameter.
7311 return FoundParameter;
7316 // Returns true when S contains at least a SCEVUnknown parameter.
7318 containsParameters(const SCEV *S) {
7320 SCEVTraversal<FindParameter> ST(F);
7323 return F.FoundParameter;
7326 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7328 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7329 for (const SCEV *T : Terms)
7330 if (containsParameters(T))
7335 // Return the number of product terms in S.
7336 static inline int numberOfTerms(const SCEV *S) {
7337 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7338 return Expr->getNumOperands();
7342 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7343 if (isa<SCEVConstant>(T))
7346 if (isa<SCEVUnknown>(T))
7349 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7350 SmallVector<const SCEV *, 2> Factors;
7351 for (const SCEV *Op : M->operands())
7352 if (!isa<SCEVConstant>(Op))
7353 Factors.push_back(Op);
7355 return SE.getMulExpr(Factors);
7361 /// Return the size of an element read or written by Inst.
7362 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7364 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7365 Ty = Store->getValueOperand()->getType();
7366 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7367 Ty = Load->getType();
7371 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7372 return getSizeOfExpr(ETy, Ty);
7375 /// Second step of delinearization: compute the array dimensions Sizes from the
7376 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7377 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7378 SmallVectorImpl<const SCEV *> &Sizes,
7379 const SCEV *ElementSize) const {
7381 if (Terms.size() < 1 || !ElementSize)
7384 // Early return when Terms do not contain parameters: we do not delinearize
7385 // non parametric SCEVs.
7386 if (!containsParameters(Terms))
7390 dbgs() << "Terms:\n";
7391 for (const SCEV *T : Terms)
7392 dbgs() << *T << "\n";
7395 // Remove duplicates.
7396 std::sort(Terms.begin(), Terms.end());
7397 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7399 // Put larger terms first.
7400 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7401 return numberOfTerms(LHS) > numberOfTerms(RHS);
7404 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7406 // Divide all terms by the element size.
7407 for (const SCEV *&Term : Terms) {
7409 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
7413 SmallVector<const SCEV *, 4> NewTerms;
7415 // Remove constant factors.
7416 for (const SCEV *T : Terms)
7417 if (const SCEV *NewT = removeConstantFactors(SE, T))
7418 NewTerms.push_back(NewT);
7421 dbgs() << "Terms after sorting:\n";
7422 for (const SCEV *T : NewTerms)
7423 dbgs() << *T << "\n";
7426 if (NewTerms.empty() ||
7427 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7432 // The last element to be pushed into Sizes is the size of an element.
7433 Sizes.push_back(ElementSize);
7436 dbgs() << "Sizes:\n";
7437 for (const SCEV *S : Sizes)
7438 dbgs() << *S << "\n";
7442 /// Third step of delinearization: compute the access functions for the
7443 /// Subscripts based on the dimensions in Sizes.
7444 void SCEVAddRecExpr::computeAccessFunctions(
7445 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7446 SmallVectorImpl<const SCEV *> &Sizes) const {
7448 // Early exit in case this SCEV is not an affine multivariate function.
7449 if (Sizes.empty() || !this->isAffine())
7452 const SCEV *Res = this;
7453 int Last = Sizes.size() - 1;
7454 for (int i = Last; i >= 0; i--) {
7456 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7459 dbgs() << "Res: " << *Res << "\n";
7460 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7461 dbgs() << "Res divided by Sizes[i]:\n";
7462 dbgs() << "Quotient: " << *Q << "\n";
7463 dbgs() << "Remainder: " << *R << "\n";
7468 // Do not record the last subscript corresponding to the size of elements in
7472 // Bail out if the remainder is too complex.
7473 if (isa<SCEVAddRecExpr>(R)) {
7482 // Record the access function for the current subscript.
7483 Subscripts.push_back(R);
7486 // Also push in last position the remainder of the last division: it will be
7487 // the access function of the innermost dimension.
7488 Subscripts.push_back(Res);
7490 std::reverse(Subscripts.begin(), Subscripts.end());
7493 dbgs() << "Subscripts:\n";
7494 for (const SCEV *S : Subscripts)
7495 dbgs() << *S << "\n";
7499 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7500 /// sizes of an array access. Returns the remainder of the delinearization that
7501 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7502 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7503 /// expressions in the stride and base of a SCEV corresponding to the
7504 /// computation of a GCD (greatest common divisor) of base and stride. When
7505 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7507 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7509 /// void foo(long n, long m, long o, double A[n][m][o]) {
7511 /// for (long i = 0; i < n; i++)
7512 /// for (long j = 0; j < m; j++)
7513 /// for (long k = 0; k < o; k++)
7514 /// A[i][j][k] = 1.0;
7517 /// the delinearization input is the following AddRec SCEV:
7519 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7521 /// From this SCEV, we are able to say that the base offset of the access is %A
7522 /// because it appears as an offset that does not divide any of the strides in
7525 /// CHECK: Base offset: %A
7527 /// and then SCEV->delinearize determines the size of some of the dimensions of
7528 /// the array as these are the multiples by which the strides are happening:
7530 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7532 /// Note that the outermost dimension remains of UnknownSize because there are
7533 /// no strides that would help identifying the size of the last dimension: when
7534 /// the array has been statically allocated, one could compute the size of that
7535 /// dimension by dividing the overall size of the array by the size of the known
7536 /// dimensions: %m * %o * 8.
7538 /// Finally delinearize provides the access functions for the array reference
7539 /// that does correspond to A[i][j][k] of the above C testcase:
7541 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7543 /// The testcases are checking the output of a function pass:
7544 /// DelinearizationPass that walks through all loads and stores of a function
7545 /// asking for the SCEV of the memory access with respect to all enclosing
7546 /// loops, calling SCEV->delinearize on that and printing the results.
7548 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7549 SmallVectorImpl<const SCEV *> &Subscripts,
7550 SmallVectorImpl<const SCEV *> &Sizes,
7551 const SCEV *ElementSize) const {
7552 // First step: collect parametric terms.
7553 SmallVector<const SCEV *, 4> Terms;
7554 collectParametricTerms(SE, Terms);
7559 // Second step: find subscript sizes.
7560 SE.findArrayDimensions(Terms, Sizes, ElementSize);
7565 // Third step: compute the access functions for each subscript.
7566 computeAccessFunctions(SE, Subscripts, Sizes);
7568 if (Subscripts.empty())
7572 dbgs() << "succeeded to delinearize " << *this << "\n";
7573 dbgs() << "ArrayDecl[UnknownSize]";
7574 for (const SCEV *S : Sizes)
7575 dbgs() << "[" << *S << "]";
7577 dbgs() << "\nArrayRef";
7578 for (const SCEV *S : Subscripts)
7579 dbgs() << "[" << *S << "]";
7584 //===----------------------------------------------------------------------===//
7585 // SCEVCallbackVH Class Implementation
7586 //===----------------------------------------------------------------------===//
7588 void ScalarEvolution::SCEVCallbackVH::deleted() {
7589 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7590 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7591 SE->ConstantEvolutionLoopExitValue.erase(PN);
7592 SE->ValueExprMap.erase(getValPtr());
7593 // this now dangles!
7596 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7597 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7599 // Forget all the expressions associated with users of the old value,
7600 // so that future queries will recompute the expressions using the new
7602 Value *Old = getValPtr();
7603 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7604 SmallPtrSet<User *, 8> Visited;
7605 while (!Worklist.empty()) {
7606 User *U = Worklist.pop_back_val();
7607 // Deleting the Old value will cause this to dangle. Postpone
7608 // that until everything else is done.
7611 if (!Visited.insert(U))
7613 if (PHINode *PN = dyn_cast<PHINode>(U))
7614 SE->ConstantEvolutionLoopExitValue.erase(PN);
7615 SE->ValueExprMap.erase(U);
7616 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7618 // Delete the Old value.
7619 if (PHINode *PN = dyn_cast<PHINode>(Old))
7620 SE->ConstantEvolutionLoopExitValue.erase(PN);
7621 SE->ValueExprMap.erase(Old);
7622 // this now dangles!
7625 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7626 : CallbackVH(V), SE(se) {}
7628 //===----------------------------------------------------------------------===//
7629 // ScalarEvolution Class Implementation
7630 //===----------------------------------------------------------------------===//
7632 ScalarEvolution::ScalarEvolution()
7633 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7634 BlockDispositions(64), FirstUnknown(nullptr) {
7635 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7638 bool ScalarEvolution::runOnFunction(Function &F) {
7640 LI = &getAnalysis<LoopInfo>();
7641 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7642 DL = DLP ? &DLP->getDataLayout() : nullptr;
7643 TLI = &getAnalysis<TargetLibraryInfo>();
7644 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7648 void ScalarEvolution::releaseMemory() {
7649 // Iterate through all the SCEVUnknown instances and call their
7650 // destructors, so that they release their references to their values.
7651 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7653 FirstUnknown = nullptr;
7655 ValueExprMap.clear();
7657 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7658 // that a loop had multiple computable exits.
7659 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7660 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7665 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7667 BackedgeTakenCounts.clear();
7668 ConstantEvolutionLoopExitValue.clear();
7669 ValuesAtScopes.clear();
7670 LoopDispositions.clear();
7671 BlockDispositions.clear();
7672 UnsignedRanges.clear();
7673 SignedRanges.clear();
7674 UniqueSCEVs.clear();
7675 SCEVAllocator.Reset();
7678 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7679 AU.setPreservesAll();
7680 AU.addRequiredTransitive<LoopInfo>();
7681 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7682 AU.addRequired<TargetLibraryInfo>();
7685 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7686 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7689 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7691 // Print all inner loops first
7692 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7693 PrintLoopInfo(OS, SE, *I);
7696 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7699 SmallVector<BasicBlock *, 8> ExitBlocks;
7700 L->getExitBlocks(ExitBlocks);
7701 if (ExitBlocks.size() != 1)
7702 OS << "<multiple exits> ";
7704 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7705 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7707 OS << "Unpredictable backedge-taken count. ";
7712 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7715 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7716 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7718 OS << "Unpredictable max backedge-taken count. ";
7724 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7725 // ScalarEvolution's implementation of the print method is to print
7726 // out SCEV values of all instructions that are interesting. Doing
7727 // this potentially causes it to create new SCEV objects though,
7728 // which technically conflicts with the const qualifier. This isn't
7729 // observable from outside the class though, so casting away the
7730 // const isn't dangerous.
7731 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7733 OS << "Classifying expressions for: ";
7734 F->printAsOperand(OS, /*PrintType=*/false);
7736 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7737 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7740 const SCEV *SV = SE.getSCEV(&*I);
7743 const Loop *L = LI->getLoopFor((*I).getParent());
7745 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
7752 OS << "\t\t" "Exits: ";
7753 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
7754 if (!SE.isLoopInvariant(ExitValue, L)) {
7755 OS << "<<Unknown>>";
7764 OS << "Determining loop execution counts for: ";
7765 F->printAsOperand(OS, /*PrintType=*/false);
7767 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
7768 PrintLoopInfo(OS, &SE, *I);
7771 ScalarEvolution::LoopDisposition
7772 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
7773 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
7774 for (unsigned u = 0; u < Values.size(); u++) {
7775 if (Values[u].first == L)
7776 return Values[u].second;
7778 Values.push_back(std::make_pair(L, LoopVariant));
7779 LoopDisposition D = computeLoopDisposition(S, L);
7780 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
7781 for (unsigned u = Values2.size(); u > 0; u--) {
7782 if (Values2[u - 1].first == L) {
7783 Values2[u - 1].second = D;
7790 ScalarEvolution::LoopDisposition
7791 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
7792 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7794 return LoopInvariant;
7798 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
7799 case scAddRecExpr: {
7800 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7802 // If L is the addrec's loop, it's computable.
7803 if (AR->getLoop() == L)
7804 return LoopComputable;
7806 // Add recurrences are never invariant in the function-body (null loop).
7810 // This recurrence is variant w.r.t. L if L contains AR's loop.
7811 if (L->contains(AR->getLoop()))
7814 // This recurrence is invariant w.r.t. L if AR's loop contains L.
7815 if (AR->getLoop()->contains(L))
7816 return LoopInvariant;
7818 // This recurrence is variant w.r.t. L if any of its operands
7820 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
7822 if (!isLoopInvariant(*I, L))
7825 // Otherwise it's loop-invariant.
7826 return LoopInvariant;
7832 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7833 bool HasVarying = false;
7834 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7836 LoopDisposition D = getLoopDisposition(*I, L);
7837 if (D == LoopVariant)
7839 if (D == LoopComputable)
7842 return HasVarying ? LoopComputable : LoopInvariant;
7845 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7846 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
7847 if (LD == LoopVariant)
7849 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
7850 if (RD == LoopVariant)
7852 return (LD == LoopInvariant && RD == LoopInvariant) ?
7853 LoopInvariant : LoopComputable;
7856 // All non-instruction values are loop invariant. All instructions are loop
7857 // invariant if they are not contained in the specified loop.
7858 // Instructions are never considered invariant in the function body
7859 // (null loop) because they are defined within the "loop".
7860 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
7861 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
7862 return LoopInvariant;
7863 case scCouldNotCompute:
7864 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7866 llvm_unreachable("Unknown SCEV kind!");
7869 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
7870 return getLoopDisposition(S, L) == LoopInvariant;
7873 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
7874 return getLoopDisposition(S, L) == LoopComputable;
7877 ScalarEvolution::BlockDisposition
7878 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7879 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
7880 for (unsigned u = 0; u < Values.size(); u++) {
7881 if (Values[u].first == BB)
7882 return Values[u].second;
7884 Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
7885 BlockDisposition D = computeBlockDisposition(S, BB);
7886 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
7887 for (unsigned u = Values2.size(); u > 0; u--) {
7888 if (Values2[u - 1].first == BB) {
7889 Values2[u - 1].second = D;
7896 ScalarEvolution::BlockDisposition
7897 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7898 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7900 return ProperlyDominatesBlock;
7904 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
7905 case scAddRecExpr: {
7906 // This uses a "dominates" query instead of "properly dominates" query
7907 // to test for proper dominance too, because the instruction which
7908 // produces the addrec's value is a PHI, and a PHI effectively properly
7909 // dominates its entire containing block.
7910 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7911 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
7912 return DoesNotDominateBlock;
7914 // FALL THROUGH into SCEVNAryExpr handling.
7919 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7921 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7923 BlockDisposition D = getBlockDisposition(*I, BB);
7924 if (D == DoesNotDominateBlock)
7925 return DoesNotDominateBlock;
7926 if (D == DominatesBlock)
7929 return Proper ? ProperlyDominatesBlock : DominatesBlock;
7932 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7933 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
7934 BlockDisposition LD = getBlockDisposition(LHS, BB);
7935 if (LD == DoesNotDominateBlock)
7936 return DoesNotDominateBlock;
7937 BlockDisposition RD = getBlockDisposition(RHS, BB);
7938 if (RD == DoesNotDominateBlock)
7939 return DoesNotDominateBlock;
7940 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
7941 ProperlyDominatesBlock : DominatesBlock;
7944 if (Instruction *I =
7945 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
7946 if (I->getParent() == BB)
7947 return DominatesBlock;
7948 if (DT->properlyDominates(I->getParent(), BB))
7949 return ProperlyDominatesBlock;
7950 return DoesNotDominateBlock;
7952 return ProperlyDominatesBlock;
7953 case scCouldNotCompute:
7954 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7956 llvm_unreachable("Unknown SCEV kind!");
7959 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
7960 return getBlockDisposition(S, BB) >= DominatesBlock;
7963 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
7964 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
7968 // Search for a SCEV expression node within an expression tree.
7969 // Implements SCEVTraversal::Visitor.
7974 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
7976 bool follow(const SCEV *S) {
7977 IsFound |= (S == Node);
7980 bool isDone() const { return IsFound; }
7984 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
7985 SCEVSearch Search(Op);
7986 visitAll(S, Search);
7987 return Search.IsFound;
7990 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
7991 ValuesAtScopes.erase(S);
7992 LoopDispositions.erase(S);
7993 BlockDispositions.erase(S);
7994 UnsignedRanges.erase(S);
7995 SignedRanges.erase(S);
7997 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7998 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
7999 BackedgeTakenInfo &BEInfo = I->second;
8000 if (BEInfo.hasOperand(S, this)) {
8002 BackedgeTakenCounts.erase(I++);
8009 typedef DenseMap<const Loop *, std::string> VerifyMap;
8011 /// replaceSubString - Replaces all occurrences of From in Str with To.
8012 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8014 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8015 Str.replace(Pos, From.size(), To.data(), To.size());
8020 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8022 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8023 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8024 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8026 std::string &S = Map[L];
8028 raw_string_ostream OS(S);
8029 SE.getBackedgeTakenCount(L)->print(OS);
8031 // false and 0 are semantically equivalent. This can happen in dead loops.
8032 replaceSubString(OS.str(), "false", "0");
8033 // Remove wrap flags, their use in SCEV is highly fragile.
8034 // FIXME: Remove this when SCEV gets smarter about them.
8035 replaceSubString(OS.str(), "<nw>", "");
8036 replaceSubString(OS.str(), "<nsw>", "");
8037 replaceSubString(OS.str(), "<nuw>", "");
8042 void ScalarEvolution::verifyAnalysis() const {
8046 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8048 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8049 // FIXME: It would be much better to store actual values instead of strings,
8050 // but SCEV pointers will change if we drop the caches.
8051 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8052 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8053 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8055 // Gather stringified backedge taken counts for all loops without using
8058 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8059 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8061 // Now compare whether they're the same with and without caches. This allows
8062 // verifying that no pass changed the cache.
8063 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8064 "New loops suddenly appeared!");
8066 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8067 OldE = BackedgeDumpsOld.end(),
8068 NewI = BackedgeDumpsNew.begin();
8069 OldI != OldE; ++OldI, ++NewI) {
8070 assert(OldI->first == NewI->first && "Loop order changed!");
8072 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8074 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8075 // means that a pass is buggy or SCEV has to learn a new pattern but is
8076 // usually not harmful.
8077 if (OldI->second != NewI->second &&
8078 OldI->second.find("undef") == std::string::npos &&
8079 NewI->second.find("undef") == std::string::npos &&
8080 OldI->second != "***COULDNOTCOMPUTE***" &&
8081 NewI->second != "***COULDNOTCOMPUTE***") {
8082 dbgs() << "SCEVValidator: SCEV for loop '"
8083 << OldI->first->getHeader()->getName()
8084 << "' changed from '" << OldI->second
8085 << "' to '" << NewI->second << "'!\n";
8090 // TODO: Verify more things.