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 APInt C1 = SC1->getValue()->getValue();
1212 APInt C2 = SC2->getValue()->getValue();
1213 APInt CDiff = C2 - C1;
1214 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1215 CDiff.isStrictlyPositive() && C2.isPowerOf2())
1216 return getAddExpr(getSignExtendExpr(SC1, Ty),
1217 getSignExtendExpr(SMul, Ty));
1222 // If the input value is a chrec scev, and we can prove that the value
1223 // did not overflow the old, smaller, value, we can sign extend all of the
1224 // operands (often constants). This allows analysis of something like
1225 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1226 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1227 if (AR->isAffine()) {
1228 const SCEV *Start = AR->getStart();
1229 const SCEV *Step = AR->getStepRecurrence(*this);
1230 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1231 const Loop *L = AR->getLoop();
1233 // If we have special knowledge that this addrec won't overflow,
1234 // we don't need to do any further analysis.
1235 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1236 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1237 getSignExtendExpr(Step, Ty),
1240 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1241 // Note that this serves two purposes: It filters out loops that are
1242 // simply not analyzable, and it covers the case where this code is
1243 // being called from within backedge-taken count analysis, such that
1244 // attempting to ask for the backedge-taken count would likely result
1245 // in infinite recursion. In the later case, the analysis code will
1246 // cope with a conservative value, and it will take care to purge
1247 // that value once it has finished.
1248 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1249 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1250 // Manually compute the final value for AR, checking for
1253 // Check whether the backedge-taken count can be losslessly casted to
1254 // the addrec's type. The count is always unsigned.
1255 const SCEV *CastedMaxBECount =
1256 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1257 const SCEV *RecastedMaxBECount =
1258 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1259 if (MaxBECount == RecastedMaxBECount) {
1260 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1261 // Check whether Start+Step*MaxBECount has no signed overflow.
1262 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1263 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1264 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1265 const SCEV *WideMaxBECount =
1266 getZeroExtendExpr(CastedMaxBECount, WideTy);
1267 const SCEV *OperandExtendedAdd =
1268 getAddExpr(WideStart,
1269 getMulExpr(WideMaxBECount,
1270 getSignExtendExpr(Step, WideTy)));
1271 if (SAdd == OperandExtendedAdd) {
1272 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1273 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1274 // Return the expression with the addrec on the outside.
1275 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1276 getSignExtendExpr(Step, Ty),
1277 L, AR->getNoWrapFlags());
1279 // Similar to above, only this time treat the step value as unsigned.
1280 // This covers loops that count up with an unsigned step.
1281 OperandExtendedAdd =
1282 getAddExpr(WideStart,
1283 getMulExpr(WideMaxBECount,
1284 getZeroExtendExpr(Step, WideTy)));
1285 if (SAdd == OperandExtendedAdd) {
1286 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1287 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1288 // Return the expression with the addrec on the outside.
1289 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1290 getZeroExtendExpr(Step, Ty),
1291 L, AR->getNoWrapFlags());
1295 // If the backedge is guarded by a comparison with the pre-inc value
1296 // the addrec is safe. Also, if the entry is guarded by a comparison
1297 // with the start value and the backedge is guarded by a comparison
1298 // with the post-inc value, the addrec is safe.
1299 ICmpInst::Predicate Pred;
1300 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1301 if (OverflowLimit &&
1302 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1303 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1304 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1306 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1307 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1308 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1309 getSignExtendExpr(Step, Ty),
1310 L, AR->getNoWrapFlags());
1313 // If Start and Step are constants, check if we can apply this
1315 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1316 auto SC1 = dyn_cast<SCEVConstant>(Start);
1317 auto SC2 = dyn_cast<SCEVConstant>(Step);
1319 APInt C1 = SC1->getValue()->getValue();
1320 APInt C2 = SC2->getValue()->getValue();
1321 APInt CDiff = C2 - C1;
1322 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1323 CDiff.isStrictlyPositive() && C2.isPowerOf2()) {
1324 Start = getSignExtendExpr(Start, Ty);
1325 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1326 L, AR->getNoWrapFlags());
1327 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1332 // The cast wasn't folded; create an explicit cast node.
1333 // Recompute the insert position, as it may have been invalidated.
1334 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1335 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1337 UniqueSCEVs.InsertNode(S, IP);
1341 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1342 /// unspecified bits out to the given type.
1344 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1346 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1347 "This is not an extending conversion!");
1348 assert(isSCEVable(Ty) &&
1349 "This is not a conversion to a SCEVable type!");
1350 Ty = getEffectiveSCEVType(Ty);
1352 // Sign-extend negative constants.
1353 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1354 if (SC->getValue()->getValue().isNegative())
1355 return getSignExtendExpr(Op, Ty);
1357 // Peel off a truncate cast.
1358 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1359 const SCEV *NewOp = T->getOperand();
1360 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1361 return getAnyExtendExpr(NewOp, Ty);
1362 return getTruncateOrNoop(NewOp, Ty);
1365 // Next try a zext cast. If the cast is folded, use it.
1366 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1367 if (!isa<SCEVZeroExtendExpr>(ZExt))
1370 // Next try a sext cast. If the cast is folded, use it.
1371 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1372 if (!isa<SCEVSignExtendExpr>(SExt))
1375 // Force the cast to be folded into the operands of an addrec.
1376 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1377 SmallVector<const SCEV *, 4> Ops;
1378 for (const SCEV *Op : AR->operands())
1379 Ops.push_back(getAnyExtendExpr(Op, Ty));
1380 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1383 // If the expression is obviously signed, use the sext cast value.
1384 if (isa<SCEVSMaxExpr>(Op))
1387 // Absent any other information, use the zext cast value.
1391 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1392 /// a list of operands to be added under the given scale, update the given
1393 /// map. This is a helper function for getAddRecExpr. As an example of
1394 /// what it does, given a sequence of operands that would form an add
1395 /// expression like this:
1397 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1399 /// where A and B are constants, update the map with these values:
1401 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1403 /// and add 13 + A*B*29 to AccumulatedConstant.
1404 /// This will allow getAddRecExpr to produce this:
1406 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1408 /// This form often exposes folding opportunities that are hidden in
1409 /// the original operand list.
1411 /// Return true iff it appears that any interesting folding opportunities
1412 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1413 /// the common case where no interesting opportunities are present, and
1414 /// is also used as a check to avoid infinite recursion.
1417 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1418 SmallVectorImpl<const SCEV *> &NewOps,
1419 APInt &AccumulatedConstant,
1420 const SCEV *const *Ops, size_t NumOperands,
1422 ScalarEvolution &SE) {
1423 bool Interesting = false;
1425 // Iterate over the add operands. They are sorted, with constants first.
1427 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1429 // Pull a buried constant out to the outside.
1430 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1432 AccumulatedConstant += Scale * C->getValue()->getValue();
1435 // Next comes everything else. We're especially interested in multiplies
1436 // here, but they're in the middle, so just visit the rest with one loop.
1437 for (; i != NumOperands; ++i) {
1438 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1439 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1441 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1442 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1443 // A multiplication of a constant with another add; recurse.
1444 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1446 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1447 Add->op_begin(), Add->getNumOperands(),
1450 // A multiplication of a constant with some other value. Update
1452 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1453 const SCEV *Key = SE.getMulExpr(MulOps);
1454 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1455 M.insert(std::make_pair(Key, NewScale));
1457 NewOps.push_back(Pair.first->first);
1459 Pair.first->second += NewScale;
1460 // The map already had an entry for this value, which may indicate
1461 // a folding opportunity.
1466 // An ordinary operand. Update the map.
1467 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1468 M.insert(std::make_pair(Ops[i], Scale));
1470 NewOps.push_back(Pair.first->first);
1472 Pair.first->second += Scale;
1473 // The map already had an entry for this value, which may indicate
1474 // a folding opportunity.
1484 struct APIntCompare {
1485 bool operator()(const APInt &LHS, const APInt &RHS) const {
1486 return LHS.ult(RHS);
1491 /// getAddExpr - Get a canonical add expression, or something simpler if
1493 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1494 SCEV::NoWrapFlags Flags) {
1495 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1496 "only nuw or nsw allowed");
1497 assert(!Ops.empty() && "Cannot get empty add!");
1498 if (Ops.size() == 1) return Ops[0];
1500 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1501 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1502 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1503 "SCEVAddExpr operand types don't match!");
1506 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1508 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1509 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1510 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1512 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1513 E = Ops.end(); I != E; ++I)
1514 if (!isKnownNonNegative(*I)) {
1518 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1521 // Sort by complexity, this groups all similar expression types together.
1522 GroupByComplexity(Ops, LI);
1524 // If there are any constants, fold them together.
1526 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1528 assert(Idx < Ops.size());
1529 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1530 // We found two constants, fold them together!
1531 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1532 RHSC->getValue()->getValue());
1533 if (Ops.size() == 2) return Ops[0];
1534 Ops.erase(Ops.begin()+1); // Erase the folded element
1535 LHSC = cast<SCEVConstant>(Ops[0]);
1538 // If we are left with a constant zero being added, strip it off.
1539 if (LHSC->getValue()->isZero()) {
1540 Ops.erase(Ops.begin());
1544 if (Ops.size() == 1) return Ops[0];
1547 // Okay, check to see if the same value occurs in the operand list more than
1548 // once. If so, merge them together into an multiply expression. Since we
1549 // sorted the list, these values are required to be adjacent.
1550 Type *Ty = Ops[0]->getType();
1551 bool FoundMatch = false;
1552 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1553 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1554 // Scan ahead to count how many equal operands there are.
1556 while (i+Count != e && Ops[i+Count] == Ops[i])
1558 // Merge the values into a multiply.
1559 const SCEV *Scale = getConstant(Ty, Count);
1560 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1561 if (Ops.size() == Count)
1564 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1565 --i; e -= Count - 1;
1569 return getAddExpr(Ops, Flags);
1571 // Check for truncates. If all the operands are truncated from the same
1572 // type, see if factoring out the truncate would permit the result to be
1573 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1574 // if the contents of the resulting outer trunc fold to something simple.
1575 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1576 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1577 Type *DstType = Trunc->getType();
1578 Type *SrcType = Trunc->getOperand()->getType();
1579 SmallVector<const SCEV *, 8> LargeOps;
1581 // Check all the operands to see if they can be represented in the
1582 // source type of the truncate.
1583 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1584 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1585 if (T->getOperand()->getType() != SrcType) {
1589 LargeOps.push_back(T->getOperand());
1590 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1591 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1592 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1593 SmallVector<const SCEV *, 8> LargeMulOps;
1594 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1595 if (const SCEVTruncateExpr *T =
1596 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1597 if (T->getOperand()->getType() != SrcType) {
1601 LargeMulOps.push_back(T->getOperand());
1602 } else if (const SCEVConstant *C =
1603 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1604 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1611 LargeOps.push_back(getMulExpr(LargeMulOps));
1618 // Evaluate the expression in the larger type.
1619 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1620 // If it folds to something simple, use it. Otherwise, don't.
1621 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1622 return getTruncateExpr(Fold, DstType);
1626 // Skip past any other cast SCEVs.
1627 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1630 // If there are add operands they would be next.
1631 if (Idx < Ops.size()) {
1632 bool DeletedAdd = false;
1633 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1634 // If we have an add, expand the add operands onto the end of the operands
1636 Ops.erase(Ops.begin()+Idx);
1637 Ops.append(Add->op_begin(), Add->op_end());
1641 // If we deleted at least one add, we added operands to the end of the list,
1642 // and they are not necessarily sorted. Recurse to resort and resimplify
1643 // any operands we just acquired.
1645 return getAddExpr(Ops);
1648 // Skip over the add expression until we get to a multiply.
1649 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1652 // Check to see if there are any folding opportunities present with
1653 // operands multiplied by constant values.
1654 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1655 uint64_t BitWidth = getTypeSizeInBits(Ty);
1656 DenseMap<const SCEV *, APInt> M;
1657 SmallVector<const SCEV *, 8> NewOps;
1658 APInt AccumulatedConstant(BitWidth, 0);
1659 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1660 Ops.data(), Ops.size(),
1661 APInt(BitWidth, 1), *this)) {
1662 // Some interesting folding opportunity is present, so its worthwhile to
1663 // re-generate the operands list. Group the operands by constant scale,
1664 // to avoid multiplying by the same constant scale multiple times.
1665 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1666 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1667 E = NewOps.end(); I != E; ++I)
1668 MulOpLists[M.find(*I)->second].push_back(*I);
1669 // Re-generate the operands list.
1671 if (AccumulatedConstant != 0)
1672 Ops.push_back(getConstant(AccumulatedConstant));
1673 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1674 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1676 Ops.push_back(getMulExpr(getConstant(I->first),
1677 getAddExpr(I->second)));
1679 return getConstant(Ty, 0);
1680 if (Ops.size() == 1)
1682 return getAddExpr(Ops);
1686 // If we are adding something to a multiply expression, make sure the
1687 // something is not already an operand of the multiply. If so, merge it into
1689 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1690 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1691 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1692 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1693 if (isa<SCEVConstant>(MulOpSCEV))
1695 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1696 if (MulOpSCEV == Ops[AddOp]) {
1697 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1698 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1699 if (Mul->getNumOperands() != 2) {
1700 // If the multiply has more than two operands, we must get the
1702 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1703 Mul->op_begin()+MulOp);
1704 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1705 InnerMul = getMulExpr(MulOps);
1707 const SCEV *One = getConstant(Ty, 1);
1708 const SCEV *AddOne = getAddExpr(One, InnerMul);
1709 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1710 if (Ops.size() == 2) return OuterMul;
1712 Ops.erase(Ops.begin()+AddOp);
1713 Ops.erase(Ops.begin()+Idx-1);
1715 Ops.erase(Ops.begin()+Idx);
1716 Ops.erase(Ops.begin()+AddOp-1);
1718 Ops.push_back(OuterMul);
1719 return getAddExpr(Ops);
1722 // Check this multiply against other multiplies being added together.
1723 for (unsigned OtherMulIdx = Idx+1;
1724 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1726 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1727 // If MulOp occurs in OtherMul, we can fold the two multiplies
1729 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1730 OMulOp != e; ++OMulOp)
1731 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1732 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1733 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1734 if (Mul->getNumOperands() != 2) {
1735 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1736 Mul->op_begin()+MulOp);
1737 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1738 InnerMul1 = getMulExpr(MulOps);
1740 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1741 if (OtherMul->getNumOperands() != 2) {
1742 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1743 OtherMul->op_begin()+OMulOp);
1744 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1745 InnerMul2 = getMulExpr(MulOps);
1747 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1748 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1749 if (Ops.size() == 2) return OuterMul;
1750 Ops.erase(Ops.begin()+Idx);
1751 Ops.erase(Ops.begin()+OtherMulIdx-1);
1752 Ops.push_back(OuterMul);
1753 return getAddExpr(Ops);
1759 // If there are any add recurrences in the operands list, see if any other
1760 // added values are loop invariant. If so, we can fold them into the
1762 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1765 // Scan over all recurrences, trying to fold loop invariants into them.
1766 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1767 // Scan all of the other operands to this add and add them to the vector if
1768 // they are loop invariant w.r.t. the recurrence.
1769 SmallVector<const SCEV *, 8> LIOps;
1770 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1771 const Loop *AddRecLoop = AddRec->getLoop();
1772 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1773 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1774 LIOps.push_back(Ops[i]);
1775 Ops.erase(Ops.begin()+i);
1779 // If we found some loop invariants, fold them into the recurrence.
1780 if (!LIOps.empty()) {
1781 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1782 LIOps.push_back(AddRec->getStart());
1784 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1786 AddRecOps[0] = getAddExpr(LIOps);
1788 // Build the new addrec. Propagate the NUW and NSW flags if both the
1789 // outer add and the inner addrec are guaranteed to have no overflow.
1790 // Always propagate NW.
1791 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1792 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1794 // If all of the other operands were loop invariant, we are done.
1795 if (Ops.size() == 1) return NewRec;
1797 // Otherwise, add the folded AddRec by the non-invariant parts.
1798 for (unsigned i = 0;; ++i)
1799 if (Ops[i] == AddRec) {
1803 return getAddExpr(Ops);
1806 // Okay, if there weren't any loop invariants to be folded, check to see if
1807 // there are multiple AddRec's with the same loop induction variable being
1808 // added together. If so, we can fold them.
1809 for (unsigned OtherIdx = Idx+1;
1810 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1812 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1813 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1814 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1816 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1818 if (const SCEVAddRecExpr *OtherAddRec =
1819 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1820 if (OtherAddRec->getLoop() == AddRecLoop) {
1821 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1823 if (i >= AddRecOps.size()) {
1824 AddRecOps.append(OtherAddRec->op_begin()+i,
1825 OtherAddRec->op_end());
1828 AddRecOps[i] = getAddExpr(AddRecOps[i],
1829 OtherAddRec->getOperand(i));
1831 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1833 // Step size has changed, so we cannot guarantee no self-wraparound.
1834 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1835 return getAddExpr(Ops);
1838 // Otherwise couldn't fold anything into this recurrence. Move onto the
1842 // Okay, it looks like we really DO need an add expr. Check to see if we
1843 // already have one, otherwise create a new one.
1844 FoldingSetNodeID ID;
1845 ID.AddInteger(scAddExpr);
1846 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1847 ID.AddPointer(Ops[i]);
1850 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1852 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1853 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1854 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1856 UniqueSCEVs.InsertNode(S, IP);
1858 S->setNoWrapFlags(Flags);
1862 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1864 if (j > 1 && k / j != i) Overflow = true;
1868 /// Compute the result of "n choose k", the binomial coefficient. If an
1869 /// intermediate computation overflows, Overflow will be set and the return will
1870 /// be garbage. Overflow is not cleared on absence of overflow.
1871 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1872 // We use the multiplicative formula:
1873 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1874 // At each iteration, we take the n-th term of the numeral and divide by the
1875 // (k-n)th term of the denominator. This division will always produce an
1876 // integral result, and helps reduce the chance of overflow in the
1877 // intermediate computations. However, we can still overflow even when the
1878 // final result would fit.
1880 if (n == 0 || n == k) return 1;
1881 if (k > n) return 0;
1887 for (uint64_t i = 1; i <= k; ++i) {
1888 r = umul_ov(r, n-(i-1), Overflow);
1894 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1896 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1897 SCEV::NoWrapFlags Flags) {
1898 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1899 "only nuw or nsw allowed");
1900 assert(!Ops.empty() && "Cannot get empty mul!");
1901 if (Ops.size() == 1) return Ops[0];
1903 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1904 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1905 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1906 "SCEVMulExpr operand types don't match!");
1909 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1911 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1912 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1913 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1915 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1916 E = Ops.end(); I != E; ++I)
1917 if (!isKnownNonNegative(*I)) {
1921 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1924 // Sort by complexity, this groups all similar expression types together.
1925 GroupByComplexity(Ops, LI);
1927 // If there are any constants, fold them together.
1929 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1931 // C1*(C2+V) -> C1*C2 + C1*V
1932 if (Ops.size() == 2)
1933 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1934 if (Add->getNumOperands() == 2 &&
1935 isa<SCEVConstant>(Add->getOperand(0)))
1936 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1937 getMulExpr(LHSC, Add->getOperand(1)));
1940 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1941 // We found two constants, fold them together!
1942 ConstantInt *Fold = ConstantInt::get(getContext(),
1943 LHSC->getValue()->getValue() *
1944 RHSC->getValue()->getValue());
1945 Ops[0] = getConstant(Fold);
1946 Ops.erase(Ops.begin()+1); // Erase the folded element
1947 if (Ops.size() == 1) return Ops[0];
1948 LHSC = cast<SCEVConstant>(Ops[0]);
1951 // If we are left with a constant one being multiplied, strip it off.
1952 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1953 Ops.erase(Ops.begin());
1955 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1956 // If we have a multiply of zero, it will always be zero.
1958 } else if (Ops[0]->isAllOnesValue()) {
1959 // If we have a mul by -1 of an add, try distributing the -1 among the
1961 if (Ops.size() == 2) {
1962 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1963 SmallVector<const SCEV *, 4> NewOps;
1964 bool AnyFolded = false;
1965 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1966 E = Add->op_end(); I != E; ++I) {
1967 const SCEV *Mul = getMulExpr(Ops[0], *I);
1968 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1969 NewOps.push_back(Mul);
1972 return getAddExpr(NewOps);
1974 else if (const SCEVAddRecExpr *
1975 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1976 // Negation preserves a recurrence's no self-wrap property.
1977 SmallVector<const SCEV *, 4> Operands;
1978 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1979 E = AddRec->op_end(); I != E; ++I) {
1980 Operands.push_back(getMulExpr(Ops[0], *I));
1982 return getAddRecExpr(Operands, AddRec->getLoop(),
1983 AddRec->getNoWrapFlags(SCEV::FlagNW));
1988 if (Ops.size() == 1)
1992 // Skip over the add expression until we get to a multiply.
1993 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1996 // If there are mul operands inline them all into this expression.
1997 if (Idx < Ops.size()) {
1998 bool DeletedMul = false;
1999 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2000 // If we have an mul, expand the mul operands onto the end of the operands
2002 Ops.erase(Ops.begin()+Idx);
2003 Ops.append(Mul->op_begin(), Mul->op_end());
2007 // If we deleted at least one mul, we added operands to the end of the list,
2008 // and they are not necessarily sorted. Recurse to resort and resimplify
2009 // any operands we just acquired.
2011 return getMulExpr(Ops);
2014 // If there are any add recurrences in the operands list, see if any other
2015 // added values are loop invariant. If so, we can fold them into the
2017 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2020 // Scan over all recurrences, trying to fold loop invariants into them.
2021 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2022 // Scan all of the other operands to this mul and add them to the vector if
2023 // they are loop invariant w.r.t. the recurrence.
2024 SmallVector<const SCEV *, 8> LIOps;
2025 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2026 const Loop *AddRecLoop = AddRec->getLoop();
2027 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2028 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2029 LIOps.push_back(Ops[i]);
2030 Ops.erase(Ops.begin()+i);
2034 // If we found some loop invariants, fold them into the recurrence.
2035 if (!LIOps.empty()) {
2036 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2037 SmallVector<const SCEV *, 4> NewOps;
2038 NewOps.reserve(AddRec->getNumOperands());
2039 const SCEV *Scale = getMulExpr(LIOps);
2040 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2041 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2043 // Build the new addrec. Propagate the NUW and NSW flags if both the
2044 // outer mul and the inner addrec are guaranteed to have no overflow.
2046 // No self-wrap cannot be guaranteed after changing the step size, but
2047 // will be inferred if either NUW or NSW is true.
2048 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2049 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2051 // If all of the other operands were loop invariant, we are done.
2052 if (Ops.size() == 1) return NewRec;
2054 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2055 for (unsigned i = 0;; ++i)
2056 if (Ops[i] == AddRec) {
2060 return getMulExpr(Ops);
2063 // Okay, if there weren't any loop invariants to be folded, check to see if
2064 // there are multiple AddRec's with the same loop induction variable being
2065 // multiplied together. If so, we can fold them.
2066 for (unsigned OtherIdx = Idx+1;
2067 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2069 if (AddRecLoop != cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop())
2072 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2073 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2074 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2075 // ]]],+,...up to x=2n}.
2076 // Note that the arguments to choose() are always integers with values
2077 // known at compile time, never SCEV objects.
2079 // The implementation avoids pointless extra computations when the two
2080 // addrec's are of different length (mathematically, it's equivalent to
2081 // an infinite stream of zeros on the right).
2082 bool OpsModified = false;
2083 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2085 const SCEVAddRecExpr *OtherAddRec =
2086 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2087 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2090 bool Overflow = false;
2091 Type *Ty = AddRec->getType();
2092 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2093 SmallVector<const SCEV*, 7> AddRecOps;
2094 for (int x = 0, xe = AddRec->getNumOperands() +
2095 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2096 const SCEV *Term = getConstant(Ty, 0);
2097 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2098 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2099 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2100 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2101 z < ze && !Overflow; ++z) {
2102 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2104 if (LargerThan64Bits)
2105 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2107 Coeff = Coeff1*Coeff2;
2108 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2109 const SCEV *Term1 = AddRec->getOperand(y-z);
2110 const SCEV *Term2 = OtherAddRec->getOperand(z);
2111 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2114 AddRecOps.push_back(Term);
2117 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2119 if (Ops.size() == 2) return NewAddRec;
2120 Ops[Idx] = NewAddRec;
2121 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2123 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2129 return getMulExpr(Ops);
2132 // Otherwise couldn't fold anything into this recurrence. Move onto the
2136 // Okay, it looks like we really DO need an mul expr. Check to see if we
2137 // already have one, otherwise create a new one.
2138 FoldingSetNodeID ID;
2139 ID.AddInteger(scMulExpr);
2140 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2141 ID.AddPointer(Ops[i]);
2144 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2146 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2147 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2148 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2150 UniqueSCEVs.InsertNode(S, IP);
2152 S->setNoWrapFlags(Flags);
2156 /// getUDivExpr - Get a canonical unsigned division expression, or something
2157 /// simpler if possible.
2158 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2160 assert(getEffectiveSCEVType(LHS->getType()) ==
2161 getEffectiveSCEVType(RHS->getType()) &&
2162 "SCEVUDivExpr operand types don't match!");
2164 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2165 if (RHSC->getValue()->equalsInt(1))
2166 return LHS; // X udiv 1 --> x
2167 // If the denominator is zero, the result of the udiv is undefined. Don't
2168 // try to analyze it, because the resolution chosen here may differ from
2169 // the resolution chosen in other parts of the compiler.
2170 if (!RHSC->getValue()->isZero()) {
2171 // Determine if the division can be folded into the operands of
2173 // TODO: Generalize this to non-constants by using known-bits information.
2174 Type *Ty = LHS->getType();
2175 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2176 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2177 // For non-power-of-two values, effectively round the value up to the
2178 // nearest power of two.
2179 if (!RHSC->getValue()->getValue().isPowerOf2())
2181 IntegerType *ExtTy =
2182 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2183 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2184 if (const SCEVConstant *Step =
2185 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2186 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2187 const APInt &StepInt = Step->getValue()->getValue();
2188 const APInt &DivInt = RHSC->getValue()->getValue();
2189 if (!StepInt.urem(DivInt) &&
2190 getZeroExtendExpr(AR, ExtTy) ==
2191 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2192 getZeroExtendExpr(Step, ExtTy),
2193 AR->getLoop(), SCEV::FlagAnyWrap)) {
2194 SmallVector<const SCEV *, 4> Operands;
2195 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2196 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2197 return getAddRecExpr(Operands, AR->getLoop(),
2200 /// Get a canonical UDivExpr for a recurrence.
2201 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2202 // We can currently only fold X%N if X is constant.
2203 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2204 if (StartC && !DivInt.urem(StepInt) &&
2205 getZeroExtendExpr(AR, ExtTy) ==
2206 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2207 getZeroExtendExpr(Step, ExtTy),
2208 AR->getLoop(), SCEV::FlagAnyWrap)) {
2209 const APInt &StartInt = StartC->getValue()->getValue();
2210 const APInt &StartRem = StartInt.urem(StepInt);
2212 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2213 AR->getLoop(), SCEV::FlagNW);
2216 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2217 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2218 SmallVector<const SCEV *, 4> Operands;
2219 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2220 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2221 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2222 // Find an operand that's safely divisible.
2223 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2224 const SCEV *Op = M->getOperand(i);
2225 const SCEV *Div = getUDivExpr(Op, RHSC);
2226 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2227 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2230 return getMulExpr(Operands);
2234 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2235 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2236 SmallVector<const SCEV *, 4> Operands;
2237 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2238 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2239 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2241 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2242 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2243 if (isa<SCEVUDivExpr>(Op) ||
2244 getMulExpr(Op, RHS) != A->getOperand(i))
2246 Operands.push_back(Op);
2248 if (Operands.size() == A->getNumOperands())
2249 return getAddExpr(Operands);
2253 // Fold if both operands are constant.
2254 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2255 Constant *LHSCV = LHSC->getValue();
2256 Constant *RHSCV = RHSC->getValue();
2257 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2263 FoldingSetNodeID ID;
2264 ID.AddInteger(scUDivExpr);
2268 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2269 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2271 UniqueSCEVs.InsertNode(S, IP);
2275 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2276 APInt A = C1->getValue()->getValue().abs();
2277 APInt B = C2->getValue()->getValue().abs();
2278 uint32_t ABW = A.getBitWidth();
2279 uint32_t BBW = B.getBitWidth();
2286 return APIntOps::GreatestCommonDivisor(A, B);
2289 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2290 /// something simpler if possible. There is no representation for an exact udiv
2291 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2292 /// We can't do this when it's not exact because the udiv may be clearing bits.
2293 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2295 // TODO: we could try to find factors in all sorts of things, but for now we
2296 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2297 // end of this file for inspiration.
2299 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2301 return getUDivExpr(LHS, RHS);
2303 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2304 // If the mulexpr multiplies by a constant, then that constant must be the
2305 // first element of the mulexpr.
2306 if (const SCEVConstant *LHSCst =
2307 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2308 if (LHSCst == RHSCst) {
2309 SmallVector<const SCEV *, 2> Operands;
2310 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2311 return getMulExpr(Operands);
2314 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2315 // that there's a factor provided by one of the other terms. We need to
2317 APInt Factor = gcd(LHSCst, RHSCst);
2318 if (!Factor.isIntN(1)) {
2319 LHSCst = cast<SCEVConstant>(
2320 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2321 RHSCst = cast<SCEVConstant>(
2322 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2323 SmallVector<const SCEV *, 2> Operands;
2324 Operands.push_back(LHSCst);
2325 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2326 LHS = getMulExpr(Operands);
2328 Mul = dyn_cast<SCEVMulExpr>(LHS);
2330 return getUDivExactExpr(LHS, RHS);
2335 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2336 if (Mul->getOperand(i) == RHS) {
2337 SmallVector<const SCEV *, 2> Operands;
2338 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2339 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2340 return getMulExpr(Operands);
2344 return getUDivExpr(LHS, RHS);
2347 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2348 /// Simplify the expression as much as possible.
2349 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2351 SCEV::NoWrapFlags Flags) {
2352 SmallVector<const SCEV *, 4> Operands;
2353 Operands.push_back(Start);
2354 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2355 if (StepChrec->getLoop() == L) {
2356 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2357 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2360 Operands.push_back(Step);
2361 return getAddRecExpr(Operands, L, Flags);
2364 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2365 /// Simplify the expression as much as possible.
2367 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2368 const Loop *L, SCEV::NoWrapFlags Flags) {
2369 if (Operands.size() == 1) return Operands[0];
2371 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2372 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2373 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2374 "SCEVAddRecExpr operand types don't match!");
2375 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2376 assert(isLoopInvariant(Operands[i], L) &&
2377 "SCEVAddRecExpr operand is not loop-invariant!");
2380 if (Operands.back()->isZero()) {
2381 Operands.pop_back();
2382 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2385 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2386 // use that information to infer NUW and NSW flags. However, computing a
2387 // BE count requires calling getAddRecExpr, so we may not yet have a
2388 // meaningful BE count at this point (and if we don't, we'd be stuck
2389 // with a SCEVCouldNotCompute as the cached BE count).
2391 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2393 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2394 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2395 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2397 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2398 E = Operands.end(); I != E; ++I)
2399 if (!isKnownNonNegative(*I)) {
2403 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2406 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2407 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2408 const Loop *NestedLoop = NestedAR->getLoop();
2409 if (L->contains(NestedLoop) ?
2410 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2411 (!NestedLoop->contains(L) &&
2412 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2413 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2414 NestedAR->op_end());
2415 Operands[0] = NestedAR->getStart();
2416 // AddRecs require their operands be loop-invariant with respect to their
2417 // loops. Don't perform this transformation if it would break this
2419 bool AllInvariant = true;
2420 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2421 if (!isLoopInvariant(Operands[i], L)) {
2422 AllInvariant = false;
2426 // Create a recurrence for the outer loop with the same step size.
2428 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2429 // inner recurrence has the same property.
2430 SCEV::NoWrapFlags OuterFlags =
2431 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2433 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2434 AllInvariant = true;
2435 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2436 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2437 AllInvariant = false;
2441 // Ok, both add recurrences are valid after the transformation.
2443 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2444 // the outer recurrence has the same property.
2445 SCEV::NoWrapFlags InnerFlags =
2446 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2447 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2450 // Reset Operands to its original state.
2451 Operands[0] = NestedAR;
2455 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2456 // already have one, otherwise create a new one.
2457 FoldingSetNodeID ID;
2458 ID.AddInteger(scAddRecExpr);
2459 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2460 ID.AddPointer(Operands[i]);
2464 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2466 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2467 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2468 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2469 O, Operands.size(), L);
2470 UniqueSCEVs.InsertNode(S, IP);
2472 S->setNoWrapFlags(Flags);
2476 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2478 SmallVector<const SCEV *, 2> Ops;
2481 return getSMaxExpr(Ops);
2485 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2486 assert(!Ops.empty() && "Cannot get empty smax!");
2487 if (Ops.size() == 1) return Ops[0];
2489 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2490 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2491 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2492 "SCEVSMaxExpr operand types don't match!");
2495 // Sort by complexity, this groups all similar expression types together.
2496 GroupByComplexity(Ops, LI);
2498 // If there are any constants, fold them together.
2500 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2502 assert(Idx < Ops.size());
2503 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2504 // We found two constants, fold them together!
2505 ConstantInt *Fold = ConstantInt::get(getContext(),
2506 APIntOps::smax(LHSC->getValue()->getValue(),
2507 RHSC->getValue()->getValue()));
2508 Ops[0] = getConstant(Fold);
2509 Ops.erase(Ops.begin()+1); // Erase the folded element
2510 if (Ops.size() == 1) return Ops[0];
2511 LHSC = cast<SCEVConstant>(Ops[0]);
2514 // If we are left with a constant minimum-int, strip it off.
2515 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2516 Ops.erase(Ops.begin());
2518 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2519 // If we have an smax with a constant maximum-int, it will always be
2524 if (Ops.size() == 1) return Ops[0];
2527 // Find the first SMax
2528 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2531 // Check to see if one of the operands is an SMax. If so, expand its operands
2532 // onto our operand list, and recurse to simplify.
2533 if (Idx < Ops.size()) {
2534 bool DeletedSMax = false;
2535 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2536 Ops.erase(Ops.begin()+Idx);
2537 Ops.append(SMax->op_begin(), SMax->op_end());
2542 return getSMaxExpr(Ops);
2545 // Okay, check to see if the same value occurs in the operand list twice. If
2546 // so, delete one. Since we sorted the list, these values are required to
2548 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2549 // X smax Y smax Y --> X smax Y
2550 // X smax Y --> X, if X is always greater than Y
2551 if (Ops[i] == Ops[i+1] ||
2552 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2553 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2555 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2556 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2560 if (Ops.size() == 1) return Ops[0];
2562 assert(!Ops.empty() && "Reduced smax down to nothing!");
2564 // Okay, it looks like we really DO need an smax expr. Check to see if we
2565 // already have one, otherwise create a new one.
2566 FoldingSetNodeID ID;
2567 ID.AddInteger(scSMaxExpr);
2568 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2569 ID.AddPointer(Ops[i]);
2571 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2572 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2573 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2574 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2576 UniqueSCEVs.InsertNode(S, IP);
2580 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2582 SmallVector<const SCEV *, 2> Ops;
2585 return getUMaxExpr(Ops);
2589 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2590 assert(!Ops.empty() && "Cannot get empty umax!");
2591 if (Ops.size() == 1) return Ops[0];
2593 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2594 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2595 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2596 "SCEVUMaxExpr operand types don't match!");
2599 // Sort by complexity, this groups all similar expression types together.
2600 GroupByComplexity(Ops, LI);
2602 // If there are any constants, fold them together.
2604 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2606 assert(Idx < Ops.size());
2607 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2608 // We found two constants, fold them together!
2609 ConstantInt *Fold = ConstantInt::get(getContext(),
2610 APIntOps::umax(LHSC->getValue()->getValue(),
2611 RHSC->getValue()->getValue()));
2612 Ops[0] = getConstant(Fold);
2613 Ops.erase(Ops.begin()+1); // Erase the folded element
2614 if (Ops.size() == 1) return Ops[0];
2615 LHSC = cast<SCEVConstant>(Ops[0]);
2618 // If we are left with a constant minimum-int, strip it off.
2619 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2620 Ops.erase(Ops.begin());
2622 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2623 // If we have an umax with a constant maximum-int, it will always be
2628 if (Ops.size() == 1) return Ops[0];
2631 // Find the first UMax
2632 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2635 // Check to see if one of the operands is a UMax. If so, expand its operands
2636 // onto our operand list, and recurse to simplify.
2637 if (Idx < Ops.size()) {
2638 bool DeletedUMax = false;
2639 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2640 Ops.erase(Ops.begin()+Idx);
2641 Ops.append(UMax->op_begin(), UMax->op_end());
2646 return getUMaxExpr(Ops);
2649 // Okay, check to see if the same value occurs in the operand list twice. If
2650 // so, delete one. Since we sorted the list, these values are required to
2652 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2653 // X umax Y umax Y --> X umax Y
2654 // X umax Y --> X, if X is always greater than Y
2655 if (Ops[i] == Ops[i+1] ||
2656 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2657 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2659 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2660 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2664 if (Ops.size() == 1) return Ops[0];
2666 assert(!Ops.empty() && "Reduced umax down to nothing!");
2668 // Okay, it looks like we really DO need a umax expr. Check to see if we
2669 // already have one, otherwise create a new one.
2670 FoldingSetNodeID ID;
2671 ID.AddInteger(scUMaxExpr);
2672 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2673 ID.AddPointer(Ops[i]);
2675 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2676 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2677 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2678 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2680 UniqueSCEVs.InsertNode(S, IP);
2684 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2686 // ~smax(~x, ~y) == smin(x, y).
2687 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2690 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2692 // ~umax(~x, ~y) == umin(x, y)
2693 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2696 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2697 // If we have DataLayout, we can bypass creating a target-independent
2698 // constant expression and then folding it back into a ConstantInt.
2699 // This is just a compile-time optimization.
2701 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
2703 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2704 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2705 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2707 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2708 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2709 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2712 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2715 // If we have DataLayout, we can bypass creating a target-independent
2716 // constant expression and then folding it back into a ConstantInt.
2717 // This is just a compile-time optimization.
2719 return getConstant(IntTy,
2720 DL->getStructLayout(STy)->getElementOffset(FieldNo));
2723 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2724 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2725 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2728 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2729 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2732 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2733 // Don't attempt to do anything other than create a SCEVUnknown object
2734 // here. createSCEV only calls getUnknown after checking for all other
2735 // interesting possibilities, and any other code that calls getUnknown
2736 // is doing so in order to hide a value from SCEV canonicalization.
2738 FoldingSetNodeID ID;
2739 ID.AddInteger(scUnknown);
2742 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2743 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2744 "Stale SCEVUnknown in uniquing map!");
2747 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2749 FirstUnknown = cast<SCEVUnknown>(S);
2750 UniqueSCEVs.InsertNode(S, IP);
2754 //===----------------------------------------------------------------------===//
2755 // Basic SCEV Analysis and PHI Idiom Recognition Code
2758 /// isSCEVable - Test if values of the given type are analyzable within
2759 /// the SCEV framework. This primarily includes integer types, and it
2760 /// can optionally include pointer types if the ScalarEvolution class
2761 /// has access to target-specific information.
2762 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2763 // Integers and pointers are always SCEVable.
2764 return Ty->isIntegerTy() || Ty->isPointerTy();
2767 /// getTypeSizeInBits - Return the size in bits of the specified type,
2768 /// for which isSCEVable must return true.
2769 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2770 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2772 // If we have a DataLayout, use it!
2774 return DL->getTypeSizeInBits(Ty);
2776 // Integer types have fixed sizes.
2777 if (Ty->isIntegerTy())
2778 return Ty->getPrimitiveSizeInBits();
2780 // The only other support type is pointer. Without DataLayout, conservatively
2781 // assume pointers are 64-bit.
2782 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2786 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2787 /// the given type and which represents how SCEV will treat the given
2788 /// type, for which isSCEVable must return true. For pointer types,
2789 /// this is the pointer-sized integer type.
2790 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2791 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2793 if (Ty->isIntegerTy()) {
2797 // The only other support type is pointer.
2798 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2801 return DL->getIntPtrType(Ty);
2803 // Without DataLayout, conservatively assume pointers are 64-bit.
2804 return Type::getInt64Ty(getContext());
2807 const SCEV *ScalarEvolution::getCouldNotCompute() {
2808 return &CouldNotCompute;
2812 // Helper class working with SCEVTraversal to figure out if a SCEV contains
2813 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
2814 // is set iff if find such SCEVUnknown.
2816 struct FindInvalidSCEVUnknown {
2818 FindInvalidSCEVUnknown() { FindOne = false; }
2819 bool follow(const SCEV *S) {
2820 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
2824 if (!cast<SCEVUnknown>(S)->getValue())
2831 bool isDone() const { return FindOne; }
2835 bool ScalarEvolution::checkValidity(const SCEV *S) const {
2836 FindInvalidSCEVUnknown F;
2837 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
2843 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2844 /// expression and create a new one.
2845 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2846 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2848 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
2849 if (I != ValueExprMap.end()) {
2850 const SCEV *S = I->second;
2851 if (checkValidity(S))
2854 ValueExprMap.erase(I);
2856 const SCEV *S = createSCEV(V);
2858 // The process of creating a SCEV for V may have caused other SCEVs
2859 // to have been created, so it's necessary to insert the new entry
2860 // from scratch, rather than trying to remember the insert position
2862 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2866 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2868 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2869 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2871 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2873 Type *Ty = V->getType();
2874 Ty = getEffectiveSCEVType(Ty);
2875 return getMulExpr(V,
2876 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2879 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2880 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2881 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2883 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2885 Type *Ty = V->getType();
2886 Ty = getEffectiveSCEVType(Ty);
2887 const SCEV *AllOnes =
2888 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2889 return getMinusSCEV(AllOnes, V);
2892 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2893 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2894 SCEV::NoWrapFlags Flags) {
2895 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2897 // Fast path: X - X --> 0.
2899 return getConstant(LHS->getType(), 0);
2902 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2905 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2906 /// input value to the specified type. If the type must be extended, it is zero
2909 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2910 Type *SrcTy = V->getType();
2911 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2912 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2913 "Cannot truncate or zero extend with non-integer arguments!");
2914 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2915 return V; // No conversion
2916 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2917 return getTruncateExpr(V, Ty);
2918 return getZeroExtendExpr(V, Ty);
2921 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2922 /// input value to the specified type. If the type must be extended, it is sign
2925 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2927 Type *SrcTy = V->getType();
2928 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2929 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2930 "Cannot truncate or zero extend with non-integer arguments!");
2931 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2932 return V; // No conversion
2933 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2934 return getTruncateExpr(V, Ty);
2935 return getSignExtendExpr(V, Ty);
2938 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2939 /// input value to the specified type. If the type must be extended, it is zero
2940 /// extended. The conversion must not be narrowing.
2942 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2943 Type *SrcTy = V->getType();
2944 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2945 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2946 "Cannot noop or zero extend with non-integer arguments!");
2947 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2948 "getNoopOrZeroExtend cannot truncate!");
2949 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2950 return V; // No conversion
2951 return getZeroExtendExpr(V, Ty);
2954 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2955 /// input value to the specified type. If the type must be extended, it is sign
2956 /// extended. The conversion must not be narrowing.
2958 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2959 Type *SrcTy = V->getType();
2960 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2961 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2962 "Cannot noop or sign extend with non-integer arguments!");
2963 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2964 "getNoopOrSignExtend cannot truncate!");
2965 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2966 return V; // No conversion
2967 return getSignExtendExpr(V, Ty);
2970 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2971 /// the input value to the specified type. If the type must be extended,
2972 /// it is extended with unspecified bits. The conversion must not be
2975 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2976 Type *SrcTy = V->getType();
2977 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2978 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2979 "Cannot noop or any extend with non-integer arguments!");
2980 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2981 "getNoopOrAnyExtend cannot truncate!");
2982 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2983 return V; // No conversion
2984 return getAnyExtendExpr(V, Ty);
2987 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2988 /// input value to the specified type. The conversion must not be widening.
2990 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2991 Type *SrcTy = V->getType();
2992 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2993 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2994 "Cannot truncate or noop with non-integer arguments!");
2995 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2996 "getTruncateOrNoop cannot extend!");
2997 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2998 return V; // No conversion
2999 return getTruncateExpr(V, Ty);
3002 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3003 /// the types using zero-extension, and then perform a umax operation
3005 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3007 const SCEV *PromotedLHS = LHS;
3008 const SCEV *PromotedRHS = RHS;
3010 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3011 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3013 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3015 return getUMaxExpr(PromotedLHS, PromotedRHS);
3018 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3019 /// the types using zero-extension, and then perform a umin operation
3021 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3023 const SCEV *PromotedLHS = LHS;
3024 const SCEV *PromotedRHS = RHS;
3026 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3027 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3029 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3031 return getUMinExpr(PromotedLHS, PromotedRHS);
3034 /// getPointerBase - Transitively follow the chain of pointer-type operands
3035 /// until reaching a SCEV that does not have a single pointer operand. This
3036 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3037 /// but corner cases do exist.
3038 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3039 // A pointer operand may evaluate to a nonpointer expression, such as null.
3040 if (!V->getType()->isPointerTy())
3043 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3044 return getPointerBase(Cast->getOperand());
3046 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3047 const SCEV *PtrOp = nullptr;
3048 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3050 if ((*I)->getType()->isPointerTy()) {
3051 // Cannot find the base of an expression with multiple pointer operands.
3059 return getPointerBase(PtrOp);
3064 /// PushDefUseChildren - Push users of the given Instruction
3065 /// onto the given Worklist.
3067 PushDefUseChildren(Instruction *I,
3068 SmallVectorImpl<Instruction *> &Worklist) {
3069 // Push the def-use children onto the Worklist stack.
3070 for (User *U : I->users())
3071 Worklist.push_back(cast<Instruction>(U));
3074 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3075 /// instructions that depend on the given instruction and removes them from
3076 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3079 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3080 SmallVector<Instruction *, 16> Worklist;
3081 PushDefUseChildren(PN, Worklist);
3083 SmallPtrSet<Instruction *, 8> Visited;
3085 while (!Worklist.empty()) {
3086 Instruction *I = Worklist.pop_back_val();
3087 if (!Visited.insert(I)) continue;
3089 ValueExprMapType::iterator It =
3090 ValueExprMap.find_as(static_cast<Value *>(I));
3091 if (It != ValueExprMap.end()) {
3092 const SCEV *Old = It->second;
3094 // Short-circuit the def-use traversal if the symbolic name
3095 // ceases to appear in expressions.
3096 if (Old != SymName && !hasOperand(Old, SymName))
3099 // SCEVUnknown for a PHI either means that it has an unrecognized
3100 // structure, it's a PHI that's in the progress of being computed
3101 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3102 // additional loop trip count information isn't going to change anything.
3103 // In the second case, createNodeForPHI will perform the necessary
3104 // updates on its own when it gets to that point. In the third, we do
3105 // want to forget the SCEVUnknown.
3106 if (!isa<PHINode>(I) ||
3107 !isa<SCEVUnknown>(Old) ||
3108 (I != PN && Old == SymName)) {
3109 forgetMemoizedResults(Old);
3110 ValueExprMap.erase(It);
3114 PushDefUseChildren(I, Worklist);
3118 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3119 /// a loop header, making it a potential recurrence, or it doesn't.
3121 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3122 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3123 if (L->getHeader() == PN->getParent()) {
3124 // The loop may have multiple entrances or multiple exits; we can analyze
3125 // this phi as an addrec if it has a unique entry value and a unique
3127 Value *BEValueV = nullptr, *StartValueV = nullptr;
3128 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3129 Value *V = PN->getIncomingValue(i);
3130 if (L->contains(PN->getIncomingBlock(i))) {
3133 } else if (BEValueV != V) {
3137 } else if (!StartValueV) {
3139 } else if (StartValueV != V) {
3140 StartValueV = nullptr;
3144 if (BEValueV && StartValueV) {
3145 // While we are analyzing this PHI node, handle its value symbolically.
3146 const SCEV *SymbolicName = getUnknown(PN);
3147 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3148 "PHI node already processed?");
3149 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3151 // Using this symbolic name for the PHI, analyze the value coming around
3153 const SCEV *BEValue = getSCEV(BEValueV);
3155 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3156 // has a special value for the first iteration of the loop.
3158 // If the value coming around the backedge is an add with the symbolic
3159 // value we just inserted, then we found a simple induction variable!
3160 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3161 // If there is a single occurrence of the symbolic value, replace it
3162 // with a recurrence.
3163 unsigned FoundIndex = Add->getNumOperands();
3164 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3165 if (Add->getOperand(i) == SymbolicName)
3166 if (FoundIndex == e) {
3171 if (FoundIndex != Add->getNumOperands()) {
3172 // Create an add with everything but the specified operand.
3173 SmallVector<const SCEV *, 8> Ops;
3174 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3175 if (i != FoundIndex)
3176 Ops.push_back(Add->getOperand(i));
3177 const SCEV *Accum = getAddExpr(Ops);
3179 // This is not a valid addrec if the step amount is varying each
3180 // loop iteration, but is not itself an addrec in this loop.
3181 if (isLoopInvariant(Accum, L) ||
3182 (isa<SCEVAddRecExpr>(Accum) &&
3183 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3184 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3186 // If the increment doesn't overflow, then neither the addrec nor
3187 // the post-increment will overflow.
3188 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3189 if (OBO->hasNoUnsignedWrap())
3190 Flags = setFlags(Flags, SCEV::FlagNUW);
3191 if (OBO->hasNoSignedWrap())
3192 Flags = setFlags(Flags, SCEV::FlagNSW);
3193 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3194 // If the increment is an inbounds GEP, then we know the address
3195 // space cannot be wrapped around. We cannot make any guarantee
3196 // about signed or unsigned overflow because pointers are
3197 // unsigned but we may have a negative index from the base
3198 // pointer. We can guarantee that no unsigned wrap occurs if the
3199 // indices form a positive value.
3200 if (GEP->isInBounds()) {
3201 Flags = setFlags(Flags, SCEV::FlagNW);
3203 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3204 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3205 Flags = setFlags(Flags, SCEV::FlagNUW);
3207 } else if (const SubOperator *OBO =
3208 dyn_cast<SubOperator>(BEValueV)) {
3209 if (OBO->hasNoUnsignedWrap())
3210 Flags = setFlags(Flags, SCEV::FlagNUW);
3211 if (OBO->hasNoSignedWrap())
3212 Flags = setFlags(Flags, SCEV::FlagNSW);
3215 const SCEV *StartVal = getSCEV(StartValueV);
3216 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3218 // Since the no-wrap flags are on the increment, they apply to the
3219 // post-incremented value as well.
3220 if (isLoopInvariant(Accum, L))
3221 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3224 // Okay, for the entire analysis of this edge we assumed the PHI
3225 // to be symbolic. We now need to go back and purge all of the
3226 // entries for the scalars that use the symbolic expression.
3227 ForgetSymbolicName(PN, SymbolicName);
3228 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3232 } else if (const SCEVAddRecExpr *AddRec =
3233 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3234 // Otherwise, this could be a loop like this:
3235 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3236 // In this case, j = {1,+,1} and BEValue is j.
3237 // Because the other in-value of i (0) fits the evolution of BEValue
3238 // i really is an addrec evolution.
3239 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3240 const SCEV *StartVal = getSCEV(StartValueV);
3242 // If StartVal = j.start - j.stride, we can use StartVal as the
3243 // initial step of the addrec evolution.
3244 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3245 AddRec->getOperand(1))) {
3246 // FIXME: For constant StartVal, we should be able to infer
3248 const SCEV *PHISCEV =
3249 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3252 // Okay, for the entire analysis of this edge we assumed the PHI
3253 // to be symbolic. We now need to go back and purge all of the
3254 // entries for the scalars that use the symbolic expression.
3255 ForgetSymbolicName(PN, SymbolicName);
3256 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3264 // If the PHI has a single incoming value, follow that value, unless the
3265 // PHI's incoming blocks are in a different loop, in which case doing so
3266 // risks breaking LCSSA form. Instcombine would normally zap these, but
3267 // it doesn't have DominatorTree information, so it may miss cases.
3268 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT))
3269 if (LI->replacementPreservesLCSSAForm(PN, V))
3272 // If it's not a loop phi, we can't handle it yet.
3273 return getUnknown(PN);
3276 /// createNodeForGEP - Expand GEP instructions into add and multiply
3277 /// operations. This allows them to be analyzed by regular SCEV code.
3279 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3280 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3281 Value *Base = GEP->getOperand(0);
3282 // Don't attempt to analyze GEPs over unsized objects.
3283 if (!Base->getType()->getPointerElementType()->isSized())
3284 return getUnknown(GEP);
3286 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3287 // Add expression, because the Instruction may be guarded by control flow
3288 // and the no-overflow bits may not be valid for the expression in any
3290 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3292 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3293 gep_type_iterator GTI = gep_type_begin(GEP);
3294 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3298 // Compute the (potentially symbolic) offset in bytes for this index.
3299 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3300 // For a struct, add the member offset.
3301 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3302 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3304 // Add the field offset to the running total offset.
3305 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3307 // For an array, add the element offset, explicitly scaled.
3308 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3309 const SCEV *IndexS = getSCEV(Index);
3310 // Getelementptr indices are signed.
3311 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3313 // Multiply the index by the element size to compute the element offset.
3314 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3316 // Add the element offset to the running total offset.
3317 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3321 // Get the SCEV for the GEP base.
3322 const SCEV *BaseS = getSCEV(Base);
3324 // Add the total offset from all the GEP indices to the base.
3325 return getAddExpr(BaseS, TotalOffset, Wrap);
3328 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3329 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3330 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3331 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3333 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3334 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3335 return C->getValue()->getValue().countTrailingZeros();
3337 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3338 return std::min(GetMinTrailingZeros(T->getOperand()),
3339 (uint32_t)getTypeSizeInBits(T->getType()));
3341 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3342 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3343 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3344 getTypeSizeInBits(E->getType()) : OpRes;
3347 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3348 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3349 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3350 getTypeSizeInBits(E->getType()) : OpRes;
3353 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3354 // The result is the min of all operands results.
3355 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3356 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3357 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3361 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3362 // The result is the sum of all operands results.
3363 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3364 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3365 for (unsigned i = 1, e = M->getNumOperands();
3366 SumOpRes != BitWidth && i != e; ++i)
3367 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3372 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3373 // The result is the min of all operands results.
3374 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3375 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3376 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3380 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3381 // The result is the min of all operands results.
3382 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3383 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3384 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3388 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3389 // The result is the min of all operands results.
3390 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3391 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3392 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3396 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3397 // For a SCEVUnknown, ask ValueTracking.
3398 unsigned BitWidth = getTypeSizeInBits(U->getType());
3399 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3400 computeKnownBits(U->getValue(), Zeros, Ones);
3401 return Zeros.countTrailingOnes();
3408 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3411 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3412 // See if we've computed this range already.
3413 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3414 if (I != UnsignedRanges.end())
3417 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3418 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3420 unsigned BitWidth = getTypeSizeInBits(S->getType());
3421 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3423 // If the value has known zeros, the maximum unsigned value will have those
3424 // known zeros as well.
3425 uint32_t TZ = GetMinTrailingZeros(S);
3427 ConservativeResult =
3428 ConstantRange(APInt::getMinValue(BitWidth),
3429 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3431 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3432 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3433 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3434 X = X.add(getUnsignedRange(Add->getOperand(i)));
3435 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3438 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3439 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3440 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3441 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3442 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3445 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3446 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3447 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3448 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3449 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3452 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3453 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3454 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3455 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3456 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3459 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3460 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3461 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3462 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3465 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3466 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3467 return setUnsignedRange(ZExt,
3468 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3471 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3472 ConstantRange X = getUnsignedRange(SExt->getOperand());
3473 return setUnsignedRange(SExt,
3474 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3477 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3478 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3479 return setUnsignedRange(Trunc,
3480 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3483 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3484 // If there's no unsigned wrap, the value will never be less than its
3486 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3487 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3488 if (!C->getValue()->isZero())
3489 ConservativeResult =
3490 ConservativeResult.intersectWith(
3491 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3493 // TODO: non-affine addrec
3494 if (AddRec->isAffine()) {
3495 Type *Ty = AddRec->getType();
3496 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3497 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3498 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3499 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3501 const SCEV *Start = AddRec->getStart();
3502 const SCEV *Step = AddRec->getStepRecurrence(*this);
3504 ConstantRange StartRange = getUnsignedRange(Start);
3505 ConstantRange StepRange = getSignedRange(Step);
3506 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3507 ConstantRange EndRange =
3508 StartRange.add(MaxBECountRange.multiply(StepRange));
3510 // Check for overflow. This must be done with ConstantRange arithmetic
3511 // because we could be called from within the ScalarEvolution overflow
3513 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3514 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3515 ConstantRange ExtMaxBECountRange =
3516 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3517 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3518 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3520 return setUnsignedRange(AddRec, ConservativeResult);
3522 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3523 EndRange.getUnsignedMin());
3524 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3525 EndRange.getUnsignedMax());
3526 if (Min.isMinValue() && Max.isMaxValue())
3527 return setUnsignedRange(AddRec, ConservativeResult);
3528 return setUnsignedRange(AddRec,
3529 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3533 return setUnsignedRange(AddRec, ConservativeResult);
3536 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3537 // For a SCEVUnknown, ask ValueTracking.
3538 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3539 computeKnownBits(U->getValue(), Zeros, Ones, DL);
3540 if (Ones == ~Zeros + 1)
3541 return setUnsignedRange(U, ConservativeResult);
3542 return setUnsignedRange(U,
3543 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3546 return setUnsignedRange(S, ConservativeResult);
3549 /// getSignedRange - Determine the signed range for a particular SCEV.
3552 ScalarEvolution::getSignedRange(const SCEV *S) {
3553 // See if we've computed this range already.
3554 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3555 if (I != SignedRanges.end())
3558 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3559 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3561 unsigned BitWidth = getTypeSizeInBits(S->getType());
3562 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3564 // If the value has known zeros, the maximum signed value will have those
3565 // known zeros as well.
3566 uint32_t TZ = GetMinTrailingZeros(S);
3568 ConservativeResult =
3569 ConstantRange(APInt::getSignedMinValue(BitWidth),
3570 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3572 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3573 ConstantRange X = getSignedRange(Add->getOperand(0));
3574 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3575 X = X.add(getSignedRange(Add->getOperand(i)));
3576 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3579 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3580 ConstantRange X = getSignedRange(Mul->getOperand(0));
3581 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3582 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3583 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3586 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3587 ConstantRange X = getSignedRange(SMax->getOperand(0));
3588 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3589 X = X.smax(getSignedRange(SMax->getOperand(i)));
3590 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3593 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3594 ConstantRange X = getSignedRange(UMax->getOperand(0));
3595 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3596 X = X.umax(getSignedRange(UMax->getOperand(i)));
3597 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3600 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3601 ConstantRange X = getSignedRange(UDiv->getLHS());
3602 ConstantRange Y = getSignedRange(UDiv->getRHS());
3603 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3606 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3607 ConstantRange X = getSignedRange(ZExt->getOperand());
3608 return setSignedRange(ZExt,
3609 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3612 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3613 ConstantRange X = getSignedRange(SExt->getOperand());
3614 return setSignedRange(SExt,
3615 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3618 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3619 ConstantRange X = getSignedRange(Trunc->getOperand());
3620 return setSignedRange(Trunc,
3621 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3624 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3625 // If there's no signed wrap, and all the operands have the same sign or
3626 // zero, the value won't ever change sign.
3627 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3628 bool AllNonNeg = true;
3629 bool AllNonPos = true;
3630 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3631 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3632 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3635 ConservativeResult = ConservativeResult.intersectWith(
3636 ConstantRange(APInt(BitWidth, 0),
3637 APInt::getSignedMinValue(BitWidth)));
3639 ConservativeResult = ConservativeResult.intersectWith(
3640 ConstantRange(APInt::getSignedMinValue(BitWidth),
3641 APInt(BitWidth, 1)));
3644 // TODO: non-affine addrec
3645 if (AddRec->isAffine()) {
3646 Type *Ty = AddRec->getType();
3647 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3648 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3649 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3650 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3652 const SCEV *Start = AddRec->getStart();
3653 const SCEV *Step = AddRec->getStepRecurrence(*this);
3655 ConstantRange StartRange = getSignedRange(Start);
3656 ConstantRange StepRange = getSignedRange(Step);
3657 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3658 ConstantRange EndRange =
3659 StartRange.add(MaxBECountRange.multiply(StepRange));
3661 // Check for overflow. This must be done with ConstantRange arithmetic
3662 // because we could be called from within the ScalarEvolution overflow
3664 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3665 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3666 ConstantRange ExtMaxBECountRange =
3667 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3668 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3669 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3671 return setSignedRange(AddRec, ConservativeResult);
3673 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3674 EndRange.getSignedMin());
3675 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3676 EndRange.getSignedMax());
3677 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3678 return setSignedRange(AddRec, ConservativeResult);
3679 return setSignedRange(AddRec,
3680 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3684 return setSignedRange(AddRec, ConservativeResult);
3687 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3688 // For a SCEVUnknown, ask ValueTracking.
3689 if (!U->getValue()->getType()->isIntegerTy() && !DL)
3690 return setSignedRange(U, ConservativeResult);
3691 unsigned NS = ComputeNumSignBits(U->getValue(), DL);
3693 return setSignedRange(U, ConservativeResult);
3694 return setSignedRange(U, ConservativeResult.intersectWith(
3695 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3696 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3699 return setSignedRange(S, ConservativeResult);
3702 /// createSCEV - We know that there is no SCEV for the specified value.
3703 /// Analyze the expression.
3705 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3706 if (!isSCEVable(V->getType()))
3707 return getUnknown(V);
3709 unsigned Opcode = Instruction::UserOp1;
3710 if (Instruction *I = dyn_cast<Instruction>(V)) {
3711 Opcode = I->getOpcode();
3713 // Don't attempt to analyze instructions in blocks that aren't
3714 // reachable. Such instructions don't matter, and they aren't required
3715 // to obey basic rules for definitions dominating uses which this
3716 // analysis depends on.
3717 if (!DT->isReachableFromEntry(I->getParent()))
3718 return getUnknown(V);
3719 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3720 Opcode = CE->getOpcode();
3721 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3722 return getConstant(CI);
3723 else if (isa<ConstantPointerNull>(V))
3724 return getConstant(V->getType(), 0);
3725 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3726 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3728 return getUnknown(V);
3730 Operator *U = cast<Operator>(V);
3732 case Instruction::Add: {
3733 // The simple thing to do would be to just call getSCEV on both operands
3734 // and call getAddExpr with the result. However if we're looking at a
3735 // bunch of things all added together, this can be quite inefficient,
3736 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3737 // Instead, gather up all the operands and make a single getAddExpr call.
3738 // LLVM IR canonical form means we need only traverse the left operands.
3740 // Don't apply this instruction's NSW or NUW flags to the new
3741 // expression. The instruction may be guarded by control flow that the
3742 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3743 // mapped to the same SCEV expression, and it would be incorrect to transfer
3744 // NSW/NUW semantics to those operations.
3745 SmallVector<const SCEV *, 4> AddOps;
3746 AddOps.push_back(getSCEV(U->getOperand(1)));
3747 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3748 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3749 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3751 U = cast<Operator>(Op);
3752 const SCEV *Op1 = getSCEV(U->getOperand(1));
3753 if (Opcode == Instruction::Sub)
3754 AddOps.push_back(getNegativeSCEV(Op1));
3756 AddOps.push_back(Op1);
3758 AddOps.push_back(getSCEV(U->getOperand(0)));
3759 return getAddExpr(AddOps);
3761 case Instruction::Mul: {
3762 // Don't transfer NSW/NUW for the same reason as AddExpr.
3763 SmallVector<const SCEV *, 4> MulOps;
3764 MulOps.push_back(getSCEV(U->getOperand(1)));
3765 for (Value *Op = U->getOperand(0);
3766 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3767 Op = U->getOperand(0)) {
3768 U = cast<Operator>(Op);
3769 MulOps.push_back(getSCEV(U->getOperand(1)));
3771 MulOps.push_back(getSCEV(U->getOperand(0)));
3772 return getMulExpr(MulOps);
3774 case Instruction::UDiv:
3775 return getUDivExpr(getSCEV(U->getOperand(0)),
3776 getSCEV(U->getOperand(1)));
3777 case Instruction::Sub:
3778 return getMinusSCEV(getSCEV(U->getOperand(0)),
3779 getSCEV(U->getOperand(1)));
3780 case Instruction::And:
3781 // For an expression like x&255 that merely masks off the high bits,
3782 // use zext(trunc(x)) as the SCEV expression.
3783 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3784 if (CI->isNullValue())
3785 return getSCEV(U->getOperand(1));
3786 if (CI->isAllOnesValue())
3787 return getSCEV(U->getOperand(0));
3788 const APInt &A = CI->getValue();
3790 // Instcombine's ShrinkDemandedConstant may strip bits out of
3791 // constants, obscuring what would otherwise be a low-bits mask.
3792 // Use computeKnownBits to compute what ShrinkDemandedConstant
3793 // knew about to reconstruct a low-bits mask value.
3794 unsigned LZ = A.countLeadingZeros();
3795 unsigned TZ = A.countTrailingZeros();
3796 unsigned BitWidth = A.getBitWidth();
3797 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3798 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL);
3800 APInt EffectiveMask =
3801 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
3802 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
3803 const SCEV *MulCount = getConstant(
3804 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
3808 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
3809 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
3816 case Instruction::Or:
3817 // If the RHS of the Or is a constant, we may have something like:
3818 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3819 // optimizations will transparently handle this case.
3821 // In order for this transformation to be safe, the LHS must be of the
3822 // form X*(2^n) and the Or constant must be less than 2^n.
3823 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3824 const SCEV *LHS = getSCEV(U->getOperand(0));
3825 const APInt &CIVal = CI->getValue();
3826 if (GetMinTrailingZeros(LHS) >=
3827 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3828 // Build a plain add SCEV.
3829 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3830 // If the LHS of the add was an addrec and it has no-wrap flags,
3831 // transfer the no-wrap flags, since an or won't introduce a wrap.
3832 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3833 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3834 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3835 OldAR->getNoWrapFlags());
3841 case Instruction::Xor:
3842 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3843 // If the RHS of the xor is a signbit, then this is just an add.
3844 // Instcombine turns add of signbit into xor as a strength reduction step.
3845 if (CI->getValue().isSignBit())
3846 return getAddExpr(getSCEV(U->getOperand(0)),
3847 getSCEV(U->getOperand(1)));
3849 // If the RHS of xor is -1, then this is a not operation.
3850 if (CI->isAllOnesValue())
3851 return getNotSCEV(getSCEV(U->getOperand(0)));
3853 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3854 // This is a variant of the check for xor with -1, and it handles
3855 // the case where instcombine has trimmed non-demanded bits out
3856 // of an xor with -1.
3857 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3858 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3859 if (BO->getOpcode() == Instruction::And &&
3860 LCI->getValue() == CI->getValue())
3861 if (const SCEVZeroExtendExpr *Z =
3862 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3863 Type *UTy = U->getType();
3864 const SCEV *Z0 = Z->getOperand();
3865 Type *Z0Ty = Z0->getType();
3866 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3868 // If C is a low-bits mask, the zero extend is serving to
3869 // mask off the high bits. Complement the operand and
3870 // re-apply the zext.
3871 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3872 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3874 // If C is a single bit, it may be in the sign-bit position
3875 // before the zero-extend. In this case, represent the xor
3876 // using an add, which is equivalent, and re-apply the zext.
3877 APInt Trunc = CI->getValue().trunc(Z0TySize);
3878 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3880 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3886 case Instruction::Shl:
3887 // Turn shift left of a constant amount into a multiply.
3888 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3889 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3891 // If the shift count is not less than the bitwidth, the result of
3892 // the shift is undefined. Don't try to analyze it, because the
3893 // resolution chosen here may differ from the resolution chosen in
3894 // other parts of the compiler.
3895 if (SA->getValue().uge(BitWidth))
3898 Constant *X = ConstantInt::get(getContext(),
3899 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3900 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3904 case Instruction::LShr:
3905 // Turn logical shift right of a constant into a unsigned divide.
3906 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3907 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3909 // If the shift count is not less than the bitwidth, the result of
3910 // the shift is undefined. Don't try to analyze it, because the
3911 // resolution chosen here may differ from the resolution chosen in
3912 // other parts of the compiler.
3913 if (SA->getValue().uge(BitWidth))
3916 Constant *X = ConstantInt::get(getContext(),
3917 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3918 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3922 case Instruction::AShr:
3923 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3924 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3925 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3926 if (L->getOpcode() == Instruction::Shl &&
3927 L->getOperand(1) == U->getOperand(1)) {
3928 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3930 // If the shift count is not less than the bitwidth, the result of
3931 // the shift is undefined. Don't try to analyze it, because the
3932 // resolution chosen here may differ from the resolution chosen in
3933 // other parts of the compiler.
3934 if (CI->getValue().uge(BitWidth))
3937 uint64_t Amt = BitWidth - CI->getZExtValue();
3938 if (Amt == BitWidth)
3939 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3941 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3942 IntegerType::get(getContext(),
3948 case Instruction::Trunc:
3949 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3951 case Instruction::ZExt:
3952 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3954 case Instruction::SExt:
3955 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3957 case Instruction::BitCast:
3958 // BitCasts are no-op casts so we just eliminate the cast.
3959 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3960 return getSCEV(U->getOperand(0));
3963 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3964 // lead to pointer expressions which cannot safely be expanded to GEPs,
3965 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3966 // simplifying integer expressions.
3968 case Instruction::GetElementPtr:
3969 return createNodeForGEP(cast<GEPOperator>(U));
3971 case Instruction::PHI:
3972 return createNodeForPHI(cast<PHINode>(U));
3974 case Instruction::Select:
3975 // This could be a smax or umax that was lowered earlier.
3976 // Try to recover it.
3977 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3978 Value *LHS = ICI->getOperand(0);
3979 Value *RHS = ICI->getOperand(1);
3980 switch (ICI->getPredicate()) {
3981 case ICmpInst::ICMP_SLT:
3982 case ICmpInst::ICMP_SLE:
3983 std::swap(LHS, RHS);
3985 case ICmpInst::ICMP_SGT:
3986 case ICmpInst::ICMP_SGE:
3987 // a >s b ? a+x : b+x -> smax(a, b)+x
3988 // a >s b ? b+x : a+x -> smin(a, b)+x
3989 if (LHS->getType() == U->getType()) {
3990 const SCEV *LS = getSCEV(LHS);
3991 const SCEV *RS = getSCEV(RHS);
3992 const SCEV *LA = getSCEV(U->getOperand(1));
3993 const SCEV *RA = getSCEV(U->getOperand(2));
3994 const SCEV *LDiff = getMinusSCEV(LA, LS);
3995 const SCEV *RDiff = getMinusSCEV(RA, RS);
3997 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3998 LDiff = getMinusSCEV(LA, RS);
3999 RDiff = getMinusSCEV(RA, LS);
4001 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4004 case ICmpInst::ICMP_ULT:
4005 case ICmpInst::ICMP_ULE:
4006 std::swap(LHS, RHS);
4008 case ICmpInst::ICMP_UGT:
4009 case ICmpInst::ICMP_UGE:
4010 // a >u b ? a+x : b+x -> umax(a, b)+x
4011 // a >u b ? b+x : a+x -> umin(a, b)+x
4012 if (LHS->getType() == U->getType()) {
4013 const SCEV *LS = getSCEV(LHS);
4014 const SCEV *RS = getSCEV(RHS);
4015 const SCEV *LA = getSCEV(U->getOperand(1));
4016 const SCEV *RA = getSCEV(U->getOperand(2));
4017 const SCEV *LDiff = getMinusSCEV(LA, LS);
4018 const SCEV *RDiff = getMinusSCEV(RA, RS);
4020 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4021 LDiff = getMinusSCEV(LA, RS);
4022 RDiff = getMinusSCEV(RA, LS);
4024 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4027 case ICmpInst::ICMP_NE:
4028 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4029 if (LHS->getType() == U->getType() &&
4030 isa<ConstantInt>(RHS) &&
4031 cast<ConstantInt>(RHS)->isZero()) {
4032 const SCEV *One = getConstant(LHS->getType(), 1);
4033 const SCEV *LS = getSCEV(LHS);
4034 const SCEV *LA = getSCEV(U->getOperand(1));
4035 const SCEV *RA = getSCEV(U->getOperand(2));
4036 const SCEV *LDiff = getMinusSCEV(LA, LS);
4037 const SCEV *RDiff = getMinusSCEV(RA, One);
4039 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4042 case ICmpInst::ICMP_EQ:
4043 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4044 if (LHS->getType() == U->getType() &&
4045 isa<ConstantInt>(RHS) &&
4046 cast<ConstantInt>(RHS)->isZero()) {
4047 const SCEV *One = getConstant(LHS->getType(), 1);
4048 const SCEV *LS = getSCEV(LHS);
4049 const SCEV *LA = getSCEV(U->getOperand(1));
4050 const SCEV *RA = getSCEV(U->getOperand(2));
4051 const SCEV *LDiff = getMinusSCEV(LA, One);
4052 const SCEV *RDiff = getMinusSCEV(RA, LS);
4054 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4062 default: // We cannot analyze this expression.
4066 return getUnknown(V);
4071 //===----------------------------------------------------------------------===//
4072 // Iteration Count Computation Code
4075 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4076 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4077 /// constant. Will also return 0 if the maximum trip count is very large (>=
4080 /// This "trip count" assumes that control exits via ExitingBlock. More
4081 /// precisely, it is the number of times that control may reach ExitingBlock
4082 /// before taking the branch. For loops with multiple exits, it may not be the
4083 /// number times that the loop header executes because the loop may exit
4084 /// prematurely via another branch.
4086 /// FIXME: We conservatively call getBackedgeTakenCount(L) instead of
4087 /// getExitCount(L, ExitingBlock) to compute a safe trip count considering all
4088 /// loop exits. getExitCount() may return an exact count for this branch
4089 /// assuming no-signed-wrap. The number of well-defined iterations may actually
4090 /// be higher than this trip count if this exit test is skipped and the loop
4091 /// exits via a different branch. Ideally, getExitCount() would know whether it
4092 /// depends on a NSW assumption, and we would only fall back to a conservative
4093 /// trip count in that case.
4094 unsigned ScalarEvolution::
4095 getSmallConstantTripCount(Loop *L, BasicBlock * /*ExitingBlock*/) {
4096 const SCEVConstant *ExitCount =
4097 dyn_cast<SCEVConstant>(getBackedgeTakenCount(L));
4101 ConstantInt *ExitConst = ExitCount->getValue();
4103 // Guard against huge trip counts.
4104 if (ExitConst->getValue().getActiveBits() > 32)
4107 // In case of integer overflow, this returns 0, which is correct.
4108 return ((unsigned)ExitConst->getZExtValue()) + 1;
4111 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4112 /// trip count of this loop as a normal unsigned value, if possible. This
4113 /// means that the actual trip count is always a multiple of the returned
4114 /// value (don't forget the trip count could very well be zero as well!).
4116 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4117 /// multiple of a constant (which is also the case if the trip count is simply
4118 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4119 /// if the trip count is very large (>= 2^32).
4121 /// As explained in the comments for getSmallConstantTripCount, this assumes
4122 /// that control exits the loop via ExitingBlock.
4123 unsigned ScalarEvolution::
4124 getSmallConstantTripMultiple(Loop *L, BasicBlock * /*ExitingBlock*/) {
4125 const SCEV *ExitCount = getBackedgeTakenCount(L);
4126 if (ExitCount == getCouldNotCompute())
4129 // Get the trip count from the BE count by adding 1.
4130 const SCEV *TCMul = getAddExpr(ExitCount,
4131 getConstant(ExitCount->getType(), 1));
4132 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4133 // to factor simple cases.
4134 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4135 TCMul = Mul->getOperand(0);
4137 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4141 ConstantInt *Result = MulC->getValue();
4143 // Guard against huge trip counts (this requires checking
4144 // for zero to handle the case where the trip count == -1 and the
4146 if (!Result || Result->getValue().getActiveBits() > 32 ||
4147 Result->getValue().getActiveBits() == 0)
4150 return (unsigned)Result->getZExtValue();
4153 // getExitCount - Get the expression for the number of loop iterations for which
4154 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4155 // SCEVCouldNotCompute.
4156 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4157 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4160 /// getBackedgeTakenCount - If the specified loop has a predictable
4161 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4162 /// object. The backedge-taken count is the number of times the loop header
4163 /// will be branched to from within the loop. This is one less than the
4164 /// trip count of the loop, since it doesn't count the first iteration,
4165 /// when the header is branched to from outside the loop.
4167 /// Note that it is not valid to call this method on a loop without a
4168 /// loop-invariant backedge-taken count (see
4169 /// hasLoopInvariantBackedgeTakenCount).
4171 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4172 return getBackedgeTakenInfo(L).getExact(this);
4175 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4176 /// return the least SCEV value that is known never to be less than the
4177 /// actual backedge taken count.
4178 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4179 return getBackedgeTakenInfo(L).getMax(this);
4182 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4183 /// onto the given Worklist.
4185 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4186 BasicBlock *Header = L->getHeader();
4188 // Push all Loop-header PHIs onto the Worklist stack.
4189 for (BasicBlock::iterator I = Header->begin();
4190 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4191 Worklist.push_back(PN);
4194 const ScalarEvolution::BackedgeTakenInfo &
4195 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4196 // Initially insert an invalid entry for this loop. If the insertion
4197 // succeeds, proceed to actually compute a backedge-taken count and
4198 // update the value. The temporary CouldNotCompute value tells SCEV
4199 // code elsewhere that it shouldn't attempt to request a new
4200 // backedge-taken count, which could result in infinite recursion.
4201 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4202 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4204 return Pair.first->second;
4206 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4207 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4208 // must be cleared in this scope.
4209 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4211 if (Result.getExact(this) != getCouldNotCompute()) {
4212 assert(isLoopInvariant(Result.getExact(this), L) &&
4213 isLoopInvariant(Result.getMax(this), L) &&
4214 "Computed backedge-taken count isn't loop invariant for loop!");
4215 ++NumTripCountsComputed;
4217 else if (Result.getMax(this) == getCouldNotCompute() &&
4218 isa<PHINode>(L->getHeader()->begin())) {
4219 // Only count loops that have phi nodes as not being computable.
4220 ++NumTripCountsNotComputed;
4223 // Now that we know more about the trip count for this loop, forget any
4224 // existing SCEV values for PHI nodes in this loop since they are only
4225 // conservative estimates made without the benefit of trip count
4226 // information. This is similar to the code in forgetLoop, except that
4227 // it handles SCEVUnknown PHI nodes specially.
4228 if (Result.hasAnyInfo()) {
4229 SmallVector<Instruction *, 16> Worklist;
4230 PushLoopPHIs(L, Worklist);
4232 SmallPtrSet<Instruction *, 8> Visited;
4233 while (!Worklist.empty()) {
4234 Instruction *I = Worklist.pop_back_val();
4235 if (!Visited.insert(I)) continue;
4237 ValueExprMapType::iterator It =
4238 ValueExprMap.find_as(static_cast<Value *>(I));
4239 if (It != ValueExprMap.end()) {
4240 const SCEV *Old = It->second;
4242 // SCEVUnknown for a PHI either means that it has an unrecognized
4243 // structure, or it's a PHI that's in the progress of being computed
4244 // by createNodeForPHI. In the former case, additional loop trip
4245 // count information isn't going to change anything. In the later
4246 // case, createNodeForPHI will perform the necessary updates on its
4247 // own when it gets to that point.
4248 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4249 forgetMemoizedResults(Old);
4250 ValueExprMap.erase(It);
4252 if (PHINode *PN = dyn_cast<PHINode>(I))
4253 ConstantEvolutionLoopExitValue.erase(PN);
4256 PushDefUseChildren(I, Worklist);
4260 // Re-lookup the insert position, since the call to
4261 // ComputeBackedgeTakenCount above could result in a
4262 // recusive call to getBackedgeTakenInfo (on a different
4263 // loop), which would invalidate the iterator computed
4265 return BackedgeTakenCounts.find(L)->second = Result;
4268 /// forgetLoop - This method should be called by the client when it has
4269 /// changed a loop in a way that may effect ScalarEvolution's ability to
4270 /// compute a trip count, or if the loop is deleted.
4271 void ScalarEvolution::forgetLoop(const Loop *L) {
4272 // Drop any stored trip count value.
4273 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4274 BackedgeTakenCounts.find(L);
4275 if (BTCPos != BackedgeTakenCounts.end()) {
4276 BTCPos->second.clear();
4277 BackedgeTakenCounts.erase(BTCPos);
4280 // Drop information about expressions based on loop-header PHIs.
4281 SmallVector<Instruction *, 16> Worklist;
4282 PushLoopPHIs(L, Worklist);
4284 SmallPtrSet<Instruction *, 8> Visited;
4285 while (!Worklist.empty()) {
4286 Instruction *I = Worklist.pop_back_val();
4287 if (!Visited.insert(I)) continue;
4289 ValueExprMapType::iterator It =
4290 ValueExprMap.find_as(static_cast<Value *>(I));
4291 if (It != ValueExprMap.end()) {
4292 forgetMemoizedResults(It->second);
4293 ValueExprMap.erase(It);
4294 if (PHINode *PN = dyn_cast<PHINode>(I))
4295 ConstantEvolutionLoopExitValue.erase(PN);
4298 PushDefUseChildren(I, Worklist);
4301 // Forget all contained loops too, to avoid dangling entries in the
4302 // ValuesAtScopes map.
4303 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4307 /// forgetValue - This method should be called by the client when it has
4308 /// changed a value in a way that may effect its value, or which may
4309 /// disconnect it from a def-use chain linking it to a loop.
4310 void ScalarEvolution::forgetValue(Value *V) {
4311 Instruction *I = dyn_cast<Instruction>(V);
4314 // Drop information about expressions based on loop-header PHIs.
4315 SmallVector<Instruction *, 16> Worklist;
4316 Worklist.push_back(I);
4318 SmallPtrSet<Instruction *, 8> Visited;
4319 while (!Worklist.empty()) {
4320 I = Worklist.pop_back_val();
4321 if (!Visited.insert(I)) continue;
4323 ValueExprMapType::iterator It =
4324 ValueExprMap.find_as(static_cast<Value *>(I));
4325 if (It != ValueExprMap.end()) {
4326 forgetMemoizedResults(It->second);
4327 ValueExprMap.erase(It);
4328 if (PHINode *PN = dyn_cast<PHINode>(I))
4329 ConstantEvolutionLoopExitValue.erase(PN);
4332 PushDefUseChildren(I, Worklist);
4336 /// getExact - Get the exact loop backedge taken count considering all loop
4337 /// exits. A computable result can only be return for loops with a single exit.
4338 /// Returning the minimum taken count among all exits is incorrect because one
4339 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4340 /// the limit of each loop test is never skipped. This is a valid assumption as
4341 /// long as the loop exits via that test. For precise results, it is the
4342 /// caller's responsibility to specify the relevant loop exit using
4343 /// getExact(ExitingBlock, SE).
4345 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4346 // If any exits were not computable, the loop is not computable.
4347 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4349 // We need exactly one computable exit.
4350 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4351 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4353 const SCEV *BECount = nullptr;
4354 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4355 ENT != nullptr; ENT = ENT->getNextExit()) {
4357 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4360 BECount = ENT->ExactNotTaken;
4361 else if (BECount != ENT->ExactNotTaken)
4362 return SE->getCouldNotCompute();
4364 assert(BECount && "Invalid not taken count for loop exit");
4368 /// getExact - Get the exact not taken count for this loop exit.
4370 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4371 ScalarEvolution *SE) const {
4372 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4373 ENT != nullptr; ENT = ENT->getNextExit()) {
4375 if (ENT->ExitingBlock == ExitingBlock)
4376 return ENT->ExactNotTaken;
4378 return SE->getCouldNotCompute();
4381 /// getMax - Get the max backedge taken count for the loop.
4383 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4384 return Max ? Max : SE->getCouldNotCompute();
4387 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4388 ScalarEvolution *SE) const {
4389 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4392 if (!ExitNotTaken.ExitingBlock)
4395 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4396 ENT != nullptr; ENT = ENT->getNextExit()) {
4398 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4399 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4406 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4407 /// computable exit into a persistent ExitNotTakenInfo array.
4408 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4409 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4410 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4413 ExitNotTaken.setIncomplete();
4415 unsigned NumExits = ExitCounts.size();
4416 if (NumExits == 0) return;
4418 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4419 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4420 if (NumExits == 1) return;
4422 // Handle the rare case of multiple computable exits.
4423 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4425 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4426 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4427 PrevENT->setNextExit(ENT);
4428 ENT->ExitingBlock = ExitCounts[i].first;
4429 ENT->ExactNotTaken = ExitCounts[i].second;
4433 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4434 void ScalarEvolution::BackedgeTakenInfo::clear() {
4435 ExitNotTaken.ExitingBlock = nullptr;
4436 ExitNotTaken.ExactNotTaken = nullptr;
4437 delete[] ExitNotTaken.getNextExit();
4440 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4441 /// of the specified loop will execute.
4442 ScalarEvolution::BackedgeTakenInfo
4443 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4444 SmallVector<BasicBlock *, 8> ExitingBlocks;
4445 L->getExitingBlocks(ExitingBlocks);
4447 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4448 bool CouldComputeBECount = true;
4449 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4450 const SCEV *MustExitMaxBECount = nullptr;
4451 const SCEV *MayExitMaxBECount = nullptr;
4453 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4454 // and compute maxBECount.
4455 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4456 BasicBlock *ExitBB = ExitingBlocks[i];
4457 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4459 // 1. For each exit that can be computed, add an entry to ExitCounts.
4460 // CouldComputeBECount is true only if all exits can be computed.
4461 if (EL.Exact == getCouldNotCompute())
4462 // We couldn't compute an exact value for this exit, so
4463 // we won't be able to compute an exact value for the loop.
4464 CouldComputeBECount = false;
4466 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4468 // 2. Derive the loop's MaxBECount from each exit's max number of
4469 // non-exiting iterations. Partition the loop exits into two kinds:
4470 // LoopMustExits and LoopMayExits.
4472 // A LoopMustExit meets two requirements:
4474 // (a) Its ExitLimit.MustExit flag must be set which indicates that the exit
4475 // test condition cannot be skipped (the tested variable has unit stride or
4476 // the test is less-than or greater-than, rather than a strict inequality).
4478 // (b) It must dominate the loop latch, hence must be tested on every loop
4481 // If any computable LoopMustExit is found, then MaxBECount is the minimum
4482 // EL.Max of computable LoopMustExits. Otherwise, MaxBECount is
4483 // conservatively the maximum EL.Max, where CouldNotCompute is considered
4484 // greater than any computable EL.Max.
4485 if (EL.MustExit && EL.Max != getCouldNotCompute() && Latch &&
4486 DT->dominates(ExitBB, Latch)) {
4487 if (!MustExitMaxBECount)
4488 MustExitMaxBECount = EL.Max;
4490 MustExitMaxBECount =
4491 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4493 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4494 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4495 MayExitMaxBECount = EL.Max;
4498 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4502 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4503 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4504 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4507 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4508 /// loop will execute if it exits via the specified block.
4509 ScalarEvolution::ExitLimit
4510 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4512 // Okay, we've chosen an exiting block. See what condition causes us to
4513 // exit at this block and remember the exit block and whether all other targets
4514 // lead to the loop header.
4515 bool MustExecuteLoopHeader = true;
4516 BasicBlock *Exit = nullptr;
4517 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4519 if (!L->contains(*SI)) {
4520 if (Exit) // Multiple exit successors.
4521 return getCouldNotCompute();
4523 } else if (*SI != L->getHeader()) {
4524 MustExecuteLoopHeader = false;
4527 // At this point, we know we have a conditional branch that determines whether
4528 // the loop is exited. However, we don't know if the branch is executed each
4529 // time through the loop. If not, then the execution count of the branch will
4530 // not be equal to the trip count of the loop.
4532 // Currently we check for this by checking to see if the Exit branch goes to
4533 // the loop header. If so, we know it will always execute the same number of
4534 // times as the loop. We also handle the case where the exit block *is* the
4535 // loop header. This is common for un-rotated loops.
4537 // If both of those tests fail, walk up the unique predecessor chain to the
4538 // header, stopping if there is an edge that doesn't exit the loop. If the
4539 // header is reached, the execution count of the branch will be equal to the
4540 // trip count of the loop.
4542 // More extensive analysis could be done to handle more cases here.
4544 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4545 // The simple checks failed, try climbing the unique predecessor chain
4546 // up to the header.
4548 for (BasicBlock *BB = ExitingBlock; BB; ) {
4549 BasicBlock *Pred = BB->getUniquePredecessor();
4551 return getCouldNotCompute();
4552 TerminatorInst *PredTerm = Pred->getTerminator();
4553 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4554 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4557 // If the predecessor has a successor that isn't BB and isn't
4558 // outside the loop, assume the worst.
4559 if (L->contains(PredSucc))
4560 return getCouldNotCompute();
4562 if (Pred == L->getHeader()) {
4569 return getCouldNotCompute();
4572 TerminatorInst *Term = ExitingBlock->getTerminator();
4573 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4574 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4575 // Proceed to the next level to examine the exit condition expression.
4576 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4577 BI->getSuccessor(1),
4578 /*IsSubExpr=*/false);
4581 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4582 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4583 /*IsSubExpr=*/false);
4585 return getCouldNotCompute();
4588 /// ComputeExitLimitFromCond - Compute the number of times the
4589 /// backedge of the specified loop will execute if its exit condition
4590 /// were a conditional branch of ExitCond, TBB, and FBB.
4592 /// @param IsSubExpr is true if ExitCond does not directly control the exit
4593 /// branch. In this case, we cannot assume that the loop only exits when the
4594 /// condition is true and cannot infer that failing to meet the condition prior
4595 /// to integer wraparound results in undefined behavior.
4596 ScalarEvolution::ExitLimit
4597 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4602 // Check if the controlling expression for this loop is an And or Or.
4603 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4604 if (BO->getOpcode() == Instruction::And) {
4605 // Recurse on the operands of the and.
4606 bool EitherMayExit = L->contains(TBB);
4607 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4608 IsSubExpr || EitherMayExit);
4609 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4610 IsSubExpr || EitherMayExit);
4611 const SCEV *BECount = getCouldNotCompute();
4612 const SCEV *MaxBECount = getCouldNotCompute();
4613 bool MustExit = false;
4614 if (EitherMayExit) {
4615 // Both conditions must be true for the loop to continue executing.
4616 // Choose the less conservative count.
4617 if (EL0.Exact == getCouldNotCompute() ||
4618 EL1.Exact == getCouldNotCompute())
4619 BECount = getCouldNotCompute();
4621 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4622 if (EL0.Max == getCouldNotCompute())
4623 MaxBECount = EL1.Max;
4624 else if (EL1.Max == getCouldNotCompute())
4625 MaxBECount = EL0.Max;
4627 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4628 MustExit = EL0.MustExit || EL1.MustExit;
4630 // Both conditions must be true at the same time for the loop to exit.
4631 // For now, be conservative.
4632 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4633 if (EL0.Max == EL1.Max)
4634 MaxBECount = EL0.Max;
4635 if (EL0.Exact == EL1.Exact)
4636 BECount = EL0.Exact;
4637 MustExit = EL0.MustExit && EL1.MustExit;
4640 return ExitLimit(BECount, MaxBECount, MustExit);
4642 if (BO->getOpcode() == Instruction::Or) {
4643 // Recurse on the operands of the or.
4644 bool EitherMayExit = L->contains(FBB);
4645 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4646 IsSubExpr || EitherMayExit);
4647 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4648 IsSubExpr || EitherMayExit);
4649 const SCEV *BECount = getCouldNotCompute();
4650 const SCEV *MaxBECount = getCouldNotCompute();
4651 bool MustExit = false;
4652 if (EitherMayExit) {
4653 // Both conditions must be false for the loop to continue executing.
4654 // Choose the less conservative count.
4655 if (EL0.Exact == getCouldNotCompute() ||
4656 EL1.Exact == getCouldNotCompute())
4657 BECount = getCouldNotCompute();
4659 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4660 if (EL0.Max == getCouldNotCompute())
4661 MaxBECount = EL1.Max;
4662 else if (EL1.Max == getCouldNotCompute())
4663 MaxBECount = EL0.Max;
4665 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4666 MustExit = EL0.MustExit || EL1.MustExit;
4668 // Both conditions must be false at the same time for the loop to exit.
4669 // For now, be conservative.
4670 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4671 if (EL0.Max == EL1.Max)
4672 MaxBECount = EL0.Max;
4673 if (EL0.Exact == EL1.Exact)
4674 BECount = EL0.Exact;
4675 MustExit = EL0.MustExit && EL1.MustExit;
4678 return ExitLimit(BECount, MaxBECount, MustExit);
4682 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4683 // Proceed to the next level to examine the icmp.
4684 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4685 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, IsSubExpr);
4687 // Check for a constant condition. These are normally stripped out by
4688 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4689 // preserve the CFG and is temporarily leaving constant conditions
4691 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4692 if (L->contains(FBB) == !CI->getZExtValue())
4693 // The backedge is always taken.
4694 return getCouldNotCompute();
4696 // The backedge is never taken.
4697 return getConstant(CI->getType(), 0);
4700 // If it's not an integer or pointer comparison then compute it the hard way.
4701 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4704 /// ComputeExitLimitFromICmp - Compute the number of times the
4705 /// backedge of the specified loop will execute if its exit condition
4706 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4707 ScalarEvolution::ExitLimit
4708 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4714 // If the condition was exit on true, convert the condition to exit on false
4715 ICmpInst::Predicate Cond;
4716 if (!L->contains(FBB))
4717 Cond = ExitCond->getPredicate();
4719 Cond = ExitCond->getInversePredicate();
4721 // Handle common loops like: for (X = "string"; *X; ++X)
4722 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4723 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4725 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4726 if (ItCnt.hasAnyInfo())
4730 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4731 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4733 // Try to evaluate any dependencies out of the loop.
4734 LHS = getSCEVAtScope(LHS, L);
4735 RHS = getSCEVAtScope(RHS, L);
4737 // At this point, we would like to compute how many iterations of the
4738 // loop the predicate will return true for these inputs.
4739 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4740 // If there is a loop-invariant, force it into the RHS.
4741 std::swap(LHS, RHS);
4742 Cond = ICmpInst::getSwappedPredicate(Cond);
4745 // Simplify the operands before analyzing them.
4746 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4748 // If we have a comparison of a chrec against a constant, try to use value
4749 // ranges to answer this query.
4750 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4751 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4752 if (AddRec->getLoop() == L) {
4753 // Form the constant range.
4754 ConstantRange CompRange(
4755 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4757 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4758 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4762 case ICmpInst::ICMP_NE: { // while (X != Y)
4763 // Convert to: while (X-Y != 0)
4764 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4765 if (EL.hasAnyInfo()) return EL;
4768 case ICmpInst::ICMP_EQ: { // while (X == Y)
4769 // Convert to: while (X-Y == 0)
4770 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4771 if (EL.hasAnyInfo()) return EL;
4774 case ICmpInst::ICMP_SLT:
4775 case ICmpInst::ICMP_ULT: { // while (X < Y)
4776 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
4777 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, IsSubExpr);
4778 if (EL.hasAnyInfo()) return EL;
4781 case ICmpInst::ICMP_SGT:
4782 case ICmpInst::ICMP_UGT: { // while (X > Y)
4783 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
4784 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, IsSubExpr);
4785 if (EL.hasAnyInfo()) return EL;
4790 dbgs() << "ComputeBackedgeTakenCount ";
4791 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4792 dbgs() << "[unsigned] ";
4793 dbgs() << *LHS << " "
4794 << Instruction::getOpcodeName(Instruction::ICmp)
4795 << " " << *RHS << "\n";
4799 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4802 ScalarEvolution::ExitLimit
4803 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
4805 BasicBlock *ExitingBlock,
4807 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
4809 // Give up if the exit is the default dest of a switch.
4810 if (Switch->getDefaultDest() == ExitingBlock)
4811 return getCouldNotCompute();
4813 assert(L->contains(Switch->getDefaultDest()) &&
4814 "Default case must not exit the loop!");
4815 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
4816 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
4818 // while (X != Y) --> while (X-Y != 0)
4819 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4820 if (EL.hasAnyInfo())
4823 return getCouldNotCompute();
4826 static ConstantInt *
4827 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4828 ScalarEvolution &SE) {
4829 const SCEV *InVal = SE.getConstant(C);
4830 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4831 assert(isa<SCEVConstant>(Val) &&
4832 "Evaluation of SCEV at constant didn't fold correctly?");
4833 return cast<SCEVConstant>(Val)->getValue();
4836 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4837 /// 'icmp op load X, cst', try to see if we can compute the backedge
4838 /// execution count.
4839 ScalarEvolution::ExitLimit
4840 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4844 ICmpInst::Predicate predicate) {
4846 if (LI->isVolatile()) return getCouldNotCompute();
4848 // Check to see if the loaded pointer is a getelementptr of a global.
4849 // TODO: Use SCEV instead of manually grubbing with GEPs.
4850 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4851 if (!GEP) return getCouldNotCompute();
4853 // Make sure that it is really a constant global we are gepping, with an
4854 // initializer, and make sure the first IDX is really 0.
4855 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4856 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4857 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4858 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4859 return getCouldNotCompute();
4861 // Okay, we allow one non-constant index into the GEP instruction.
4862 Value *VarIdx = nullptr;
4863 std::vector<Constant*> Indexes;
4864 unsigned VarIdxNum = 0;
4865 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4866 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4867 Indexes.push_back(CI);
4868 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4869 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4870 VarIdx = GEP->getOperand(i);
4872 Indexes.push_back(nullptr);
4875 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4877 return getCouldNotCompute();
4879 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4880 // Check to see if X is a loop variant variable value now.
4881 const SCEV *Idx = getSCEV(VarIdx);
4882 Idx = getSCEVAtScope(Idx, L);
4884 // We can only recognize very limited forms of loop index expressions, in
4885 // particular, only affine AddRec's like {C1,+,C2}.
4886 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4887 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4888 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4889 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4890 return getCouldNotCompute();
4892 unsigned MaxSteps = MaxBruteForceIterations;
4893 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4894 ConstantInt *ItCst = ConstantInt::get(
4895 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4896 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4898 // Form the GEP offset.
4899 Indexes[VarIdxNum] = Val;
4901 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4903 if (!Result) break; // Cannot compute!
4905 // Evaluate the condition for this iteration.
4906 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4907 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4908 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4910 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4911 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4914 ++NumArrayLenItCounts;
4915 return getConstant(ItCst); // Found terminating iteration!
4918 return getCouldNotCompute();
4922 /// CanConstantFold - Return true if we can constant fold an instruction of the
4923 /// specified type, assuming that all operands were constants.
4924 static bool CanConstantFold(const Instruction *I) {
4925 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4926 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4930 if (const CallInst *CI = dyn_cast<CallInst>(I))
4931 if (const Function *F = CI->getCalledFunction())
4932 return canConstantFoldCallTo(F);
4936 /// Determine whether this instruction can constant evolve within this loop
4937 /// assuming its operands can all constant evolve.
4938 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4939 // An instruction outside of the loop can't be derived from a loop PHI.
4940 if (!L->contains(I)) return false;
4942 if (isa<PHINode>(I)) {
4943 if (L->getHeader() == I->getParent())
4946 // We don't currently keep track of the control flow needed to evaluate
4947 // PHIs, so we cannot handle PHIs inside of loops.
4951 // If we won't be able to constant fold this expression even if the operands
4952 // are constants, bail early.
4953 return CanConstantFold(I);
4956 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4957 /// recursing through each instruction operand until reaching a loop header phi.
4959 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4960 DenseMap<Instruction *, PHINode *> &PHIMap) {
4962 // Otherwise, we can evaluate this instruction if all of its operands are
4963 // constant or derived from a PHI node themselves.
4964 PHINode *PHI = nullptr;
4965 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4966 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4968 if (isa<Constant>(*OpI)) continue;
4970 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4971 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
4973 PHINode *P = dyn_cast<PHINode>(OpInst);
4975 // If this operand is already visited, reuse the prior result.
4976 // We may have P != PHI if this is the deepest point at which the
4977 // inconsistent paths meet.
4978 P = PHIMap.lookup(OpInst);
4980 // Recurse and memoize the results, whether a phi is found or not.
4981 // This recursive call invalidates pointers into PHIMap.
4982 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4986 return nullptr; // Not evolving from PHI
4987 if (PHI && PHI != P)
4988 return nullptr; // Evolving from multiple different PHIs.
4991 // This is a expression evolving from a constant PHI!
4995 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4996 /// in the loop that V is derived from. We allow arbitrary operations along the
4997 /// way, but the operands of an operation must either be constants or a value
4998 /// derived from a constant PHI. If this expression does not fit with these
4999 /// constraints, return null.
5000 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5001 Instruction *I = dyn_cast<Instruction>(V);
5002 if (!I || !canConstantEvolve(I, L)) return nullptr;
5004 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5008 // Record non-constant instructions contained by the loop.
5009 DenseMap<Instruction *, PHINode *> PHIMap;
5010 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5013 /// EvaluateExpression - Given an expression that passes the
5014 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5015 /// in the loop has the value PHIVal. If we can't fold this expression for some
5016 /// reason, return null.
5017 static Constant *EvaluateExpression(Value *V, const Loop *L,
5018 DenseMap<Instruction *, Constant *> &Vals,
5019 const DataLayout *DL,
5020 const TargetLibraryInfo *TLI) {
5021 // Convenient constant check, but redundant for recursive calls.
5022 if (Constant *C = dyn_cast<Constant>(V)) return C;
5023 Instruction *I = dyn_cast<Instruction>(V);
5024 if (!I) return nullptr;
5026 if (Constant *C = Vals.lookup(I)) return C;
5028 // An instruction inside the loop depends on a value outside the loop that we
5029 // weren't given a mapping for, or a value such as a call inside the loop.
5030 if (!canConstantEvolve(I, L)) return nullptr;
5032 // An unmapped PHI can be due to a branch or another loop inside this loop,
5033 // or due to this not being the initial iteration through a loop where we
5034 // couldn't compute the evolution of this particular PHI last time.
5035 if (isa<PHINode>(I)) return nullptr;
5037 std::vector<Constant*> Operands(I->getNumOperands());
5039 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5040 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5042 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5043 if (!Operands[i]) return nullptr;
5046 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5048 if (!C) return nullptr;
5052 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5053 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5054 Operands[1], DL, TLI);
5055 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5056 if (!LI->isVolatile())
5057 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5059 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5063 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5064 /// in the header of its containing loop, we know the loop executes a
5065 /// constant number of times, and the PHI node is just a recurrence
5066 /// involving constants, fold it.
5068 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5071 DenseMap<PHINode*, Constant*>::const_iterator I =
5072 ConstantEvolutionLoopExitValue.find(PN);
5073 if (I != ConstantEvolutionLoopExitValue.end())
5076 if (BEs.ugt(MaxBruteForceIterations))
5077 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5079 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5081 DenseMap<Instruction *, Constant *> CurrentIterVals;
5082 BasicBlock *Header = L->getHeader();
5083 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5085 // Since the loop is canonicalized, the PHI node must have two entries. One
5086 // entry must be a constant (coming in from outside of the loop), and the
5087 // second must be derived from the same PHI.
5088 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5089 PHINode *PHI = nullptr;
5090 for (BasicBlock::iterator I = Header->begin();
5091 (PHI = dyn_cast<PHINode>(I)); ++I) {
5092 Constant *StartCST =
5093 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5094 if (!StartCST) continue;
5095 CurrentIterVals[PHI] = StartCST;
5097 if (!CurrentIterVals.count(PN))
5098 return RetVal = nullptr;
5100 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5102 // Execute the loop symbolically to determine the exit value.
5103 if (BEs.getActiveBits() >= 32)
5104 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5106 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5107 unsigned IterationNum = 0;
5108 for (; ; ++IterationNum) {
5109 if (IterationNum == NumIterations)
5110 return RetVal = CurrentIterVals[PN]; // Got exit value!
5112 // Compute the value of the PHIs for the next iteration.
5113 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5114 DenseMap<Instruction *, Constant *> NextIterVals;
5115 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5118 return nullptr; // Couldn't evaluate!
5119 NextIterVals[PN] = NextPHI;
5121 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5123 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5124 // cease to be able to evaluate one of them or if they stop evolving,
5125 // because that doesn't necessarily prevent us from computing PN.
5126 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5127 for (DenseMap<Instruction *, Constant *>::const_iterator
5128 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5129 PHINode *PHI = dyn_cast<PHINode>(I->first);
5130 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5131 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5133 // We use two distinct loops because EvaluateExpression may invalidate any
5134 // iterators into CurrentIterVals.
5135 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5136 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5137 PHINode *PHI = I->first;
5138 Constant *&NextPHI = NextIterVals[PHI];
5139 if (!NextPHI) { // Not already computed.
5140 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5141 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5143 if (NextPHI != I->second)
5144 StoppedEvolving = false;
5147 // If all entries in CurrentIterVals == NextIterVals then we can stop
5148 // iterating, the loop can't continue to change.
5149 if (StoppedEvolving)
5150 return RetVal = CurrentIterVals[PN];
5152 CurrentIterVals.swap(NextIterVals);
5156 /// ComputeExitCountExhaustively - If the loop is known to execute a
5157 /// constant number of times (the condition evolves only from constants),
5158 /// try to evaluate a few iterations of the loop until we get the exit
5159 /// condition gets a value of ExitWhen (true or false). If we cannot
5160 /// evaluate the trip count of the loop, return getCouldNotCompute().
5161 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5164 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5165 if (!PN) return getCouldNotCompute();
5167 // If the loop is canonicalized, the PHI will have exactly two entries.
5168 // That's the only form we support here.
5169 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5171 DenseMap<Instruction *, Constant *> CurrentIterVals;
5172 BasicBlock *Header = L->getHeader();
5173 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5175 // One entry must be a constant (coming in from outside of the loop), and the
5176 // second must be derived from the same PHI.
5177 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5178 PHINode *PHI = nullptr;
5179 for (BasicBlock::iterator I = Header->begin();
5180 (PHI = dyn_cast<PHINode>(I)); ++I) {
5181 Constant *StartCST =
5182 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5183 if (!StartCST) continue;
5184 CurrentIterVals[PHI] = StartCST;
5186 if (!CurrentIterVals.count(PN))
5187 return getCouldNotCompute();
5189 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5190 // the loop symbolically to determine when the condition gets a value of
5193 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5194 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5195 ConstantInt *CondVal =
5196 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5199 // Couldn't symbolically evaluate.
5200 if (!CondVal) return getCouldNotCompute();
5202 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5203 ++NumBruteForceTripCountsComputed;
5204 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5207 // Update all the PHI nodes for the next iteration.
5208 DenseMap<Instruction *, Constant *> NextIterVals;
5210 // Create a list of which PHIs we need to compute. We want to do this before
5211 // calling EvaluateExpression on them because that may invalidate iterators
5212 // into CurrentIterVals.
5213 SmallVector<PHINode *, 8> PHIsToCompute;
5214 for (DenseMap<Instruction *, Constant *>::const_iterator
5215 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5216 PHINode *PHI = dyn_cast<PHINode>(I->first);
5217 if (!PHI || PHI->getParent() != Header) continue;
5218 PHIsToCompute.push_back(PHI);
5220 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5221 E = PHIsToCompute.end(); I != E; ++I) {
5223 Constant *&NextPHI = NextIterVals[PHI];
5224 if (NextPHI) continue; // Already computed!
5226 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5227 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5229 CurrentIterVals.swap(NextIterVals);
5232 // Too many iterations were needed to evaluate.
5233 return getCouldNotCompute();
5236 /// getSCEVAtScope - Return a SCEV expression for the specified value
5237 /// at the specified scope in the program. The L value specifies a loop
5238 /// nest to evaluate the expression at, where null is the top-level or a
5239 /// specified loop is immediately inside of the loop.
5241 /// This method can be used to compute the exit value for a variable defined
5242 /// in a loop by querying what the value will hold in the parent loop.
5244 /// In the case that a relevant loop exit value cannot be computed, the
5245 /// original value V is returned.
5246 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5247 // Check to see if we've folded this expression at this loop before.
5248 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5249 for (unsigned u = 0; u < Values.size(); u++) {
5250 if (Values[u].first == L)
5251 return Values[u].second ? Values[u].second : V;
5253 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5254 // Otherwise compute it.
5255 const SCEV *C = computeSCEVAtScope(V, L);
5256 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5257 for (unsigned u = Values2.size(); u > 0; u--) {
5258 if (Values2[u - 1].first == L) {
5259 Values2[u - 1].second = C;
5266 /// This builds up a Constant using the ConstantExpr interface. That way, we
5267 /// will return Constants for objects which aren't represented by a
5268 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5269 /// Returns NULL if the SCEV isn't representable as a Constant.
5270 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5271 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5272 case scCouldNotCompute:
5276 return cast<SCEVConstant>(V)->getValue();
5278 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5279 case scSignExtend: {
5280 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5281 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5282 return ConstantExpr::getSExt(CastOp, SS->getType());
5285 case scZeroExtend: {
5286 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5287 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5288 return ConstantExpr::getZExt(CastOp, SZ->getType());
5292 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5293 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5294 return ConstantExpr::getTrunc(CastOp, ST->getType());
5298 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5299 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5300 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5301 unsigned AS = PTy->getAddressSpace();
5302 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5303 C = ConstantExpr::getBitCast(C, DestPtrTy);
5305 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5306 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5307 if (!C2) return nullptr;
5310 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5311 unsigned AS = C2->getType()->getPointerAddressSpace();
5313 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5314 // The offsets have been converted to bytes. We can add bytes to an
5315 // i8* by GEP with the byte count in the first index.
5316 C = ConstantExpr::getBitCast(C, DestPtrTy);
5319 // Don't bother trying to sum two pointers. We probably can't
5320 // statically compute a load that results from it anyway.
5321 if (C2->getType()->isPointerTy())
5324 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5325 if (PTy->getElementType()->isStructTy())
5326 C2 = ConstantExpr::getIntegerCast(
5327 C2, Type::getInt32Ty(C->getContext()), true);
5328 C = ConstantExpr::getGetElementPtr(C, C2);
5330 C = ConstantExpr::getAdd(C, C2);
5337 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5338 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5339 // Don't bother with pointers at all.
5340 if (C->getType()->isPointerTy()) return nullptr;
5341 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5342 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5343 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5344 C = ConstantExpr::getMul(C, C2);
5351 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5352 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5353 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5354 if (LHS->getType() == RHS->getType())
5355 return ConstantExpr::getUDiv(LHS, RHS);
5360 break; // TODO: smax, umax.
5365 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5366 if (isa<SCEVConstant>(V)) return V;
5368 // If this instruction is evolved from a constant-evolving PHI, compute the
5369 // exit value from the loop without using SCEVs.
5370 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5371 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5372 const Loop *LI = (*this->LI)[I->getParent()];
5373 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5374 if (PHINode *PN = dyn_cast<PHINode>(I))
5375 if (PN->getParent() == LI->getHeader()) {
5376 // Okay, there is no closed form solution for the PHI node. Check
5377 // to see if the loop that contains it has a known backedge-taken
5378 // count. If so, we may be able to force computation of the exit
5380 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5381 if (const SCEVConstant *BTCC =
5382 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5383 // Okay, we know how many times the containing loop executes. If
5384 // this is a constant evolving PHI node, get the final value at
5385 // the specified iteration number.
5386 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5387 BTCC->getValue()->getValue(),
5389 if (RV) return getSCEV(RV);
5393 // Okay, this is an expression that we cannot symbolically evaluate
5394 // into a SCEV. Check to see if it's possible to symbolically evaluate
5395 // the arguments into constants, and if so, try to constant propagate the
5396 // result. This is particularly useful for computing loop exit values.
5397 if (CanConstantFold(I)) {
5398 SmallVector<Constant *, 4> Operands;
5399 bool MadeImprovement = false;
5400 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5401 Value *Op = I->getOperand(i);
5402 if (Constant *C = dyn_cast<Constant>(Op)) {
5403 Operands.push_back(C);
5407 // If any of the operands is non-constant and if they are
5408 // non-integer and non-pointer, don't even try to analyze them
5409 // with scev techniques.
5410 if (!isSCEVable(Op->getType()))
5413 const SCEV *OrigV = getSCEV(Op);
5414 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5415 MadeImprovement |= OrigV != OpV;
5417 Constant *C = BuildConstantFromSCEV(OpV);
5419 if (C->getType() != Op->getType())
5420 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5424 Operands.push_back(C);
5427 // Check to see if getSCEVAtScope actually made an improvement.
5428 if (MadeImprovement) {
5429 Constant *C = nullptr;
5430 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5431 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5432 Operands[0], Operands[1], DL,
5434 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5435 if (!LI->isVolatile())
5436 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5438 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5446 // This is some other type of SCEVUnknown, just return it.
5450 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5451 // Avoid performing the look-up in the common case where the specified
5452 // expression has no loop-variant portions.
5453 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5454 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5455 if (OpAtScope != Comm->getOperand(i)) {
5456 // Okay, at least one of these operands is loop variant but might be
5457 // foldable. Build a new instance of the folded commutative expression.
5458 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5459 Comm->op_begin()+i);
5460 NewOps.push_back(OpAtScope);
5462 for (++i; i != e; ++i) {
5463 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5464 NewOps.push_back(OpAtScope);
5466 if (isa<SCEVAddExpr>(Comm))
5467 return getAddExpr(NewOps);
5468 if (isa<SCEVMulExpr>(Comm))
5469 return getMulExpr(NewOps);
5470 if (isa<SCEVSMaxExpr>(Comm))
5471 return getSMaxExpr(NewOps);
5472 if (isa<SCEVUMaxExpr>(Comm))
5473 return getUMaxExpr(NewOps);
5474 llvm_unreachable("Unknown commutative SCEV type!");
5477 // If we got here, all operands are loop invariant.
5481 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5482 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5483 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5484 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5485 return Div; // must be loop invariant
5486 return getUDivExpr(LHS, RHS);
5489 // If this is a loop recurrence for a loop that does not contain L, then we
5490 // are dealing with the final value computed by the loop.
5491 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5492 // First, attempt to evaluate each operand.
5493 // Avoid performing the look-up in the common case where the specified
5494 // expression has no loop-variant portions.
5495 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5496 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5497 if (OpAtScope == AddRec->getOperand(i))
5500 // Okay, at least one of these operands is loop variant but might be
5501 // foldable. Build a new instance of the folded commutative expression.
5502 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5503 AddRec->op_begin()+i);
5504 NewOps.push_back(OpAtScope);
5505 for (++i; i != e; ++i)
5506 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5508 const SCEV *FoldedRec =
5509 getAddRecExpr(NewOps, AddRec->getLoop(),
5510 AddRec->getNoWrapFlags(SCEV::FlagNW));
5511 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5512 // The addrec may be folded to a nonrecurrence, for example, if the
5513 // induction variable is multiplied by zero after constant folding. Go
5514 // ahead and return the folded value.
5520 // If the scope is outside the addrec's loop, evaluate it by using the
5521 // loop exit value of the addrec.
5522 if (!AddRec->getLoop()->contains(L)) {
5523 // To evaluate this recurrence, we need to know how many times the AddRec
5524 // loop iterates. Compute this now.
5525 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5526 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5528 // Then, evaluate the AddRec.
5529 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5535 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5536 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5537 if (Op == Cast->getOperand())
5538 return Cast; // must be loop invariant
5539 return getZeroExtendExpr(Op, Cast->getType());
5542 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5543 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5544 if (Op == Cast->getOperand())
5545 return Cast; // must be loop invariant
5546 return getSignExtendExpr(Op, Cast->getType());
5549 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5550 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5551 if (Op == Cast->getOperand())
5552 return Cast; // must be loop invariant
5553 return getTruncateExpr(Op, Cast->getType());
5556 llvm_unreachable("Unknown SCEV type!");
5559 /// getSCEVAtScope - This is a convenience function which does
5560 /// getSCEVAtScope(getSCEV(V), L).
5561 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5562 return getSCEVAtScope(getSCEV(V), L);
5565 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5566 /// following equation:
5568 /// A * X = B (mod N)
5570 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5571 /// A and B isn't important.
5573 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5574 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5575 ScalarEvolution &SE) {
5576 uint32_t BW = A.getBitWidth();
5577 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5578 assert(A != 0 && "A must be non-zero.");
5582 // The gcd of A and N may have only one prime factor: 2. The number of
5583 // trailing zeros in A is its multiplicity
5584 uint32_t Mult2 = A.countTrailingZeros();
5587 // 2. Check if B is divisible by D.
5589 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5590 // is not less than multiplicity of this prime factor for D.
5591 if (B.countTrailingZeros() < Mult2)
5592 return SE.getCouldNotCompute();
5594 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5597 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5598 // bit width during computations.
5599 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5600 APInt Mod(BW + 1, 0);
5601 Mod.setBit(BW - Mult2); // Mod = N / D
5602 APInt I = AD.multiplicativeInverse(Mod);
5604 // 4. Compute the minimum unsigned root of the equation:
5605 // I * (B / D) mod (N / D)
5606 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5608 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5610 return SE.getConstant(Result.trunc(BW));
5613 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5614 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5615 /// might be the same) or two SCEVCouldNotCompute objects.
5617 static std::pair<const SCEV *,const SCEV *>
5618 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5619 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5620 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5621 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5622 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5624 // We currently can only solve this if the coefficients are constants.
5625 if (!LC || !MC || !NC) {
5626 const SCEV *CNC = SE.getCouldNotCompute();
5627 return std::make_pair(CNC, CNC);
5630 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5631 const APInt &L = LC->getValue()->getValue();
5632 const APInt &M = MC->getValue()->getValue();
5633 const APInt &N = NC->getValue()->getValue();
5634 APInt Two(BitWidth, 2);
5635 APInt Four(BitWidth, 4);
5638 using namespace APIntOps;
5640 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5641 // The B coefficient is M-N/2
5645 // The A coefficient is N/2
5646 APInt A(N.sdiv(Two));
5648 // Compute the B^2-4ac term.
5651 SqrtTerm -= Four * (A * C);
5653 if (SqrtTerm.isNegative()) {
5654 // The loop is provably infinite.
5655 const SCEV *CNC = SE.getCouldNotCompute();
5656 return std::make_pair(CNC, CNC);
5659 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5660 // integer value or else APInt::sqrt() will assert.
5661 APInt SqrtVal(SqrtTerm.sqrt());
5663 // Compute the two solutions for the quadratic formula.
5664 // The divisions must be performed as signed divisions.
5667 if (TwoA.isMinValue()) {
5668 const SCEV *CNC = SE.getCouldNotCompute();
5669 return std::make_pair(CNC, CNC);
5672 LLVMContext &Context = SE.getContext();
5674 ConstantInt *Solution1 =
5675 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5676 ConstantInt *Solution2 =
5677 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5679 return std::make_pair(SE.getConstant(Solution1),
5680 SE.getConstant(Solution2));
5681 } // end APIntOps namespace
5684 /// HowFarToZero - Return the number of times a backedge comparing the specified
5685 /// value to zero will execute. If not computable, return CouldNotCompute.
5687 /// This is only used for loops with a "x != y" exit test. The exit condition is
5688 /// now expressed as a single expression, V = x-y. So the exit test is
5689 /// effectively V != 0. We know and take advantage of the fact that this
5690 /// expression only being used in a comparison by zero context.
5691 ScalarEvolution::ExitLimit
5692 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
5693 // If the value is a constant
5694 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5695 // If the value is already zero, the branch will execute zero times.
5696 if (C->getValue()->isZero()) return C;
5697 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5700 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5701 if (!AddRec || AddRec->getLoop() != L)
5702 return getCouldNotCompute();
5704 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5705 // the quadratic equation to solve it.
5706 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5707 std::pair<const SCEV *,const SCEV *> Roots =
5708 SolveQuadraticEquation(AddRec, *this);
5709 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5710 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5713 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5714 << " sol#2: " << *R2 << "\n";
5716 // Pick the smallest positive root value.
5717 if (ConstantInt *CB =
5718 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5721 if (CB->getZExtValue() == false)
5722 std::swap(R1, R2); // R1 is the minimum root now.
5724 // We can only use this value if the chrec ends up with an exact zero
5725 // value at this index. When solving for "X*X != 5", for example, we
5726 // should not accept a root of 2.
5727 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5729 return R1; // We found a quadratic root!
5732 return getCouldNotCompute();
5735 // Otherwise we can only handle this if it is affine.
5736 if (!AddRec->isAffine())
5737 return getCouldNotCompute();
5739 // If this is an affine expression, the execution count of this branch is
5740 // the minimum unsigned root of the following equation:
5742 // Start + Step*N = 0 (mod 2^BW)
5746 // Step*N = -Start (mod 2^BW)
5748 // where BW is the common bit width of Start and Step.
5750 // Get the initial value for the loop.
5751 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5752 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5754 // For now we handle only constant steps.
5756 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5757 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5758 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5759 // We have not yet seen any such cases.
5760 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5761 if (!StepC || StepC->getValue()->equalsInt(0))
5762 return getCouldNotCompute();
5764 // For positive steps (counting up until unsigned overflow):
5765 // N = -Start/Step (as unsigned)
5766 // For negative steps (counting down to zero):
5768 // First compute the unsigned distance from zero in the direction of Step.
5769 bool CountDown = StepC->getValue()->getValue().isNegative();
5770 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5772 // Handle unitary steps, which cannot wraparound.
5773 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5774 // N = Distance (as unsigned)
5775 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5776 ConstantRange CR = getUnsignedRange(Start);
5777 const SCEV *MaxBECount;
5778 if (!CountDown && CR.getUnsignedMin().isMinValue())
5779 // When counting up, the worst starting value is 1, not 0.
5780 MaxBECount = CR.getUnsignedMax().isMinValue()
5781 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5782 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5784 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5785 : -CR.getUnsignedMin());
5786 return ExitLimit(Distance, MaxBECount, /*MustExit=*/true);
5789 // If the recurrence is known not to wraparound, unsigned divide computes the
5790 // back edge count. (Ideally we would have an "isexact" bit for udiv). We know
5791 // that the value will either become zero (and thus the loop terminates), that
5792 // the loop will terminate through some other exit condition first, or that
5793 // the loop has undefined behavior. This means we can't "miss" the exit
5794 // value, even with nonunit stride, and exit later via the same branch. Note
5795 // that we can skip this exit if loop later exits via a different
5796 // branch. Hence MustExit=false.
5798 // This is only valid for expressions that directly compute the loop exit. It
5799 // is invalid for subexpressions in which the loop may exit through this
5800 // branch even if this subexpression is false. In that case, the trip count
5801 // computed by this udiv could be smaller than the number of well-defined
5803 if (!IsSubExpr && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5805 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5806 return ExitLimit(Exact, Exact, /*MustExit=*/false);
5809 // If Step is a power of two that evenly divides Start we know that the loop
5810 // will always terminate. Start may not be a constant so we just have the
5811 // number of trailing zeros available. This is safe even in presence of
5812 // overflow as the recurrence will overflow to exactly 0.
5813 const APInt &StepV = StepC->getValue()->getValue();
5814 if (StepV.isPowerOf2() &&
5815 GetMinTrailingZeros(getNegativeSCEV(Start)) >= StepV.countTrailingZeros())
5816 return getUDivExactExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5818 // Then, try to solve the above equation provided that Start is constant.
5819 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5820 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5821 -StartC->getValue()->getValue(),
5823 return getCouldNotCompute();
5826 /// HowFarToNonZero - Return the number of times a backedge checking the
5827 /// specified value for nonzero will execute. If not computable, return
5829 ScalarEvolution::ExitLimit
5830 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5831 // Loops that look like: while (X == 0) are very strange indeed. We don't
5832 // handle them yet except for the trivial case. This could be expanded in the
5833 // future as needed.
5835 // If the value is a constant, check to see if it is known to be non-zero
5836 // already. If so, the backedge will execute zero times.
5837 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5838 if (!C->getValue()->isNullValue())
5839 return getConstant(C->getType(), 0);
5840 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5843 // We could implement others, but I really doubt anyone writes loops like
5844 // this, and if they did, they would already be constant folded.
5845 return getCouldNotCompute();
5848 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5849 /// (which may not be an immediate predecessor) which has exactly one
5850 /// successor from which BB is reachable, or null if no such block is
5853 std::pair<BasicBlock *, BasicBlock *>
5854 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5855 // If the block has a unique predecessor, then there is no path from the
5856 // predecessor to the block that does not go through the direct edge
5857 // from the predecessor to the block.
5858 if (BasicBlock *Pred = BB->getSinglePredecessor())
5859 return std::make_pair(Pred, BB);
5861 // A loop's header is defined to be a block that dominates the loop.
5862 // If the header has a unique predecessor outside the loop, it must be
5863 // a block that has exactly one successor that can reach the loop.
5864 if (Loop *L = LI->getLoopFor(BB))
5865 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5867 return std::pair<BasicBlock *, BasicBlock *>();
5870 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5871 /// testing whether two expressions are equal, however for the purposes of
5872 /// looking for a condition guarding a loop, it can be useful to be a little
5873 /// more general, since a front-end may have replicated the controlling
5876 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5877 // Quick check to see if they are the same SCEV.
5878 if (A == B) return true;
5880 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5881 // two different instructions with the same value. Check for this case.
5882 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5883 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5884 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5885 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5886 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5889 // Otherwise assume they may have a different value.
5893 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5894 /// predicate Pred. Return true iff any changes were made.
5896 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5897 const SCEV *&LHS, const SCEV *&RHS,
5899 bool Changed = false;
5901 // If we hit the max recursion limit bail out.
5905 // Canonicalize a constant to the right side.
5906 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5907 // Check for both operands constant.
5908 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5909 if (ConstantExpr::getICmp(Pred,
5911 RHSC->getValue())->isNullValue())
5912 goto trivially_false;
5914 goto trivially_true;
5916 // Otherwise swap the operands to put the constant on the right.
5917 std::swap(LHS, RHS);
5918 Pred = ICmpInst::getSwappedPredicate(Pred);
5922 // If we're comparing an addrec with a value which is loop-invariant in the
5923 // addrec's loop, put the addrec on the left. Also make a dominance check,
5924 // as both operands could be addrecs loop-invariant in each other's loop.
5925 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5926 const Loop *L = AR->getLoop();
5927 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5928 std::swap(LHS, RHS);
5929 Pred = ICmpInst::getSwappedPredicate(Pred);
5934 // If there's a constant operand, canonicalize comparisons with boundary
5935 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5936 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5937 const APInt &RA = RC->getValue()->getValue();
5939 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5940 case ICmpInst::ICMP_EQ:
5941 case ICmpInst::ICMP_NE:
5942 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5944 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5945 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5946 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5947 ME->getOperand(0)->isAllOnesValue()) {
5948 RHS = AE->getOperand(1);
5949 LHS = ME->getOperand(1);
5953 case ICmpInst::ICMP_UGE:
5954 if ((RA - 1).isMinValue()) {
5955 Pred = ICmpInst::ICMP_NE;
5956 RHS = getConstant(RA - 1);
5960 if (RA.isMaxValue()) {
5961 Pred = ICmpInst::ICMP_EQ;
5965 if (RA.isMinValue()) goto trivially_true;
5967 Pred = ICmpInst::ICMP_UGT;
5968 RHS = getConstant(RA - 1);
5971 case ICmpInst::ICMP_ULE:
5972 if ((RA + 1).isMaxValue()) {
5973 Pred = ICmpInst::ICMP_NE;
5974 RHS = getConstant(RA + 1);
5978 if (RA.isMinValue()) {
5979 Pred = ICmpInst::ICMP_EQ;
5983 if (RA.isMaxValue()) goto trivially_true;
5985 Pred = ICmpInst::ICMP_ULT;
5986 RHS = getConstant(RA + 1);
5989 case ICmpInst::ICMP_SGE:
5990 if ((RA - 1).isMinSignedValue()) {
5991 Pred = ICmpInst::ICMP_NE;
5992 RHS = getConstant(RA - 1);
5996 if (RA.isMaxSignedValue()) {
5997 Pred = ICmpInst::ICMP_EQ;
6001 if (RA.isMinSignedValue()) goto trivially_true;
6003 Pred = ICmpInst::ICMP_SGT;
6004 RHS = getConstant(RA - 1);
6007 case ICmpInst::ICMP_SLE:
6008 if ((RA + 1).isMaxSignedValue()) {
6009 Pred = ICmpInst::ICMP_NE;
6010 RHS = getConstant(RA + 1);
6014 if (RA.isMinSignedValue()) {
6015 Pred = ICmpInst::ICMP_EQ;
6019 if (RA.isMaxSignedValue()) goto trivially_true;
6021 Pred = ICmpInst::ICMP_SLT;
6022 RHS = getConstant(RA + 1);
6025 case ICmpInst::ICMP_UGT:
6026 if (RA.isMinValue()) {
6027 Pred = ICmpInst::ICMP_NE;
6031 if ((RA + 1).isMaxValue()) {
6032 Pred = ICmpInst::ICMP_EQ;
6033 RHS = getConstant(RA + 1);
6037 if (RA.isMaxValue()) goto trivially_false;
6039 case ICmpInst::ICMP_ULT:
6040 if (RA.isMaxValue()) {
6041 Pred = ICmpInst::ICMP_NE;
6045 if ((RA - 1).isMinValue()) {
6046 Pred = ICmpInst::ICMP_EQ;
6047 RHS = getConstant(RA - 1);
6051 if (RA.isMinValue()) goto trivially_false;
6053 case ICmpInst::ICMP_SGT:
6054 if (RA.isMinSignedValue()) {
6055 Pred = ICmpInst::ICMP_NE;
6059 if ((RA + 1).isMaxSignedValue()) {
6060 Pred = ICmpInst::ICMP_EQ;
6061 RHS = getConstant(RA + 1);
6065 if (RA.isMaxSignedValue()) goto trivially_false;
6067 case ICmpInst::ICMP_SLT:
6068 if (RA.isMaxSignedValue()) {
6069 Pred = ICmpInst::ICMP_NE;
6073 if ((RA - 1).isMinSignedValue()) {
6074 Pred = ICmpInst::ICMP_EQ;
6075 RHS = getConstant(RA - 1);
6079 if (RA.isMinSignedValue()) goto trivially_false;
6084 // Check for obvious equality.
6085 if (HasSameValue(LHS, RHS)) {
6086 if (ICmpInst::isTrueWhenEqual(Pred))
6087 goto trivially_true;
6088 if (ICmpInst::isFalseWhenEqual(Pred))
6089 goto trivially_false;
6092 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6093 // adding or subtracting 1 from one of the operands.
6095 case ICmpInst::ICMP_SLE:
6096 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6097 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6099 Pred = ICmpInst::ICMP_SLT;
6101 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6102 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6104 Pred = ICmpInst::ICMP_SLT;
6108 case ICmpInst::ICMP_SGE:
6109 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6110 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6112 Pred = ICmpInst::ICMP_SGT;
6114 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6115 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6117 Pred = ICmpInst::ICMP_SGT;
6121 case ICmpInst::ICMP_ULE:
6122 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6123 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6125 Pred = ICmpInst::ICMP_ULT;
6127 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6128 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6130 Pred = ICmpInst::ICMP_ULT;
6134 case ICmpInst::ICMP_UGE:
6135 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6136 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6138 Pred = ICmpInst::ICMP_UGT;
6140 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6141 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6143 Pred = ICmpInst::ICMP_UGT;
6151 // TODO: More simplifications are possible here.
6153 // Recursively simplify until we either hit a recursion limit or nothing
6156 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6162 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6163 Pred = ICmpInst::ICMP_EQ;
6168 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6169 Pred = ICmpInst::ICMP_NE;
6173 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6174 return getSignedRange(S).getSignedMax().isNegative();
6177 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6178 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6181 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6182 return !getSignedRange(S).getSignedMin().isNegative();
6185 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6186 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6189 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6190 return isKnownNegative(S) || isKnownPositive(S);
6193 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6194 const SCEV *LHS, const SCEV *RHS) {
6195 // Canonicalize the inputs first.
6196 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6198 // If LHS or RHS is an addrec, check to see if the condition is true in
6199 // every iteration of the loop.
6200 // If LHS and RHS are both addrec, both conditions must be true in
6201 // every iteration of the loop.
6202 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6203 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6204 bool LeftGuarded = false;
6205 bool RightGuarded = false;
6207 const Loop *L = LAR->getLoop();
6208 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6209 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6210 if (!RAR) return true;
6215 const Loop *L = RAR->getLoop();
6216 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6217 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6218 if (!LAR) return true;
6219 RightGuarded = true;
6222 if (LeftGuarded && RightGuarded)
6225 // Otherwise see what can be done with known constant ranges.
6226 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6230 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6231 const SCEV *LHS, const SCEV *RHS) {
6232 if (HasSameValue(LHS, RHS))
6233 return ICmpInst::isTrueWhenEqual(Pred);
6235 // This code is split out from isKnownPredicate because it is called from
6236 // within isLoopEntryGuardedByCond.
6239 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6240 case ICmpInst::ICMP_SGT:
6241 std::swap(LHS, RHS);
6242 case ICmpInst::ICMP_SLT: {
6243 ConstantRange LHSRange = getSignedRange(LHS);
6244 ConstantRange RHSRange = getSignedRange(RHS);
6245 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6247 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6251 case ICmpInst::ICMP_SGE:
6252 std::swap(LHS, RHS);
6253 case ICmpInst::ICMP_SLE: {
6254 ConstantRange LHSRange = getSignedRange(LHS);
6255 ConstantRange RHSRange = getSignedRange(RHS);
6256 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6258 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6262 case ICmpInst::ICMP_UGT:
6263 std::swap(LHS, RHS);
6264 case ICmpInst::ICMP_ULT: {
6265 ConstantRange LHSRange = getUnsignedRange(LHS);
6266 ConstantRange RHSRange = getUnsignedRange(RHS);
6267 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6269 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6273 case ICmpInst::ICMP_UGE:
6274 std::swap(LHS, RHS);
6275 case ICmpInst::ICMP_ULE: {
6276 ConstantRange LHSRange = getUnsignedRange(LHS);
6277 ConstantRange RHSRange = getUnsignedRange(RHS);
6278 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6280 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6284 case ICmpInst::ICMP_NE: {
6285 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6287 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6290 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6291 if (isKnownNonZero(Diff))
6295 case ICmpInst::ICMP_EQ:
6296 // The check at the top of the function catches the case where
6297 // the values are known to be equal.
6303 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6304 /// protected by a conditional between LHS and RHS. This is used to
6305 /// to eliminate casts.
6307 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6308 ICmpInst::Predicate Pred,
6309 const SCEV *LHS, const SCEV *RHS) {
6310 // Interpret a null as meaning no loop, where there is obviously no guard
6311 // (interprocedural conditions notwithstanding).
6312 if (!L) return true;
6314 BasicBlock *Latch = L->getLoopLatch();
6318 BranchInst *LoopContinuePredicate =
6319 dyn_cast<BranchInst>(Latch->getTerminator());
6320 if (!LoopContinuePredicate ||
6321 LoopContinuePredicate->isUnconditional())
6324 return isImpliedCond(Pred, LHS, RHS,
6325 LoopContinuePredicate->getCondition(),
6326 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6329 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6330 /// by a conditional between LHS and RHS. This is used to help avoid max
6331 /// expressions in loop trip counts, and to eliminate casts.
6333 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6334 ICmpInst::Predicate Pred,
6335 const SCEV *LHS, const SCEV *RHS) {
6336 // Interpret a null as meaning no loop, where there is obviously no guard
6337 // (interprocedural conditions notwithstanding).
6338 if (!L) return false;
6340 // Starting at the loop predecessor, climb up the predecessor chain, as long
6341 // as there are predecessors that can be found that have unique successors
6342 // leading to the original header.
6343 for (std::pair<BasicBlock *, BasicBlock *>
6344 Pair(L->getLoopPredecessor(), L->getHeader());
6346 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6348 BranchInst *LoopEntryPredicate =
6349 dyn_cast<BranchInst>(Pair.first->getTerminator());
6350 if (!LoopEntryPredicate ||
6351 LoopEntryPredicate->isUnconditional())
6354 if (isImpliedCond(Pred, LHS, RHS,
6355 LoopEntryPredicate->getCondition(),
6356 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6363 /// RAII wrapper to prevent recursive application of isImpliedCond.
6364 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6365 /// currently evaluating isImpliedCond.
6366 struct MarkPendingLoopPredicate {
6368 DenseSet<Value*> &LoopPreds;
6371 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6372 : Cond(C), LoopPreds(LP) {
6373 Pending = !LoopPreds.insert(Cond).second;
6375 ~MarkPendingLoopPredicate() {
6377 LoopPreds.erase(Cond);
6381 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6382 /// and RHS is true whenever the given Cond value evaluates to true.
6383 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6384 const SCEV *LHS, const SCEV *RHS,
6385 Value *FoundCondValue,
6387 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6391 // Recursively handle And and Or conditions.
6392 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6393 if (BO->getOpcode() == Instruction::And) {
6395 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6396 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6397 } else if (BO->getOpcode() == Instruction::Or) {
6399 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6400 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6404 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6405 if (!ICI) return false;
6407 // Bail if the ICmp's operands' types are wider than the needed type
6408 // before attempting to call getSCEV on them. This avoids infinite
6409 // recursion, since the analysis of widening casts can require loop
6410 // exit condition information for overflow checking, which would
6412 if (getTypeSizeInBits(LHS->getType()) <
6413 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6416 // Now that we found a conditional branch that dominates the loop or controls
6417 // the loop latch. Check to see if it is the comparison we are looking for.
6418 ICmpInst::Predicate FoundPred;
6420 FoundPred = ICI->getInversePredicate();
6422 FoundPred = ICI->getPredicate();
6424 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6425 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6427 // Balance the types. The case where FoundLHS' type is wider than
6428 // LHS' type is checked for above.
6429 if (getTypeSizeInBits(LHS->getType()) >
6430 getTypeSizeInBits(FoundLHS->getType())) {
6431 if (CmpInst::isSigned(FoundPred)) {
6432 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6433 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6435 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6436 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6440 // Canonicalize the query to match the way instcombine will have
6441 // canonicalized the comparison.
6442 if (SimplifyICmpOperands(Pred, LHS, RHS))
6444 return CmpInst::isTrueWhenEqual(Pred);
6445 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6446 if (FoundLHS == FoundRHS)
6447 return CmpInst::isFalseWhenEqual(FoundPred);
6449 // Check to see if we can make the LHS or RHS match.
6450 if (LHS == FoundRHS || RHS == FoundLHS) {
6451 if (isa<SCEVConstant>(RHS)) {
6452 std::swap(FoundLHS, FoundRHS);
6453 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6455 std::swap(LHS, RHS);
6456 Pred = ICmpInst::getSwappedPredicate(Pred);
6460 // Check whether the found predicate is the same as the desired predicate.
6461 if (FoundPred == Pred)
6462 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6464 // Check whether swapping the found predicate makes it the same as the
6465 // desired predicate.
6466 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6467 if (isa<SCEVConstant>(RHS))
6468 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6470 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6471 RHS, LHS, FoundLHS, FoundRHS);
6474 // Check whether the actual condition is beyond sufficient.
6475 if (FoundPred == ICmpInst::ICMP_EQ)
6476 if (ICmpInst::isTrueWhenEqual(Pred))
6477 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6479 if (Pred == ICmpInst::ICMP_NE)
6480 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6481 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6484 // Otherwise assume the worst.
6488 /// isImpliedCondOperands - Test whether the condition described by Pred,
6489 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6490 /// and FoundRHS is true.
6491 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6492 const SCEV *LHS, const SCEV *RHS,
6493 const SCEV *FoundLHS,
6494 const SCEV *FoundRHS) {
6495 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6496 FoundLHS, FoundRHS) ||
6497 // ~x < ~y --> x > y
6498 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6499 getNotSCEV(FoundRHS),
6500 getNotSCEV(FoundLHS));
6503 /// isImpliedCondOperandsHelper - Test whether the condition described by
6504 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6505 /// FoundLHS, and FoundRHS is true.
6507 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6508 const SCEV *LHS, const SCEV *RHS,
6509 const SCEV *FoundLHS,
6510 const SCEV *FoundRHS) {
6512 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6513 case ICmpInst::ICMP_EQ:
6514 case ICmpInst::ICMP_NE:
6515 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6518 case ICmpInst::ICMP_SLT:
6519 case ICmpInst::ICMP_SLE:
6520 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6521 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6524 case ICmpInst::ICMP_SGT:
6525 case ICmpInst::ICMP_SGE:
6526 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6527 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6530 case ICmpInst::ICMP_ULT:
6531 case ICmpInst::ICMP_ULE:
6532 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6533 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6536 case ICmpInst::ICMP_UGT:
6537 case ICmpInst::ICMP_UGE:
6538 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6539 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6547 // Verify if an linear IV with positive stride can overflow when in a
6548 // less-than comparison, knowing the invariant term of the comparison, the
6549 // stride and the knowledge of NSW/NUW flags on the recurrence.
6550 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
6551 bool IsSigned, bool NoWrap) {
6552 if (NoWrap) return false;
6554 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6555 const SCEV *One = getConstant(Stride->getType(), 1);
6558 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
6559 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
6560 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6563 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
6564 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
6567 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
6568 APInt MaxValue = APInt::getMaxValue(BitWidth);
6569 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6572 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
6573 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
6576 // Verify if an linear IV with negative stride can overflow when in a
6577 // greater-than comparison, knowing the invariant term of the comparison,
6578 // the stride and the knowledge of NSW/NUW flags on the recurrence.
6579 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
6580 bool IsSigned, bool NoWrap) {
6581 if (NoWrap) return false;
6583 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6584 const SCEV *One = getConstant(Stride->getType(), 1);
6587 APInt MinRHS = getSignedRange(RHS).getSignedMin();
6588 APInt MinValue = APInt::getSignedMinValue(BitWidth);
6589 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6592 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
6593 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
6596 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
6597 APInt MinValue = APInt::getMinValue(BitWidth);
6598 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6601 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
6602 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
6605 // Compute the backedge taken count knowing the interval difference, the
6606 // stride and presence of the equality in the comparison.
6607 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
6609 const SCEV *One = getConstant(Step->getType(), 1);
6610 Delta = Equality ? getAddExpr(Delta, Step)
6611 : getAddExpr(Delta, getMinusSCEV(Step, One));
6612 return getUDivExpr(Delta, Step);
6615 /// HowManyLessThans - Return the number of times a backedge containing the
6616 /// specified less-than comparison will execute. If not computable, return
6617 /// CouldNotCompute.
6619 /// @param IsSubExpr is true when the LHS < RHS condition does not directly
6620 /// control the branch. In this case, we can only compute an iteration count for
6621 /// a subexpression that cannot overflow before evaluating true.
6622 ScalarEvolution::ExitLimit
6623 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6624 const Loop *L, bool IsSigned,
6626 // We handle only IV < Invariant
6627 if (!isLoopInvariant(RHS, L))
6628 return getCouldNotCompute();
6630 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6632 // Avoid weird loops
6633 if (!IV || IV->getLoop() != L || !IV->isAffine())
6634 return getCouldNotCompute();
6636 bool NoWrap = !IsSubExpr &&
6637 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6639 const SCEV *Stride = IV->getStepRecurrence(*this);
6641 // Avoid negative or zero stride values
6642 if (!isKnownPositive(Stride))
6643 return getCouldNotCompute();
6645 // Avoid proven overflow cases: this will ensure that the backedge taken count
6646 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6647 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6648 // behaviors like the case of C language.
6649 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
6650 return getCouldNotCompute();
6652 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
6653 : ICmpInst::ICMP_ULT;
6654 const SCEV *Start = IV->getStart();
6655 const SCEV *End = RHS;
6656 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
6657 End = IsSigned ? getSMaxExpr(RHS, Start)
6658 : getUMaxExpr(RHS, Start);
6660 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
6662 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
6663 : getUnsignedRange(Start).getUnsignedMin();
6665 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6666 : getUnsignedRange(Stride).getUnsignedMin();
6668 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6669 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
6670 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
6672 // Although End can be a MAX expression we estimate MaxEnd considering only
6673 // the case End = RHS. This is safe because in the other case (End - Start)
6674 // is zero, leading to a zero maximum backedge taken count.
6676 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
6677 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
6679 const SCEV *MaxBECount;
6680 if (isa<SCEVConstant>(BECount))
6681 MaxBECount = BECount;
6683 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
6684 getConstant(MinStride), false);
6686 if (isa<SCEVCouldNotCompute>(MaxBECount))
6687 MaxBECount = BECount;
6689 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6692 ScalarEvolution::ExitLimit
6693 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
6694 const Loop *L, bool IsSigned,
6696 // We handle only IV > Invariant
6697 if (!isLoopInvariant(RHS, L))
6698 return getCouldNotCompute();
6700 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6702 // Avoid weird loops
6703 if (!IV || IV->getLoop() != L || !IV->isAffine())
6704 return getCouldNotCompute();
6706 bool NoWrap = !IsSubExpr &&
6707 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6709 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
6711 // Avoid negative or zero stride values
6712 if (!isKnownPositive(Stride))
6713 return getCouldNotCompute();
6715 // Avoid proven overflow cases: this will ensure that the backedge taken count
6716 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6717 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6718 // behaviors like the case of C language.
6719 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
6720 return getCouldNotCompute();
6722 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
6723 : ICmpInst::ICMP_UGT;
6725 const SCEV *Start = IV->getStart();
6726 const SCEV *End = RHS;
6727 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
6728 End = IsSigned ? getSMinExpr(RHS, Start)
6729 : getUMinExpr(RHS, Start);
6731 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
6733 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
6734 : getUnsignedRange(Start).getUnsignedMax();
6736 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6737 : getUnsignedRange(Stride).getUnsignedMin();
6739 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6740 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
6741 : APInt::getMinValue(BitWidth) + (MinStride - 1);
6743 // Although End can be a MIN expression we estimate MinEnd considering only
6744 // the case End = RHS. This is safe because in the other case (Start - End)
6745 // is zero, leading to a zero maximum backedge taken count.
6747 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
6748 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
6751 const SCEV *MaxBECount = getCouldNotCompute();
6752 if (isa<SCEVConstant>(BECount))
6753 MaxBECount = BECount;
6755 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
6756 getConstant(MinStride), false);
6758 if (isa<SCEVCouldNotCompute>(MaxBECount))
6759 MaxBECount = BECount;
6761 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6764 /// getNumIterationsInRange - Return the number of iterations of this loop that
6765 /// produce values in the specified constant range. Another way of looking at
6766 /// this is that it returns the first iteration number where the value is not in
6767 /// the condition, thus computing the exit count. If the iteration count can't
6768 /// be computed, an instance of SCEVCouldNotCompute is returned.
6769 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6770 ScalarEvolution &SE) const {
6771 if (Range.isFullSet()) // Infinite loop.
6772 return SE.getCouldNotCompute();
6774 // If the start is a non-zero constant, shift the range to simplify things.
6775 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6776 if (!SC->getValue()->isZero()) {
6777 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6778 Operands[0] = SE.getConstant(SC->getType(), 0);
6779 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6780 getNoWrapFlags(FlagNW));
6781 if (const SCEVAddRecExpr *ShiftedAddRec =
6782 dyn_cast<SCEVAddRecExpr>(Shifted))
6783 return ShiftedAddRec->getNumIterationsInRange(
6784 Range.subtract(SC->getValue()->getValue()), SE);
6785 // This is strange and shouldn't happen.
6786 return SE.getCouldNotCompute();
6789 // The only time we can solve this is when we have all constant indices.
6790 // Otherwise, we cannot determine the overflow conditions.
6791 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6792 if (!isa<SCEVConstant>(getOperand(i)))
6793 return SE.getCouldNotCompute();
6796 // Okay at this point we know that all elements of the chrec are constants and
6797 // that the start element is zero.
6799 // First check to see if the range contains zero. If not, the first
6801 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6802 if (!Range.contains(APInt(BitWidth, 0)))
6803 return SE.getConstant(getType(), 0);
6806 // If this is an affine expression then we have this situation:
6807 // Solve {0,+,A} in Range === Ax in Range
6809 // We know that zero is in the range. If A is positive then we know that
6810 // the upper value of the range must be the first possible exit value.
6811 // If A is negative then the lower of the range is the last possible loop
6812 // value. Also note that we already checked for a full range.
6813 APInt One(BitWidth,1);
6814 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6815 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6817 // The exit value should be (End+A)/A.
6818 APInt ExitVal = (End + A).udiv(A);
6819 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6821 // Evaluate at the exit value. If we really did fall out of the valid
6822 // range, then we computed our trip count, otherwise wrap around or other
6823 // things must have happened.
6824 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6825 if (Range.contains(Val->getValue()))
6826 return SE.getCouldNotCompute(); // Something strange happened
6828 // Ensure that the previous value is in the range. This is a sanity check.
6829 assert(Range.contains(
6830 EvaluateConstantChrecAtConstant(this,
6831 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6832 "Linear scev computation is off in a bad way!");
6833 return SE.getConstant(ExitValue);
6834 } else if (isQuadratic()) {
6835 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6836 // quadratic equation to solve it. To do this, we must frame our problem in
6837 // terms of figuring out when zero is crossed, instead of when
6838 // Range.getUpper() is crossed.
6839 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6840 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6841 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6842 // getNoWrapFlags(FlagNW)
6845 // Next, solve the constructed addrec
6846 std::pair<const SCEV *,const SCEV *> Roots =
6847 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6848 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6849 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6851 // Pick the smallest positive root value.
6852 if (ConstantInt *CB =
6853 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6854 R1->getValue(), R2->getValue()))) {
6855 if (CB->getZExtValue() == false)
6856 std::swap(R1, R2); // R1 is the minimum root now.
6858 // Make sure the root is not off by one. The returned iteration should
6859 // not be in the range, but the previous one should be. When solving
6860 // for "X*X < 5", for example, we should not return a root of 2.
6861 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6864 if (Range.contains(R1Val->getValue())) {
6865 // The next iteration must be out of the range...
6866 ConstantInt *NextVal =
6867 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6869 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6870 if (!Range.contains(R1Val->getValue()))
6871 return SE.getConstant(NextVal);
6872 return SE.getCouldNotCompute(); // Something strange happened
6875 // If R1 was not in the range, then it is a good return value. Make
6876 // sure that R1-1 WAS in the range though, just in case.
6877 ConstantInt *NextVal =
6878 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6879 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6880 if (Range.contains(R1Val->getValue()))
6882 return SE.getCouldNotCompute(); // Something strange happened
6887 return SE.getCouldNotCompute();
6893 FindUndefs() : Found(false) {}
6895 bool follow(const SCEV *S) {
6896 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
6897 if (isa<UndefValue>(C->getValue()))
6899 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
6900 if (isa<UndefValue>(C->getValue()))
6904 // Keep looking if we haven't found it yet.
6907 bool isDone() const {
6908 // Stop recursion if we have found an undef.
6914 // Return true when S contains at least an undef value.
6916 containsUndefs(const SCEV *S) {
6918 SCEVTraversal<FindUndefs> ST(F);
6925 // Collect all steps of SCEV expressions.
6926 struct SCEVCollectStrides {
6927 ScalarEvolution &SE;
6928 SmallVectorImpl<const SCEV *> &Strides;
6930 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
6931 : SE(SE), Strides(S) {}
6933 bool follow(const SCEV *S) {
6934 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
6935 Strides.push_back(AR->getStepRecurrence(SE));
6938 bool isDone() const { return false; }
6941 // Collect all SCEVUnknown and SCEVMulExpr expressions.
6942 struct SCEVCollectTerms {
6943 SmallVectorImpl<const SCEV *> &Terms;
6945 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
6948 bool follow(const SCEV *S) {
6949 if (isa<SCEVUnknown>(S) || isa<SCEVConstant>(S) || isa<SCEVMulExpr>(S)) {
6950 if (!containsUndefs(S))
6953 // Stop recursion: once we collected a term, do not walk its operands.
6960 bool isDone() const { return false; }
6964 /// Find parametric terms in this SCEVAddRecExpr.
6965 void SCEVAddRecExpr::collectParametricTerms(
6966 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
6967 SmallVector<const SCEV *, 4> Strides;
6968 SCEVCollectStrides StrideCollector(SE, Strides);
6969 visitAll(this, StrideCollector);
6972 dbgs() << "Strides:\n";
6973 for (const SCEV *S : Strides)
6974 dbgs() << *S << "\n";
6977 for (const SCEV *S : Strides) {
6978 SCEVCollectTerms TermCollector(Terms);
6979 visitAll(S, TermCollector);
6983 dbgs() << "Terms:\n";
6984 for (const SCEV *T : Terms)
6985 dbgs() << *T << "\n";
6989 static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
6990 APInt A = C1->getValue()->getValue();
6991 APInt B = C2->getValue()->getValue();
6992 uint32_t ABW = A.getBitWidth();
6993 uint32_t BBW = B.getBitWidth();
7000 return APIntOps::srem(A, B);
7003 static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
7004 APInt A = C1->getValue()->getValue();
7005 APInt B = C2->getValue()->getValue();
7006 uint32_t ABW = A.getBitWidth();
7007 uint32_t BBW = B.getBitWidth();
7014 return APIntOps::sdiv(A, B);
7018 struct FindSCEVSize {
7020 FindSCEVSize() : Size(0) {}
7022 bool follow(const SCEV *S) {
7024 // Keep looking at all operands of S.
7027 bool isDone() const {
7033 // Returns the size of the SCEV S.
7034 static inline int sizeOfSCEV(const SCEV *S) {
7036 SCEVTraversal<FindSCEVSize> ST(F);
7043 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
7045 // Computes the Quotient and Remainder of the division of Numerator by
7047 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
7048 const SCEV *Denominator, const SCEV **Quotient,
7049 const SCEV **Remainder) {
7050 assert(Numerator && Denominator && "Uninitialized SCEV");
7052 SCEVDivision D(SE, Numerator, Denominator);
7054 // Check for the trivial case here to avoid having to check for it in the
7055 // rest of the code.
7056 if (Numerator == Denominator) {
7058 *Remainder = D.Zero;
7062 if (Numerator->isZero()) {
7064 *Remainder = D.Zero;
7068 // Split the Denominator when it is a product.
7069 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
7071 *Quotient = Numerator;
7072 for (const SCEV *Op : T->operands()) {
7073 divide(SE, *Quotient, Op, &Q, &R);
7076 // Bail out when the Numerator is not divisible by one of the terms of
7080 *Remainder = Numerator;
7084 *Remainder = D.Zero;
7089 *Quotient = D.Quotient;
7090 *Remainder = D.Remainder;
7093 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator, const SCEV *Denominator)
7094 : SE(S), Denominator(Denominator) {
7095 Zero = SE.getConstant(Denominator->getType(), 0);
7096 One = SE.getConstant(Denominator->getType(), 1);
7098 // By default, we don't know how to divide Expr by Denominator.
7099 // Providing the default here simplifies the rest of the code.
7101 Remainder = Numerator;
7104 // Except in the trivial case described above, we do not know how to divide
7105 // Expr by Denominator for the following functions with empty implementation.
7106 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
7107 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
7108 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
7109 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
7110 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
7111 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
7112 void visitUnknown(const SCEVUnknown *Numerator) {}
7113 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
7115 void visitConstant(const SCEVConstant *Numerator) {
7116 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
7117 Quotient = SE.getConstant(sdiv(Numerator, D));
7118 Remainder = SE.getConstant(srem(Numerator, D));
7123 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
7124 const SCEV *StartQ, *StartR, *StepQ, *StepR;
7125 assert(Numerator->isAffine() && "Numerator should be affine");
7126 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
7127 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
7128 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
7129 Numerator->getNoWrapFlags());
7130 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
7131 Numerator->getNoWrapFlags());
7134 void visitAddExpr(const SCEVAddExpr *Numerator) {
7135 SmallVector<const SCEV *, 2> Qs, Rs;
7136 for (const SCEV *Op : Numerator->operands()) {
7138 divide(SE, Op, Denominator, &Q, &R);
7143 if (Qs.size() == 1) {
7149 Quotient = SE.getAddExpr(Qs);
7150 Remainder = SE.getAddExpr(Rs);
7153 void visitMulExpr(const SCEVMulExpr *Numerator) {
7154 SmallVector<const SCEV *, 2> Qs;
7156 bool FoundDenominatorTerm = false;
7157 for (const SCEV *Op : Numerator->operands()) {
7158 if (FoundDenominatorTerm) {
7163 // Check whether Denominator divides one of the product operands.
7165 divide(SE, Op, Denominator, &Q, &R);
7170 FoundDenominatorTerm = true;
7174 if (FoundDenominatorTerm) {
7179 Quotient = SE.getMulExpr(Qs);
7183 if (!isa<SCEVUnknown>(Denominator)) {
7185 Remainder = Numerator;
7189 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
7190 ValueToValueMap RewriteMap;
7191 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
7192 cast<SCEVConstant>(Zero)->getValue();
7193 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
7195 // Quotient is (Numerator - Remainder) divided by Denominator.
7197 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
7198 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
7199 // This SCEV does not seem to simplify: fail the division here.
7201 Remainder = Numerator;
7204 divide(SE, Diff, Denominator, &Q, &R);
7206 "(Numerator - Remainder) should evenly divide Denominator");
7211 ScalarEvolution &SE;
7212 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
7216 // Find the Greatest Common Divisor of A and B.
7218 findGCD(ScalarEvolution &SE, const SCEV *A, const SCEV *B) {
7220 if (const SCEVConstant *CA = dyn_cast<SCEVConstant>(A))
7221 if (const SCEVConstant *CB = dyn_cast<SCEVConstant>(B))
7222 return SE.getConstant(gcd(CA, CB));
7224 const SCEV *One = SE.getConstant(A->getType(), 1);
7225 if (isa<SCEVConstant>(A) && isa<SCEVUnknown>(B))
7227 if (isa<SCEVUnknown>(A) && isa<SCEVConstant>(B))
7231 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(A)) {
7232 SmallVector<const SCEV *, 2> Qs;
7233 for (const SCEV *Op : M->operands())
7234 Qs.push_back(findGCD(SE, Op, B));
7235 return SE.getMulExpr(Qs);
7237 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(B)) {
7238 SmallVector<const SCEV *, 2> Qs;
7239 for (const SCEV *Op : M->operands())
7240 Qs.push_back(findGCD(SE, A, Op));
7241 return SE.getMulExpr(Qs);
7244 SCEVDivision::divide(SE, A, B, &Q, &R);
7248 SCEVDivision::divide(SE, B, A, &Q, &R);
7255 // Find the Greatest Common Divisor of all the SCEVs in Terms.
7257 findGCD(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) {
7258 assert(Terms.size() > 0 && "Terms vector is empty");
7260 const SCEV *GCD = Terms[0];
7261 for (const SCEV *T : Terms)
7262 GCD = findGCD(SE, GCD, T);
7267 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7268 SmallVectorImpl<const SCEV *> &Terms,
7269 SmallVectorImpl<const SCEV *> &Sizes) {
7270 // The GCD of all Terms is the dimension of the innermost dimension.
7271 const SCEV *GCD = findGCD(SE, Terms);
7273 // End of recursion.
7274 if (Terms.size() == 1) {
7275 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(GCD)) {
7276 SmallVector<const SCEV *, 2> Qs;
7277 for (const SCEV *Op : M->operands())
7278 if (!isa<SCEVConstant>(Op))
7281 GCD = SE.getMulExpr(Qs);
7284 Sizes.push_back(GCD);
7288 for (const SCEV *&Term : Terms) {
7289 // Normalize the terms before the next call to findArrayDimensionsRec.
7291 SCEVDivision::divide(SE, Term, GCD, &Q, &R);
7293 // Bail out when GCD does not evenly divide one of the terms.
7300 // Remove all SCEVConstants.
7301 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7302 return isa<SCEVConstant>(E);
7306 if (Terms.size() > 0)
7307 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7310 Sizes.push_back(GCD);
7315 struct FindParameter {
7316 bool FoundParameter;
7317 FindParameter() : FoundParameter(false) {}
7319 bool follow(const SCEV *S) {
7320 if (isa<SCEVUnknown>(S)) {
7321 FoundParameter = true;
7322 // Stop recursion: we found a parameter.
7328 bool isDone() const {
7329 // Stop recursion if we have found a parameter.
7330 return FoundParameter;
7335 // Returns true when S contains at least a SCEVUnknown parameter.
7337 containsParameters(const SCEV *S) {
7339 SCEVTraversal<FindParameter> ST(F);
7342 return F.FoundParameter;
7345 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7347 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7348 for (const SCEV *T : Terms)
7349 if (containsParameters(T))
7354 // Return the number of product terms in S.
7355 static inline int numberOfTerms(const SCEV *S) {
7356 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7357 return Expr->getNumOperands();
7361 /// Second step of delinearization: compute the array dimensions Sizes from the
7362 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7363 void ScalarEvolution::findArrayDimensions(
7364 SmallVectorImpl<const SCEV *> &Terms,
7365 SmallVectorImpl<const SCEV *> &Sizes) const {
7367 if (Terms.size() < 2)
7370 // Early return when Terms do not contain parameters: we do not delinearize
7371 // non parametric SCEVs.
7372 if (!containsParameters(Terms))
7376 dbgs() << "Terms:\n";
7377 for (const SCEV *T : Terms)
7378 dbgs() << *T << "\n";
7381 // Remove duplicates.
7382 std::sort(Terms.begin(), Terms.end());
7383 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7385 // Put larger terms first.
7386 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7387 return numberOfTerms(LHS) > numberOfTerms(RHS);
7391 dbgs() << "Terms after sorting:\n";
7392 for (const SCEV *T : Terms)
7393 dbgs() << *T << "\n";
7396 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7397 bool Res = findArrayDimensionsRec(SE, Terms, Sizes);
7405 dbgs() << "Sizes:\n";
7406 for (const SCEV *S : Sizes)
7407 dbgs() << *S << "\n";
7411 /// Third step of delinearization: compute the access functions for the
7412 /// Subscripts based on the dimensions in Sizes.
7413 const SCEV *SCEVAddRecExpr::computeAccessFunctions(
7414 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7415 SmallVectorImpl<const SCEV *> &Sizes) const {
7417 // Early exit in case this SCEV is not an affine multivariate function.
7418 if (Sizes.empty() || !this->isAffine())
7421 const SCEV *Zero = SE.getConstant(this->getType(), 0);
7422 const SCEV *Res = this, *Remainder = Zero;
7423 int Last = Sizes.size() - 1;
7424 for (int i = Last; i >= 0; i--) {
7426 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7429 dbgs() << "Res: " << *Res << "\n";
7430 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7431 dbgs() << "Res divided by Sizes[i]:\n";
7432 dbgs() << "Quotient: " << *Q << "\n";
7433 dbgs() << "Remainder: " << *R << "\n";
7439 // Do not record the last subscript corresponding to the size of elements
7445 // Record the access function for the current subscript.
7446 Subscripts.push_back(R);
7449 // Also push in last position the remainder of the last division: it will be
7450 // the access function of the innermost dimension.
7451 Subscripts.push_back(Res);
7453 std::reverse(Subscripts.begin(), Subscripts.end());
7456 dbgs() << "Subscripts:\n";
7457 for (const SCEV *S : Subscripts)
7458 dbgs() << *S << "\n";
7463 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7464 /// sizes of an array access. Returns the remainder of the delinearization that
7465 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7466 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7467 /// expressions in the stride and base of a SCEV corresponding to the
7468 /// computation of a GCD (greatest common divisor) of base and stride. When
7469 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7471 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7473 /// void foo(long n, long m, long o, double A[n][m][o]) {
7475 /// for (long i = 0; i < n; i++)
7476 /// for (long j = 0; j < m; j++)
7477 /// for (long k = 0; k < o; k++)
7478 /// A[i][j][k] = 1.0;
7481 /// the delinearization input is the following AddRec SCEV:
7483 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7485 /// From this SCEV, we are able to say that the base offset of the access is %A
7486 /// because it appears as an offset that does not divide any of the strides in
7489 /// CHECK: Base offset: %A
7491 /// and then SCEV->delinearize determines the size of some of the dimensions of
7492 /// the array as these are the multiples by which the strides are happening:
7494 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7496 /// Note that the outermost dimension remains of UnknownSize because there are
7497 /// no strides that would help identifying the size of the last dimension: when
7498 /// the array has been statically allocated, one could compute the size of that
7499 /// dimension by dividing the overall size of the array by the size of the known
7500 /// dimensions: %m * %o * 8.
7502 /// Finally delinearize provides the access functions for the array reference
7503 /// that does correspond to A[i][j][k] of the above C testcase:
7505 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7507 /// The testcases are checking the output of a function pass:
7508 /// DelinearizationPass that walks through all loads and stores of a function
7509 /// asking for the SCEV of the memory access with respect to all enclosing
7510 /// loops, calling SCEV->delinearize on that and printing the results.
7513 SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7514 SmallVectorImpl<const SCEV *> &Subscripts,
7515 SmallVectorImpl<const SCEV *> &Sizes) const {
7516 // First step: collect parametric terms.
7517 SmallVector<const SCEV *, 4> Terms;
7518 collectParametricTerms(SE, Terms);
7523 // Second step: find subscript sizes.
7524 SE.findArrayDimensions(Terms, Sizes);
7529 // Third step: compute the access functions for each subscript.
7530 const SCEV *Remainder = computeAccessFunctions(SE, Subscripts, Sizes);
7532 if (!Remainder || Subscripts.empty())
7536 dbgs() << "succeeded to delinearize " << *this << "\n";
7537 dbgs() << "ArrayDecl[UnknownSize]";
7538 for (const SCEV *S : Sizes)
7539 dbgs() << "[" << *S << "]";
7541 dbgs() << "\nArrayRef";
7542 for (const SCEV *S : Subscripts)
7543 dbgs() << "[" << *S << "]";
7550 //===----------------------------------------------------------------------===//
7551 // SCEVCallbackVH Class Implementation
7552 //===----------------------------------------------------------------------===//
7554 void ScalarEvolution::SCEVCallbackVH::deleted() {
7555 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7556 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7557 SE->ConstantEvolutionLoopExitValue.erase(PN);
7558 SE->ValueExprMap.erase(getValPtr());
7559 // this now dangles!
7562 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7563 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7565 // Forget all the expressions associated with users of the old value,
7566 // so that future queries will recompute the expressions using the new
7568 Value *Old = getValPtr();
7569 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7570 SmallPtrSet<User *, 8> Visited;
7571 while (!Worklist.empty()) {
7572 User *U = Worklist.pop_back_val();
7573 // Deleting the Old value will cause this to dangle. Postpone
7574 // that until everything else is done.
7577 if (!Visited.insert(U))
7579 if (PHINode *PN = dyn_cast<PHINode>(U))
7580 SE->ConstantEvolutionLoopExitValue.erase(PN);
7581 SE->ValueExprMap.erase(U);
7582 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7584 // Delete the Old value.
7585 if (PHINode *PN = dyn_cast<PHINode>(Old))
7586 SE->ConstantEvolutionLoopExitValue.erase(PN);
7587 SE->ValueExprMap.erase(Old);
7588 // this now dangles!
7591 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7592 : CallbackVH(V), SE(se) {}
7594 //===----------------------------------------------------------------------===//
7595 // ScalarEvolution Class Implementation
7596 //===----------------------------------------------------------------------===//
7598 ScalarEvolution::ScalarEvolution()
7599 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7600 BlockDispositions(64), FirstUnknown(nullptr) {
7601 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7604 bool ScalarEvolution::runOnFunction(Function &F) {
7606 LI = &getAnalysis<LoopInfo>();
7607 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7608 DL = DLP ? &DLP->getDataLayout() : nullptr;
7609 TLI = &getAnalysis<TargetLibraryInfo>();
7610 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7614 void ScalarEvolution::releaseMemory() {
7615 // Iterate through all the SCEVUnknown instances and call their
7616 // destructors, so that they release their references to their values.
7617 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7619 FirstUnknown = nullptr;
7621 ValueExprMap.clear();
7623 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7624 // that a loop had multiple computable exits.
7625 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7626 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7631 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7633 BackedgeTakenCounts.clear();
7634 ConstantEvolutionLoopExitValue.clear();
7635 ValuesAtScopes.clear();
7636 LoopDispositions.clear();
7637 BlockDispositions.clear();
7638 UnsignedRanges.clear();
7639 SignedRanges.clear();
7640 UniqueSCEVs.clear();
7641 SCEVAllocator.Reset();
7644 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7645 AU.setPreservesAll();
7646 AU.addRequiredTransitive<LoopInfo>();
7647 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7648 AU.addRequired<TargetLibraryInfo>();
7651 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7652 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7655 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7657 // Print all inner loops first
7658 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7659 PrintLoopInfo(OS, SE, *I);
7662 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7665 SmallVector<BasicBlock *, 8> ExitBlocks;
7666 L->getExitBlocks(ExitBlocks);
7667 if (ExitBlocks.size() != 1)
7668 OS << "<multiple exits> ";
7670 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7671 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7673 OS << "Unpredictable backedge-taken count. ";
7678 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7681 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7682 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7684 OS << "Unpredictable max backedge-taken count. ";
7690 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7691 // ScalarEvolution's implementation of the print method is to print
7692 // out SCEV values of all instructions that are interesting. Doing
7693 // this potentially causes it to create new SCEV objects though,
7694 // which technically conflicts with the const qualifier. This isn't
7695 // observable from outside the class though, so casting away the
7696 // const isn't dangerous.
7697 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7699 OS << "Classifying expressions for: ";
7700 F->printAsOperand(OS, /*PrintType=*/false);
7702 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7703 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7706 const SCEV *SV = SE.getSCEV(&*I);
7709 const Loop *L = LI->getLoopFor((*I).getParent());
7711 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
7718 OS << "\t\t" "Exits: ";
7719 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
7720 if (!SE.isLoopInvariant(ExitValue, L)) {
7721 OS << "<<Unknown>>";
7730 OS << "Determining loop execution counts for: ";
7731 F->printAsOperand(OS, /*PrintType=*/false);
7733 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
7734 PrintLoopInfo(OS, &SE, *I);
7737 ScalarEvolution::LoopDisposition
7738 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
7739 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
7740 for (unsigned u = 0; u < Values.size(); u++) {
7741 if (Values[u].first == L)
7742 return Values[u].second;
7744 Values.push_back(std::make_pair(L, LoopVariant));
7745 LoopDisposition D = computeLoopDisposition(S, L);
7746 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
7747 for (unsigned u = Values2.size(); u > 0; u--) {
7748 if (Values2[u - 1].first == L) {
7749 Values2[u - 1].second = D;
7756 ScalarEvolution::LoopDisposition
7757 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
7758 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7760 return LoopInvariant;
7764 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
7765 case scAddRecExpr: {
7766 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7768 // If L is the addrec's loop, it's computable.
7769 if (AR->getLoop() == L)
7770 return LoopComputable;
7772 // Add recurrences are never invariant in the function-body (null loop).
7776 // This recurrence is variant w.r.t. L if L contains AR's loop.
7777 if (L->contains(AR->getLoop()))
7780 // This recurrence is invariant w.r.t. L if AR's loop contains L.
7781 if (AR->getLoop()->contains(L))
7782 return LoopInvariant;
7784 // This recurrence is variant w.r.t. L if any of its operands
7786 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
7788 if (!isLoopInvariant(*I, L))
7791 // Otherwise it's loop-invariant.
7792 return LoopInvariant;
7798 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7799 bool HasVarying = false;
7800 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7802 LoopDisposition D = getLoopDisposition(*I, L);
7803 if (D == LoopVariant)
7805 if (D == LoopComputable)
7808 return HasVarying ? LoopComputable : LoopInvariant;
7811 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7812 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
7813 if (LD == LoopVariant)
7815 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
7816 if (RD == LoopVariant)
7818 return (LD == LoopInvariant && RD == LoopInvariant) ?
7819 LoopInvariant : LoopComputable;
7822 // All non-instruction values are loop invariant. All instructions are loop
7823 // invariant if they are not contained in the specified loop.
7824 // Instructions are never considered invariant in the function body
7825 // (null loop) because they are defined within the "loop".
7826 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
7827 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
7828 return LoopInvariant;
7829 case scCouldNotCompute:
7830 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7832 llvm_unreachable("Unknown SCEV kind!");
7835 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
7836 return getLoopDisposition(S, L) == LoopInvariant;
7839 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
7840 return getLoopDisposition(S, L) == LoopComputable;
7843 ScalarEvolution::BlockDisposition
7844 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7845 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
7846 for (unsigned u = 0; u < Values.size(); u++) {
7847 if (Values[u].first == BB)
7848 return Values[u].second;
7850 Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
7851 BlockDisposition D = computeBlockDisposition(S, BB);
7852 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
7853 for (unsigned u = Values2.size(); u > 0; u--) {
7854 if (Values2[u - 1].first == BB) {
7855 Values2[u - 1].second = D;
7862 ScalarEvolution::BlockDisposition
7863 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7864 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7866 return ProperlyDominatesBlock;
7870 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
7871 case scAddRecExpr: {
7872 // This uses a "dominates" query instead of "properly dominates" query
7873 // to test for proper dominance too, because the instruction which
7874 // produces the addrec's value is a PHI, and a PHI effectively properly
7875 // dominates its entire containing block.
7876 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7877 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
7878 return DoesNotDominateBlock;
7880 // FALL THROUGH into SCEVNAryExpr handling.
7885 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7887 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7889 BlockDisposition D = getBlockDisposition(*I, BB);
7890 if (D == DoesNotDominateBlock)
7891 return DoesNotDominateBlock;
7892 if (D == DominatesBlock)
7895 return Proper ? ProperlyDominatesBlock : DominatesBlock;
7898 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7899 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
7900 BlockDisposition LD = getBlockDisposition(LHS, BB);
7901 if (LD == DoesNotDominateBlock)
7902 return DoesNotDominateBlock;
7903 BlockDisposition RD = getBlockDisposition(RHS, BB);
7904 if (RD == DoesNotDominateBlock)
7905 return DoesNotDominateBlock;
7906 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
7907 ProperlyDominatesBlock : DominatesBlock;
7910 if (Instruction *I =
7911 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
7912 if (I->getParent() == BB)
7913 return DominatesBlock;
7914 if (DT->properlyDominates(I->getParent(), BB))
7915 return ProperlyDominatesBlock;
7916 return DoesNotDominateBlock;
7918 return ProperlyDominatesBlock;
7919 case scCouldNotCompute:
7920 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7922 llvm_unreachable("Unknown SCEV kind!");
7925 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
7926 return getBlockDisposition(S, BB) >= DominatesBlock;
7929 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
7930 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
7934 // Search for a SCEV expression node within an expression tree.
7935 // Implements SCEVTraversal::Visitor.
7940 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
7942 bool follow(const SCEV *S) {
7943 IsFound |= (S == Node);
7946 bool isDone() const { return IsFound; }
7950 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
7951 SCEVSearch Search(Op);
7952 visitAll(S, Search);
7953 return Search.IsFound;
7956 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
7957 ValuesAtScopes.erase(S);
7958 LoopDispositions.erase(S);
7959 BlockDispositions.erase(S);
7960 UnsignedRanges.erase(S);
7961 SignedRanges.erase(S);
7963 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7964 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
7965 BackedgeTakenInfo &BEInfo = I->second;
7966 if (BEInfo.hasOperand(S, this)) {
7968 BackedgeTakenCounts.erase(I++);
7975 typedef DenseMap<const Loop *, std::string> VerifyMap;
7977 /// replaceSubString - Replaces all occurrences of From in Str with To.
7978 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
7980 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
7981 Str.replace(Pos, From.size(), To.data(), To.size());
7986 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
7988 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
7989 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
7990 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
7992 std::string &S = Map[L];
7994 raw_string_ostream OS(S);
7995 SE.getBackedgeTakenCount(L)->print(OS);
7997 // false and 0 are semantically equivalent. This can happen in dead loops.
7998 replaceSubString(OS.str(), "false", "0");
7999 // Remove wrap flags, their use in SCEV is highly fragile.
8000 // FIXME: Remove this when SCEV gets smarter about them.
8001 replaceSubString(OS.str(), "<nw>", "");
8002 replaceSubString(OS.str(), "<nsw>", "");
8003 replaceSubString(OS.str(), "<nuw>", "");
8008 void ScalarEvolution::verifyAnalysis() const {
8012 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8014 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8015 // FIXME: It would be much better to store actual values instead of strings,
8016 // but SCEV pointers will change if we drop the caches.
8017 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8018 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8019 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8021 // Gather stringified backedge taken counts for all loops without using
8024 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8025 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8027 // Now compare whether they're the same with and without caches. This allows
8028 // verifying that no pass changed the cache.
8029 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8030 "New loops suddenly appeared!");
8032 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8033 OldE = BackedgeDumpsOld.end(),
8034 NewI = BackedgeDumpsNew.begin();
8035 OldI != OldE; ++OldI, ++NewI) {
8036 assert(OldI->first == NewI->first && "Loop order changed!");
8038 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8040 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8041 // means that a pass is buggy or SCEV has to learn a new pattern but is
8042 // usually not harmful.
8043 if (OldI->second != NewI->second &&
8044 OldI->second.find("undef") == std::string::npos &&
8045 NewI->second.find("undef") == std::string::npos &&
8046 OldI->second != "***COULDNOTCOMPUTE***" &&
8047 NewI->second != "***COULDNOTCOMPUTE***") {
8048 dbgs() << "SCEVValidator: SCEV for loop '"
8049 << OldI->first->getHeader()->getName()
8050 << "' changed from '" << OldI->second
8051 << "' to '" << NewI->second << "'!\n";
8056 // TODO: Verify more things.