1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/STLExtras.h"
63 #include "llvm/ADT/SmallPtrSet.h"
64 #include "llvm/ADT/Statistic.h"
65 #include "llvm/Analysis/ConstantFolding.h"
66 #include "llvm/Analysis/InstructionSimplify.h"
67 #include "llvm/Analysis/LoopInfo.h"
68 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
69 #include "llvm/Analysis/ValueTracking.h"
70 #include "llvm/IR/ConstantRange.h"
71 #include "llvm/IR/Constants.h"
72 #include "llvm/IR/DataLayout.h"
73 #include "llvm/IR/DerivedTypes.h"
74 #include "llvm/IR/Dominators.h"
75 #include "llvm/IR/GetElementPtrTypeIterator.h"
76 #include "llvm/IR/GlobalAlias.h"
77 #include "llvm/IR/GlobalVariable.h"
78 #include "llvm/IR/InstIterator.h"
79 #include "llvm/IR/Instructions.h"
80 #include "llvm/IR/LLVMContext.h"
81 #include "llvm/IR/Operator.h"
82 #include "llvm/Support/CommandLine.h"
83 #include "llvm/Support/Debug.h"
84 #include "llvm/Support/ErrorHandling.h"
85 #include "llvm/Support/MathExtras.h"
86 #include "llvm/Support/raw_ostream.h"
87 #include "llvm/Target/TargetLibraryInfo.h"
91 #define DEBUG_TYPE "scalar-evolution"
93 STATISTIC(NumArrayLenItCounts,
94 "Number of trip counts computed with array length");
95 STATISTIC(NumTripCountsComputed,
96 "Number of loops with predictable loop counts");
97 STATISTIC(NumTripCountsNotComputed,
98 "Number of loops without predictable loop counts");
99 STATISTIC(NumBruteForceTripCountsComputed,
100 "Number of loops with trip counts computed by force");
102 static cl::opt<unsigned>
103 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
104 cl::desc("Maximum number of iterations SCEV will "
105 "symbolically execute a constant "
109 // FIXME: Enable this with XDEBUG when the test suite is clean.
111 VerifySCEV("verify-scev",
112 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
114 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
115 "Scalar Evolution Analysis", false, true)
116 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
117 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
118 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
119 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
120 "Scalar Evolution Analysis", false, true)
121 char ScalarEvolution::ID = 0;
123 //===----------------------------------------------------------------------===//
124 // SCEV class definitions
125 //===----------------------------------------------------------------------===//
127 //===----------------------------------------------------------------------===//
128 // Implementation of the SCEV class.
131 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
132 void SCEV::dump() const {
138 void SCEV::print(raw_ostream &OS) const {
139 switch (static_cast<SCEVTypes>(getSCEVType())) {
141 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
144 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
145 const SCEV *Op = Trunc->getOperand();
146 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
147 << *Trunc->getType() << ")";
151 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
152 const SCEV *Op = ZExt->getOperand();
153 OS << "(zext " << *Op->getType() << " " << *Op << " to "
154 << *ZExt->getType() << ")";
158 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
159 const SCEV *Op = SExt->getOperand();
160 OS << "(sext " << *Op->getType() << " " << *Op << " to "
161 << *SExt->getType() << ")";
165 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
166 OS << "{" << *AR->getOperand(0);
167 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
168 OS << ",+," << *AR->getOperand(i);
170 if (AR->getNoWrapFlags(FlagNUW))
172 if (AR->getNoWrapFlags(FlagNSW))
174 if (AR->getNoWrapFlags(FlagNW) &&
175 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
177 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
185 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
186 const char *OpStr = nullptr;
187 switch (NAry->getSCEVType()) {
188 case scAddExpr: OpStr = " + "; break;
189 case scMulExpr: OpStr = " * "; break;
190 case scUMaxExpr: OpStr = " umax "; break;
191 case scSMaxExpr: OpStr = " smax "; break;
194 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
197 if (std::next(I) != E)
201 switch (NAry->getSCEVType()) {
204 if (NAry->getNoWrapFlags(FlagNUW))
206 if (NAry->getNoWrapFlags(FlagNSW))
212 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
213 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
217 const SCEVUnknown *U = cast<SCEVUnknown>(this);
219 if (U->isSizeOf(AllocTy)) {
220 OS << "sizeof(" << *AllocTy << ")";
223 if (U->isAlignOf(AllocTy)) {
224 OS << "alignof(" << *AllocTy << ")";
230 if (U->isOffsetOf(CTy, FieldNo)) {
231 OS << "offsetof(" << *CTy << ", ";
232 FieldNo->printAsOperand(OS, false);
237 // Otherwise just print it normally.
238 U->getValue()->printAsOperand(OS, false);
241 case scCouldNotCompute:
242 OS << "***COULDNOTCOMPUTE***";
245 llvm_unreachable("Unknown SCEV kind!");
248 Type *SCEV::getType() const {
249 switch (static_cast<SCEVTypes>(getSCEVType())) {
251 return cast<SCEVConstant>(this)->getType();
255 return cast<SCEVCastExpr>(this)->getType();
260 return cast<SCEVNAryExpr>(this)->getType();
262 return cast<SCEVAddExpr>(this)->getType();
264 return cast<SCEVUDivExpr>(this)->getType();
266 return cast<SCEVUnknown>(this)->getType();
267 case scCouldNotCompute:
268 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
270 llvm_unreachable("Unknown SCEV kind!");
273 bool SCEV::isZero() const {
274 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
275 return SC->getValue()->isZero();
279 bool SCEV::isOne() const {
280 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
281 return SC->getValue()->isOne();
285 bool SCEV::isAllOnesValue() const {
286 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
287 return SC->getValue()->isAllOnesValue();
291 /// isNonConstantNegative - Return true if the specified scev is negated, but
293 bool SCEV::isNonConstantNegative() const {
294 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
295 if (!Mul) return false;
297 // If there is a constant factor, it will be first.
298 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
299 if (!SC) return false;
301 // Return true if the value is negative, this matches things like (-42 * V).
302 return SC->getValue()->getValue().isNegative();
305 SCEVCouldNotCompute::SCEVCouldNotCompute() :
306 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
308 bool SCEVCouldNotCompute::classof(const SCEV *S) {
309 return S->getSCEVType() == scCouldNotCompute;
312 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
314 ID.AddInteger(scConstant);
317 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
318 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
319 UniqueSCEVs.InsertNode(S, IP);
323 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
324 return getConstant(ConstantInt::get(getContext(), Val));
328 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
329 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
330 return getConstant(ConstantInt::get(ITy, V, isSigned));
333 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
334 unsigned SCEVTy, const SCEV *op, Type *ty)
335 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
337 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
338 const SCEV *op, Type *ty)
339 : SCEVCastExpr(ID, scTruncate, op, ty) {
340 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
341 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
342 "Cannot truncate non-integer value!");
345 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
346 const SCEV *op, Type *ty)
347 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
348 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
349 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
350 "Cannot zero extend non-integer value!");
353 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
354 const SCEV *op, Type *ty)
355 : SCEVCastExpr(ID, scSignExtend, op, ty) {
356 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
357 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
358 "Cannot sign extend non-integer value!");
361 void SCEVUnknown::deleted() {
362 // Clear this SCEVUnknown from various maps.
363 SE->forgetMemoizedResults(this);
365 // Remove this SCEVUnknown from the uniquing map.
366 SE->UniqueSCEVs.RemoveNode(this);
368 // Release the value.
372 void SCEVUnknown::allUsesReplacedWith(Value *New) {
373 // Clear this SCEVUnknown from various maps.
374 SE->forgetMemoizedResults(this);
376 // Remove this SCEVUnknown from the uniquing map.
377 SE->UniqueSCEVs.RemoveNode(this);
379 // Update this SCEVUnknown to point to the new value. This is needed
380 // because there may still be outstanding SCEVs which still point to
385 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
386 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
387 if (VCE->getOpcode() == Instruction::PtrToInt)
388 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
389 if (CE->getOpcode() == Instruction::GetElementPtr &&
390 CE->getOperand(0)->isNullValue() &&
391 CE->getNumOperands() == 2)
392 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
394 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
402 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
403 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
404 if (VCE->getOpcode() == Instruction::PtrToInt)
405 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
406 if (CE->getOpcode() == Instruction::GetElementPtr &&
407 CE->getOperand(0)->isNullValue()) {
409 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
410 if (StructType *STy = dyn_cast<StructType>(Ty))
411 if (!STy->isPacked() &&
412 CE->getNumOperands() == 3 &&
413 CE->getOperand(1)->isNullValue()) {
414 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
416 STy->getNumElements() == 2 &&
417 STy->getElementType(0)->isIntegerTy(1)) {
418 AllocTy = STy->getElementType(1);
427 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
428 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
429 if (VCE->getOpcode() == Instruction::PtrToInt)
430 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
431 if (CE->getOpcode() == Instruction::GetElementPtr &&
432 CE->getNumOperands() == 3 &&
433 CE->getOperand(0)->isNullValue() &&
434 CE->getOperand(1)->isNullValue()) {
436 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
437 // Ignore vector types here so that ScalarEvolutionExpander doesn't
438 // emit getelementptrs that index into vectors.
439 if (Ty->isStructTy() || Ty->isArrayTy()) {
441 FieldNo = CE->getOperand(2);
449 //===----------------------------------------------------------------------===//
451 //===----------------------------------------------------------------------===//
454 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
455 /// than the complexity of the RHS. This comparator is used to canonicalize
457 class SCEVComplexityCompare {
458 const LoopInfo *const LI;
460 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
462 // Return true or false if LHS is less than, or at least RHS, respectively.
463 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
464 return compare(LHS, RHS) < 0;
467 // Return negative, zero, or positive, if LHS is less than, equal to, or
468 // greater than RHS, respectively. A three-way result allows recursive
469 // comparisons to be more efficient.
470 int compare(const SCEV *LHS, const SCEV *RHS) const {
471 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
475 // Primarily, sort the SCEVs by their getSCEVType().
476 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
478 return (int)LType - (int)RType;
480 // Aside from the getSCEVType() ordering, the particular ordering
481 // isn't very important except that it's beneficial to be consistent,
482 // so that (a + b) and (b + a) don't end up as different expressions.
483 switch (static_cast<SCEVTypes>(LType)) {
485 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
486 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
488 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
489 // not as complete as it could be.
490 const Value *LV = LU->getValue(), *RV = RU->getValue();
492 // Order pointer values after integer values. This helps SCEVExpander
494 bool LIsPointer = LV->getType()->isPointerTy(),
495 RIsPointer = RV->getType()->isPointerTy();
496 if (LIsPointer != RIsPointer)
497 return (int)LIsPointer - (int)RIsPointer;
499 // Compare getValueID values.
500 unsigned LID = LV->getValueID(),
501 RID = RV->getValueID();
503 return (int)LID - (int)RID;
505 // Sort arguments by their position.
506 if (const Argument *LA = dyn_cast<Argument>(LV)) {
507 const Argument *RA = cast<Argument>(RV);
508 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
509 return (int)LArgNo - (int)RArgNo;
512 // For instructions, compare their loop depth, and their operand
513 // count. This is pretty loose.
514 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
515 const Instruction *RInst = cast<Instruction>(RV);
517 // Compare loop depths.
518 const BasicBlock *LParent = LInst->getParent(),
519 *RParent = RInst->getParent();
520 if (LParent != RParent) {
521 unsigned LDepth = LI->getLoopDepth(LParent),
522 RDepth = LI->getLoopDepth(RParent);
523 if (LDepth != RDepth)
524 return (int)LDepth - (int)RDepth;
527 // Compare the number of operands.
528 unsigned LNumOps = LInst->getNumOperands(),
529 RNumOps = RInst->getNumOperands();
530 return (int)LNumOps - (int)RNumOps;
537 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
538 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
540 // Compare constant values.
541 const APInt &LA = LC->getValue()->getValue();
542 const APInt &RA = RC->getValue()->getValue();
543 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
544 if (LBitWidth != RBitWidth)
545 return (int)LBitWidth - (int)RBitWidth;
546 return LA.ult(RA) ? -1 : 1;
550 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
551 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
553 // Compare addrec loop depths.
554 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
555 if (LLoop != RLoop) {
556 unsigned LDepth = LLoop->getLoopDepth(),
557 RDepth = RLoop->getLoopDepth();
558 if (LDepth != RDepth)
559 return (int)LDepth - (int)RDepth;
562 // Addrec complexity grows with operand count.
563 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
564 if (LNumOps != RNumOps)
565 return (int)LNumOps - (int)RNumOps;
567 // Lexicographically compare.
568 for (unsigned i = 0; i != LNumOps; ++i) {
569 long X = compare(LA->getOperand(i), RA->getOperand(i));
581 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
582 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
584 // Lexicographically compare n-ary expressions.
585 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
586 if (LNumOps != RNumOps)
587 return (int)LNumOps - (int)RNumOps;
589 for (unsigned i = 0; i != LNumOps; ++i) {
592 long X = compare(LC->getOperand(i), RC->getOperand(i));
596 return (int)LNumOps - (int)RNumOps;
600 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
601 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
603 // Lexicographically compare udiv expressions.
604 long X = compare(LC->getLHS(), RC->getLHS());
607 return compare(LC->getRHS(), RC->getRHS());
613 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
614 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
616 // Compare cast expressions by operand.
617 return compare(LC->getOperand(), RC->getOperand());
620 case scCouldNotCompute:
621 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
623 llvm_unreachable("Unknown SCEV kind!");
628 /// GroupByComplexity - Given a list of SCEV objects, order them by their
629 /// complexity, and group objects of the same complexity together by value.
630 /// When this routine is finished, we know that any duplicates in the vector are
631 /// consecutive and that complexity is monotonically increasing.
633 /// Note that we go take special precautions to ensure that we get deterministic
634 /// results from this routine. In other words, we don't want the results of
635 /// this to depend on where the addresses of various SCEV objects happened to
638 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
640 if (Ops.size() < 2) return; // Noop
641 if (Ops.size() == 2) {
642 // This is the common case, which also happens to be trivially simple.
644 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
645 if (SCEVComplexityCompare(LI)(RHS, LHS))
650 // Do the rough sort by complexity.
651 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
653 // Now that we are sorted by complexity, group elements of the same
654 // complexity. Note that this is, at worst, N^2, but the vector is likely to
655 // be extremely short in practice. Note that we take this approach because we
656 // do not want to depend on the addresses of the objects we are grouping.
657 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
658 const SCEV *S = Ops[i];
659 unsigned Complexity = S->getSCEVType();
661 // If there are any objects of the same complexity and same value as this
663 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
664 if (Ops[j] == S) { // Found a duplicate.
665 // Move it to immediately after i'th element.
666 std::swap(Ops[i+1], Ops[j]);
667 ++i; // no need to rescan it.
668 if (i == e-2) return; // Done!
676 //===----------------------------------------------------------------------===//
677 // Simple SCEV method implementations
678 //===----------------------------------------------------------------------===//
680 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
682 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
685 // Handle the simplest case efficiently.
687 return SE.getTruncateOrZeroExtend(It, ResultTy);
689 // We are using the following formula for BC(It, K):
691 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
693 // Suppose, W is the bitwidth of the return value. We must be prepared for
694 // overflow. Hence, we must assure that the result of our computation is
695 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
696 // safe in modular arithmetic.
698 // However, this code doesn't use exactly that formula; the formula it uses
699 // is something like the following, where T is the number of factors of 2 in
700 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
703 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
705 // This formula is trivially equivalent to the previous formula. However,
706 // this formula can be implemented much more efficiently. The trick is that
707 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
708 // arithmetic. To do exact division in modular arithmetic, all we have
709 // to do is multiply by the inverse. Therefore, this step can be done at
712 // The next issue is how to safely do the division by 2^T. The way this
713 // is done is by doing the multiplication step at a width of at least W + T
714 // bits. This way, the bottom W+T bits of the product are accurate. Then,
715 // when we perform the division by 2^T (which is equivalent to a right shift
716 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
717 // truncated out after the division by 2^T.
719 // In comparison to just directly using the first formula, this technique
720 // is much more efficient; using the first formula requires W * K bits,
721 // but this formula less than W + K bits. Also, the first formula requires
722 // a division step, whereas this formula only requires multiplies and shifts.
724 // It doesn't matter whether the subtraction step is done in the calculation
725 // width or the input iteration count's width; if the subtraction overflows,
726 // the result must be zero anyway. We prefer here to do it in the width of
727 // the induction variable because it helps a lot for certain cases; CodeGen
728 // isn't smart enough to ignore the overflow, which leads to much less
729 // efficient code if the width of the subtraction is wider than the native
732 // (It's possible to not widen at all by pulling out factors of 2 before
733 // the multiplication; for example, K=2 can be calculated as
734 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
735 // extra arithmetic, so it's not an obvious win, and it gets
736 // much more complicated for K > 3.)
738 // Protection from insane SCEVs; this bound is conservative,
739 // but it probably doesn't matter.
741 return SE.getCouldNotCompute();
743 unsigned W = SE.getTypeSizeInBits(ResultTy);
745 // Calculate K! / 2^T and T; we divide out the factors of two before
746 // multiplying for calculating K! / 2^T to avoid overflow.
747 // Other overflow doesn't matter because we only care about the bottom
748 // W bits of the result.
749 APInt OddFactorial(W, 1);
751 for (unsigned i = 3; i <= K; ++i) {
753 unsigned TwoFactors = Mult.countTrailingZeros();
755 Mult = Mult.lshr(TwoFactors);
756 OddFactorial *= Mult;
759 // We need at least W + T bits for the multiplication step
760 unsigned CalculationBits = W + T;
762 // Calculate 2^T, at width T+W.
763 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
765 // Calculate the multiplicative inverse of K! / 2^T;
766 // this multiplication factor will perform the exact division by
768 APInt Mod = APInt::getSignedMinValue(W+1);
769 APInt MultiplyFactor = OddFactorial.zext(W+1);
770 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
771 MultiplyFactor = MultiplyFactor.trunc(W);
773 // Calculate the product, at width T+W
774 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
776 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
777 for (unsigned i = 1; i != K; ++i) {
778 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
779 Dividend = SE.getMulExpr(Dividend,
780 SE.getTruncateOrZeroExtend(S, CalculationTy));
784 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
786 // Truncate the result, and divide by K! / 2^T.
788 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
789 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
792 /// evaluateAtIteration - Return the value of this chain of recurrences at
793 /// the specified iteration number. We can evaluate this recurrence by
794 /// multiplying each element in the chain by the binomial coefficient
795 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
797 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
799 /// where BC(It, k) stands for binomial coefficient.
801 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
802 ScalarEvolution &SE) const {
803 const SCEV *Result = getStart();
804 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
805 // The computation is correct in the face of overflow provided that the
806 // multiplication is performed _after_ the evaluation of the binomial
808 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
809 if (isa<SCEVCouldNotCompute>(Coeff))
812 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
817 //===----------------------------------------------------------------------===//
818 // SCEV Expression folder implementations
819 //===----------------------------------------------------------------------===//
821 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
823 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
824 "This is not a truncating conversion!");
825 assert(isSCEVable(Ty) &&
826 "This is not a conversion to a SCEVable type!");
827 Ty = getEffectiveSCEVType(Ty);
830 ID.AddInteger(scTruncate);
834 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
836 // Fold if the operand is constant.
837 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
839 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
841 // trunc(trunc(x)) --> trunc(x)
842 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
843 return getTruncateExpr(ST->getOperand(), Ty);
845 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
846 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
847 return getTruncateOrSignExtend(SS->getOperand(), Ty);
849 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
850 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
851 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
853 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
854 // eliminate all the truncates.
855 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
856 SmallVector<const SCEV *, 4> Operands;
857 bool hasTrunc = false;
858 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
859 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
860 hasTrunc = isa<SCEVTruncateExpr>(S);
861 Operands.push_back(S);
864 return getAddExpr(Operands);
865 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
868 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
869 // eliminate all the truncates.
870 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
871 SmallVector<const SCEV *, 4> Operands;
872 bool hasTrunc = false;
873 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
874 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
875 hasTrunc = isa<SCEVTruncateExpr>(S);
876 Operands.push_back(S);
879 return getMulExpr(Operands);
880 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
883 // If the input value is a chrec scev, truncate the chrec's operands.
884 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
885 SmallVector<const SCEV *, 4> Operands;
886 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
887 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
888 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
891 // The cast wasn't folded; create an explicit cast node. We can reuse
892 // the existing insert position since if we get here, we won't have
893 // made any changes which would invalidate it.
894 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
896 UniqueSCEVs.InsertNode(S, IP);
900 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
902 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
903 "This is not an extending conversion!");
904 assert(isSCEVable(Ty) &&
905 "This is not a conversion to a SCEVable type!");
906 Ty = getEffectiveSCEVType(Ty);
908 // Fold if the operand is constant.
909 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
911 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
913 // zext(zext(x)) --> zext(x)
914 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
915 return getZeroExtendExpr(SZ->getOperand(), Ty);
917 // Before doing any expensive analysis, check to see if we've already
918 // computed a SCEV for this Op and Ty.
920 ID.AddInteger(scZeroExtend);
924 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
926 // zext(trunc(x)) --> zext(x) or x or trunc(x)
927 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
928 // It's possible the bits taken off by the truncate were all zero bits. If
929 // so, we should be able to simplify this further.
930 const SCEV *X = ST->getOperand();
931 ConstantRange CR = getUnsignedRange(X);
932 unsigned TruncBits = getTypeSizeInBits(ST->getType());
933 unsigned NewBits = getTypeSizeInBits(Ty);
934 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
935 CR.zextOrTrunc(NewBits)))
936 return getTruncateOrZeroExtend(X, Ty);
939 // If the input value is a chrec scev, and we can prove that the value
940 // did not overflow the old, smaller, value, we can zero extend all of the
941 // operands (often constants). This allows analysis of something like
942 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
943 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
944 if (AR->isAffine()) {
945 const SCEV *Start = AR->getStart();
946 const SCEV *Step = AR->getStepRecurrence(*this);
947 unsigned BitWidth = getTypeSizeInBits(AR->getType());
948 const Loop *L = AR->getLoop();
950 // If we have special knowledge that this addrec won't overflow,
951 // we don't need to do any further analysis.
952 if (AR->getNoWrapFlags(SCEV::FlagNUW))
953 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
954 getZeroExtendExpr(Step, Ty),
955 L, AR->getNoWrapFlags());
957 // Check whether the backedge-taken count is SCEVCouldNotCompute.
958 // Note that this serves two purposes: It filters out loops that are
959 // simply not analyzable, and it covers the case where this code is
960 // being called from within backedge-taken count analysis, such that
961 // attempting to ask for the backedge-taken count would likely result
962 // in infinite recursion. In the later case, the analysis code will
963 // cope with a conservative value, and it will take care to purge
964 // that value once it has finished.
965 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
966 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
967 // Manually compute the final value for AR, checking for
970 // Check whether the backedge-taken count can be losslessly casted to
971 // the addrec's type. The count is always unsigned.
972 const SCEV *CastedMaxBECount =
973 getTruncateOrZeroExtend(MaxBECount, Start->getType());
974 const SCEV *RecastedMaxBECount =
975 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
976 if (MaxBECount == RecastedMaxBECount) {
977 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
978 // Check whether Start+Step*MaxBECount has no unsigned overflow.
979 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
980 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
981 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
982 const SCEV *WideMaxBECount =
983 getZeroExtendExpr(CastedMaxBECount, WideTy);
984 const SCEV *OperandExtendedAdd =
985 getAddExpr(WideStart,
986 getMulExpr(WideMaxBECount,
987 getZeroExtendExpr(Step, WideTy)));
988 if (ZAdd == OperandExtendedAdd) {
989 // Cache knowledge of AR NUW, which is propagated to this AddRec.
990 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
991 // Return the expression with the addrec on the outside.
992 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
993 getZeroExtendExpr(Step, Ty),
994 L, AR->getNoWrapFlags());
996 // Similar to above, only this time treat the step value as signed.
997 // This covers loops that count down.
999 getAddExpr(WideStart,
1000 getMulExpr(WideMaxBECount,
1001 getSignExtendExpr(Step, WideTy)));
1002 if (ZAdd == OperandExtendedAdd) {
1003 // Cache knowledge of AR NW, which is propagated to this AddRec.
1004 // Negative step causes unsigned wrap, but it still can't self-wrap.
1005 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1006 // Return the expression with the addrec on the outside.
1007 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1008 getSignExtendExpr(Step, Ty),
1009 L, AR->getNoWrapFlags());
1013 // If the backedge is guarded by a comparison with the pre-inc value
1014 // the addrec is safe. Also, if the entry is guarded by a comparison
1015 // with the start value and the backedge is guarded by a comparison
1016 // with the post-inc value, the addrec is safe.
1017 if (isKnownPositive(Step)) {
1018 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1019 getUnsignedRange(Step).getUnsignedMax());
1020 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1021 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1022 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1023 AR->getPostIncExpr(*this), N))) {
1024 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1025 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1026 // Return the expression with the addrec on the outside.
1027 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1028 getZeroExtendExpr(Step, Ty),
1029 L, AR->getNoWrapFlags());
1031 } else if (isKnownNegative(Step)) {
1032 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1033 getSignedRange(Step).getSignedMin());
1034 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1035 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1036 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1037 AR->getPostIncExpr(*this), N))) {
1038 // Cache knowledge of AR NW, which is propagated to this AddRec.
1039 // Negative step causes unsigned wrap, but it still can't self-wrap.
1040 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1041 // Return the expression with the addrec on the outside.
1042 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1043 getSignExtendExpr(Step, Ty),
1044 L, AR->getNoWrapFlags());
1050 // The cast wasn't folded; create an explicit cast node.
1051 // Recompute the insert position, as it may have been invalidated.
1052 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1053 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1055 UniqueSCEVs.InsertNode(S, IP);
1059 // Get the limit of a recurrence such that incrementing by Step cannot cause
1060 // signed overflow as long as the value of the recurrence within the loop does
1061 // not exceed this limit before incrementing.
1062 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1063 ICmpInst::Predicate *Pred,
1064 ScalarEvolution *SE) {
1065 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1066 if (SE->isKnownPositive(Step)) {
1067 *Pred = ICmpInst::ICMP_SLT;
1068 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1069 SE->getSignedRange(Step).getSignedMax());
1071 if (SE->isKnownNegative(Step)) {
1072 *Pred = ICmpInst::ICMP_SGT;
1073 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1074 SE->getSignedRange(Step).getSignedMin());
1079 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1080 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1081 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1082 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1083 // result, the expression "Step + sext(PreIncAR)" is congruent with
1084 // "sext(PostIncAR)"
1085 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1087 ScalarEvolution *SE) {
1088 const Loop *L = AR->getLoop();
1089 const SCEV *Start = AR->getStart();
1090 const SCEV *Step = AR->getStepRecurrence(*SE);
1092 // Check for a simple looking step prior to loop entry.
1093 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1097 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1098 // subtraction is expensive. For this purpose, perform a quick and dirty
1099 // difference, by checking for Step in the operand list.
1100 SmallVector<const SCEV *, 4> DiffOps;
1101 for (const SCEV *Op : SA->operands())
1103 DiffOps.push_back(Op);
1105 if (DiffOps.size() == SA->getNumOperands())
1108 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1109 // same three conditions that getSignExtendedExpr checks.
1111 // 1. NSW flags on the step increment.
1112 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1113 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1114 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1116 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1119 // 2. Direct overflow check on the step operation's expression.
1120 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1121 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1122 const SCEV *OperandExtendedStart =
1123 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1124 SE->getSignExtendExpr(Step, WideTy));
1125 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1126 // Cache knowledge of PreAR NSW.
1128 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1129 // FIXME: this optimization needs a unit test
1130 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1134 // 3. Loop precondition.
1135 ICmpInst::Predicate Pred;
1136 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1138 if (OverflowLimit &&
1139 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1145 // Get the normalized sign-extended expression for this AddRec's Start.
1146 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1148 ScalarEvolution *SE) {
1149 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1151 return SE->getSignExtendExpr(AR->getStart(), Ty);
1153 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1154 SE->getSignExtendExpr(PreStart, Ty));
1157 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1159 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1160 "This is not an extending conversion!");
1161 assert(isSCEVable(Ty) &&
1162 "This is not a conversion to a SCEVable type!");
1163 Ty = getEffectiveSCEVType(Ty);
1165 // Fold if the operand is constant.
1166 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1168 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1170 // sext(sext(x)) --> sext(x)
1171 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1172 return getSignExtendExpr(SS->getOperand(), Ty);
1174 // sext(zext(x)) --> zext(x)
1175 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1176 return getZeroExtendExpr(SZ->getOperand(), Ty);
1178 // Before doing any expensive analysis, check to see if we've already
1179 // computed a SCEV for this Op and Ty.
1180 FoldingSetNodeID ID;
1181 ID.AddInteger(scSignExtend);
1185 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1187 // If the input value is provably positive, build a zext instead.
1188 if (isKnownNonNegative(Op))
1189 return getZeroExtendExpr(Op, Ty);
1191 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1192 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1193 // It's possible the bits taken off by the truncate were all sign bits. If
1194 // so, we should be able to simplify this further.
1195 const SCEV *X = ST->getOperand();
1196 ConstantRange CR = getSignedRange(X);
1197 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1198 unsigned NewBits = getTypeSizeInBits(Ty);
1199 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1200 CR.sextOrTrunc(NewBits)))
1201 return getTruncateOrSignExtend(X, Ty);
1204 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1205 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1206 if (SA->getNumOperands() == 2) {
1207 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1208 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1210 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1211 const APInt &C1 = SC1->getValue()->getValue();
1212 const APInt &C2 = SC2->getValue()->getValue();
1213 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1214 C2.ugt(C1) && C2.isPowerOf2())
1215 return getAddExpr(getSignExtendExpr(SC1, Ty),
1216 getSignExtendExpr(SMul, Ty));
1221 // If the input value is a chrec scev, and we can prove that the value
1222 // did not overflow the old, smaller, value, we can sign extend all of the
1223 // operands (often constants). This allows analysis of something like
1224 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1225 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1226 if (AR->isAffine()) {
1227 const SCEV *Start = AR->getStart();
1228 const SCEV *Step = AR->getStepRecurrence(*this);
1229 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1230 const Loop *L = AR->getLoop();
1232 // If we have special knowledge that this addrec won't overflow,
1233 // we don't need to do any further analysis.
1234 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1235 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1236 getSignExtendExpr(Step, Ty),
1239 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1240 // Note that this serves two purposes: It filters out loops that are
1241 // simply not analyzable, and it covers the case where this code is
1242 // being called from within backedge-taken count analysis, such that
1243 // attempting to ask for the backedge-taken count would likely result
1244 // in infinite recursion. In the later case, the analysis code will
1245 // cope with a conservative value, and it will take care to purge
1246 // that value once it has finished.
1247 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1248 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1249 // Manually compute the final value for AR, checking for
1252 // Check whether the backedge-taken count can be losslessly casted to
1253 // the addrec's type. The count is always unsigned.
1254 const SCEV *CastedMaxBECount =
1255 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1256 const SCEV *RecastedMaxBECount =
1257 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1258 if (MaxBECount == RecastedMaxBECount) {
1259 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1260 // Check whether Start+Step*MaxBECount has no signed overflow.
1261 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1262 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1263 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1264 const SCEV *WideMaxBECount =
1265 getZeroExtendExpr(CastedMaxBECount, WideTy);
1266 const SCEV *OperandExtendedAdd =
1267 getAddExpr(WideStart,
1268 getMulExpr(WideMaxBECount,
1269 getSignExtendExpr(Step, WideTy)));
1270 if (SAdd == OperandExtendedAdd) {
1271 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1272 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1273 // Return the expression with the addrec on the outside.
1274 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1275 getSignExtendExpr(Step, Ty),
1276 L, AR->getNoWrapFlags());
1278 // Similar to above, only this time treat the step value as unsigned.
1279 // This covers loops that count up with an unsigned step.
1280 OperandExtendedAdd =
1281 getAddExpr(WideStart,
1282 getMulExpr(WideMaxBECount,
1283 getZeroExtendExpr(Step, WideTy)));
1284 if (SAdd == OperandExtendedAdd) {
1285 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1286 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1287 // Return the expression with the addrec on the outside.
1288 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1289 getZeroExtendExpr(Step, Ty),
1290 L, AR->getNoWrapFlags());
1294 // If the backedge is guarded by a comparison with the pre-inc value
1295 // the addrec is safe. Also, if the entry is guarded by a comparison
1296 // with the start value and the backedge is guarded by a comparison
1297 // with the post-inc value, the addrec is safe.
1298 ICmpInst::Predicate Pred;
1299 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1300 if (OverflowLimit &&
1301 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1302 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1303 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1305 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1306 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1307 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1308 getSignExtendExpr(Step, Ty),
1309 L, AR->getNoWrapFlags());
1312 // If Start and Step are constants, check if we can apply this
1314 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1315 auto SC1 = dyn_cast<SCEVConstant>(Start);
1316 auto SC2 = dyn_cast<SCEVConstant>(Step);
1318 const APInt &C1 = SC1->getValue()->getValue();
1319 const APInt &C2 = SC2->getValue()->getValue();
1320 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1322 Start = getSignExtendExpr(Start, Ty);
1323 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1324 L, AR->getNoWrapFlags());
1325 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1330 // The cast wasn't folded; create an explicit cast node.
1331 // Recompute the insert position, as it may have been invalidated.
1332 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1333 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1335 UniqueSCEVs.InsertNode(S, IP);
1339 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1340 /// unspecified bits out to the given type.
1342 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1344 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1345 "This is not an extending conversion!");
1346 assert(isSCEVable(Ty) &&
1347 "This is not a conversion to a SCEVable type!");
1348 Ty = getEffectiveSCEVType(Ty);
1350 // Sign-extend negative constants.
1351 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1352 if (SC->getValue()->getValue().isNegative())
1353 return getSignExtendExpr(Op, Ty);
1355 // Peel off a truncate cast.
1356 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1357 const SCEV *NewOp = T->getOperand();
1358 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1359 return getAnyExtendExpr(NewOp, Ty);
1360 return getTruncateOrNoop(NewOp, Ty);
1363 // Next try a zext cast. If the cast is folded, use it.
1364 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1365 if (!isa<SCEVZeroExtendExpr>(ZExt))
1368 // Next try a sext cast. If the cast is folded, use it.
1369 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1370 if (!isa<SCEVSignExtendExpr>(SExt))
1373 // Force the cast to be folded into the operands of an addrec.
1374 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1375 SmallVector<const SCEV *, 4> Ops;
1376 for (const SCEV *Op : AR->operands())
1377 Ops.push_back(getAnyExtendExpr(Op, Ty));
1378 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1381 // If the expression is obviously signed, use the sext cast value.
1382 if (isa<SCEVSMaxExpr>(Op))
1385 // Absent any other information, use the zext cast value.
1389 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1390 /// a list of operands to be added under the given scale, update the given
1391 /// map. This is a helper function for getAddRecExpr. As an example of
1392 /// what it does, given a sequence of operands that would form an add
1393 /// expression like this:
1395 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1397 /// where A and B are constants, update the map with these values:
1399 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1401 /// and add 13 + A*B*29 to AccumulatedConstant.
1402 /// This will allow getAddRecExpr to produce this:
1404 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1406 /// This form often exposes folding opportunities that are hidden in
1407 /// the original operand list.
1409 /// Return true iff it appears that any interesting folding opportunities
1410 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1411 /// the common case where no interesting opportunities are present, and
1412 /// is also used as a check to avoid infinite recursion.
1415 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1416 SmallVectorImpl<const SCEV *> &NewOps,
1417 APInt &AccumulatedConstant,
1418 const SCEV *const *Ops, size_t NumOperands,
1420 ScalarEvolution &SE) {
1421 bool Interesting = false;
1423 // Iterate over the add operands. They are sorted, with constants first.
1425 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1427 // Pull a buried constant out to the outside.
1428 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1430 AccumulatedConstant += Scale * C->getValue()->getValue();
1433 // Next comes everything else. We're especially interested in multiplies
1434 // here, but they're in the middle, so just visit the rest with one loop.
1435 for (; i != NumOperands; ++i) {
1436 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1437 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1439 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1440 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1441 // A multiplication of a constant with another add; recurse.
1442 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1444 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1445 Add->op_begin(), Add->getNumOperands(),
1448 // A multiplication of a constant with some other value. Update
1450 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1451 const SCEV *Key = SE.getMulExpr(MulOps);
1452 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1453 M.insert(std::make_pair(Key, NewScale));
1455 NewOps.push_back(Pair.first->first);
1457 Pair.first->second += NewScale;
1458 // The map already had an entry for this value, which may indicate
1459 // a folding opportunity.
1464 // An ordinary operand. Update the map.
1465 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1466 M.insert(std::make_pair(Ops[i], Scale));
1468 NewOps.push_back(Pair.first->first);
1470 Pair.first->second += Scale;
1471 // The map already had an entry for this value, which may indicate
1472 // a folding opportunity.
1482 struct APIntCompare {
1483 bool operator()(const APInt &LHS, const APInt &RHS) const {
1484 return LHS.ult(RHS);
1489 /// getAddExpr - Get a canonical add expression, or something simpler if
1491 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1492 SCEV::NoWrapFlags Flags) {
1493 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1494 "only nuw or nsw allowed");
1495 assert(!Ops.empty() && "Cannot get empty add!");
1496 if (Ops.size() == 1) return Ops[0];
1498 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1499 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1500 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1501 "SCEVAddExpr operand types don't match!");
1504 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1506 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1507 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1508 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1510 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1511 E = Ops.end(); I != E; ++I)
1512 if (!isKnownNonNegative(*I)) {
1516 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1519 // Sort by complexity, this groups all similar expression types together.
1520 GroupByComplexity(Ops, LI);
1522 // If there are any constants, fold them together.
1524 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1526 assert(Idx < Ops.size());
1527 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1528 // We found two constants, fold them together!
1529 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1530 RHSC->getValue()->getValue());
1531 if (Ops.size() == 2) return Ops[0];
1532 Ops.erase(Ops.begin()+1); // Erase the folded element
1533 LHSC = cast<SCEVConstant>(Ops[0]);
1536 // If we are left with a constant zero being added, strip it off.
1537 if (LHSC->getValue()->isZero()) {
1538 Ops.erase(Ops.begin());
1542 if (Ops.size() == 1) return Ops[0];
1545 // Okay, check to see if the same value occurs in the operand list more than
1546 // once. If so, merge them together into an multiply expression. Since we
1547 // sorted the list, these values are required to be adjacent.
1548 Type *Ty = Ops[0]->getType();
1549 bool FoundMatch = false;
1550 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1551 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1552 // Scan ahead to count how many equal operands there are.
1554 while (i+Count != e && Ops[i+Count] == Ops[i])
1556 // Merge the values into a multiply.
1557 const SCEV *Scale = getConstant(Ty, Count);
1558 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1559 if (Ops.size() == Count)
1562 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1563 --i; e -= Count - 1;
1567 return getAddExpr(Ops, Flags);
1569 // Check for truncates. If all the operands are truncated from the same
1570 // type, see if factoring out the truncate would permit the result to be
1571 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1572 // if the contents of the resulting outer trunc fold to something simple.
1573 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1574 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1575 Type *DstType = Trunc->getType();
1576 Type *SrcType = Trunc->getOperand()->getType();
1577 SmallVector<const SCEV *, 8> LargeOps;
1579 // Check all the operands to see if they can be represented in the
1580 // source type of the truncate.
1581 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1582 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1583 if (T->getOperand()->getType() != SrcType) {
1587 LargeOps.push_back(T->getOperand());
1588 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1589 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1590 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1591 SmallVector<const SCEV *, 8> LargeMulOps;
1592 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1593 if (const SCEVTruncateExpr *T =
1594 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1595 if (T->getOperand()->getType() != SrcType) {
1599 LargeMulOps.push_back(T->getOperand());
1600 } else if (const SCEVConstant *C =
1601 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1602 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1609 LargeOps.push_back(getMulExpr(LargeMulOps));
1616 // Evaluate the expression in the larger type.
1617 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1618 // If it folds to something simple, use it. Otherwise, don't.
1619 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1620 return getTruncateExpr(Fold, DstType);
1624 // Skip past any other cast SCEVs.
1625 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1628 // If there are add operands they would be next.
1629 if (Idx < Ops.size()) {
1630 bool DeletedAdd = false;
1631 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1632 // If we have an add, expand the add operands onto the end of the operands
1634 Ops.erase(Ops.begin()+Idx);
1635 Ops.append(Add->op_begin(), Add->op_end());
1639 // If we deleted at least one add, we added operands to the end of the list,
1640 // and they are not necessarily sorted. Recurse to resort and resimplify
1641 // any operands we just acquired.
1643 return getAddExpr(Ops);
1646 // Skip over the add expression until we get to a multiply.
1647 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1650 // Check to see if there are any folding opportunities present with
1651 // operands multiplied by constant values.
1652 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1653 uint64_t BitWidth = getTypeSizeInBits(Ty);
1654 DenseMap<const SCEV *, APInt> M;
1655 SmallVector<const SCEV *, 8> NewOps;
1656 APInt AccumulatedConstant(BitWidth, 0);
1657 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1658 Ops.data(), Ops.size(),
1659 APInt(BitWidth, 1), *this)) {
1660 // Some interesting folding opportunity is present, so its worthwhile to
1661 // re-generate the operands list. Group the operands by constant scale,
1662 // to avoid multiplying by the same constant scale multiple times.
1663 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1664 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1665 E = NewOps.end(); I != E; ++I)
1666 MulOpLists[M.find(*I)->second].push_back(*I);
1667 // Re-generate the operands list.
1669 if (AccumulatedConstant != 0)
1670 Ops.push_back(getConstant(AccumulatedConstant));
1671 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1672 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1674 Ops.push_back(getMulExpr(getConstant(I->first),
1675 getAddExpr(I->second)));
1677 return getConstant(Ty, 0);
1678 if (Ops.size() == 1)
1680 return getAddExpr(Ops);
1684 // If we are adding something to a multiply expression, make sure the
1685 // something is not already an operand of the multiply. If so, merge it into
1687 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1688 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1689 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1690 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1691 if (isa<SCEVConstant>(MulOpSCEV))
1693 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1694 if (MulOpSCEV == Ops[AddOp]) {
1695 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1696 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1697 if (Mul->getNumOperands() != 2) {
1698 // If the multiply has more than two operands, we must get the
1700 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1701 Mul->op_begin()+MulOp);
1702 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1703 InnerMul = getMulExpr(MulOps);
1705 const SCEV *One = getConstant(Ty, 1);
1706 const SCEV *AddOne = getAddExpr(One, InnerMul);
1707 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1708 if (Ops.size() == 2) return OuterMul;
1710 Ops.erase(Ops.begin()+AddOp);
1711 Ops.erase(Ops.begin()+Idx-1);
1713 Ops.erase(Ops.begin()+Idx);
1714 Ops.erase(Ops.begin()+AddOp-1);
1716 Ops.push_back(OuterMul);
1717 return getAddExpr(Ops);
1720 // Check this multiply against other multiplies being added together.
1721 for (unsigned OtherMulIdx = Idx+1;
1722 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1724 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1725 // If MulOp occurs in OtherMul, we can fold the two multiplies
1727 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1728 OMulOp != e; ++OMulOp)
1729 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1730 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1731 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1732 if (Mul->getNumOperands() != 2) {
1733 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1734 Mul->op_begin()+MulOp);
1735 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1736 InnerMul1 = getMulExpr(MulOps);
1738 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1739 if (OtherMul->getNumOperands() != 2) {
1740 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1741 OtherMul->op_begin()+OMulOp);
1742 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1743 InnerMul2 = getMulExpr(MulOps);
1745 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1746 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1747 if (Ops.size() == 2) return OuterMul;
1748 Ops.erase(Ops.begin()+Idx);
1749 Ops.erase(Ops.begin()+OtherMulIdx-1);
1750 Ops.push_back(OuterMul);
1751 return getAddExpr(Ops);
1757 // If there are any add recurrences in the operands list, see if any other
1758 // added values are loop invariant. If so, we can fold them into the
1760 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1763 // Scan over all recurrences, trying to fold loop invariants into them.
1764 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1765 // Scan all of the other operands to this add and add them to the vector if
1766 // they are loop invariant w.r.t. the recurrence.
1767 SmallVector<const SCEV *, 8> LIOps;
1768 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1769 const Loop *AddRecLoop = AddRec->getLoop();
1770 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1771 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1772 LIOps.push_back(Ops[i]);
1773 Ops.erase(Ops.begin()+i);
1777 // If we found some loop invariants, fold them into the recurrence.
1778 if (!LIOps.empty()) {
1779 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1780 LIOps.push_back(AddRec->getStart());
1782 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1784 AddRecOps[0] = getAddExpr(LIOps);
1786 // Build the new addrec. Propagate the NUW and NSW flags if both the
1787 // outer add and the inner addrec are guaranteed to have no overflow.
1788 // Always propagate NW.
1789 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1790 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1792 // If all of the other operands were loop invariant, we are done.
1793 if (Ops.size() == 1) return NewRec;
1795 // Otherwise, add the folded AddRec by the non-invariant parts.
1796 for (unsigned i = 0;; ++i)
1797 if (Ops[i] == AddRec) {
1801 return getAddExpr(Ops);
1804 // Okay, if there weren't any loop invariants to be folded, check to see if
1805 // there are multiple AddRec's with the same loop induction variable being
1806 // added together. If so, we can fold them.
1807 for (unsigned OtherIdx = Idx+1;
1808 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1810 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1811 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1812 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1814 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1816 if (const SCEVAddRecExpr *OtherAddRec =
1817 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1818 if (OtherAddRec->getLoop() == AddRecLoop) {
1819 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1821 if (i >= AddRecOps.size()) {
1822 AddRecOps.append(OtherAddRec->op_begin()+i,
1823 OtherAddRec->op_end());
1826 AddRecOps[i] = getAddExpr(AddRecOps[i],
1827 OtherAddRec->getOperand(i));
1829 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1831 // Step size has changed, so we cannot guarantee no self-wraparound.
1832 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1833 return getAddExpr(Ops);
1836 // Otherwise couldn't fold anything into this recurrence. Move onto the
1840 // Okay, it looks like we really DO need an add expr. Check to see if we
1841 // already have one, otherwise create a new one.
1842 FoldingSetNodeID ID;
1843 ID.AddInteger(scAddExpr);
1844 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1845 ID.AddPointer(Ops[i]);
1848 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1850 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1851 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1852 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1854 UniqueSCEVs.InsertNode(S, IP);
1856 S->setNoWrapFlags(Flags);
1860 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1862 if (j > 1 && k / j != i) Overflow = true;
1866 /// Compute the result of "n choose k", the binomial coefficient. If an
1867 /// intermediate computation overflows, Overflow will be set and the return will
1868 /// be garbage. Overflow is not cleared on absence of overflow.
1869 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1870 // We use the multiplicative formula:
1871 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1872 // At each iteration, we take the n-th term of the numeral and divide by the
1873 // (k-n)th term of the denominator. This division will always produce an
1874 // integral result, and helps reduce the chance of overflow in the
1875 // intermediate computations. However, we can still overflow even when the
1876 // final result would fit.
1878 if (n == 0 || n == k) return 1;
1879 if (k > n) return 0;
1885 for (uint64_t i = 1; i <= k; ++i) {
1886 r = umul_ov(r, n-(i-1), Overflow);
1892 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1894 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1895 SCEV::NoWrapFlags Flags) {
1896 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1897 "only nuw or nsw allowed");
1898 assert(!Ops.empty() && "Cannot get empty mul!");
1899 if (Ops.size() == 1) return Ops[0];
1901 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1902 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1903 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1904 "SCEVMulExpr operand types don't match!");
1907 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1909 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1910 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1911 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1913 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1914 E = Ops.end(); I != E; ++I)
1915 if (!isKnownNonNegative(*I)) {
1919 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1922 // Sort by complexity, this groups all similar expression types together.
1923 GroupByComplexity(Ops, LI);
1925 // If there are any constants, fold them together.
1927 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1929 // C1*(C2+V) -> C1*C2 + C1*V
1930 if (Ops.size() == 2)
1931 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1932 if (Add->getNumOperands() == 2 &&
1933 isa<SCEVConstant>(Add->getOperand(0)))
1934 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1935 getMulExpr(LHSC, Add->getOperand(1)));
1938 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1939 // We found two constants, fold them together!
1940 ConstantInt *Fold = ConstantInt::get(getContext(),
1941 LHSC->getValue()->getValue() *
1942 RHSC->getValue()->getValue());
1943 Ops[0] = getConstant(Fold);
1944 Ops.erase(Ops.begin()+1); // Erase the folded element
1945 if (Ops.size() == 1) return Ops[0];
1946 LHSC = cast<SCEVConstant>(Ops[0]);
1949 // If we are left with a constant one being multiplied, strip it off.
1950 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1951 Ops.erase(Ops.begin());
1953 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1954 // If we have a multiply of zero, it will always be zero.
1956 } else if (Ops[0]->isAllOnesValue()) {
1957 // If we have a mul by -1 of an add, try distributing the -1 among the
1959 if (Ops.size() == 2) {
1960 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1961 SmallVector<const SCEV *, 4> NewOps;
1962 bool AnyFolded = false;
1963 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1964 E = Add->op_end(); I != E; ++I) {
1965 const SCEV *Mul = getMulExpr(Ops[0], *I);
1966 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1967 NewOps.push_back(Mul);
1970 return getAddExpr(NewOps);
1972 else if (const SCEVAddRecExpr *
1973 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1974 // Negation preserves a recurrence's no self-wrap property.
1975 SmallVector<const SCEV *, 4> Operands;
1976 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1977 E = AddRec->op_end(); I != E; ++I) {
1978 Operands.push_back(getMulExpr(Ops[0], *I));
1980 return getAddRecExpr(Operands, AddRec->getLoop(),
1981 AddRec->getNoWrapFlags(SCEV::FlagNW));
1986 if (Ops.size() == 1)
1990 // Skip over the add expression until we get to a multiply.
1991 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1994 // If there are mul operands inline them all into this expression.
1995 if (Idx < Ops.size()) {
1996 bool DeletedMul = false;
1997 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1998 // If we have an mul, expand the mul operands onto the end of the operands
2000 Ops.erase(Ops.begin()+Idx);
2001 Ops.append(Mul->op_begin(), Mul->op_end());
2005 // If we deleted at least one mul, we added operands to the end of the list,
2006 // and they are not necessarily sorted. Recurse to resort and resimplify
2007 // any operands we just acquired.
2009 return getMulExpr(Ops);
2012 // If there are any add recurrences in the operands list, see if any other
2013 // added values are loop invariant. If so, we can fold them into the
2015 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2018 // Scan over all recurrences, trying to fold loop invariants into them.
2019 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2020 // Scan all of the other operands to this mul and add them to the vector if
2021 // they are loop invariant w.r.t. the recurrence.
2022 SmallVector<const SCEV *, 8> LIOps;
2023 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2024 const Loop *AddRecLoop = AddRec->getLoop();
2025 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2026 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2027 LIOps.push_back(Ops[i]);
2028 Ops.erase(Ops.begin()+i);
2032 // If we found some loop invariants, fold them into the recurrence.
2033 if (!LIOps.empty()) {
2034 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2035 SmallVector<const SCEV *, 4> NewOps;
2036 NewOps.reserve(AddRec->getNumOperands());
2037 const SCEV *Scale = getMulExpr(LIOps);
2038 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2039 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2041 // Build the new addrec. Propagate the NUW and NSW flags if both the
2042 // outer mul and the inner addrec are guaranteed to have no overflow.
2044 // No self-wrap cannot be guaranteed after changing the step size, but
2045 // will be inferred if either NUW or NSW is true.
2046 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2047 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2049 // If all of the other operands were loop invariant, we are done.
2050 if (Ops.size() == 1) return NewRec;
2052 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2053 for (unsigned i = 0;; ++i)
2054 if (Ops[i] == AddRec) {
2058 return getMulExpr(Ops);
2061 // Okay, if there weren't any loop invariants to be folded, check to see if
2062 // there are multiple AddRec's with the same loop induction variable being
2063 // multiplied together. If so, we can fold them.
2065 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2066 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2067 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2068 // ]]],+,...up to x=2n}.
2069 // Note that the arguments to choose() are always integers with values
2070 // known at compile time, never SCEV objects.
2072 // The implementation avoids pointless extra computations when the two
2073 // addrec's are of different length (mathematically, it's equivalent to
2074 // an infinite stream of zeros on the right).
2075 bool OpsModified = false;
2076 for (unsigned OtherIdx = Idx+1;
2077 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2079 const SCEVAddRecExpr *OtherAddRec =
2080 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2081 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2084 bool Overflow = false;
2085 Type *Ty = AddRec->getType();
2086 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2087 SmallVector<const SCEV*, 7> AddRecOps;
2088 for (int x = 0, xe = AddRec->getNumOperands() +
2089 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2090 const SCEV *Term = getConstant(Ty, 0);
2091 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2092 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2093 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2094 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2095 z < ze && !Overflow; ++z) {
2096 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2098 if (LargerThan64Bits)
2099 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2101 Coeff = Coeff1*Coeff2;
2102 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2103 const SCEV *Term1 = AddRec->getOperand(y-z);
2104 const SCEV *Term2 = OtherAddRec->getOperand(z);
2105 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2108 AddRecOps.push_back(Term);
2111 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2113 if (Ops.size() == 2) return NewAddRec;
2114 Ops[Idx] = NewAddRec;
2115 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2117 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2123 return getMulExpr(Ops);
2125 // Otherwise couldn't fold anything into this recurrence. Move onto the
2129 // Okay, it looks like we really DO need an mul expr. Check to see if we
2130 // already have one, otherwise create a new one.
2131 FoldingSetNodeID ID;
2132 ID.AddInteger(scMulExpr);
2133 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2134 ID.AddPointer(Ops[i]);
2137 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2139 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2140 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2141 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2143 UniqueSCEVs.InsertNode(S, IP);
2145 S->setNoWrapFlags(Flags);
2149 /// getUDivExpr - Get a canonical unsigned division expression, or something
2150 /// simpler if possible.
2151 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2153 assert(getEffectiveSCEVType(LHS->getType()) ==
2154 getEffectiveSCEVType(RHS->getType()) &&
2155 "SCEVUDivExpr operand types don't match!");
2157 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2158 if (RHSC->getValue()->equalsInt(1))
2159 return LHS; // X udiv 1 --> x
2160 // If the denominator is zero, the result of the udiv is undefined. Don't
2161 // try to analyze it, because the resolution chosen here may differ from
2162 // the resolution chosen in other parts of the compiler.
2163 if (!RHSC->getValue()->isZero()) {
2164 // Determine if the division can be folded into the operands of
2166 // TODO: Generalize this to non-constants by using known-bits information.
2167 Type *Ty = LHS->getType();
2168 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2169 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2170 // For non-power-of-two values, effectively round the value up to the
2171 // nearest power of two.
2172 if (!RHSC->getValue()->getValue().isPowerOf2())
2174 IntegerType *ExtTy =
2175 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2176 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2177 if (const SCEVConstant *Step =
2178 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2179 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2180 const APInt &StepInt = Step->getValue()->getValue();
2181 const APInt &DivInt = RHSC->getValue()->getValue();
2182 if (!StepInt.urem(DivInt) &&
2183 getZeroExtendExpr(AR, ExtTy) ==
2184 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2185 getZeroExtendExpr(Step, ExtTy),
2186 AR->getLoop(), SCEV::FlagAnyWrap)) {
2187 SmallVector<const SCEV *, 4> Operands;
2188 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2189 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2190 return getAddRecExpr(Operands, AR->getLoop(),
2193 /// Get a canonical UDivExpr for a recurrence.
2194 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2195 // We can currently only fold X%N if X is constant.
2196 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2197 if (StartC && !DivInt.urem(StepInt) &&
2198 getZeroExtendExpr(AR, ExtTy) ==
2199 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2200 getZeroExtendExpr(Step, ExtTy),
2201 AR->getLoop(), SCEV::FlagAnyWrap)) {
2202 const APInt &StartInt = StartC->getValue()->getValue();
2203 const APInt &StartRem = StartInt.urem(StepInt);
2205 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2206 AR->getLoop(), SCEV::FlagNW);
2209 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2210 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2211 SmallVector<const SCEV *, 4> Operands;
2212 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2213 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2214 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2215 // Find an operand that's safely divisible.
2216 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2217 const SCEV *Op = M->getOperand(i);
2218 const SCEV *Div = getUDivExpr(Op, RHSC);
2219 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2220 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2223 return getMulExpr(Operands);
2227 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2228 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2229 SmallVector<const SCEV *, 4> Operands;
2230 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2231 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2232 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2234 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2235 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2236 if (isa<SCEVUDivExpr>(Op) ||
2237 getMulExpr(Op, RHS) != A->getOperand(i))
2239 Operands.push_back(Op);
2241 if (Operands.size() == A->getNumOperands())
2242 return getAddExpr(Operands);
2246 // Fold if both operands are constant.
2247 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2248 Constant *LHSCV = LHSC->getValue();
2249 Constant *RHSCV = RHSC->getValue();
2250 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2256 FoldingSetNodeID ID;
2257 ID.AddInteger(scUDivExpr);
2261 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2262 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2264 UniqueSCEVs.InsertNode(S, IP);
2268 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2269 APInt A = C1->getValue()->getValue().abs();
2270 APInt B = C2->getValue()->getValue().abs();
2271 uint32_t ABW = A.getBitWidth();
2272 uint32_t BBW = B.getBitWidth();
2279 return APIntOps::GreatestCommonDivisor(A, B);
2282 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2283 /// something simpler if possible. There is no representation for an exact udiv
2284 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2285 /// We can't do this when it's not exact because the udiv may be clearing bits.
2286 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2288 // TODO: we could try to find factors in all sorts of things, but for now we
2289 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2290 // end of this file for inspiration.
2292 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2294 return getUDivExpr(LHS, RHS);
2296 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2297 // If the mulexpr multiplies by a constant, then that constant must be the
2298 // first element of the mulexpr.
2299 if (const SCEVConstant *LHSCst =
2300 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2301 if (LHSCst == RHSCst) {
2302 SmallVector<const SCEV *, 2> Operands;
2303 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2304 return getMulExpr(Operands);
2307 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2308 // that there's a factor provided by one of the other terms. We need to
2310 APInt Factor = gcd(LHSCst, RHSCst);
2311 if (!Factor.isIntN(1)) {
2312 LHSCst = cast<SCEVConstant>(
2313 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2314 RHSCst = cast<SCEVConstant>(
2315 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2316 SmallVector<const SCEV *, 2> Operands;
2317 Operands.push_back(LHSCst);
2318 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2319 LHS = getMulExpr(Operands);
2321 Mul = dyn_cast<SCEVMulExpr>(LHS);
2323 return getUDivExactExpr(LHS, RHS);
2328 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2329 if (Mul->getOperand(i) == RHS) {
2330 SmallVector<const SCEV *, 2> Operands;
2331 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2332 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2333 return getMulExpr(Operands);
2337 return getUDivExpr(LHS, RHS);
2340 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2341 /// Simplify the expression as much as possible.
2342 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2344 SCEV::NoWrapFlags Flags) {
2345 SmallVector<const SCEV *, 4> Operands;
2346 Operands.push_back(Start);
2347 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2348 if (StepChrec->getLoop() == L) {
2349 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2350 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2353 Operands.push_back(Step);
2354 return getAddRecExpr(Operands, L, Flags);
2357 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2358 /// Simplify the expression as much as possible.
2360 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2361 const Loop *L, SCEV::NoWrapFlags Flags) {
2362 if (Operands.size() == 1) return Operands[0];
2364 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2365 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2366 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2367 "SCEVAddRecExpr operand types don't match!");
2368 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2369 assert(isLoopInvariant(Operands[i], L) &&
2370 "SCEVAddRecExpr operand is not loop-invariant!");
2373 if (Operands.back()->isZero()) {
2374 Operands.pop_back();
2375 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2378 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2379 // use that information to infer NUW and NSW flags. However, computing a
2380 // BE count requires calling getAddRecExpr, so we may not yet have a
2381 // meaningful BE count at this point (and if we don't, we'd be stuck
2382 // with a SCEVCouldNotCompute as the cached BE count).
2384 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2386 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2387 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2388 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2390 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2391 E = Operands.end(); I != E; ++I)
2392 if (!isKnownNonNegative(*I)) {
2396 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2399 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2400 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2401 const Loop *NestedLoop = NestedAR->getLoop();
2402 if (L->contains(NestedLoop) ?
2403 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2404 (!NestedLoop->contains(L) &&
2405 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2406 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2407 NestedAR->op_end());
2408 Operands[0] = NestedAR->getStart();
2409 // AddRecs require their operands be loop-invariant with respect to their
2410 // loops. Don't perform this transformation if it would break this
2412 bool AllInvariant = true;
2413 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2414 if (!isLoopInvariant(Operands[i], L)) {
2415 AllInvariant = false;
2419 // Create a recurrence for the outer loop with the same step size.
2421 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2422 // inner recurrence has the same property.
2423 SCEV::NoWrapFlags OuterFlags =
2424 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2426 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2427 AllInvariant = true;
2428 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2429 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2430 AllInvariant = false;
2434 // Ok, both add recurrences are valid after the transformation.
2436 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2437 // the outer recurrence has the same property.
2438 SCEV::NoWrapFlags InnerFlags =
2439 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2440 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2443 // Reset Operands to its original state.
2444 Operands[0] = NestedAR;
2448 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2449 // already have one, otherwise create a new one.
2450 FoldingSetNodeID ID;
2451 ID.AddInteger(scAddRecExpr);
2452 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2453 ID.AddPointer(Operands[i]);
2457 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2459 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2460 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2461 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2462 O, Operands.size(), L);
2463 UniqueSCEVs.InsertNode(S, IP);
2465 S->setNoWrapFlags(Flags);
2469 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2471 SmallVector<const SCEV *, 2> Ops;
2474 return getSMaxExpr(Ops);
2478 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2479 assert(!Ops.empty() && "Cannot get empty smax!");
2480 if (Ops.size() == 1) return Ops[0];
2482 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2483 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2484 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2485 "SCEVSMaxExpr operand types don't match!");
2488 // Sort by complexity, this groups all similar expression types together.
2489 GroupByComplexity(Ops, LI);
2491 // If there are any constants, fold them together.
2493 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2495 assert(Idx < Ops.size());
2496 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2497 // We found two constants, fold them together!
2498 ConstantInt *Fold = ConstantInt::get(getContext(),
2499 APIntOps::smax(LHSC->getValue()->getValue(),
2500 RHSC->getValue()->getValue()));
2501 Ops[0] = getConstant(Fold);
2502 Ops.erase(Ops.begin()+1); // Erase the folded element
2503 if (Ops.size() == 1) return Ops[0];
2504 LHSC = cast<SCEVConstant>(Ops[0]);
2507 // If we are left with a constant minimum-int, strip it off.
2508 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2509 Ops.erase(Ops.begin());
2511 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2512 // If we have an smax with a constant maximum-int, it will always be
2517 if (Ops.size() == 1) return Ops[0];
2520 // Find the first SMax
2521 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2524 // Check to see if one of the operands is an SMax. If so, expand its operands
2525 // onto our operand list, and recurse to simplify.
2526 if (Idx < Ops.size()) {
2527 bool DeletedSMax = false;
2528 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2529 Ops.erase(Ops.begin()+Idx);
2530 Ops.append(SMax->op_begin(), SMax->op_end());
2535 return getSMaxExpr(Ops);
2538 // Okay, check to see if the same value occurs in the operand list twice. If
2539 // so, delete one. Since we sorted the list, these values are required to
2541 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2542 // X smax Y smax Y --> X smax Y
2543 // X smax Y --> X, if X is always greater than Y
2544 if (Ops[i] == Ops[i+1] ||
2545 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2546 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2548 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2549 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2553 if (Ops.size() == 1) return Ops[0];
2555 assert(!Ops.empty() && "Reduced smax down to nothing!");
2557 // Okay, it looks like we really DO need an smax expr. Check to see if we
2558 // already have one, otherwise create a new one.
2559 FoldingSetNodeID ID;
2560 ID.AddInteger(scSMaxExpr);
2561 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2562 ID.AddPointer(Ops[i]);
2564 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2565 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2566 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2567 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2569 UniqueSCEVs.InsertNode(S, IP);
2573 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2575 SmallVector<const SCEV *, 2> Ops;
2578 return getUMaxExpr(Ops);
2582 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2583 assert(!Ops.empty() && "Cannot get empty umax!");
2584 if (Ops.size() == 1) return Ops[0];
2586 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2587 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2588 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2589 "SCEVUMaxExpr operand types don't match!");
2592 // Sort by complexity, this groups all similar expression types together.
2593 GroupByComplexity(Ops, LI);
2595 // If there are any constants, fold them together.
2597 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2599 assert(Idx < Ops.size());
2600 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2601 // We found two constants, fold them together!
2602 ConstantInt *Fold = ConstantInt::get(getContext(),
2603 APIntOps::umax(LHSC->getValue()->getValue(),
2604 RHSC->getValue()->getValue()));
2605 Ops[0] = getConstant(Fold);
2606 Ops.erase(Ops.begin()+1); // Erase the folded element
2607 if (Ops.size() == 1) return Ops[0];
2608 LHSC = cast<SCEVConstant>(Ops[0]);
2611 // If we are left with a constant minimum-int, strip it off.
2612 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2613 Ops.erase(Ops.begin());
2615 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2616 // If we have an umax with a constant maximum-int, it will always be
2621 if (Ops.size() == 1) return Ops[0];
2624 // Find the first UMax
2625 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2628 // Check to see if one of the operands is a UMax. If so, expand its operands
2629 // onto our operand list, and recurse to simplify.
2630 if (Idx < Ops.size()) {
2631 bool DeletedUMax = false;
2632 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2633 Ops.erase(Ops.begin()+Idx);
2634 Ops.append(UMax->op_begin(), UMax->op_end());
2639 return getUMaxExpr(Ops);
2642 // Okay, check to see if the same value occurs in the operand list twice. If
2643 // so, delete one. Since we sorted the list, these values are required to
2645 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2646 // X umax Y umax Y --> X umax Y
2647 // X umax Y --> X, if X is always greater than Y
2648 if (Ops[i] == Ops[i+1] ||
2649 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2650 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2652 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2653 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2657 if (Ops.size() == 1) return Ops[0];
2659 assert(!Ops.empty() && "Reduced umax down to nothing!");
2661 // Okay, it looks like we really DO need a umax expr. Check to see if we
2662 // already have one, otherwise create a new one.
2663 FoldingSetNodeID ID;
2664 ID.AddInteger(scUMaxExpr);
2665 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2666 ID.AddPointer(Ops[i]);
2668 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2669 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2670 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2671 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2673 UniqueSCEVs.InsertNode(S, IP);
2677 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2679 // ~smax(~x, ~y) == smin(x, y).
2680 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2683 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2685 // ~umax(~x, ~y) == umin(x, y)
2686 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2689 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2690 // If we have DataLayout, we can bypass creating a target-independent
2691 // constant expression and then folding it back into a ConstantInt.
2692 // This is just a compile-time optimization.
2694 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
2696 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2697 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2698 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2700 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2701 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2702 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2705 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2708 // If we have DataLayout, we can bypass creating a target-independent
2709 // constant expression and then folding it back into a ConstantInt.
2710 // This is just a compile-time optimization.
2712 return getConstant(IntTy,
2713 DL->getStructLayout(STy)->getElementOffset(FieldNo));
2716 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2717 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2718 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2721 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2722 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2725 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2726 // Don't attempt to do anything other than create a SCEVUnknown object
2727 // here. createSCEV only calls getUnknown after checking for all other
2728 // interesting possibilities, and any other code that calls getUnknown
2729 // is doing so in order to hide a value from SCEV canonicalization.
2731 FoldingSetNodeID ID;
2732 ID.AddInteger(scUnknown);
2735 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2736 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2737 "Stale SCEVUnknown in uniquing map!");
2740 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2742 FirstUnknown = cast<SCEVUnknown>(S);
2743 UniqueSCEVs.InsertNode(S, IP);
2747 //===----------------------------------------------------------------------===//
2748 // Basic SCEV Analysis and PHI Idiom Recognition Code
2751 /// isSCEVable - Test if values of the given type are analyzable within
2752 /// the SCEV framework. This primarily includes integer types, and it
2753 /// can optionally include pointer types if the ScalarEvolution class
2754 /// has access to target-specific information.
2755 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2756 // Integers and pointers are always SCEVable.
2757 return Ty->isIntegerTy() || Ty->isPointerTy();
2760 /// getTypeSizeInBits - Return the size in bits of the specified type,
2761 /// for which isSCEVable must return true.
2762 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2763 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2765 // If we have a DataLayout, use it!
2767 return DL->getTypeSizeInBits(Ty);
2769 // Integer types have fixed sizes.
2770 if (Ty->isIntegerTy())
2771 return Ty->getPrimitiveSizeInBits();
2773 // The only other support type is pointer. Without DataLayout, conservatively
2774 // assume pointers are 64-bit.
2775 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2779 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2780 /// the given type and which represents how SCEV will treat the given
2781 /// type, for which isSCEVable must return true. For pointer types,
2782 /// this is the pointer-sized integer type.
2783 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2784 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2786 if (Ty->isIntegerTy()) {
2790 // The only other support type is pointer.
2791 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2794 return DL->getIntPtrType(Ty);
2796 // Without DataLayout, conservatively assume pointers are 64-bit.
2797 return Type::getInt64Ty(getContext());
2800 const SCEV *ScalarEvolution::getCouldNotCompute() {
2801 return &CouldNotCompute;
2805 // Helper class working with SCEVTraversal to figure out if a SCEV contains
2806 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
2807 // is set iff if find such SCEVUnknown.
2809 struct FindInvalidSCEVUnknown {
2811 FindInvalidSCEVUnknown() { FindOne = false; }
2812 bool follow(const SCEV *S) {
2813 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
2817 if (!cast<SCEVUnknown>(S)->getValue())
2824 bool isDone() const { return FindOne; }
2828 bool ScalarEvolution::checkValidity(const SCEV *S) const {
2829 FindInvalidSCEVUnknown F;
2830 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
2836 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2837 /// expression and create a new one.
2838 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2839 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2841 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
2842 if (I != ValueExprMap.end()) {
2843 const SCEV *S = I->second;
2844 if (checkValidity(S))
2847 ValueExprMap.erase(I);
2849 const SCEV *S = createSCEV(V);
2851 // The process of creating a SCEV for V may have caused other SCEVs
2852 // to have been created, so it's necessary to insert the new entry
2853 // from scratch, rather than trying to remember the insert position
2855 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2859 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2861 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2862 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2864 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2866 Type *Ty = V->getType();
2867 Ty = getEffectiveSCEVType(Ty);
2868 return getMulExpr(V,
2869 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2872 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2873 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2874 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2876 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2878 Type *Ty = V->getType();
2879 Ty = getEffectiveSCEVType(Ty);
2880 const SCEV *AllOnes =
2881 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2882 return getMinusSCEV(AllOnes, V);
2885 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2886 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2887 SCEV::NoWrapFlags Flags) {
2888 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2890 // Fast path: X - X --> 0.
2892 return getConstant(LHS->getType(), 0);
2895 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2898 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2899 /// input value to the specified type. If the type must be extended, it is zero
2902 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2903 Type *SrcTy = V->getType();
2904 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2905 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2906 "Cannot truncate or zero extend with non-integer arguments!");
2907 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2908 return V; // No conversion
2909 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2910 return getTruncateExpr(V, Ty);
2911 return getZeroExtendExpr(V, Ty);
2914 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2915 /// input value to the specified type. If the type must be extended, it is sign
2918 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2920 Type *SrcTy = V->getType();
2921 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2922 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2923 "Cannot truncate or zero extend with non-integer arguments!");
2924 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2925 return V; // No conversion
2926 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2927 return getTruncateExpr(V, Ty);
2928 return getSignExtendExpr(V, Ty);
2931 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2932 /// input value to the specified type. If the type must be extended, it is zero
2933 /// extended. The conversion must not be narrowing.
2935 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2936 Type *SrcTy = V->getType();
2937 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2938 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2939 "Cannot noop or zero extend with non-integer arguments!");
2940 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2941 "getNoopOrZeroExtend cannot truncate!");
2942 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2943 return V; // No conversion
2944 return getZeroExtendExpr(V, Ty);
2947 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2948 /// input value to the specified type. If the type must be extended, it is sign
2949 /// extended. The conversion must not be narrowing.
2951 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2952 Type *SrcTy = V->getType();
2953 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2954 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2955 "Cannot noop or sign extend with non-integer arguments!");
2956 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2957 "getNoopOrSignExtend cannot truncate!");
2958 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2959 return V; // No conversion
2960 return getSignExtendExpr(V, Ty);
2963 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2964 /// the input value to the specified type. If the type must be extended,
2965 /// it is extended with unspecified bits. The conversion must not be
2968 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2969 Type *SrcTy = V->getType();
2970 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2971 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2972 "Cannot noop or any extend with non-integer arguments!");
2973 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2974 "getNoopOrAnyExtend cannot truncate!");
2975 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2976 return V; // No conversion
2977 return getAnyExtendExpr(V, Ty);
2980 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2981 /// input value to the specified type. The conversion must not be widening.
2983 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2984 Type *SrcTy = V->getType();
2985 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2986 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2987 "Cannot truncate or noop with non-integer arguments!");
2988 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2989 "getTruncateOrNoop cannot extend!");
2990 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2991 return V; // No conversion
2992 return getTruncateExpr(V, Ty);
2995 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2996 /// the types using zero-extension, and then perform a umax operation
2998 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3000 const SCEV *PromotedLHS = LHS;
3001 const SCEV *PromotedRHS = RHS;
3003 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3004 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3006 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3008 return getUMaxExpr(PromotedLHS, PromotedRHS);
3011 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3012 /// the types using zero-extension, and then perform a umin operation
3014 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3016 const SCEV *PromotedLHS = LHS;
3017 const SCEV *PromotedRHS = RHS;
3019 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3020 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3022 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3024 return getUMinExpr(PromotedLHS, PromotedRHS);
3027 /// getPointerBase - Transitively follow the chain of pointer-type operands
3028 /// until reaching a SCEV that does not have a single pointer operand. This
3029 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3030 /// but corner cases do exist.
3031 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3032 // A pointer operand may evaluate to a nonpointer expression, such as null.
3033 if (!V->getType()->isPointerTy())
3036 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3037 return getPointerBase(Cast->getOperand());
3039 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3040 const SCEV *PtrOp = nullptr;
3041 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3043 if ((*I)->getType()->isPointerTy()) {
3044 // Cannot find the base of an expression with multiple pointer operands.
3052 return getPointerBase(PtrOp);
3057 /// PushDefUseChildren - Push users of the given Instruction
3058 /// onto the given Worklist.
3060 PushDefUseChildren(Instruction *I,
3061 SmallVectorImpl<Instruction *> &Worklist) {
3062 // Push the def-use children onto the Worklist stack.
3063 for (User *U : I->users())
3064 Worklist.push_back(cast<Instruction>(U));
3067 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3068 /// instructions that depend on the given instruction and removes them from
3069 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3072 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3073 SmallVector<Instruction *, 16> Worklist;
3074 PushDefUseChildren(PN, Worklist);
3076 SmallPtrSet<Instruction *, 8> Visited;
3078 while (!Worklist.empty()) {
3079 Instruction *I = Worklist.pop_back_val();
3080 if (!Visited.insert(I)) continue;
3082 ValueExprMapType::iterator It =
3083 ValueExprMap.find_as(static_cast<Value *>(I));
3084 if (It != ValueExprMap.end()) {
3085 const SCEV *Old = It->second;
3087 // Short-circuit the def-use traversal if the symbolic name
3088 // ceases to appear in expressions.
3089 if (Old != SymName && !hasOperand(Old, SymName))
3092 // SCEVUnknown for a PHI either means that it has an unrecognized
3093 // structure, it's a PHI that's in the progress of being computed
3094 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3095 // additional loop trip count information isn't going to change anything.
3096 // In the second case, createNodeForPHI will perform the necessary
3097 // updates on its own when it gets to that point. In the third, we do
3098 // want to forget the SCEVUnknown.
3099 if (!isa<PHINode>(I) ||
3100 !isa<SCEVUnknown>(Old) ||
3101 (I != PN && Old == SymName)) {
3102 forgetMemoizedResults(Old);
3103 ValueExprMap.erase(It);
3107 PushDefUseChildren(I, Worklist);
3111 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3112 /// a loop header, making it a potential recurrence, or it doesn't.
3114 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3115 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3116 if (L->getHeader() == PN->getParent()) {
3117 // The loop may have multiple entrances or multiple exits; we can analyze
3118 // this phi as an addrec if it has a unique entry value and a unique
3120 Value *BEValueV = nullptr, *StartValueV = nullptr;
3121 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3122 Value *V = PN->getIncomingValue(i);
3123 if (L->contains(PN->getIncomingBlock(i))) {
3126 } else if (BEValueV != V) {
3130 } else if (!StartValueV) {
3132 } else if (StartValueV != V) {
3133 StartValueV = nullptr;
3137 if (BEValueV && StartValueV) {
3138 // While we are analyzing this PHI node, handle its value symbolically.
3139 const SCEV *SymbolicName = getUnknown(PN);
3140 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3141 "PHI node already processed?");
3142 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3144 // Using this symbolic name for the PHI, analyze the value coming around
3146 const SCEV *BEValue = getSCEV(BEValueV);
3148 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3149 // has a special value for the first iteration of the loop.
3151 // If the value coming around the backedge is an add with the symbolic
3152 // value we just inserted, then we found a simple induction variable!
3153 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3154 // If there is a single occurrence of the symbolic value, replace it
3155 // with a recurrence.
3156 unsigned FoundIndex = Add->getNumOperands();
3157 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3158 if (Add->getOperand(i) == SymbolicName)
3159 if (FoundIndex == e) {
3164 if (FoundIndex != Add->getNumOperands()) {
3165 // Create an add with everything but the specified operand.
3166 SmallVector<const SCEV *, 8> Ops;
3167 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3168 if (i != FoundIndex)
3169 Ops.push_back(Add->getOperand(i));
3170 const SCEV *Accum = getAddExpr(Ops);
3172 // This is not a valid addrec if the step amount is varying each
3173 // loop iteration, but is not itself an addrec in this loop.
3174 if (isLoopInvariant(Accum, L) ||
3175 (isa<SCEVAddRecExpr>(Accum) &&
3176 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3177 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3179 // If the increment doesn't overflow, then neither the addrec nor
3180 // the post-increment will overflow.
3181 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3182 if (OBO->hasNoUnsignedWrap())
3183 Flags = setFlags(Flags, SCEV::FlagNUW);
3184 if (OBO->hasNoSignedWrap())
3185 Flags = setFlags(Flags, SCEV::FlagNSW);
3186 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3187 // If the increment is an inbounds GEP, then we know the address
3188 // space cannot be wrapped around. We cannot make any guarantee
3189 // about signed or unsigned overflow because pointers are
3190 // unsigned but we may have a negative index from the base
3191 // pointer. We can guarantee that no unsigned wrap occurs if the
3192 // indices form a positive value.
3193 if (GEP->isInBounds()) {
3194 Flags = setFlags(Flags, SCEV::FlagNW);
3196 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3197 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3198 Flags = setFlags(Flags, SCEV::FlagNUW);
3200 } else if (const SubOperator *OBO =
3201 dyn_cast<SubOperator>(BEValueV)) {
3202 if (OBO->hasNoUnsignedWrap())
3203 Flags = setFlags(Flags, SCEV::FlagNUW);
3204 if (OBO->hasNoSignedWrap())
3205 Flags = setFlags(Flags, SCEV::FlagNSW);
3208 const SCEV *StartVal = getSCEV(StartValueV);
3209 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3211 // Since the no-wrap flags are on the increment, they apply to the
3212 // post-incremented value as well.
3213 if (isLoopInvariant(Accum, L))
3214 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3217 // Okay, for the entire analysis of this edge we assumed the PHI
3218 // to be symbolic. We now need to go back and purge all of the
3219 // entries for the scalars that use the symbolic expression.
3220 ForgetSymbolicName(PN, SymbolicName);
3221 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3225 } else if (const SCEVAddRecExpr *AddRec =
3226 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3227 // Otherwise, this could be a loop like this:
3228 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3229 // In this case, j = {1,+,1} and BEValue is j.
3230 // Because the other in-value of i (0) fits the evolution of BEValue
3231 // i really is an addrec evolution.
3232 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3233 const SCEV *StartVal = getSCEV(StartValueV);
3235 // If StartVal = j.start - j.stride, we can use StartVal as the
3236 // initial step of the addrec evolution.
3237 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3238 AddRec->getOperand(1))) {
3239 // FIXME: For constant StartVal, we should be able to infer
3241 const SCEV *PHISCEV =
3242 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3245 // Okay, for the entire analysis of this edge we assumed the PHI
3246 // to be symbolic. We now need to go back and purge all of the
3247 // entries for the scalars that use the symbolic expression.
3248 ForgetSymbolicName(PN, SymbolicName);
3249 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3257 // If the PHI has a single incoming value, follow that value, unless the
3258 // PHI's incoming blocks are in a different loop, in which case doing so
3259 // risks breaking LCSSA form. Instcombine would normally zap these, but
3260 // it doesn't have DominatorTree information, so it may miss cases.
3261 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT))
3262 if (LI->replacementPreservesLCSSAForm(PN, V))
3265 // If it's not a loop phi, we can't handle it yet.
3266 return getUnknown(PN);
3269 /// createNodeForGEP - Expand GEP instructions into add and multiply
3270 /// operations. This allows them to be analyzed by regular SCEV code.
3272 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3273 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3274 Value *Base = GEP->getOperand(0);
3275 // Don't attempt to analyze GEPs over unsized objects.
3276 if (!Base->getType()->getPointerElementType()->isSized())
3277 return getUnknown(GEP);
3279 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3280 // Add expression, because the Instruction may be guarded by control flow
3281 // and the no-overflow bits may not be valid for the expression in any
3283 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3285 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3286 gep_type_iterator GTI = gep_type_begin(GEP);
3287 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3291 // Compute the (potentially symbolic) offset in bytes for this index.
3292 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3293 // For a struct, add the member offset.
3294 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3295 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3297 // Add the field offset to the running total offset.
3298 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3300 // For an array, add the element offset, explicitly scaled.
3301 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3302 const SCEV *IndexS = getSCEV(Index);
3303 // Getelementptr indices are signed.
3304 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3306 // Multiply the index by the element size to compute the element offset.
3307 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3309 // Add the element offset to the running total offset.
3310 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3314 // Get the SCEV for the GEP base.
3315 const SCEV *BaseS = getSCEV(Base);
3317 // Add the total offset from all the GEP indices to the base.
3318 return getAddExpr(BaseS, TotalOffset, Wrap);
3321 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3322 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3323 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3324 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3326 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3327 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3328 return C->getValue()->getValue().countTrailingZeros();
3330 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3331 return std::min(GetMinTrailingZeros(T->getOperand()),
3332 (uint32_t)getTypeSizeInBits(T->getType()));
3334 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3335 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3336 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3337 getTypeSizeInBits(E->getType()) : OpRes;
3340 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3341 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3342 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3343 getTypeSizeInBits(E->getType()) : OpRes;
3346 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3347 // The result is the min of all operands results.
3348 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3349 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3350 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3354 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3355 // The result is the sum of all operands results.
3356 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3357 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3358 for (unsigned i = 1, e = M->getNumOperands();
3359 SumOpRes != BitWidth && i != e; ++i)
3360 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3365 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3366 // The result is the min of all operands results.
3367 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3368 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3369 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3373 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3374 // The result is the min of all operands results.
3375 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3376 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3377 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3381 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3382 // The result is the min of all operands results.
3383 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3384 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3385 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3389 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3390 // For a SCEVUnknown, ask ValueTracking.
3391 unsigned BitWidth = getTypeSizeInBits(U->getType());
3392 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3393 computeKnownBits(U->getValue(), Zeros, Ones);
3394 return Zeros.countTrailingOnes();
3401 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3404 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3405 // See if we've computed this range already.
3406 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3407 if (I != UnsignedRanges.end())
3410 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3411 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3413 unsigned BitWidth = getTypeSizeInBits(S->getType());
3414 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3416 // If the value has known zeros, the maximum unsigned value will have those
3417 // known zeros as well.
3418 uint32_t TZ = GetMinTrailingZeros(S);
3420 ConservativeResult =
3421 ConstantRange(APInt::getMinValue(BitWidth),
3422 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3424 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3425 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3426 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3427 X = X.add(getUnsignedRange(Add->getOperand(i)));
3428 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3431 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3432 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3433 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3434 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3435 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3438 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3439 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3440 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3441 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3442 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3445 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3446 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3447 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3448 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3449 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3452 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3453 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3454 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3455 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3458 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3459 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3460 return setUnsignedRange(ZExt,
3461 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3464 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3465 ConstantRange X = getUnsignedRange(SExt->getOperand());
3466 return setUnsignedRange(SExt,
3467 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3470 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3471 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3472 return setUnsignedRange(Trunc,
3473 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3476 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3477 // If there's no unsigned wrap, the value will never be less than its
3479 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3480 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3481 if (!C->getValue()->isZero())
3482 ConservativeResult =
3483 ConservativeResult.intersectWith(
3484 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3486 // TODO: non-affine addrec
3487 if (AddRec->isAffine()) {
3488 Type *Ty = AddRec->getType();
3489 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3490 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3491 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3492 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3494 const SCEV *Start = AddRec->getStart();
3495 const SCEV *Step = AddRec->getStepRecurrence(*this);
3497 ConstantRange StartRange = getUnsignedRange(Start);
3498 ConstantRange StepRange = getSignedRange(Step);
3499 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3500 ConstantRange EndRange =
3501 StartRange.add(MaxBECountRange.multiply(StepRange));
3503 // Check for overflow. This must be done with ConstantRange arithmetic
3504 // because we could be called from within the ScalarEvolution overflow
3506 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3507 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3508 ConstantRange ExtMaxBECountRange =
3509 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3510 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3511 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3513 return setUnsignedRange(AddRec, ConservativeResult);
3515 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3516 EndRange.getUnsignedMin());
3517 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3518 EndRange.getUnsignedMax());
3519 if (Min.isMinValue() && Max.isMaxValue())
3520 return setUnsignedRange(AddRec, ConservativeResult);
3521 return setUnsignedRange(AddRec,
3522 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3526 return setUnsignedRange(AddRec, ConservativeResult);
3529 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3530 // For a SCEVUnknown, ask ValueTracking.
3531 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3532 computeKnownBits(U->getValue(), Zeros, Ones, DL);
3533 if (Ones == ~Zeros + 1)
3534 return setUnsignedRange(U, ConservativeResult);
3535 return setUnsignedRange(U,
3536 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3539 return setUnsignedRange(S, ConservativeResult);
3542 /// getSignedRange - Determine the signed range for a particular SCEV.
3545 ScalarEvolution::getSignedRange(const SCEV *S) {
3546 // See if we've computed this range already.
3547 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3548 if (I != SignedRanges.end())
3551 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3552 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3554 unsigned BitWidth = getTypeSizeInBits(S->getType());
3555 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3557 // If the value has known zeros, the maximum signed value will have those
3558 // known zeros as well.
3559 uint32_t TZ = GetMinTrailingZeros(S);
3561 ConservativeResult =
3562 ConstantRange(APInt::getSignedMinValue(BitWidth),
3563 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3565 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3566 ConstantRange X = getSignedRange(Add->getOperand(0));
3567 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3568 X = X.add(getSignedRange(Add->getOperand(i)));
3569 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3572 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3573 ConstantRange X = getSignedRange(Mul->getOperand(0));
3574 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3575 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3576 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3579 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3580 ConstantRange X = getSignedRange(SMax->getOperand(0));
3581 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3582 X = X.smax(getSignedRange(SMax->getOperand(i)));
3583 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3586 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3587 ConstantRange X = getSignedRange(UMax->getOperand(0));
3588 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3589 X = X.umax(getSignedRange(UMax->getOperand(i)));
3590 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3593 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3594 ConstantRange X = getSignedRange(UDiv->getLHS());
3595 ConstantRange Y = getSignedRange(UDiv->getRHS());
3596 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3599 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3600 ConstantRange X = getSignedRange(ZExt->getOperand());
3601 return setSignedRange(ZExt,
3602 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3605 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3606 ConstantRange X = getSignedRange(SExt->getOperand());
3607 return setSignedRange(SExt,
3608 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3611 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3612 ConstantRange X = getSignedRange(Trunc->getOperand());
3613 return setSignedRange(Trunc,
3614 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3617 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3618 // If there's no signed wrap, and all the operands have the same sign or
3619 // zero, the value won't ever change sign.
3620 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3621 bool AllNonNeg = true;
3622 bool AllNonPos = true;
3623 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3624 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3625 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3628 ConservativeResult = ConservativeResult.intersectWith(
3629 ConstantRange(APInt(BitWidth, 0),
3630 APInt::getSignedMinValue(BitWidth)));
3632 ConservativeResult = ConservativeResult.intersectWith(
3633 ConstantRange(APInt::getSignedMinValue(BitWidth),
3634 APInt(BitWidth, 1)));
3637 // TODO: non-affine addrec
3638 if (AddRec->isAffine()) {
3639 Type *Ty = AddRec->getType();
3640 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3641 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3642 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3643 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3645 const SCEV *Start = AddRec->getStart();
3646 const SCEV *Step = AddRec->getStepRecurrence(*this);
3648 ConstantRange StartRange = getSignedRange(Start);
3649 ConstantRange StepRange = getSignedRange(Step);
3650 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3651 ConstantRange EndRange =
3652 StartRange.add(MaxBECountRange.multiply(StepRange));
3654 // Check for overflow. This must be done with ConstantRange arithmetic
3655 // because we could be called from within the ScalarEvolution overflow
3657 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3658 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3659 ConstantRange ExtMaxBECountRange =
3660 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3661 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3662 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3664 return setSignedRange(AddRec, ConservativeResult);
3666 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3667 EndRange.getSignedMin());
3668 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3669 EndRange.getSignedMax());
3670 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3671 return setSignedRange(AddRec, ConservativeResult);
3672 return setSignedRange(AddRec,
3673 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3677 return setSignedRange(AddRec, ConservativeResult);
3680 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3681 // For a SCEVUnknown, ask ValueTracking.
3682 if (!U->getValue()->getType()->isIntegerTy() && !DL)
3683 return setSignedRange(U, ConservativeResult);
3684 unsigned NS = ComputeNumSignBits(U->getValue(), DL);
3686 return setSignedRange(U, ConservativeResult);
3687 return setSignedRange(U, ConservativeResult.intersectWith(
3688 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3689 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3692 return setSignedRange(S, ConservativeResult);
3695 /// createSCEV - We know that there is no SCEV for the specified value.
3696 /// Analyze the expression.
3698 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3699 if (!isSCEVable(V->getType()))
3700 return getUnknown(V);
3702 unsigned Opcode = Instruction::UserOp1;
3703 if (Instruction *I = dyn_cast<Instruction>(V)) {
3704 Opcode = I->getOpcode();
3706 // Don't attempt to analyze instructions in blocks that aren't
3707 // reachable. Such instructions don't matter, and they aren't required
3708 // to obey basic rules for definitions dominating uses which this
3709 // analysis depends on.
3710 if (!DT->isReachableFromEntry(I->getParent()))
3711 return getUnknown(V);
3712 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3713 Opcode = CE->getOpcode();
3714 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3715 return getConstant(CI);
3716 else if (isa<ConstantPointerNull>(V))
3717 return getConstant(V->getType(), 0);
3718 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3719 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3721 return getUnknown(V);
3723 Operator *U = cast<Operator>(V);
3725 case Instruction::Add: {
3726 // The simple thing to do would be to just call getSCEV on both operands
3727 // and call getAddExpr with the result. However if we're looking at a
3728 // bunch of things all added together, this can be quite inefficient,
3729 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3730 // Instead, gather up all the operands and make a single getAddExpr call.
3731 // LLVM IR canonical form means we need only traverse the left operands.
3733 // Don't apply this instruction's NSW or NUW flags to the new
3734 // expression. The instruction may be guarded by control flow that the
3735 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3736 // mapped to the same SCEV expression, and it would be incorrect to transfer
3737 // NSW/NUW semantics to those operations.
3738 SmallVector<const SCEV *, 4> AddOps;
3739 AddOps.push_back(getSCEV(U->getOperand(1)));
3740 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3741 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3742 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3744 U = cast<Operator>(Op);
3745 const SCEV *Op1 = getSCEV(U->getOperand(1));
3746 if (Opcode == Instruction::Sub)
3747 AddOps.push_back(getNegativeSCEV(Op1));
3749 AddOps.push_back(Op1);
3751 AddOps.push_back(getSCEV(U->getOperand(0)));
3752 return getAddExpr(AddOps);
3754 case Instruction::Mul: {
3755 // Don't transfer NSW/NUW for the same reason as AddExpr.
3756 SmallVector<const SCEV *, 4> MulOps;
3757 MulOps.push_back(getSCEV(U->getOperand(1)));
3758 for (Value *Op = U->getOperand(0);
3759 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3760 Op = U->getOperand(0)) {
3761 U = cast<Operator>(Op);
3762 MulOps.push_back(getSCEV(U->getOperand(1)));
3764 MulOps.push_back(getSCEV(U->getOperand(0)));
3765 return getMulExpr(MulOps);
3767 case Instruction::UDiv:
3768 return getUDivExpr(getSCEV(U->getOperand(0)),
3769 getSCEV(U->getOperand(1)));
3770 case Instruction::Sub:
3771 return getMinusSCEV(getSCEV(U->getOperand(0)),
3772 getSCEV(U->getOperand(1)));
3773 case Instruction::And:
3774 // For an expression like x&255 that merely masks off the high bits,
3775 // use zext(trunc(x)) as the SCEV expression.
3776 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3777 if (CI->isNullValue())
3778 return getSCEV(U->getOperand(1));
3779 if (CI->isAllOnesValue())
3780 return getSCEV(U->getOperand(0));
3781 const APInt &A = CI->getValue();
3783 // Instcombine's ShrinkDemandedConstant may strip bits out of
3784 // constants, obscuring what would otherwise be a low-bits mask.
3785 // Use computeKnownBits to compute what ShrinkDemandedConstant
3786 // knew about to reconstruct a low-bits mask value.
3787 unsigned LZ = A.countLeadingZeros();
3788 unsigned TZ = A.countTrailingZeros();
3789 unsigned BitWidth = A.getBitWidth();
3790 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3791 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL);
3793 APInt EffectiveMask =
3794 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
3795 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
3796 const SCEV *MulCount = getConstant(
3797 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
3801 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
3802 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
3809 case Instruction::Or:
3810 // If the RHS of the Or is a constant, we may have something like:
3811 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3812 // optimizations will transparently handle this case.
3814 // In order for this transformation to be safe, the LHS must be of the
3815 // form X*(2^n) and the Or constant must be less than 2^n.
3816 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3817 const SCEV *LHS = getSCEV(U->getOperand(0));
3818 const APInt &CIVal = CI->getValue();
3819 if (GetMinTrailingZeros(LHS) >=
3820 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3821 // Build a plain add SCEV.
3822 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3823 // If the LHS of the add was an addrec and it has no-wrap flags,
3824 // transfer the no-wrap flags, since an or won't introduce a wrap.
3825 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3826 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3827 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3828 OldAR->getNoWrapFlags());
3834 case Instruction::Xor:
3835 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3836 // If the RHS of the xor is a signbit, then this is just an add.
3837 // Instcombine turns add of signbit into xor as a strength reduction step.
3838 if (CI->getValue().isSignBit())
3839 return getAddExpr(getSCEV(U->getOperand(0)),
3840 getSCEV(U->getOperand(1)));
3842 // If the RHS of xor is -1, then this is a not operation.
3843 if (CI->isAllOnesValue())
3844 return getNotSCEV(getSCEV(U->getOperand(0)));
3846 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3847 // This is a variant of the check for xor with -1, and it handles
3848 // the case where instcombine has trimmed non-demanded bits out
3849 // of an xor with -1.
3850 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3851 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3852 if (BO->getOpcode() == Instruction::And &&
3853 LCI->getValue() == CI->getValue())
3854 if (const SCEVZeroExtendExpr *Z =
3855 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3856 Type *UTy = U->getType();
3857 const SCEV *Z0 = Z->getOperand();
3858 Type *Z0Ty = Z0->getType();
3859 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3861 // If C is a low-bits mask, the zero extend is serving to
3862 // mask off the high bits. Complement the operand and
3863 // re-apply the zext.
3864 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3865 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3867 // If C is a single bit, it may be in the sign-bit position
3868 // before the zero-extend. In this case, represent the xor
3869 // using an add, which is equivalent, and re-apply the zext.
3870 APInt Trunc = CI->getValue().trunc(Z0TySize);
3871 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3873 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3879 case Instruction::Shl:
3880 // Turn shift left of a constant amount into a multiply.
3881 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3882 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3884 // If the shift count is not less than the bitwidth, the result of
3885 // the shift is undefined. Don't try to analyze it, because the
3886 // resolution chosen here may differ from the resolution chosen in
3887 // other parts of the compiler.
3888 if (SA->getValue().uge(BitWidth))
3891 Constant *X = ConstantInt::get(getContext(),
3892 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3893 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3897 case Instruction::LShr:
3898 // Turn logical shift right of a constant into a unsigned divide.
3899 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3900 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3902 // If the shift count is not less than the bitwidth, the result of
3903 // the shift is undefined. Don't try to analyze it, because the
3904 // resolution chosen here may differ from the resolution chosen in
3905 // other parts of the compiler.
3906 if (SA->getValue().uge(BitWidth))
3909 Constant *X = ConstantInt::get(getContext(),
3910 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3911 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3915 case Instruction::AShr:
3916 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3917 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3918 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3919 if (L->getOpcode() == Instruction::Shl &&
3920 L->getOperand(1) == U->getOperand(1)) {
3921 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3923 // If the shift count is not less than the bitwidth, the result of
3924 // the shift is undefined. Don't try to analyze it, because the
3925 // resolution chosen here may differ from the resolution chosen in
3926 // other parts of the compiler.
3927 if (CI->getValue().uge(BitWidth))
3930 uint64_t Amt = BitWidth - CI->getZExtValue();
3931 if (Amt == BitWidth)
3932 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3934 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3935 IntegerType::get(getContext(),
3941 case Instruction::Trunc:
3942 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3944 case Instruction::ZExt:
3945 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3947 case Instruction::SExt:
3948 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3950 case Instruction::BitCast:
3951 // BitCasts are no-op casts so we just eliminate the cast.
3952 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3953 return getSCEV(U->getOperand(0));
3956 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3957 // lead to pointer expressions which cannot safely be expanded to GEPs,
3958 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3959 // simplifying integer expressions.
3961 case Instruction::GetElementPtr:
3962 return createNodeForGEP(cast<GEPOperator>(U));
3964 case Instruction::PHI:
3965 return createNodeForPHI(cast<PHINode>(U));
3967 case Instruction::Select:
3968 // This could be a smax or umax that was lowered earlier.
3969 // Try to recover it.
3970 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3971 Value *LHS = ICI->getOperand(0);
3972 Value *RHS = ICI->getOperand(1);
3973 switch (ICI->getPredicate()) {
3974 case ICmpInst::ICMP_SLT:
3975 case ICmpInst::ICMP_SLE:
3976 std::swap(LHS, RHS);
3978 case ICmpInst::ICMP_SGT:
3979 case ICmpInst::ICMP_SGE:
3980 // a >s b ? a+x : b+x -> smax(a, b)+x
3981 // a >s b ? b+x : a+x -> smin(a, b)+x
3982 if (LHS->getType() == U->getType()) {
3983 const SCEV *LS = getSCEV(LHS);
3984 const SCEV *RS = getSCEV(RHS);
3985 const SCEV *LA = getSCEV(U->getOperand(1));
3986 const SCEV *RA = getSCEV(U->getOperand(2));
3987 const SCEV *LDiff = getMinusSCEV(LA, LS);
3988 const SCEV *RDiff = getMinusSCEV(RA, RS);
3990 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3991 LDiff = getMinusSCEV(LA, RS);
3992 RDiff = getMinusSCEV(RA, LS);
3994 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3997 case ICmpInst::ICMP_ULT:
3998 case ICmpInst::ICMP_ULE:
3999 std::swap(LHS, RHS);
4001 case ICmpInst::ICMP_UGT:
4002 case ICmpInst::ICMP_UGE:
4003 // a >u b ? a+x : b+x -> umax(a, b)+x
4004 // a >u b ? b+x : a+x -> umin(a, b)+x
4005 if (LHS->getType() == U->getType()) {
4006 const SCEV *LS = getSCEV(LHS);
4007 const SCEV *RS = getSCEV(RHS);
4008 const SCEV *LA = getSCEV(U->getOperand(1));
4009 const SCEV *RA = getSCEV(U->getOperand(2));
4010 const SCEV *LDiff = getMinusSCEV(LA, LS);
4011 const SCEV *RDiff = getMinusSCEV(RA, RS);
4013 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4014 LDiff = getMinusSCEV(LA, RS);
4015 RDiff = getMinusSCEV(RA, LS);
4017 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4020 case ICmpInst::ICMP_NE:
4021 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4022 if (LHS->getType() == U->getType() &&
4023 isa<ConstantInt>(RHS) &&
4024 cast<ConstantInt>(RHS)->isZero()) {
4025 const SCEV *One = getConstant(LHS->getType(), 1);
4026 const SCEV *LS = getSCEV(LHS);
4027 const SCEV *LA = getSCEV(U->getOperand(1));
4028 const SCEV *RA = getSCEV(U->getOperand(2));
4029 const SCEV *LDiff = getMinusSCEV(LA, LS);
4030 const SCEV *RDiff = getMinusSCEV(RA, One);
4032 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4035 case ICmpInst::ICMP_EQ:
4036 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4037 if (LHS->getType() == U->getType() &&
4038 isa<ConstantInt>(RHS) &&
4039 cast<ConstantInt>(RHS)->isZero()) {
4040 const SCEV *One = getConstant(LHS->getType(), 1);
4041 const SCEV *LS = getSCEV(LHS);
4042 const SCEV *LA = getSCEV(U->getOperand(1));
4043 const SCEV *RA = getSCEV(U->getOperand(2));
4044 const SCEV *LDiff = getMinusSCEV(LA, One);
4045 const SCEV *RDiff = getMinusSCEV(RA, LS);
4047 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4055 default: // We cannot analyze this expression.
4059 return getUnknown(V);
4064 //===----------------------------------------------------------------------===//
4065 // Iteration Count Computation Code
4068 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4069 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4070 /// constant. Will also return 0 if the maximum trip count is very large (>=
4073 /// This "trip count" assumes that control exits via ExitingBlock. More
4074 /// precisely, it is the number of times that control may reach ExitingBlock
4075 /// before taking the branch. For loops with multiple exits, it may not be the
4076 /// number times that the loop header executes because the loop may exit
4077 /// prematurely via another branch.
4079 /// FIXME: We conservatively call getBackedgeTakenCount(L) instead of
4080 /// getExitCount(L, ExitingBlock) to compute a safe trip count considering all
4081 /// loop exits. getExitCount() may return an exact count for this branch
4082 /// assuming no-signed-wrap. The number of well-defined iterations may actually
4083 /// be higher than this trip count if this exit test is skipped and the loop
4084 /// exits via a different branch. Ideally, getExitCount() would know whether it
4085 /// depends on a NSW assumption, and we would only fall back to a conservative
4086 /// trip count in that case.
4087 unsigned ScalarEvolution::
4088 getSmallConstantTripCount(Loop *L, BasicBlock * /*ExitingBlock*/) {
4089 const SCEVConstant *ExitCount =
4090 dyn_cast<SCEVConstant>(getBackedgeTakenCount(L));
4094 ConstantInt *ExitConst = ExitCount->getValue();
4096 // Guard against huge trip counts.
4097 if (ExitConst->getValue().getActiveBits() > 32)
4100 // In case of integer overflow, this returns 0, which is correct.
4101 return ((unsigned)ExitConst->getZExtValue()) + 1;
4104 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4105 /// trip count of this loop as a normal unsigned value, if possible. This
4106 /// means that the actual trip count is always a multiple of the returned
4107 /// value (don't forget the trip count could very well be zero as well!).
4109 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4110 /// multiple of a constant (which is also the case if the trip count is simply
4111 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4112 /// if the trip count is very large (>= 2^32).
4114 /// As explained in the comments for getSmallConstantTripCount, this assumes
4115 /// that control exits the loop via ExitingBlock.
4116 unsigned ScalarEvolution::
4117 getSmallConstantTripMultiple(Loop *L, BasicBlock * /*ExitingBlock*/) {
4118 const SCEV *ExitCount = getBackedgeTakenCount(L);
4119 if (ExitCount == getCouldNotCompute())
4122 // Get the trip count from the BE count by adding 1.
4123 const SCEV *TCMul = getAddExpr(ExitCount,
4124 getConstant(ExitCount->getType(), 1));
4125 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4126 // to factor simple cases.
4127 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4128 TCMul = Mul->getOperand(0);
4130 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4134 ConstantInt *Result = MulC->getValue();
4136 // Guard against huge trip counts (this requires checking
4137 // for zero to handle the case where the trip count == -1 and the
4139 if (!Result || Result->getValue().getActiveBits() > 32 ||
4140 Result->getValue().getActiveBits() == 0)
4143 return (unsigned)Result->getZExtValue();
4146 // getExitCount - Get the expression for the number of loop iterations for which
4147 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4148 // SCEVCouldNotCompute.
4149 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4150 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4153 /// getBackedgeTakenCount - If the specified loop has a predictable
4154 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4155 /// object. The backedge-taken count is the number of times the loop header
4156 /// will be branched to from within the loop. This is one less than the
4157 /// trip count of the loop, since it doesn't count the first iteration,
4158 /// when the header is branched to from outside the loop.
4160 /// Note that it is not valid to call this method on a loop without a
4161 /// loop-invariant backedge-taken count (see
4162 /// hasLoopInvariantBackedgeTakenCount).
4164 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4165 return getBackedgeTakenInfo(L).getExact(this);
4168 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4169 /// return the least SCEV value that is known never to be less than the
4170 /// actual backedge taken count.
4171 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4172 return getBackedgeTakenInfo(L).getMax(this);
4175 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4176 /// onto the given Worklist.
4178 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4179 BasicBlock *Header = L->getHeader();
4181 // Push all Loop-header PHIs onto the Worklist stack.
4182 for (BasicBlock::iterator I = Header->begin();
4183 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4184 Worklist.push_back(PN);
4187 const ScalarEvolution::BackedgeTakenInfo &
4188 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4189 // Initially insert an invalid entry for this loop. If the insertion
4190 // succeeds, proceed to actually compute a backedge-taken count and
4191 // update the value. The temporary CouldNotCompute value tells SCEV
4192 // code elsewhere that it shouldn't attempt to request a new
4193 // backedge-taken count, which could result in infinite recursion.
4194 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4195 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4197 return Pair.first->second;
4199 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4200 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4201 // must be cleared in this scope.
4202 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4204 if (Result.getExact(this) != getCouldNotCompute()) {
4205 assert(isLoopInvariant(Result.getExact(this), L) &&
4206 isLoopInvariant(Result.getMax(this), L) &&
4207 "Computed backedge-taken count isn't loop invariant for loop!");
4208 ++NumTripCountsComputed;
4210 else if (Result.getMax(this) == getCouldNotCompute() &&
4211 isa<PHINode>(L->getHeader()->begin())) {
4212 // Only count loops that have phi nodes as not being computable.
4213 ++NumTripCountsNotComputed;
4216 // Now that we know more about the trip count for this loop, forget any
4217 // existing SCEV values for PHI nodes in this loop since they are only
4218 // conservative estimates made without the benefit of trip count
4219 // information. This is similar to the code in forgetLoop, except that
4220 // it handles SCEVUnknown PHI nodes specially.
4221 if (Result.hasAnyInfo()) {
4222 SmallVector<Instruction *, 16> Worklist;
4223 PushLoopPHIs(L, Worklist);
4225 SmallPtrSet<Instruction *, 8> Visited;
4226 while (!Worklist.empty()) {
4227 Instruction *I = Worklist.pop_back_val();
4228 if (!Visited.insert(I)) continue;
4230 ValueExprMapType::iterator It =
4231 ValueExprMap.find_as(static_cast<Value *>(I));
4232 if (It != ValueExprMap.end()) {
4233 const SCEV *Old = It->second;
4235 // SCEVUnknown for a PHI either means that it has an unrecognized
4236 // structure, or it's a PHI that's in the progress of being computed
4237 // by createNodeForPHI. In the former case, additional loop trip
4238 // count information isn't going to change anything. In the later
4239 // case, createNodeForPHI will perform the necessary updates on its
4240 // own when it gets to that point.
4241 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4242 forgetMemoizedResults(Old);
4243 ValueExprMap.erase(It);
4245 if (PHINode *PN = dyn_cast<PHINode>(I))
4246 ConstantEvolutionLoopExitValue.erase(PN);
4249 PushDefUseChildren(I, Worklist);
4253 // Re-lookup the insert position, since the call to
4254 // ComputeBackedgeTakenCount above could result in a
4255 // recusive call to getBackedgeTakenInfo (on a different
4256 // loop), which would invalidate the iterator computed
4258 return BackedgeTakenCounts.find(L)->second = Result;
4261 /// forgetLoop - This method should be called by the client when it has
4262 /// changed a loop in a way that may effect ScalarEvolution's ability to
4263 /// compute a trip count, or if the loop is deleted.
4264 void ScalarEvolution::forgetLoop(const Loop *L) {
4265 // Drop any stored trip count value.
4266 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4267 BackedgeTakenCounts.find(L);
4268 if (BTCPos != BackedgeTakenCounts.end()) {
4269 BTCPos->second.clear();
4270 BackedgeTakenCounts.erase(BTCPos);
4273 // Drop information about expressions based on loop-header PHIs.
4274 SmallVector<Instruction *, 16> Worklist;
4275 PushLoopPHIs(L, Worklist);
4277 SmallPtrSet<Instruction *, 8> Visited;
4278 while (!Worklist.empty()) {
4279 Instruction *I = Worklist.pop_back_val();
4280 if (!Visited.insert(I)) continue;
4282 ValueExprMapType::iterator It =
4283 ValueExprMap.find_as(static_cast<Value *>(I));
4284 if (It != ValueExprMap.end()) {
4285 forgetMemoizedResults(It->second);
4286 ValueExprMap.erase(It);
4287 if (PHINode *PN = dyn_cast<PHINode>(I))
4288 ConstantEvolutionLoopExitValue.erase(PN);
4291 PushDefUseChildren(I, Worklist);
4294 // Forget all contained loops too, to avoid dangling entries in the
4295 // ValuesAtScopes map.
4296 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4300 /// forgetValue - This method should be called by the client when it has
4301 /// changed a value in a way that may effect its value, or which may
4302 /// disconnect it from a def-use chain linking it to a loop.
4303 void ScalarEvolution::forgetValue(Value *V) {
4304 Instruction *I = dyn_cast<Instruction>(V);
4307 // Drop information about expressions based on loop-header PHIs.
4308 SmallVector<Instruction *, 16> Worklist;
4309 Worklist.push_back(I);
4311 SmallPtrSet<Instruction *, 8> Visited;
4312 while (!Worklist.empty()) {
4313 I = Worklist.pop_back_val();
4314 if (!Visited.insert(I)) continue;
4316 ValueExprMapType::iterator It =
4317 ValueExprMap.find_as(static_cast<Value *>(I));
4318 if (It != ValueExprMap.end()) {
4319 forgetMemoizedResults(It->second);
4320 ValueExprMap.erase(It);
4321 if (PHINode *PN = dyn_cast<PHINode>(I))
4322 ConstantEvolutionLoopExitValue.erase(PN);
4325 PushDefUseChildren(I, Worklist);
4329 /// getExact - Get the exact loop backedge taken count considering all loop
4330 /// exits. A computable result can only be return for loops with a single exit.
4331 /// Returning the minimum taken count among all exits is incorrect because one
4332 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4333 /// the limit of each loop test is never skipped. This is a valid assumption as
4334 /// long as the loop exits via that test. For precise results, it is the
4335 /// caller's responsibility to specify the relevant loop exit using
4336 /// getExact(ExitingBlock, SE).
4338 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4339 // If any exits were not computable, the loop is not computable.
4340 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4342 // We need exactly one computable exit.
4343 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4344 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4346 const SCEV *BECount = nullptr;
4347 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4348 ENT != nullptr; ENT = ENT->getNextExit()) {
4350 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4353 BECount = ENT->ExactNotTaken;
4354 else if (BECount != ENT->ExactNotTaken)
4355 return SE->getCouldNotCompute();
4357 assert(BECount && "Invalid not taken count for loop exit");
4361 /// getExact - Get the exact not taken count for this loop exit.
4363 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4364 ScalarEvolution *SE) const {
4365 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4366 ENT != nullptr; ENT = ENT->getNextExit()) {
4368 if (ENT->ExitingBlock == ExitingBlock)
4369 return ENT->ExactNotTaken;
4371 return SE->getCouldNotCompute();
4374 /// getMax - Get the max backedge taken count for the loop.
4376 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4377 return Max ? Max : SE->getCouldNotCompute();
4380 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4381 ScalarEvolution *SE) const {
4382 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4385 if (!ExitNotTaken.ExitingBlock)
4388 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4389 ENT != nullptr; ENT = ENT->getNextExit()) {
4391 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4392 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4399 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4400 /// computable exit into a persistent ExitNotTakenInfo array.
4401 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4402 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4403 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4406 ExitNotTaken.setIncomplete();
4408 unsigned NumExits = ExitCounts.size();
4409 if (NumExits == 0) return;
4411 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4412 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4413 if (NumExits == 1) return;
4415 // Handle the rare case of multiple computable exits.
4416 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4418 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4419 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4420 PrevENT->setNextExit(ENT);
4421 ENT->ExitingBlock = ExitCounts[i].first;
4422 ENT->ExactNotTaken = ExitCounts[i].second;
4426 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4427 void ScalarEvolution::BackedgeTakenInfo::clear() {
4428 ExitNotTaken.ExitingBlock = nullptr;
4429 ExitNotTaken.ExactNotTaken = nullptr;
4430 delete[] ExitNotTaken.getNextExit();
4433 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4434 /// of the specified loop will execute.
4435 ScalarEvolution::BackedgeTakenInfo
4436 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4437 SmallVector<BasicBlock *, 8> ExitingBlocks;
4438 L->getExitingBlocks(ExitingBlocks);
4440 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4441 bool CouldComputeBECount = true;
4442 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4443 const SCEV *MustExitMaxBECount = nullptr;
4444 const SCEV *MayExitMaxBECount = nullptr;
4446 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4447 // and compute maxBECount.
4448 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4449 BasicBlock *ExitBB = ExitingBlocks[i];
4450 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4452 // 1. For each exit that can be computed, add an entry to ExitCounts.
4453 // CouldComputeBECount is true only if all exits can be computed.
4454 if (EL.Exact == getCouldNotCompute())
4455 // We couldn't compute an exact value for this exit, so
4456 // we won't be able to compute an exact value for the loop.
4457 CouldComputeBECount = false;
4459 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4461 // 2. Derive the loop's MaxBECount from each exit's max number of
4462 // non-exiting iterations. Partition the loop exits into two kinds:
4463 // LoopMustExits and LoopMayExits.
4465 // A LoopMustExit meets two requirements:
4467 // (a) Its ExitLimit.MustExit flag must be set which indicates that the exit
4468 // test condition cannot be skipped (the tested variable has unit stride or
4469 // the test is less-than or greater-than, rather than a strict inequality).
4471 // (b) It must dominate the loop latch, hence must be tested on every loop
4474 // If any computable LoopMustExit is found, then MaxBECount is the minimum
4475 // EL.Max of computable LoopMustExits. Otherwise, MaxBECount is
4476 // conservatively the maximum EL.Max, where CouldNotCompute is considered
4477 // greater than any computable EL.Max.
4478 if (EL.MustExit && EL.Max != getCouldNotCompute() && Latch &&
4479 DT->dominates(ExitBB, Latch)) {
4480 if (!MustExitMaxBECount)
4481 MustExitMaxBECount = EL.Max;
4483 MustExitMaxBECount =
4484 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4486 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4487 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4488 MayExitMaxBECount = EL.Max;
4491 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4495 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4496 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4497 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4500 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4501 /// loop will execute if it exits via the specified block.
4502 ScalarEvolution::ExitLimit
4503 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4505 // Okay, we've chosen an exiting block. See what condition causes us to
4506 // exit at this block and remember the exit block and whether all other targets
4507 // lead to the loop header.
4508 bool MustExecuteLoopHeader = true;
4509 BasicBlock *Exit = nullptr;
4510 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4512 if (!L->contains(*SI)) {
4513 if (Exit) // Multiple exit successors.
4514 return getCouldNotCompute();
4516 } else if (*SI != L->getHeader()) {
4517 MustExecuteLoopHeader = false;
4520 // At this point, we know we have a conditional branch that determines whether
4521 // the loop is exited. However, we don't know if the branch is executed each
4522 // time through the loop. If not, then the execution count of the branch will
4523 // not be equal to the trip count of the loop.
4525 // Currently we check for this by checking to see if the Exit branch goes to
4526 // the loop header. If so, we know it will always execute the same number of
4527 // times as the loop. We also handle the case where the exit block *is* the
4528 // loop header. This is common for un-rotated loops.
4530 // If both of those tests fail, walk up the unique predecessor chain to the
4531 // header, stopping if there is an edge that doesn't exit the loop. If the
4532 // header is reached, the execution count of the branch will be equal to the
4533 // trip count of the loop.
4535 // More extensive analysis could be done to handle more cases here.
4537 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4538 // The simple checks failed, try climbing the unique predecessor chain
4539 // up to the header.
4541 for (BasicBlock *BB = ExitingBlock; BB; ) {
4542 BasicBlock *Pred = BB->getUniquePredecessor();
4544 return getCouldNotCompute();
4545 TerminatorInst *PredTerm = Pred->getTerminator();
4546 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4547 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4550 // If the predecessor has a successor that isn't BB and isn't
4551 // outside the loop, assume the worst.
4552 if (L->contains(PredSucc))
4553 return getCouldNotCompute();
4555 if (Pred == L->getHeader()) {
4562 return getCouldNotCompute();
4565 TerminatorInst *Term = ExitingBlock->getTerminator();
4566 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4567 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4568 // Proceed to the next level to examine the exit condition expression.
4569 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4570 BI->getSuccessor(1),
4571 /*IsSubExpr=*/false);
4574 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4575 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4576 /*IsSubExpr=*/false);
4578 return getCouldNotCompute();
4581 /// ComputeExitLimitFromCond - Compute the number of times the
4582 /// backedge of the specified loop will execute if its exit condition
4583 /// were a conditional branch of ExitCond, TBB, and FBB.
4585 /// @param IsSubExpr is true if ExitCond does not directly control the exit
4586 /// branch. In this case, we cannot assume that the loop only exits when the
4587 /// condition is true and cannot infer that failing to meet the condition prior
4588 /// to integer wraparound results in undefined behavior.
4589 ScalarEvolution::ExitLimit
4590 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4595 // Check if the controlling expression for this loop is an And or Or.
4596 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4597 if (BO->getOpcode() == Instruction::And) {
4598 // Recurse on the operands of the and.
4599 bool EitherMayExit = L->contains(TBB);
4600 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4601 IsSubExpr || EitherMayExit);
4602 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4603 IsSubExpr || EitherMayExit);
4604 const SCEV *BECount = getCouldNotCompute();
4605 const SCEV *MaxBECount = getCouldNotCompute();
4606 bool MustExit = false;
4607 if (EitherMayExit) {
4608 // Both conditions must be true for the loop to continue executing.
4609 // Choose the less conservative count.
4610 if (EL0.Exact == getCouldNotCompute() ||
4611 EL1.Exact == getCouldNotCompute())
4612 BECount = getCouldNotCompute();
4614 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4615 if (EL0.Max == getCouldNotCompute())
4616 MaxBECount = EL1.Max;
4617 else if (EL1.Max == getCouldNotCompute())
4618 MaxBECount = EL0.Max;
4620 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4621 MustExit = EL0.MustExit || EL1.MustExit;
4623 // Both conditions must be true at the same time for the loop to exit.
4624 // For now, be conservative.
4625 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4626 if (EL0.Max == EL1.Max)
4627 MaxBECount = EL0.Max;
4628 if (EL0.Exact == EL1.Exact)
4629 BECount = EL0.Exact;
4630 MustExit = EL0.MustExit && EL1.MustExit;
4633 return ExitLimit(BECount, MaxBECount, MustExit);
4635 if (BO->getOpcode() == Instruction::Or) {
4636 // Recurse on the operands of the or.
4637 bool EitherMayExit = L->contains(FBB);
4638 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4639 IsSubExpr || EitherMayExit);
4640 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4641 IsSubExpr || EitherMayExit);
4642 const SCEV *BECount = getCouldNotCompute();
4643 const SCEV *MaxBECount = getCouldNotCompute();
4644 bool MustExit = false;
4645 if (EitherMayExit) {
4646 // Both conditions must be false for the loop to continue executing.
4647 // Choose the less conservative count.
4648 if (EL0.Exact == getCouldNotCompute() ||
4649 EL1.Exact == getCouldNotCompute())
4650 BECount = getCouldNotCompute();
4652 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4653 if (EL0.Max == getCouldNotCompute())
4654 MaxBECount = EL1.Max;
4655 else if (EL1.Max == getCouldNotCompute())
4656 MaxBECount = EL0.Max;
4658 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4659 MustExit = EL0.MustExit || EL1.MustExit;
4661 // Both conditions must be false at the same time for the loop to exit.
4662 // For now, be conservative.
4663 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4664 if (EL0.Max == EL1.Max)
4665 MaxBECount = EL0.Max;
4666 if (EL0.Exact == EL1.Exact)
4667 BECount = EL0.Exact;
4668 MustExit = EL0.MustExit && EL1.MustExit;
4671 return ExitLimit(BECount, MaxBECount, MustExit);
4675 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4676 // Proceed to the next level to examine the icmp.
4677 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4678 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, IsSubExpr);
4680 // Check for a constant condition. These are normally stripped out by
4681 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4682 // preserve the CFG and is temporarily leaving constant conditions
4684 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4685 if (L->contains(FBB) == !CI->getZExtValue())
4686 // The backedge is always taken.
4687 return getCouldNotCompute();
4689 // The backedge is never taken.
4690 return getConstant(CI->getType(), 0);
4693 // If it's not an integer or pointer comparison then compute it the hard way.
4694 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4697 /// ComputeExitLimitFromICmp - Compute the number of times the
4698 /// backedge of the specified loop will execute if its exit condition
4699 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4700 ScalarEvolution::ExitLimit
4701 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4707 // If the condition was exit on true, convert the condition to exit on false
4708 ICmpInst::Predicate Cond;
4709 if (!L->contains(FBB))
4710 Cond = ExitCond->getPredicate();
4712 Cond = ExitCond->getInversePredicate();
4714 // Handle common loops like: for (X = "string"; *X; ++X)
4715 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4716 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4718 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4719 if (ItCnt.hasAnyInfo())
4723 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4724 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4726 // Try to evaluate any dependencies out of the loop.
4727 LHS = getSCEVAtScope(LHS, L);
4728 RHS = getSCEVAtScope(RHS, L);
4730 // At this point, we would like to compute how many iterations of the
4731 // loop the predicate will return true for these inputs.
4732 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4733 // If there is a loop-invariant, force it into the RHS.
4734 std::swap(LHS, RHS);
4735 Cond = ICmpInst::getSwappedPredicate(Cond);
4738 // Simplify the operands before analyzing them.
4739 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4741 // If we have a comparison of a chrec against a constant, try to use value
4742 // ranges to answer this query.
4743 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4744 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4745 if (AddRec->getLoop() == L) {
4746 // Form the constant range.
4747 ConstantRange CompRange(
4748 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4750 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4751 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4755 case ICmpInst::ICMP_NE: { // while (X != Y)
4756 // Convert to: while (X-Y != 0)
4757 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4758 if (EL.hasAnyInfo()) return EL;
4761 case ICmpInst::ICMP_EQ: { // while (X == Y)
4762 // Convert to: while (X-Y == 0)
4763 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4764 if (EL.hasAnyInfo()) return EL;
4767 case ICmpInst::ICMP_SLT:
4768 case ICmpInst::ICMP_ULT: { // while (X < Y)
4769 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
4770 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, IsSubExpr);
4771 if (EL.hasAnyInfo()) return EL;
4774 case ICmpInst::ICMP_SGT:
4775 case ICmpInst::ICMP_UGT: { // while (X > Y)
4776 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
4777 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, IsSubExpr);
4778 if (EL.hasAnyInfo()) return EL;
4783 dbgs() << "ComputeBackedgeTakenCount ";
4784 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4785 dbgs() << "[unsigned] ";
4786 dbgs() << *LHS << " "
4787 << Instruction::getOpcodeName(Instruction::ICmp)
4788 << " " << *RHS << "\n";
4792 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4795 ScalarEvolution::ExitLimit
4796 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
4798 BasicBlock *ExitingBlock,
4800 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
4802 // Give up if the exit is the default dest of a switch.
4803 if (Switch->getDefaultDest() == ExitingBlock)
4804 return getCouldNotCompute();
4806 assert(L->contains(Switch->getDefaultDest()) &&
4807 "Default case must not exit the loop!");
4808 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
4809 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
4811 // while (X != Y) --> while (X-Y != 0)
4812 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4813 if (EL.hasAnyInfo())
4816 return getCouldNotCompute();
4819 static ConstantInt *
4820 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4821 ScalarEvolution &SE) {
4822 const SCEV *InVal = SE.getConstant(C);
4823 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4824 assert(isa<SCEVConstant>(Val) &&
4825 "Evaluation of SCEV at constant didn't fold correctly?");
4826 return cast<SCEVConstant>(Val)->getValue();
4829 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4830 /// 'icmp op load X, cst', try to see if we can compute the backedge
4831 /// execution count.
4832 ScalarEvolution::ExitLimit
4833 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4837 ICmpInst::Predicate predicate) {
4839 if (LI->isVolatile()) return getCouldNotCompute();
4841 // Check to see if the loaded pointer is a getelementptr of a global.
4842 // TODO: Use SCEV instead of manually grubbing with GEPs.
4843 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4844 if (!GEP) return getCouldNotCompute();
4846 // Make sure that it is really a constant global we are gepping, with an
4847 // initializer, and make sure the first IDX is really 0.
4848 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4849 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4850 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4851 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4852 return getCouldNotCompute();
4854 // Okay, we allow one non-constant index into the GEP instruction.
4855 Value *VarIdx = nullptr;
4856 std::vector<Constant*> Indexes;
4857 unsigned VarIdxNum = 0;
4858 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4859 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4860 Indexes.push_back(CI);
4861 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4862 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4863 VarIdx = GEP->getOperand(i);
4865 Indexes.push_back(nullptr);
4868 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4870 return getCouldNotCompute();
4872 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4873 // Check to see if X is a loop variant variable value now.
4874 const SCEV *Idx = getSCEV(VarIdx);
4875 Idx = getSCEVAtScope(Idx, L);
4877 // We can only recognize very limited forms of loop index expressions, in
4878 // particular, only affine AddRec's like {C1,+,C2}.
4879 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4880 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4881 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4882 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4883 return getCouldNotCompute();
4885 unsigned MaxSteps = MaxBruteForceIterations;
4886 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4887 ConstantInt *ItCst = ConstantInt::get(
4888 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4889 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4891 // Form the GEP offset.
4892 Indexes[VarIdxNum] = Val;
4894 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4896 if (!Result) break; // Cannot compute!
4898 // Evaluate the condition for this iteration.
4899 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4900 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4901 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4903 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4904 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4907 ++NumArrayLenItCounts;
4908 return getConstant(ItCst); // Found terminating iteration!
4911 return getCouldNotCompute();
4915 /// CanConstantFold - Return true if we can constant fold an instruction of the
4916 /// specified type, assuming that all operands were constants.
4917 static bool CanConstantFold(const Instruction *I) {
4918 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4919 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4923 if (const CallInst *CI = dyn_cast<CallInst>(I))
4924 if (const Function *F = CI->getCalledFunction())
4925 return canConstantFoldCallTo(F);
4929 /// Determine whether this instruction can constant evolve within this loop
4930 /// assuming its operands can all constant evolve.
4931 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4932 // An instruction outside of the loop can't be derived from a loop PHI.
4933 if (!L->contains(I)) return false;
4935 if (isa<PHINode>(I)) {
4936 if (L->getHeader() == I->getParent())
4939 // We don't currently keep track of the control flow needed to evaluate
4940 // PHIs, so we cannot handle PHIs inside of loops.
4944 // If we won't be able to constant fold this expression even if the operands
4945 // are constants, bail early.
4946 return CanConstantFold(I);
4949 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4950 /// recursing through each instruction operand until reaching a loop header phi.
4952 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4953 DenseMap<Instruction *, PHINode *> &PHIMap) {
4955 // Otherwise, we can evaluate this instruction if all of its operands are
4956 // constant or derived from a PHI node themselves.
4957 PHINode *PHI = nullptr;
4958 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4959 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4961 if (isa<Constant>(*OpI)) continue;
4963 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4964 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
4966 PHINode *P = dyn_cast<PHINode>(OpInst);
4968 // If this operand is already visited, reuse the prior result.
4969 // We may have P != PHI if this is the deepest point at which the
4970 // inconsistent paths meet.
4971 P = PHIMap.lookup(OpInst);
4973 // Recurse and memoize the results, whether a phi is found or not.
4974 // This recursive call invalidates pointers into PHIMap.
4975 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4979 return nullptr; // Not evolving from PHI
4980 if (PHI && PHI != P)
4981 return nullptr; // Evolving from multiple different PHIs.
4984 // This is a expression evolving from a constant PHI!
4988 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4989 /// in the loop that V is derived from. We allow arbitrary operations along the
4990 /// way, but the operands of an operation must either be constants or a value
4991 /// derived from a constant PHI. If this expression does not fit with these
4992 /// constraints, return null.
4993 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4994 Instruction *I = dyn_cast<Instruction>(V);
4995 if (!I || !canConstantEvolve(I, L)) return nullptr;
4997 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5001 // Record non-constant instructions contained by the loop.
5002 DenseMap<Instruction *, PHINode *> PHIMap;
5003 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5006 /// EvaluateExpression - Given an expression that passes the
5007 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5008 /// in the loop has the value PHIVal. If we can't fold this expression for some
5009 /// reason, return null.
5010 static Constant *EvaluateExpression(Value *V, const Loop *L,
5011 DenseMap<Instruction *, Constant *> &Vals,
5012 const DataLayout *DL,
5013 const TargetLibraryInfo *TLI) {
5014 // Convenient constant check, but redundant for recursive calls.
5015 if (Constant *C = dyn_cast<Constant>(V)) return C;
5016 Instruction *I = dyn_cast<Instruction>(V);
5017 if (!I) return nullptr;
5019 if (Constant *C = Vals.lookup(I)) return C;
5021 // An instruction inside the loop depends on a value outside the loop that we
5022 // weren't given a mapping for, or a value such as a call inside the loop.
5023 if (!canConstantEvolve(I, L)) return nullptr;
5025 // An unmapped PHI can be due to a branch or another loop inside this loop,
5026 // or due to this not being the initial iteration through a loop where we
5027 // couldn't compute the evolution of this particular PHI last time.
5028 if (isa<PHINode>(I)) return nullptr;
5030 std::vector<Constant*> Operands(I->getNumOperands());
5032 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5033 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5035 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5036 if (!Operands[i]) return nullptr;
5039 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5041 if (!C) return nullptr;
5045 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5046 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5047 Operands[1], DL, TLI);
5048 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5049 if (!LI->isVolatile())
5050 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5052 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5056 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5057 /// in the header of its containing loop, we know the loop executes a
5058 /// constant number of times, and the PHI node is just a recurrence
5059 /// involving constants, fold it.
5061 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5064 DenseMap<PHINode*, Constant*>::const_iterator I =
5065 ConstantEvolutionLoopExitValue.find(PN);
5066 if (I != ConstantEvolutionLoopExitValue.end())
5069 if (BEs.ugt(MaxBruteForceIterations))
5070 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5072 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5074 DenseMap<Instruction *, Constant *> CurrentIterVals;
5075 BasicBlock *Header = L->getHeader();
5076 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5078 // Since the loop is canonicalized, the PHI node must have two entries. One
5079 // entry must be a constant (coming in from outside of the loop), and the
5080 // second must be derived from the same PHI.
5081 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5082 PHINode *PHI = nullptr;
5083 for (BasicBlock::iterator I = Header->begin();
5084 (PHI = dyn_cast<PHINode>(I)); ++I) {
5085 Constant *StartCST =
5086 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5087 if (!StartCST) continue;
5088 CurrentIterVals[PHI] = StartCST;
5090 if (!CurrentIterVals.count(PN))
5091 return RetVal = nullptr;
5093 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5095 // Execute the loop symbolically to determine the exit value.
5096 if (BEs.getActiveBits() >= 32)
5097 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5099 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5100 unsigned IterationNum = 0;
5101 for (; ; ++IterationNum) {
5102 if (IterationNum == NumIterations)
5103 return RetVal = CurrentIterVals[PN]; // Got exit value!
5105 // Compute the value of the PHIs for the next iteration.
5106 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5107 DenseMap<Instruction *, Constant *> NextIterVals;
5108 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5111 return nullptr; // Couldn't evaluate!
5112 NextIterVals[PN] = NextPHI;
5114 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5116 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5117 // cease to be able to evaluate one of them or if they stop evolving,
5118 // because that doesn't necessarily prevent us from computing PN.
5119 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5120 for (DenseMap<Instruction *, Constant *>::const_iterator
5121 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5122 PHINode *PHI = dyn_cast<PHINode>(I->first);
5123 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5124 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5126 // We use two distinct loops because EvaluateExpression may invalidate any
5127 // iterators into CurrentIterVals.
5128 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5129 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5130 PHINode *PHI = I->first;
5131 Constant *&NextPHI = NextIterVals[PHI];
5132 if (!NextPHI) { // Not already computed.
5133 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5134 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5136 if (NextPHI != I->second)
5137 StoppedEvolving = false;
5140 // If all entries in CurrentIterVals == NextIterVals then we can stop
5141 // iterating, the loop can't continue to change.
5142 if (StoppedEvolving)
5143 return RetVal = CurrentIterVals[PN];
5145 CurrentIterVals.swap(NextIterVals);
5149 /// ComputeExitCountExhaustively - If the loop is known to execute a
5150 /// constant number of times (the condition evolves only from constants),
5151 /// try to evaluate a few iterations of the loop until we get the exit
5152 /// condition gets a value of ExitWhen (true or false). If we cannot
5153 /// evaluate the trip count of the loop, return getCouldNotCompute().
5154 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5157 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5158 if (!PN) return getCouldNotCompute();
5160 // If the loop is canonicalized, the PHI will have exactly two entries.
5161 // That's the only form we support here.
5162 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5164 DenseMap<Instruction *, Constant *> CurrentIterVals;
5165 BasicBlock *Header = L->getHeader();
5166 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5168 // One entry must be a constant (coming in from outside of the loop), and the
5169 // second must be derived from the same PHI.
5170 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5171 PHINode *PHI = nullptr;
5172 for (BasicBlock::iterator I = Header->begin();
5173 (PHI = dyn_cast<PHINode>(I)); ++I) {
5174 Constant *StartCST =
5175 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5176 if (!StartCST) continue;
5177 CurrentIterVals[PHI] = StartCST;
5179 if (!CurrentIterVals.count(PN))
5180 return getCouldNotCompute();
5182 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5183 // the loop symbolically to determine when the condition gets a value of
5186 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5187 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5188 ConstantInt *CondVal =
5189 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5192 // Couldn't symbolically evaluate.
5193 if (!CondVal) return getCouldNotCompute();
5195 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5196 ++NumBruteForceTripCountsComputed;
5197 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5200 // Update all the PHI nodes for the next iteration.
5201 DenseMap<Instruction *, Constant *> NextIterVals;
5203 // Create a list of which PHIs we need to compute. We want to do this before
5204 // calling EvaluateExpression on them because that may invalidate iterators
5205 // into CurrentIterVals.
5206 SmallVector<PHINode *, 8> PHIsToCompute;
5207 for (DenseMap<Instruction *, Constant *>::const_iterator
5208 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5209 PHINode *PHI = dyn_cast<PHINode>(I->first);
5210 if (!PHI || PHI->getParent() != Header) continue;
5211 PHIsToCompute.push_back(PHI);
5213 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5214 E = PHIsToCompute.end(); I != E; ++I) {
5216 Constant *&NextPHI = NextIterVals[PHI];
5217 if (NextPHI) continue; // Already computed!
5219 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5220 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5222 CurrentIterVals.swap(NextIterVals);
5225 // Too many iterations were needed to evaluate.
5226 return getCouldNotCompute();
5229 /// getSCEVAtScope - Return a SCEV expression for the specified value
5230 /// at the specified scope in the program. The L value specifies a loop
5231 /// nest to evaluate the expression at, where null is the top-level or a
5232 /// specified loop is immediately inside of the loop.
5234 /// This method can be used to compute the exit value for a variable defined
5235 /// in a loop by querying what the value will hold in the parent loop.
5237 /// In the case that a relevant loop exit value cannot be computed, the
5238 /// original value V is returned.
5239 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5240 // Check to see if we've folded this expression at this loop before.
5241 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5242 for (unsigned u = 0; u < Values.size(); u++) {
5243 if (Values[u].first == L)
5244 return Values[u].second ? Values[u].second : V;
5246 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5247 // Otherwise compute it.
5248 const SCEV *C = computeSCEVAtScope(V, L);
5249 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5250 for (unsigned u = Values2.size(); u > 0; u--) {
5251 if (Values2[u - 1].first == L) {
5252 Values2[u - 1].second = C;
5259 /// This builds up a Constant using the ConstantExpr interface. That way, we
5260 /// will return Constants for objects which aren't represented by a
5261 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5262 /// Returns NULL if the SCEV isn't representable as a Constant.
5263 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5264 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5265 case scCouldNotCompute:
5269 return cast<SCEVConstant>(V)->getValue();
5271 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5272 case scSignExtend: {
5273 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5274 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5275 return ConstantExpr::getSExt(CastOp, SS->getType());
5278 case scZeroExtend: {
5279 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5280 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5281 return ConstantExpr::getZExt(CastOp, SZ->getType());
5285 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5286 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5287 return ConstantExpr::getTrunc(CastOp, ST->getType());
5291 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5292 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5293 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5294 unsigned AS = PTy->getAddressSpace();
5295 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5296 C = ConstantExpr::getBitCast(C, DestPtrTy);
5298 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5299 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5300 if (!C2) return nullptr;
5303 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5304 unsigned AS = C2->getType()->getPointerAddressSpace();
5306 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5307 // The offsets have been converted to bytes. We can add bytes to an
5308 // i8* by GEP with the byte count in the first index.
5309 C = ConstantExpr::getBitCast(C, DestPtrTy);
5312 // Don't bother trying to sum two pointers. We probably can't
5313 // statically compute a load that results from it anyway.
5314 if (C2->getType()->isPointerTy())
5317 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5318 if (PTy->getElementType()->isStructTy())
5319 C2 = ConstantExpr::getIntegerCast(
5320 C2, Type::getInt32Ty(C->getContext()), true);
5321 C = ConstantExpr::getGetElementPtr(C, C2);
5323 C = ConstantExpr::getAdd(C, C2);
5330 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5331 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5332 // Don't bother with pointers at all.
5333 if (C->getType()->isPointerTy()) return nullptr;
5334 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5335 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5336 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5337 C = ConstantExpr::getMul(C, C2);
5344 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5345 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5346 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5347 if (LHS->getType() == RHS->getType())
5348 return ConstantExpr::getUDiv(LHS, RHS);
5353 break; // TODO: smax, umax.
5358 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5359 if (isa<SCEVConstant>(V)) return V;
5361 // If this instruction is evolved from a constant-evolving PHI, compute the
5362 // exit value from the loop without using SCEVs.
5363 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5364 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5365 const Loop *LI = (*this->LI)[I->getParent()];
5366 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5367 if (PHINode *PN = dyn_cast<PHINode>(I))
5368 if (PN->getParent() == LI->getHeader()) {
5369 // Okay, there is no closed form solution for the PHI node. Check
5370 // to see if the loop that contains it has a known backedge-taken
5371 // count. If so, we may be able to force computation of the exit
5373 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5374 if (const SCEVConstant *BTCC =
5375 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5376 // Okay, we know how many times the containing loop executes. If
5377 // this is a constant evolving PHI node, get the final value at
5378 // the specified iteration number.
5379 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5380 BTCC->getValue()->getValue(),
5382 if (RV) return getSCEV(RV);
5386 // Okay, this is an expression that we cannot symbolically evaluate
5387 // into a SCEV. Check to see if it's possible to symbolically evaluate
5388 // the arguments into constants, and if so, try to constant propagate the
5389 // result. This is particularly useful for computing loop exit values.
5390 if (CanConstantFold(I)) {
5391 SmallVector<Constant *, 4> Operands;
5392 bool MadeImprovement = false;
5393 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5394 Value *Op = I->getOperand(i);
5395 if (Constant *C = dyn_cast<Constant>(Op)) {
5396 Operands.push_back(C);
5400 // If any of the operands is non-constant and if they are
5401 // non-integer and non-pointer, don't even try to analyze them
5402 // with scev techniques.
5403 if (!isSCEVable(Op->getType()))
5406 const SCEV *OrigV = getSCEV(Op);
5407 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5408 MadeImprovement |= OrigV != OpV;
5410 Constant *C = BuildConstantFromSCEV(OpV);
5412 if (C->getType() != Op->getType())
5413 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5417 Operands.push_back(C);
5420 // Check to see if getSCEVAtScope actually made an improvement.
5421 if (MadeImprovement) {
5422 Constant *C = nullptr;
5423 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5424 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5425 Operands[0], Operands[1], DL,
5427 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5428 if (!LI->isVolatile())
5429 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5431 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5439 // This is some other type of SCEVUnknown, just return it.
5443 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5444 // Avoid performing the look-up in the common case where the specified
5445 // expression has no loop-variant portions.
5446 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5447 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5448 if (OpAtScope != Comm->getOperand(i)) {
5449 // Okay, at least one of these operands is loop variant but might be
5450 // foldable. Build a new instance of the folded commutative expression.
5451 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5452 Comm->op_begin()+i);
5453 NewOps.push_back(OpAtScope);
5455 for (++i; i != e; ++i) {
5456 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5457 NewOps.push_back(OpAtScope);
5459 if (isa<SCEVAddExpr>(Comm))
5460 return getAddExpr(NewOps);
5461 if (isa<SCEVMulExpr>(Comm))
5462 return getMulExpr(NewOps);
5463 if (isa<SCEVSMaxExpr>(Comm))
5464 return getSMaxExpr(NewOps);
5465 if (isa<SCEVUMaxExpr>(Comm))
5466 return getUMaxExpr(NewOps);
5467 llvm_unreachable("Unknown commutative SCEV type!");
5470 // If we got here, all operands are loop invariant.
5474 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5475 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5476 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5477 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5478 return Div; // must be loop invariant
5479 return getUDivExpr(LHS, RHS);
5482 // If this is a loop recurrence for a loop that does not contain L, then we
5483 // are dealing with the final value computed by the loop.
5484 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5485 // First, attempt to evaluate each operand.
5486 // Avoid performing the look-up in the common case where the specified
5487 // expression has no loop-variant portions.
5488 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5489 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5490 if (OpAtScope == AddRec->getOperand(i))
5493 // Okay, at least one of these operands is loop variant but might be
5494 // foldable. Build a new instance of the folded commutative expression.
5495 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5496 AddRec->op_begin()+i);
5497 NewOps.push_back(OpAtScope);
5498 for (++i; i != e; ++i)
5499 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5501 const SCEV *FoldedRec =
5502 getAddRecExpr(NewOps, AddRec->getLoop(),
5503 AddRec->getNoWrapFlags(SCEV::FlagNW));
5504 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5505 // The addrec may be folded to a nonrecurrence, for example, if the
5506 // induction variable is multiplied by zero after constant folding. Go
5507 // ahead and return the folded value.
5513 // If the scope is outside the addrec's loop, evaluate it by using the
5514 // loop exit value of the addrec.
5515 if (!AddRec->getLoop()->contains(L)) {
5516 // To evaluate this recurrence, we need to know how many times the AddRec
5517 // loop iterates. Compute this now.
5518 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5519 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5521 // Then, evaluate the AddRec.
5522 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5528 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5529 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5530 if (Op == Cast->getOperand())
5531 return Cast; // must be loop invariant
5532 return getZeroExtendExpr(Op, Cast->getType());
5535 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5536 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5537 if (Op == Cast->getOperand())
5538 return Cast; // must be loop invariant
5539 return getSignExtendExpr(Op, Cast->getType());
5542 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5543 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5544 if (Op == Cast->getOperand())
5545 return Cast; // must be loop invariant
5546 return getTruncateExpr(Op, Cast->getType());
5549 llvm_unreachable("Unknown SCEV type!");
5552 /// getSCEVAtScope - This is a convenience function which does
5553 /// getSCEVAtScope(getSCEV(V), L).
5554 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5555 return getSCEVAtScope(getSCEV(V), L);
5558 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5559 /// following equation:
5561 /// A * X = B (mod N)
5563 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5564 /// A and B isn't important.
5566 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5567 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5568 ScalarEvolution &SE) {
5569 uint32_t BW = A.getBitWidth();
5570 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5571 assert(A != 0 && "A must be non-zero.");
5575 // The gcd of A and N may have only one prime factor: 2. The number of
5576 // trailing zeros in A is its multiplicity
5577 uint32_t Mult2 = A.countTrailingZeros();
5580 // 2. Check if B is divisible by D.
5582 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5583 // is not less than multiplicity of this prime factor for D.
5584 if (B.countTrailingZeros() < Mult2)
5585 return SE.getCouldNotCompute();
5587 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5590 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5591 // bit width during computations.
5592 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5593 APInt Mod(BW + 1, 0);
5594 Mod.setBit(BW - Mult2); // Mod = N / D
5595 APInt I = AD.multiplicativeInverse(Mod);
5597 // 4. Compute the minimum unsigned root of the equation:
5598 // I * (B / D) mod (N / D)
5599 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5601 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5603 return SE.getConstant(Result.trunc(BW));
5606 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5607 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5608 /// might be the same) or two SCEVCouldNotCompute objects.
5610 static std::pair<const SCEV *,const SCEV *>
5611 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5612 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5613 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5614 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5615 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5617 // We currently can only solve this if the coefficients are constants.
5618 if (!LC || !MC || !NC) {
5619 const SCEV *CNC = SE.getCouldNotCompute();
5620 return std::make_pair(CNC, CNC);
5623 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5624 const APInt &L = LC->getValue()->getValue();
5625 const APInt &M = MC->getValue()->getValue();
5626 const APInt &N = NC->getValue()->getValue();
5627 APInt Two(BitWidth, 2);
5628 APInt Four(BitWidth, 4);
5631 using namespace APIntOps;
5633 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5634 // The B coefficient is M-N/2
5638 // The A coefficient is N/2
5639 APInt A(N.sdiv(Two));
5641 // Compute the B^2-4ac term.
5644 SqrtTerm -= Four * (A * C);
5646 if (SqrtTerm.isNegative()) {
5647 // The loop is provably infinite.
5648 const SCEV *CNC = SE.getCouldNotCompute();
5649 return std::make_pair(CNC, CNC);
5652 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5653 // integer value or else APInt::sqrt() will assert.
5654 APInt SqrtVal(SqrtTerm.sqrt());
5656 // Compute the two solutions for the quadratic formula.
5657 // The divisions must be performed as signed divisions.
5660 if (TwoA.isMinValue()) {
5661 const SCEV *CNC = SE.getCouldNotCompute();
5662 return std::make_pair(CNC, CNC);
5665 LLVMContext &Context = SE.getContext();
5667 ConstantInt *Solution1 =
5668 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5669 ConstantInt *Solution2 =
5670 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5672 return std::make_pair(SE.getConstant(Solution1),
5673 SE.getConstant(Solution2));
5674 } // end APIntOps namespace
5677 /// HowFarToZero - Return the number of times a backedge comparing the specified
5678 /// value to zero will execute. If not computable, return CouldNotCompute.
5680 /// This is only used for loops with a "x != y" exit test. The exit condition is
5681 /// now expressed as a single expression, V = x-y. So the exit test is
5682 /// effectively V != 0. We know and take advantage of the fact that this
5683 /// expression only being used in a comparison by zero context.
5684 ScalarEvolution::ExitLimit
5685 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
5686 // If the value is a constant
5687 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5688 // If the value is already zero, the branch will execute zero times.
5689 if (C->getValue()->isZero()) return C;
5690 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5693 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5694 if (!AddRec || AddRec->getLoop() != L)
5695 return getCouldNotCompute();
5697 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5698 // the quadratic equation to solve it.
5699 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5700 std::pair<const SCEV *,const SCEV *> Roots =
5701 SolveQuadraticEquation(AddRec, *this);
5702 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5703 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5706 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5707 << " sol#2: " << *R2 << "\n";
5709 // Pick the smallest positive root value.
5710 if (ConstantInt *CB =
5711 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5714 if (CB->getZExtValue() == false)
5715 std::swap(R1, R2); // R1 is the minimum root now.
5717 // We can only use this value if the chrec ends up with an exact zero
5718 // value at this index. When solving for "X*X != 5", for example, we
5719 // should not accept a root of 2.
5720 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5722 return R1; // We found a quadratic root!
5725 return getCouldNotCompute();
5728 // Otherwise we can only handle this if it is affine.
5729 if (!AddRec->isAffine())
5730 return getCouldNotCompute();
5732 // If this is an affine expression, the execution count of this branch is
5733 // the minimum unsigned root of the following equation:
5735 // Start + Step*N = 0 (mod 2^BW)
5739 // Step*N = -Start (mod 2^BW)
5741 // where BW is the common bit width of Start and Step.
5743 // Get the initial value for the loop.
5744 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5745 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5747 // For now we handle only constant steps.
5749 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5750 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5751 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5752 // We have not yet seen any such cases.
5753 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5754 if (!StepC || StepC->getValue()->equalsInt(0))
5755 return getCouldNotCompute();
5757 // For positive steps (counting up until unsigned overflow):
5758 // N = -Start/Step (as unsigned)
5759 // For negative steps (counting down to zero):
5761 // First compute the unsigned distance from zero in the direction of Step.
5762 bool CountDown = StepC->getValue()->getValue().isNegative();
5763 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5765 // Handle unitary steps, which cannot wraparound.
5766 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5767 // N = Distance (as unsigned)
5768 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5769 ConstantRange CR = getUnsignedRange(Start);
5770 const SCEV *MaxBECount;
5771 if (!CountDown && CR.getUnsignedMin().isMinValue())
5772 // When counting up, the worst starting value is 1, not 0.
5773 MaxBECount = CR.getUnsignedMax().isMinValue()
5774 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5775 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5777 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5778 : -CR.getUnsignedMin());
5779 return ExitLimit(Distance, MaxBECount, /*MustExit=*/true);
5782 // If the recurrence is known not to wraparound, unsigned divide computes the
5783 // back edge count. (Ideally we would have an "isexact" bit for udiv). We know
5784 // that the value will either become zero (and thus the loop terminates), that
5785 // the loop will terminate through some other exit condition first, or that
5786 // the loop has undefined behavior. This means we can't "miss" the exit
5787 // value, even with nonunit stride, and exit later via the same branch. Note
5788 // that we can skip this exit if loop later exits via a different
5789 // branch. Hence MustExit=false.
5791 // This is only valid for expressions that directly compute the loop exit. It
5792 // is invalid for subexpressions in which the loop may exit through this
5793 // branch even if this subexpression is false. In that case, the trip count
5794 // computed by this udiv could be smaller than the number of well-defined
5796 if (!IsSubExpr && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5798 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5799 return ExitLimit(Exact, Exact, /*MustExit=*/false);
5802 // If Step is a power of two that evenly divides Start we know that the loop
5803 // will always terminate. Start may not be a constant so we just have the
5804 // number of trailing zeros available. This is safe even in presence of
5805 // overflow as the recurrence will overflow to exactly 0.
5806 const APInt &StepV = StepC->getValue()->getValue();
5807 if (StepV.isPowerOf2() &&
5808 GetMinTrailingZeros(getNegativeSCEV(Start)) >= StepV.countTrailingZeros())
5809 return getUDivExactExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5811 // Then, try to solve the above equation provided that Start is constant.
5812 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5813 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5814 -StartC->getValue()->getValue(),
5816 return getCouldNotCompute();
5819 /// HowFarToNonZero - Return the number of times a backedge checking the
5820 /// specified value for nonzero will execute. If not computable, return
5822 ScalarEvolution::ExitLimit
5823 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5824 // Loops that look like: while (X == 0) are very strange indeed. We don't
5825 // handle them yet except for the trivial case. This could be expanded in the
5826 // future as needed.
5828 // If the value is a constant, check to see if it is known to be non-zero
5829 // already. If so, the backedge will execute zero times.
5830 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5831 if (!C->getValue()->isNullValue())
5832 return getConstant(C->getType(), 0);
5833 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5836 // We could implement others, but I really doubt anyone writes loops like
5837 // this, and if they did, they would already be constant folded.
5838 return getCouldNotCompute();
5841 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5842 /// (which may not be an immediate predecessor) which has exactly one
5843 /// successor from which BB is reachable, or null if no such block is
5846 std::pair<BasicBlock *, BasicBlock *>
5847 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5848 // If the block has a unique predecessor, then there is no path from the
5849 // predecessor to the block that does not go through the direct edge
5850 // from the predecessor to the block.
5851 if (BasicBlock *Pred = BB->getSinglePredecessor())
5852 return std::make_pair(Pred, BB);
5854 // A loop's header is defined to be a block that dominates the loop.
5855 // If the header has a unique predecessor outside the loop, it must be
5856 // a block that has exactly one successor that can reach the loop.
5857 if (Loop *L = LI->getLoopFor(BB))
5858 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5860 return std::pair<BasicBlock *, BasicBlock *>();
5863 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5864 /// testing whether two expressions are equal, however for the purposes of
5865 /// looking for a condition guarding a loop, it can be useful to be a little
5866 /// more general, since a front-end may have replicated the controlling
5869 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5870 // Quick check to see if they are the same SCEV.
5871 if (A == B) return true;
5873 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5874 // two different instructions with the same value. Check for this case.
5875 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5876 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5877 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5878 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5879 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5882 // Otherwise assume they may have a different value.
5886 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5887 /// predicate Pred. Return true iff any changes were made.
5889 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5890 const SCEV *&LHS, const SCEV *&RHS,
5892 bool Changed = false;
5894 // If we hit the max recursion limit bail out.
5898 // Canonicalize a constant to the right side.
5899 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5900 // Check for both operands constant.
5901 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5902 if (ConstantExpr::getICmp(Pred,
5904 RHSC->getValue())->isNullValue())
5905 goto trivially_false;
5907 goto trivially_true;
5909 // Otherwise swap the operands to put the constant on the right.
5910 std::swap(LHS, RHS);
5911 Pred = ICmpInst::getSwappedPredicate(Pred);
5915 // If we're comparing an addrec with a value which is loop-invariant in the
5916 // addrec's loop, put the addrec on the left. Also make a dominance check,
5917 // as both operands could be addrecs loop-invariant in each other's loop.
5918 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5919 const Loop *L = AR->getLoop();
5920 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5921 std::swap(LHS, RHS);
5922 Pred = ICmpInst::getSwappedPredicate(Pred);
5927 // If there's a constant operand, canonicalize comparisons with boundary
5928 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5929 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5930 const APInt &RA = RC->getValue()->getValue();
5932 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5933 case ICmpInst::ICMP_EQ:
5934 case ICmpInst::ICMP_NE:
5935 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5937 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5938 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5939 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5940 ME->getOperand(0)->isAllOnesValue()) {
5941 RHS = AE->getOperand(1);
5942 LHS = ME->getOperand(1);
5946 case ICmpInst::ICMP_UGE:
5947 if ((RA - 1).isMinValue()) {
5948 Pred = ICmpInst::ICMP_NE;
5949 RHS = getConstant(RA - 1);
5953 if (RA.isMaxValue()) {
5954 Pred = ICmpInst::ICMP_EQ;
5958 if (RA.isMinValue()) goto trivially_true;
5960 Pred = ICmpInst::ICMP_UGT;
5961 RHS = getConstant(RA - 1);
5964 case ICmpInst::ICMP_ULE:
5965 if ((RA + 1).isMaxValue()) {
5966 Pred = ICmpInst::ICMP_NE;
5967 RHS = getConstant(RA + 1);
5971 if (RA.isMinValue()) {
5972 Pred = ICmpInst::ICMP_EQ;
5976 if (RA.isMaxValue()) goto trivially_true;
5978 Pred = ICmpInst::ICMP_ULT;
5979 RHS = getConstant(RA + 1);
5982 case ICmpInst::ICMP_SGE:
5983 if ((RA - 1).isMinSignedValue()) {
5984 Pred = ICmpInst::ICMP_NE;
5985 RHS = getConstant(RA - 1);
5989 if (RA.isMaxSignedValue()) {
5990 Pred = ICmpInst::ICMP_EQ;
5994 if (RA.isMinSignedValue()) goto trivially_true;
5996 Pred = ICmpInst::ICMP_SGT;
5997 RHS = getConstant(RA - 1);
6000 case ICmpInst::ICMP_SLE:
6001 if ((RA + 1).isMaxSignedValue()) {
6002 Pred = ICmpInst::ICMP_NE;
6003 RHS = getConstant(RA + 1);
6007 if (RA.isMinSignedValue()) {
6008 Pred = ICmpInst::ICMP_EQ;
6012 if (RA.isMaxSignedValue()) goto trivially_true;
6014 Pred = ICmpInst::ICMP_SLT;
6015 RHS = getConstant(RA + 1);
6018 case ICmpInst::ICMP_UGT:
6019 if (RA.isMinValue()) {
6020 Pred = ICmpInst::ICMP_NE;
6024 if ((RA + 1).isMaxValue()) {
6025 Pred = ICmpInst::ICMP_EQ;
6026 RHS = getConstant(RA + 1);
6030 if (RA.isMaxValue()) goto trivially_false;
6032 case ICmpInst::ICMP_ULT:
6033 if (RA.isMaxValue()) {
6034 Pred = ICmpInst::ICMP_NE;
6038 if ((RA - 1).isMinValue()) {
6039 Pred = ICmpInst::ICMP_EQ;
6040 RHS = getConstant(RA - 1);
6044 if (RA.isMinValue()) goto trivially_false;
6046 case ICmpInst::ICMP_SGT:
6047 if (RA.isMinSignedValue()) {
6048 Pred = ICmpInst::ICMP_NE;
6052 if ((RA + 1).isMaxSignedValue()) {
6053 Pred = ICmpInst::ICMP_EQ;
6054 RHS = getConstant(RA + 1);
6058 if (RA.isMaxSignedValue()) goto trivially_false;
6060 case ICmpInst::ICMP_SLT:
6061 if (RA.isMaxSignedValue()) {
6062 Pred = ICmpInst::ICMP_NE;
6066 if ((RA - 1).isMinSignedValue()) {
6067 Pred = ICmpInst::ICMP_EQ;
6068 RHS = getConstant(RA - 1);
6072 if (RA.isMinSignedValue()) goto trivially_false;
6077 // Check for obvious equality.
6078 if (HasSameValue(LHS, RHS)) {
6079 if (ICmpInst::isTrueWhenEqual(Pred))
6080 goto trivially_true;
6081 if (ICmpInst::isFalseWhenEqual(Pred))
6082 goto trivially_false;
6085 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6086 // adding or subtracting 1 from one of the operands.
6088 case ICmpInst::ICMP_SLE:
6089 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6090 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6092 Pred = ICmpInst::ICMP_SLT;
6094 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6095 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6097 Pred = ICmpInst::ICMP_SLT;
6101 case ICmpInst::ICMP_SGE:
6102 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6103 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6105 Pred = ICmpInst::ICMP_SGT;
6107 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6108 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6110 Pred = ICmpInst::ICMP_SGT;
6114 case ICmpInst::ICMP_ULE:
6115 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6116 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6118 Pred = ICmpInst::ICMP_ULT;
6120 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6121 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6123 Pred = ICmpInst::ICMP_ULT;
6127 case ICmpInst::ICMP_UGE:
6128 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6129 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6131 Pred = ICmpInst::ICMP_UGT;
6133 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6134 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6136 Pred = ICmpInst::ICMP_UGT;
6144 // TODO: More simplifications are possible here.
6146 // Recursively simplify until we either hit a recursion limit or nothing
6149 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6155 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6156 Pred = ICmpInst::ICMP_EQ;
6161 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6162 Pred = ICmpInst::ICMP_NE;
6166 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6167 return getSignedRange(S).getSignedMax().isNegative();
6170 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6171 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6174 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6175 return !getSignedRange(S).getSignedMin().isNegative();
6178 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6179 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6182 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6183 return isKnownNegative(S) || isKnownPositive(S);
6186 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6187 const SCEV *LHS, const SCEV *RHS) {
6188 // Canonicalize the inputs first.
6189 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6191 // If LHS or RHS is an addrec, check to see if the condition is true in
6192 // every iteration of the loop.
6193 // If LHS and RHS are both addrec, both conditions must be true in
6194 // every iteration of the loop.
6195 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6196 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6197 bool LeftGuarded = false;
6198 bool RightGuarded = false;
6200 const Loop *L = LAR->getLoop();
6201 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6202 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6203 if (!RAR) return true;
6208 const Loop *L = RAR->getLoop();
6209 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6210 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6211 if (!LAR) return true;
6212 RightGuarded = true;
6215 if (LeftGuarded && RightGuarded)
6218 // Otherwise see what can be done with known constant ranges.
6219 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6223 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6224 const SCEV *LHS, const SCEV *RHS) {
6225 if (HasSameValue(LHS, RHS))
6226 return ICmpInst::isTrueWhenEqual(Pred);
6228 // This code is split out from isKnownPredicate because it is called from
6229 // within isLoopEntryGuardedByCond.
6232 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6233 case ICmpInst::ICMP_SGT:
6234 std::swap(LHS, RHS);
6235 case ICmpInst::ICMP_SLT: {
6236 ConstantRange LHSRange = getSignedRange(LHS);
6237 ConstantRange RHSRange = getSignedRange(RHS);
6238 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6240 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6244 case ICmpInst::ICMP_SGE:
6245 std::swap(LHS, RHS);
6246 case ICmpInst::ICMP_SLE: {
6247 ConstantRange LHSRange = getSignedRange(LHS);
6248 ConstantRange RHSRange = getSignedRange(RHS);
6249 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6251 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6255 case ICmpInst::ICMP_UGT:
6256 std::swap(LHS, RHS);
6257 case ICmpInst::ICMP_ULT: {
6258 ConstantRange LHSRange = getUnsignedRange(LHS);
6259 ConstantRange RHSRange = getUnsignedRange(RHS);
6260 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6262 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6266 case ICmpInst::ICMP_UGE:
6267 std::swap(LHS, RHS);
6268 case ICmpInst::ICMP_ULE: {
6269 ConstantRange LHSRange = getUnsignedRange(LHS);
6270 ConstantRange RHSRange = getUnsignedRange(RHS);
6271 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6273 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6277 case ICmpInst::ICMP_NE: {
6278 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6280 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6283 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6284 if (isKnownNonZero(Diff))
6288 case ICmpInst::ICMP_EQ:
6289 // The check at the top of the function catches the case where
6290 // the values are known to be equal.
6296 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6297 /// protected by a conditional between LHS and RHS. This is used to
6298 /// to eliminate casts.
6300 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6301 ICmpInst::Predicate Pred,
6302 const SCEV *LHS, const SCEV *RHS) {
6303 // Interpret a null as meaning no loop, where there is obviously no guard
6304 // (interprocedural conditions notwithstanding).
6305 if (!L) return true;
6307 BasicBlock *Latch = L->getLoopLatch();
6311 BranchInst *LoopContinuePredicate =
6312 dyn_cast<BranchInst>(Latch->getTerminator());
6313 if (!LoopContinuePredicate ||
6314 LoopContinuePredicate->isUnconditional())
6317 return isImpliedCond(Pred, LHS, RHS,
6318 LoopContinuePredicate->getCondition(),
6319 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6322 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6323 /// by a conditional between LHS and RHS. This is used to help avoid max
6324 /// expressions in loop trip counts, and to eliminate casts.
6326 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6327 ICmpInst::Predicate Pred,
6328 const SCEV *LHS, const SCEV *RHS) {
6329 // Interpret a null as meaning no loop, where there is obviously no guard
6330 // (interprocedural conditions notwithstanding).
6331 if (!L) return false;
6333 // Starting at the loop predecessor, climb up the predecessor chain, as long
6334 // as there are predecessors that can be found that have unique successors
6335 // leading to the original header.
6336 for (std::pair<BasicBlock *, BasicBlock *>
6337 Pair(L->getLoopPredecessor(), L->getHeader());
6339 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6341 BranchInst *LoopEntryPredicate =
6342 dyn_cast<BranchInst>(Pair.first->getTerminator());
6343 if (!LoopEntryPredicate ||
6344 LoopEntryPredicate->isUnconditional())
6347 if (isImpliedCond(Pred, LHS, RHS,
6348 LoopEntryPredicate->getCondition(),
6349 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6356 /// RAII wrapper to prevent recursive application of isImpliedCond.
6357 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6358 /// currently evaluating isImpliedCond.
6359 struct MarkPendingLoopPredicate {
6361 DenseSet<Value*> &LoopPreds;
6364 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6365 : Cond(C), LoopPreds(LP) {
6366 Pending = !LoopPreds.insert(Cond).second;
6368 ~MarkPendingLoopPredicate() {
6370 LoopPreds.erase(Cond);
6374 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6375 /// and RHS is true whenever the given Cond value evaluates to true.
6376 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6377 const SCEV *LHS, const SCEV *RHS,
6378 Value *FoundCondValue,
6380 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6384 // Recursively handle And and Or conditions.
6385 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6386 if (BO->getOpcode() == Instruction::And) {
6388 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6389 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6390 } else if (BO->getOpcode() == Instruction::Or) {
6392 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6393 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6397 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6398 if (!ICI) return false;
6400 // Bail if the ICmp's operands' types are wider than the needed type
6401 // before attempting to call getSCEV on them. This avoids infinite
6402 // recursion, since the analysis of widening casts can require loop
6403 // exit condition information for overflow checking, which would
6405 if (getTypeSizeInBits(LHS->getType()) <
6406 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6409 // Now that we found a conditional branch that dominates the loop or controls
6410 // the loop latch. Check to see if it is the comparison we are looking for.
6411 ICmpInst::Predicate FoundPred;
6413 FoundPred = ICI->getInversePredicate();
6415 FoundPred = ICI->getPredicate();
6417 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6418 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6420 // Balance the types. The case where FoundLHS' type is wider than
6421 // LHS' type is checked for above.
6422 if (getTypeSizeInBits(LHS->getType()) >
6423 getTypeSizeInBits(FoundLHS->getType())) {
6424 if (CmpInst::isSigned(FoundPred)) {
6425 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6426 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6428 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6429 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6433 // Canonicalize the query to match the way instcombine will have
6434 // canonicalized the comparison.
6435 if (SimplifyICmpOperands(Pred, LHS, RHS))
6437 return CmpInst::isTrueWhenEqual(Pred);
6438 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6439 if (FoundLHS == FoundRHS)
6440 return CmpInst::isFalseWhenEqual(FoundPred);
6442 // Check to see if we can make the LHS or RHS match.
6443 if (LHS == FoundRHS || RHS == FoundLHS) {
6444 if (isa<SCEVConstant>(RHS)) {
6445 std::swap(FoundLHS, FoundRHS);
6446 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6448 std::swap(LHS, RHS);
6449 Pred = ICmpInst::getSwappedPredicate(Pred);
6453 // Check whether the found predicate is the same as the desired predicate.
6454 if (FoundPred == Pred)
6455 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6457 // Check whether swapping the found predicate makes it the same as the
6458 // desired predicate.
6459 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6460 if (isa<SCEVConstant>(RHS))
6461 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6463 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6464 RHS, LHS, FoundLHS, FoundRHS);
6467 // Check whether the actual condition is beyond sufficient.
6468 if (FoundPred == ICmpInst::ICMP_EQ)
6469 if (ICmpInst::isTrueWhenEqual(Pred))
6470 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6472 if (Pred == ICmpInst::ICMP_NE)
6473 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6474 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6477 // Otherwise assume the worst.
6481 /// isImpliedCondOperands - Test whether the condition described by Pred,
6482 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6483 /// and FoundRHS is true.
6484 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6485 const SCEV *LHS, const SCEV *RHS,
6486 const SCEV *FoundLHS,
6487 const SCEV *FoundRHS) {
6488 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6489 FoundLHS, FoundRHS) ||
6490 // ~x < ~y --> x > y
6491 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6492 getNotSCEV(FoundRHS),
6493 getNotSCEV(FoundLHS));
6496 /// isImpliedCondOperandsHelper - Test whether the condition described by
6497 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6498 /// FoundLHS, and FoundRHS is true.
6500 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6501 const SCEV *LHS, const SCEV *RHS,
6502 const SCEV *FoundLHS,
6503 const SCEV *FoundRHS) {
6505 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6506 case ICmpInst::ICMP_EQ:
6507 case ICmpInst::ICMP_NE:
6508 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6511 case ICmpInst::ICMP_SLT:
6512 case ICmpInst::ICMP_SLE:
6513 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6514 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6517 case ICmpInst::ICMP_SGT:
6518 case ICmpInst::ICMP_SGE:
6519 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6520 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6523 case ICmpInst::ICMP_ULT:
6524 case ICmpInst::ICMP_ULE:
6525 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6526 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6529 case ICmpInst::ICMP_UGT:
6530 case ICmpInst::ICMP_UGE:
6531 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6532 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6540 // Verify if an linear IV with positive stride can overflow when in a
6541 // less-than comparison, knowing the invariant term of the comparison, the
6542 // stride and the knowledge of NSW/NUW flags on the recurrence.
6543 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
6544 bool IsSigned, bool NoWrap) {
6545 if (NoWrap) return false;
6547 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6548 const SCEV *One = getConstant(Stride->getType(), 1);
6551 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
6552 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
6553 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6556 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
6557 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
6560 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
6561 APInt MaxValue = APInt::getMaxValue(BitWidth);
6562 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6565 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
6566 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
6569 // Verify if an linear IV with negative stride can overflow when in a
6570 // greater-than comparison, knowing the invariant term of the comparison,
6571 // the stride and the knowledge of NSW/NUW flags on the recurrence.
6572 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
6573 bool IsSigned, bool NoWrap) {
6574 if (NoWrap) return false;
6576 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6577 const SCEV *One = getConstant(Stride->getType(), 1);
6580 APInt MinRHS = getSignedRange(RHS).getSignedMin();
6581 APInt MinValue = APInt::getSignedMinValue(BitWidth);
6582 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6585 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
6586 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
6589 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
6590 APInt MinValue = APInt::getMinValue(BitWidth);
6591 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6594 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
6595 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
6598 // Compute the backedge taken count knowing the interval difference, the
6599 // stride and presence of the equality in the comparison.
6600 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
6602 const SCEV *One = getConstant(Step->getType(), 1);
6603 Delta = Equality ? getAddExpr(Delta, Step)
6604 : getAddExpr(Delta, getMinusSCEV(Step, One));
6605 return getUDivExpr(Delta, Step);
6608 /// HowManyLessThans - Return the number of times a backedge containing the
6609 /// specified less-than comparison will execute. If not computable, return
6610 /// CouldNotCompute.
6612 /// @param IsSubExpr is true when the LHS < RHS condition does not directly
6613 /// control the branch. In this case, we can only compute an iteration count for
6614 /// a subexpression that cannot overflow before evaluating true.
6615 ScalarEvolution::ExitLimit
6616 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6617 const Loop *L, bool IsSigned,
6619 // We handle only IV < Invariant
6620 if (!isLoopInvariant(RHS, L))
6621 return getCouldNotCompute();
6623 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6625 // Avoid weird loops
6626 if (!IV || IV->getLoop() != L || !IV->isAffine())
6627 return getCouldNotCompute();
6629 bool NoWrap = !IsSubExpr &&
6630 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6632 const SCEV *Stride = IV->getStepRecurrence(*this);
6634 // Avoid negative or zero stride values
6635 if (!isKnownPositive(Stride))
6636 return getCouldNotCompute();
6638 // Avoid proven overflow cases: this will ensure that the backedge taken count
6639 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6640 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6641 // behaviors like the case of C language.
6642 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
6643 return getCouldNotCompute();
6645 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
6646 : ICmpInst::ICMP_ULT;
6647 const SCEV *Start = IV->getStart();
6648 const SCEV *End = RHS;
6649 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
6650 End = IsSigned ? getSMaxExpr(RHS, Start)
6651 : getUMaxExpr(RHS, Start);
6653 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
6655 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
6656 : getUnsignedRange(Start).getUnsignedMin();
6658 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6659 : getUnsignedRange(Stride).getUnsignedMin();
6661 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6662 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
6663 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
6665 // Although End can be a MAX expression we estimate MaxEnd considering only
6666 // the case End = RHS. This is safe because in the other case (End - Start)
6667 // is zero, leading to a zero maximum backedge taken count.
6669 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
6670 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
6672 const SCEV *MaxBECount;
6673 if (isa<SCEVConstant>(BECount))
6674 MaxBECount = BECount;
6676 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
6677 getConstant(MinStride), false);
6679 if (isa<SCEVCouldNotCompute>(MaxBECount))
6680 MaxBECount = BECount;
6682 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6685 ScalarEvolution::ExitLimit
6686 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
6687 const Loop *L, bool IsSigned,
6689 // We handle only IV > Invariant
6690 if (!isLoopInvariant(RHS, L))
6691 return getCouldNotCompute();
6693 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6695 // Avoid weird loops
6696 if (!IV || IV->getLoop() != L || !IV->isAffine())
6697 return getCouldNotCompute();
6699 bool NoWrap = !IsSubExpr &&
6700 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6702 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
6704 // Avoid negative or zero stride values
6705 if (!isKnownPositive(Stride))
6706 return getCouldNotCompute();
6708 // Avoid proven overflow cases: this will ensure that the backedge taken count
6709 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6710 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6711 // behaviors like the case of C language.
6712 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
6713 return getCouldNotCompute();
6715 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
6716 : ICmpInst::ICMP_UGT;
6718 const SCEV *Start = IV->getStart();
6719 const SCEV *End = RHS;
6720 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
6721 End = IsSigned ? getSMinExpr(RHS, Start)
6722 : getUMinExpr(RHS, Start);
6724 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
6726 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
6727 : getUnsignedRange(Start).getUnsignedMax();
6729 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6730 : getUnsignedRange(Stride).getUnsignedMin();
6732 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6733 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
6734 : APInt::getMinValue(BitWidth) + (MinStride - 1);
6736 // Although End can be a MIN expression we estimate MinEnd considering only
6737 // the case End = RHS. This is safe because in the other case (Start - End)
6738 // is zero, leading to a zero maximum backedge taken count.
6740 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
6741 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
6744 const SCEV *MaxBECount = getCouldNotCompute();
6745 if (isa<SCEVConstant>(BECount))
6746 MaxBECount = BECount;
6748 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
6749 getConstant(MinStride), false);
6751 if (isa<SCEVCouldNotCompute>(MaxBECount))
6752 MaxBECount = BECount;
6754 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6757 /// getNumIterationsInRange - Return the number of iterations of this loop that
6758 /// produce values in the specified constant range. Another way of looking at
6759 /// this is that it returns the first iteration number where the value is not in
6760 /// the condition, thus computing the exit count. If the iteration count can't
6761 /// be computed, an instance of SCEVCouldNotCompute is returned.
6762 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6763 ScalarEvolution &SE) const {
6764 if (Range.isFullSet()) // Infinite loop.
6765 return SE.getCouldNotCompute();
6767 // If the start is a non-zero constant, shift the range to simplify things.
6768 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6769 if (!SC->getValue()->isZero()) {
6770 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6771 Operands[0] = SE.getConstant(SC->getType(), 0);
6772 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6773 getNoWrapFlags(FlagNW));
6774 if (const SCEVAddRecExpr *ShiftedAddRec =
6775 dyn_cast<SCEVAddRecExpr>(Shifted))
6776 return ShiftedAddRec->getNumIterationsInRange(
6777 Range.subtract(SC->getValue()->getValue()), SE);
6778 // This is strange and shouldn't happen.
6779 return SE.getCouldNotCompute();
6782 // The only time we can solve this is when we have all constant indices.
6783 // Otherwise, we cannot determine the overflow conditions.
6784 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6785 if (!isa<SCEVConstant>(getOperand(i)))
6786 return SE.getCouldNotCompute();
6789 // Okay at this point we know that all elements of the chrec are constants and
6790 // that the start element is zero.
6792 // First check to see if the range contains zero. If not, the first
6794 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6795 if (!Range.contains(APInt(BitWidth, 0)))
6796 return SE.getConstant(getType(), 0);
6799 // If this is an affine expression then we have this situation:
6800 // Solve {0,+,A} in Range === Ax in Range
6802 // We know that zero is in the range. If A is positive then we know that
6803 // the upper value of the range must be the first possible exit value.
6804 // If A is negative then the lower of the range is the last possible loop
6805 // value. Also note that we already checked for a full range.
6806 APInt One(BitWidth,1);
6807 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6808 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6810 // The exit value should be (End+A)/A.
6811 APInt ExitVal = (End + A).udiv(A);
6812 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6814 // Evaluate at the exit value. If we really did fall out of the valid
6815 // range, then we computed our trip count, otherwise wrap around or other
6816 // things must have happened.
6817 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6818 if (Range.contains(Val->getValue()))
6819 return SE.getCouldNotCompute(); // Something strange happened
6821 // Ensure that the previous value is in the range. This is a sanity check.
6822 assert(Range.contains(
6823 EvaluateConstantChrecAtConstant(this,
6824 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6825 "Linear scev computation is off in a bad way!");
6826 return SE.getConstant(ExitValue);
6827 } else if (isQuadratic()) {
6828 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6829 // quadratic equation to solve it. To do this, we must frame our problem in
6830 // terms of figuring out when zero is crossed, instead of when
6831 // Range.getUpper() is crossed.
6832 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6833 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6834 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6835 // getNoWrapFlags(FlagNW)
6838 // Next, solve the constructed addrec
6839 std::pair<const SCEV *,const SCEV *> Roots =
6840 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6841 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6842 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6844 // Pick the smallest positive root value.
6845 if (ConstantInt *CB =
6846 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6847 R1->getValue(), R2->getValue()))) {
6848 if (CB->getZExtValue() == false)
6849 std::swap(R1, R2); // R1 is the minimum root now.
6851 // Make sure the root is not off by one. The returned iteration should
6852 // not be in the range, but the previous one should be. When solving
6853 // for "X*X < 5", for example, we should not return a root of 2.
6854 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6857 if (Range.contains(R1Val->getValue())) {
6858 // The next iteration must be out of the range...
6859 ConstantInt *NextVal =
6860 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6862 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6863 if (!Range.contains(R1Val->getValue()))
6864 return SE.getConstant(NextVal);
6865 return SE.getCouldNotCompute(); // Something strange happened
6868 // If R1 was not in the range, then it is a good return value. Make
6869 // sure that R1-1 WAS in the range though, just in case.
6870 ConstantInt *NextVal =
6871 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6872 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6873 if (Range.contains(R1Val->getValue()))
6875 return SE.getCouldNotCompute(); // Something strange happened
6880 return SE.getCouldNotCompute();
6886 FindUndefs() : Found(false) {}
6888 bool follow(const SCEV *S) {
6889 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
6890 if (isa<UndefValue>(C->getValue()))
6892 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
6893 if (isa<UndefValue>(C->getValue()))
6897 // Keep looking if we haven't found it yet.
6900 bool isDone() const {
6901 // Stop recursion if we have found an undef.
6907 // Return true when S contains at least an undef value.
6909 containsUndefs(const SCEV *S) {
6911 SCEVTraversal<FindUndefs> ST(F);
6918 // Collect all steps of SCEV expressions.
6919 struct SCEVCollectStrides {
6920 ScalarEvolution &SE;
6921 SmallVectorImpl<const SCEV *> &Strides;
6923 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
6924 : SE(SE), Strides(S) {}
6926 bool follow(const SCEV *S) {
6927 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
6928 Strides.push_back(AR->getStepRecurrence(SE));
6931 bool isDone() const { return false; }
6934 // Collect all SCEVUnknown and SCEVMulExpr expressions.
6935 struct SCEVCollectTerms {
6936 SmallVectorImpl<const SCEV *> &Terms;
6938 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
6941 bool follow(const SCEV *S) {
6942 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
6943 if (!containsUndefs(S))
6946 // Stop recursion: once we collected a term, do not walk its operands.
6953 bool isDone() const { return false; }
6957 /// Find parametric terms in this SCEVAddRecExpr.
6958 void SCEVAddRecExpr::collectParametricTerms(
6959 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
6960 SmallVector<const SCEV *, 4> Strides;
6961 SCEVCollectStrides StrideCollector(SE, Strides);
6962 visitAll(this, StrideCollector);
6965 dbgs() << "Strides:\n";
6966 for (const SCEV *S : Strides)
6967 dbgs() << *S << "\n";
6970 for (const SCEV *S : Strides) {
6971 SCEVCollectTerms TermCollector(Terms);
6972 visitAll(S, TermCollector);
6976 dbgs() << "Terms:\n";
6977 for (const SCEV *T : Terms)
6978 dbgs() << *T << "\n";
6982 static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
6983 APInt A = C1->getValue()->getValue();
6984 APInt B = C2->getValue()->getValue();
6985 uint32_t ABW = A.getBitWidth();
6986 uint32_t BBW = B.getBitWidth();
6993 return APIntOps::srem(A, B);
6996 static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
6997 APInt A = C1->getValue()->getValue();
6998 APInt B = C2->getValue()->getValue();
6999 uint32_t ABW = A.getBitWidth();
7000 uint32_t BBW = B.getBitWidth();
7007 return APIntOps::sdiv(A, B);
7011 struct FindSCEVSize {
7013 FindSCEVSize() : Size(0) {}
7015 bool follow(const SCEV *S) {
7017 // Keep looking at all operands of S.
7020 bool isDone() const {
7026 // Returns the size of the SCEV S.
7027 static inline int sizeOfSCEV(const SCEV *S) {
7029 SCEVTraversal<FindSCEVSize> ST(F);
7036 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
7038 // Computes the Quotient and Remainder of the division of Numerator by
7040 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
7041 const SCEV *Denominator, const SCEV **Quotient,
7042 const SCEV **Remainder) {
7043 assert(Numerator && Denominator && "Uninitialized SCEV");
7045 SCEVDivision D(SE, Numerator, Denominator);
7047 // Check for the trivial case here to avoid having to check for it in the
7048 // rest of the code.
7049 if (Numerator == Denominator) {
7051 *Remainder = D.Zero;
7055 if (Numerator->isZero()) {
7057 *Remainder = D.Zero;
7061 // Split the Denominator when it is a product.
7062 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
7064 *Quotient = Numerator;
7065 for (const SCEV *Op : T->operands()) {
7066 divide(SE, *Quotient, Op, &Q, &R);
7069 // Bail out when the Numerator is not divisible by one of the terms of
7073 *Remainder = Numerator;
7077 *Remainder = D.Zero;
7082 *Quotient = D.Quotient;
7083 *Remainder = D.Remainder;
7086 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator, const SCEV *Denominator)
7087 : SE(S), Denominator(Denominator) {
7088 Zero = SE.getConstant(Denominator->getType(), 0);
7089 One = SE.getConstant(Denominator->getType(), 1);
7091 // By default, we don't know how to divide Expr by Denominator.
7092 // Providing the default here simplifies the rest of the code.
7094 Remainder = Numerator;
7097 // Except in the trivial case described above, we do not know how to divide
7098 // Expr by Denominator for the following functions with empty implementation.
7099 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
7100 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
7101 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
7102 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
7103 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
7104 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
7105 void visitUnknown(const SCEVUnknown *Numerator) {}
7106 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
7108 void visitConstant(const SCEVConstant *Numerator) {
7109 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
7110 Quotient = SE.getConstant(sdiv(Numerator, D));
7111 Remainder = SE.getConstant(srem(Numerator, D));
7116 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
7117 const SCEV *StartQ, *StartR, *StepQ, *StepR;
7118 assert(Numerator->isAffine() && "Numerator should be affine");
7119 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
7120 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
7121 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
7122 Numerator->getNoWrapFlags());
7123 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
7124 Numerator->getNoWrapFlags());
7127 void visitAddExpr(const SCEVAddExpr *Numerator) {
7128 SmallVector<const SCEV *, 2> Qs, Rs;
7129 Type *Ty = Denominator->getType();
7131 for (const SCEV *Op : Numerator->operands()) {
7133 divide(SE, Op, Denominator, &Q, &R);
7135 // Bail out if types do not match.
7136 if (Ty != Q->getType() || Ty != R->getType()) {
7138 Remainder = Numerator;
7146 if (Qs.size() == 1) {
7152 Quotient = SE.getAddExpr(Qs);
7153 Remainder = SE.getAddExpr(Rs);
7156 void visitMulExpr(const SCEVMulExpr *Numerator) {
7157 SmallVector<const SCEV *, 2> Qs;
7158 Type *Ty = Denominator->getType();
7160 bool FoundDenominatorTerm = false;
7161 for (const SCEV *Op : Numerator->operands()) {
7162 // Bail out if types do not match.
7163 if (Ty != Op->getType()) {
7165 Remainder = Numerator;
7169 if (FoundDenominatorTerm) {
7174 // Check whether Denominator divides one of the product operands.
7176 divide(SE, Op, Denominator, &Q, &R);
7182 // Bail out if types do not match.
7183 if (Ty != Q->getType()) {
7185 Remainder = Numerator;
7189 FoundDenominatorTerm = true;
7193 if (FoundDenominatorTerm) {
7198 Quotient = SE.getMulExpr(Qs);
7202 if (!isa<SCEVUnknown>(Denominator)) {
7204 Remainder = Numerator;
7208 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
7209 ValueToValueMap RewriteMap;
7210 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
7211 cast<SCEVConstant>(Zero)->getValue();
7212 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
7214 if (Remainder->isZero()) {
7215 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
7216 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
7217 cast<SCEVConstant>(One)->getValue();
7219 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
7223 // Quotient is (Numerator - Remainder) divided by Denominator.
7225 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
7226 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
7227 // This SCEV does not seem to simplify: fail the division here.
7229 Remainder = Numerator;
7232 divide(SE, Diff, Denominator, &Q, &R);
7234 "(Numerator - Remainder) should evenly divide Denominator");
7239 ScalarEvolution &SE;
7240 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
7244 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7245 SmallVectorImpl<const SCEV *> &Terms,
7246 SmallVectorImpl<const SCEV *> &Sizes) {
7247 int Last = Terms.size() - 1;
7248 const SCEV *Step = Terms[Last];
7250 // End of recursion.
7252 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7253 SmallVector<const SCEV *, 2> Qs;
7254 for (const SCEV *Op : M->operands())
7255 if (!isa<SCEVConstant>(Op))
7258 Step = SE.getMulExpr(Qs);
7261 Sizes.push_back(Step);
7265 for (const SCEV *&Term : Terms) {
7266 // Normalize the terms before the next call to findArrayDimensionsRec.
7268 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7270 // Bail out when GCD does not evenly divide one of the terms.
7277 // Remove all SCEVConstants.
7278 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7279 return isa<SCEVConstant>(E);
7283 if (Terms.size() > 0)
7284 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7287 Sizes.push_back(Step);
7292 struct FindParameter {
7293 bool FoundParameter;
7294 FindParameter() : FoundParameter(false) {}
7296 bool follow(const SCEV *S) {
7297 if (isa<SCEVUnknown>(S)) {
7298 FoundParameter = true;
7299 // Stop recursion: we found a parameter.
7305 bool isDone() const {
7306 // Stop recursion if we have found a parameter.
7307 return FoundParameter;
7312 // Returns true when S contains at least a SCEVUnknown parameter.
7314 containsParameters(const SCEV *S) {
7316 SCEVTraversal<FindParameter> ST(F);
7319 return F.FoundParameter;
7322 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7324 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7325 for (const SCEV *T : Terms)
7326 if (containsParameters(T))
7331 // Return the number of product terms in S.
7332 static inline int numberOfTerms(const SCEV *S) {
7333 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7334 return Expr->getNumOperands();
7338 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7339 if (isa<SCEVConstant>(T))
7342 if (isa<SCEVUnknown>(T))
7345 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7346 SmallVector<const SCEV *, 2> Factors;
7347 for (const SCEV *Op : M->operands())
7348 if (!isa<SCEVConstant>(Op))
7349 Factors.push_back(Op);
7351 return SE.getMulExpr(Factors);
7357 /// Return the size of an element read or written by Inst.
7358 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7360 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7361 Ty = Store->getValueOperand()->getType();
7362 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7363 Ty = Load->getType();
7367 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7368 return getSizeOfExpr(ETy, Ty);
7371 /// Second step of delinearization: compute the array dimensions Sizes from the
7372 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7373 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7374 SmallVectorImpl<const SCEV *> &Sizes,
7375 const SCEV *ElementSize) const {
7377 if (Terms.size() < 1 || !ElementSize)
7380 // Early return when Terms do not contain parameters: we do not delinearize
7381 // non parametric SCEVs.
7382 if (!containsParameters(Terms))
7386 dbgs() << "Terms:\n";
7387 for (const SCEV *T : Terms)
7388 dbgs() << *T << "\n";
7391 // Remove duplicates.
7392 std::sort(Terms.begin(), Terms.end());
7393 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7395 // Put larger terms first.
7396 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7397 return numberOfTerms(LHS) > numberOfTerms(RHS);
7400 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7402 // Divide all terms by the element size.
7403 for (const SCEV *&Term : Terms) {
7405 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
7409 SmallVector<const SCEV *, 4> NewTerms;
7411 // Remove constant factors.
7412 for (const SCEV *T : Terms)
7413 if (const SCEV *NewT = removeConstantFactors(SE, T))
7414 NewTerms.push_back(NewT);
7417 dbgs() << "Terms after sorting:\n";
7418 for (const SCEV *T : NewTerms)
7419 dbgs() << *T << "\n";
7422 if (NewTerms.empty() ||
7423 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7428 // The last element to be pushed into Sizes is the size of an element.
7429 Sizes.push_back(ElementSize);
7432 dbgs() << "Sizes:\n";
7433 for (const SCEV *S : Sizes)
7434 dbgs() << *S << "\n";
7438 /// Third step of delinearization: compute the access functions for the
7439 /// Subscripts based on the dimensions in Sizes.
7440 void SCEVAddRecExpr::computeAccessFunctions(
7441 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7442 SmallVectorImpl<const SCEV *> &Sizes) const {
7444 // Early exit in case this SCEV is not an affine multivariate function.
7445 if (Sizes.empty() || !this->isAffine())
7448 const SCEV *Res = this;
7449 int Last = Sizes.size() - 1;
7450 for (int i = Last; i >= 0; i--) {
7452 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7455 dbgs() << "Res: " << *Res << "\n";
7456 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7457 dbgs() << "Res divided by Sizes[i]:\n";
7458 dbgs() << "Quotient: " << *Q << "\n";
7459 dbgs() << "Remainder: " << *R << "\n";
7464 // Do not record the last subscript corresponding to the size of elements in
7468 // Bail out if the remainder is too complex.
7469 if (isa<SCEVAddRecExpr>(R)) {
7478 // Record the access function for the current subscript.
7479 Subscripts.push_back(R);
7482 // Also push in last position the remainder of the last division: it will be
7483 // the access function of the innermost dimension.
7484 Subscripts.push_back(Res);
7486 std::reverse(Subscripts.begin(), Subscripts.end());
7489 dbgs() << "Subscripts:\n";
7490 for (const SCEV *S : Subscripts)
7491 dbgs() << *S << "\n";
7495 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7496 /// sizes of an array access. Returns the remainder of the delinearization that
7497 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7498 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7499 /// expressions in the stride and base of a SCEV corresponding to the
7500 /// computation of a GCD (greatest common divisor) of base and stride. When
7501 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7503 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7505 /// void foo(long n, long m, long o, double A[n][m][o]) {
7507 /// for (long i = 0; i < n; i++)
7508 /// for (long j = 0; j < m; j++)
7509 /// for (long k = 0; k < o; k++)
7510 /// A[i][j][k] = 1.0;
7513 /// the delinearization input is the following AddRec SCEV:
7515 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7517 /// From this SCEV, we are able to say that the base offset of the access is %A
7518 /// because it appears as an offset that does not divide any of the strides in
7521 /// CHECK: Base offset: %A
7523 /// and then SCEV->delinearize determines the size of some of the dimensions of
7524 /// the array as these are the multiples by which the strides are happening:
7526 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7528 /// Note that the outermost dimension remains of UnknownSize because there are
7529 /// no strides that would help identifying the size of the last dimension: when
7530 /// the array has been statically allocated, one could compute the size of that
7531 /// dimension by dividing the overall size of the array by the size of the known
7532 /// dimensions: %m * %o * 8.
7534 /// Finally delinearize provides the access functions for the array reference
7535 /// that does correspond to A[i][j][k] of the above C testcase:
7537 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7539 /// The testcases are checking the output of a function pass:
7540 /// DelinearizationPass that walks through all loads and stores of a function
7541 /// asking for the SCEV of the memory access with respect to all enclosing
7542 /// loops, calling SCEV->delinearize on that and printing the results.
7544 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7545 SmallVectorImpl<const SCEV *> &Subscripts,
7546 SmallVectorImpl<const SCEV *> &Sizes,
7547 const SCEV *ElementSize) const {
7548 // First step: collect parametric terms.
7549 SmallVector<const SCEV *, 4> Terms;
7550 collectParametricTerms(SE, Terms);
7555 // Second step: find subscript sizes.
7556 SE.findArrayDimensions(Terms, Sizes, ElementSize);
7561 // Third step: compute the access functions for each subscript.
7562 computeAccessFunctions(SE, Subscripts, Sizes);
7564 if (Subscripts.empty())
7568 dbgs() << "succeeded to delinearize " << *this << "\n";
7569 dbgs() << "ArrayDecl[UnknownSize]";
7570 for (const SCEV *S : Sizes)
7571 dbgs() << "[" << *S << "]";
7573 dbgs() << "\nArrayRef";
7574 for (const SCEV *S : Subscripts)
7575 dbgs() << "[" << *S << "]";
7580 //===----------------------------------------------------------------------===//
7581 // SCEVCallbackVH Class Implementation
7582 //===----------------------------------------------------------------------===//
7584 void ScalarEvolution::SCEVCallbackVH::deleted() {
7585 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7586 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7587 SE->ConstantEvolutionLoopExitValue.erase(PN);
7588 SE->ValueExprMap.erase(getValPtr());
7589 // this now dangles!
7592 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7593 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7595 // Forget all the expressions associated with users of the old value,
7596 // so that future queries will recompute the expressions using the new
7598 Value *Old = getValPtr();
7599 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7600 SmallPtrSet<User *, 8> Visited;
7601 while (!Worklist.empty()) {
7602 User *U = Worklist.pop_back_val();
7603 // Deleting the Old value will cause this to dangle. Postpone
7604 // that until everything else is done.
7607 if (!Visited.insert(U))
7609 if (PHINode *PN = dyn_cast<PHINode>(U))
7610 SE->ConstantEvolutionLoopExitValue.erase(PN);
7611 SE->ValueExprMap.erase(U);
7612 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7614 // Delete the Old value.
7615 if (PHINode *PN = dyn_cast<PHINode>(Old))
7616 SE->ConstantEvolutionLoopExitValue.erase(PN);
7617 SE->ValueExprMap.erase(Old);
7618 // this now dangles!
7621 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7622 : CallbackVH(V), SE(se) {}
7624 //===----------------------------------------------------------------------===//
7625 // ScalarEvolution Class Implementation
7626 //===----------------------------------------------------------------------===//
7628 ScalarEvolution::ScalarEvolution()
7629 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7630 BlockDispositions(64), FirstUnknown(nullptr) {
7631 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7634 bool ScalarEvolution::runOnFunction(Function &F) {
7636 LI = &getAnalysis<LoopInfo>();
7637 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7638 DL = DLP ? &DLP->getDataLayout() : nullptr;
7639 TLI = &getAnalysis<TargetLibraryInfo>();
7640 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7644 void ScalarEvolution::releaseMemory() {
7645 // Iterate through all the SCEVUnknown instances and call their
7646 // destructors, so that they release their references to their values.
7647 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7649 FirstUnknown = nullptr;
7651 ValueExprMap.clear();
7653 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7654 // that a loop had multiple computable exits.
7655 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7656 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7661 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7663 BackedgeTakenCounts.clear();
7664 ConstantEvolutionLoopExitValue.clear();
7665 ValuesAtScopes.clear();
7666 LoopDispositions.clear();
7667 BlockDispositions.clear();
7668 UnsignedRanges.clear();
7669 SignedRanges.clear();
7670 UniqueSCEVs.clear();
7671 SCEVAllocator.Reset();
7674 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7675 AU.setPreservesAll();
7676 AU.addRequiredTransitive<LoopInfo>();
7677 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7678 AU.addRequired<TargetLibraryInfo>();
7681 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7682 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7685 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7687 // Print all inner loops first
7688 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7689 PrintLoopInfo(OS, SE, *I);
7692 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7695 SmallVector<BasicBlock *, 8> ExitBlocks;
7696 L->getExitBlocks(ExitBlocks);
7697 if (ExitBlocks.size() != 1)
7698 OS << "<multiple exits> ";
7700 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7701 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7703 OS << "Unpredictable backedge-taken count. ";
7708 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7711 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7712 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7714 OS << "Unpredictable max backedge-taken count. ";
7720 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7721 // ScalarEvolution's implementation of the print method is to print
7722 // out SCEV values of all instructions that are interesting. Doing
7723 // this potentially causes it to create new SCEV objects though,
7724 // which technically conflicts with the const qualifier. This isn't
7725 // observable from outside the class though, so casting away the
7726 // const isn't dangerous.
7727 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7729 OS << "Classifying expressions for: ";
7730 F->printAsOperand(OS, /*PrintType=*/false);
7732 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7733 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7736 const SCEV *SV = SE.getSCEV(&*I);
7739 const Loop *L = LI->getLoopFor((*I).getParent());
7741 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
7748 OS << "\t\t" "Exits: ";
7749 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
7750 if (!SE.isLoopInvariant(ExitValue, L)) {
7751 OS << "<<Unknown>>";
7760 OS << "Determining loop execution counts for: ";
7761 F->printAsOperand(OS, /*PrintType=*/false);
7763 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
7764 PrintLoopInfo(OS, &SE, *I);
7767 ScalarEvolution::LoopDisposition
7768 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
7769 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
7770 for (unsigned u = 0; u < Values.size(); u++) {
7771 if (Values[u].first == L)
7772 return Values[u].second;
7774 Values.push_back(std::make_pair(L, LoopVariant));
7775 LoopDisposition D = computeLoopDisposition(S, L);
7776 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
7777 for (unsigned u = Values2.size(); u > 0; u--) {
7778 if (Values2[u - 1].first == L) {
7779 Values2[u - 1].second = D;
7786 ScalarEvolution::LoopDisposition
7787 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
7788 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7790 return LoopInvariant;
7794 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
7795 case scAddRecExpr: {
7796 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7798 // If L is the addrec's loop, it's computable.
7799 if (AR->getLoop() == L)
7800 return LoopComputable;
7802 // Add recurrences are never invariant in the function-body (null loop).
7806 // This recurrence is variant w.r.t. L if L contains AR's loop.
7807 if (L->contains(AR->getLoop()))
7810 // This recurrence is invariant w.r.t. L if AR's loop contains L.
7811 if (AR->getLoop()->contains(L))
7812 return LoopInvariant;
7814 // This recurrence is variant w.r.t. L if any of its operands
7816 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
7818 if (!isLoopInvariant(*I, L))
7821 // Otherwise it's loop-invariant.
7822 return LoopInvariant;
7828 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7829 bool HasVarying = false;
7830 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7832 LoopDisposition D = getLoopDisposition(*I, L);
7833 if (D == LoopVariant)
7835 if (D == LoopComputable)
7838 return HasVarying ? LoopComputable : LoopInvariant;
7841 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7842 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
7843 if (LD == LoopVariant)
7845 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
7846 if (RD == LoopVariant)
7848 return (LD == LoopInvariant && RD == LoopInvariant) ?
7849 LoopInvariant : LoopComputable;
7852 // All non-instruction values are loop invariant. All instructions are loop
7853 // invariant if they are not contained in the specified loop.
7854 // Instructions are never considered invariant in the function body
7855 // (null loop) because they are defined within the "loop".
7856 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
7857 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
7858 return LoopInvariant;
7859 case scCouldNotCompute:
7860 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7862 llvm_unreachable("Unknown SCEV kind!");
7865 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
7866 return getLoopDisposition(S, L) == LoopInvariant;
7869 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
7870 return getLoopDisposition(S, L) == LoopComputable;
7873 ScalarEvolution::BlockDisposition
7874 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7875 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
7876 for (unsigned u = 0; u < Values.size(); u++) {
7877 if (Values[u].first == BB)
7878 return Values[u].second;
7880 Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
7881 BlockDisposition D = computeBlockDisposition(S, BB);
7882 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
7883 for (unsigned u = Values2.size(); u > 0; u--) {
7884 if (Values2[u - 1].first == BB) {
7885 Values2[u - 1].second = D;
7892 ScalarEvolution::BlockDisposition
7893 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7894 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7896 return ProperlyDominatesBlock;
7900 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
7901 case scAddRecExpr: {
7902 // This uses a "dominates" query instead of "properly dominates" query
7903 // to test for proper dominance too, because the instruction which
7904 // produces the addrec's value is a PHI, and a PHI effectively properly
7905 // dominates its entire containing block.
7906 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7907 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
7908 return DoesNotDominateBlock;
7910 // FALL THROUGH into SCEVNAryExpr handling.
7915 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7917 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7919 BlockDisposition D = getBlockDisposition(*I, BB);
7920 if (D == DoesNotDominateBlock)
7921 return DoesNotDominateBlock;
7922 if (D == DominatesBlock)
7925 return Proper ? ProperlyDominatesBlock : DominatesBlock;
7928 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7929 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
7930 BlockDisposition LD = getBlockDisposition(LHS, BB);
7931 if (LD == DoesNotDominateBlock)
7932 return DoesNotDominateBlock;
7933 BlockDisposition RD = getBlockDisposition(RHS, BB);
7934 if (RD == DoesNotDominateBlock)
7935 return DoesNotDominateBlock;
7936 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
7937 ProperlyDominatesBlock : DominatesBlock;
7940 if (Instruction *I =
7941 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
7942 if (I->getParent() == BB)
7943 return DominatesBlock;
7944 if (DT->properlyDominates(I->getParent(), BB))
7945 return ProperlyDominatesBlock;
7946 return DoesNotDominateBlock;
7948 return ProperlyDominatesBlock;
7949 case scCouldNotCompute:
7950 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7952 llvm_unreachable("Unknown SCEV kind!");
7955 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
7956 return getBlockDisposition(S, BB) >= DominatesBlock;
7959 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
7960 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
7964 // Search for a SCEV expression node within an expression tree.
7965 // Implements SCEVTraversal::Visitor.
7970 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
7972 bool follow(const SCEV *S) {
7973 IsFound |= (S == Node);
7976 bool isDone() const { return IsFound; }
7980 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
7981 SCEVSearch Search(Op);
7982 visitAll(S, Search);
7983 return Search.IsFound;
7986 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
7987 ValuesAtScopes.erase(S);
7988 LoopDispositions.erase(S);
7989 BlockDispositions.erase(S);
7990 UnsignedRanges.erase(S);
7991 SignedRanges.erase(S);
7993 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7994 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
7995 BackedgeTakenInfo &BEInfo = I->second;
7996 if (BEInfo.hasOperand(S, this)) {
7998 BackedgeTakenCounts.erase(I++);
8005 typedef DenseMap<const Loop *, std::string> VerifyMap;
8007 /// replaceSubString - Replaces all occurrences of From in Str with To.
8008 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8010 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8011 Str.replace(Pos, From.size(), To.data(), To.size());
8016 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8018 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8019 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8020 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8022 std::string &S = Map[L];
8024 raw_string_ostream OS(S);
8025 SE.getBackedgeTakenCount(L)->print(OS);
8027 // false and 0 are semantically equivalent. This can happen in dead loops.
8028 replaceSubString(OS.str(), "false", "0");
8029 // Remove wrap flags, their use in SCEV is highly fragile.
8030 // FIXME: Remove this when SCEV gets smarter about them.
8031 replaceSubString(OS.str(), "<nw>", "");
8032 replaceSubString(OS.str(), "<nsw>", "");
8033 replaceSubString(OS.str(), "<nuw>", "");
8038 void ScalarEvolution::verifyAnalysis() const {
8042 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8044 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8045 // FIXME: It would be much better to store actual values instead of strings,
8046 // but SCEV pointers will change if we drop the caches.
8047 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8048 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8049 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8051 // Gather stringified backedge taken counts for all loops without using
8054 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8055 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8057 // Now compare whether they're the same with and without caches. This allows
8058 // verifying that no pass changed the cache.
8059 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8060 "New loops suddenly appeared!");
8062 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8063 OldE = BackedgeDumpsOld.end(),
8064 NewI = BackedgeDumpsNew.begin();
8065 OldI != OldE; ++OldI, ++NewI) {
8066 assert(OldI->first == NewI->first && "Loop order changed!");
8068 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8070 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8071 // means that a pass is buggy or SCEV has to learn a new pattern but is
8072 // usually not harmful.
8073 if (OldI->second != NewI->second &&
8074 OldI->second.find("undef") == std::string::npos &&
8075 NewI->second.find("undef") == std::string::npos &&
8076 OldI->second != "***COULDNOTCOMPUTE***" &&
8077 NewI->second != "***COULDNOTCOMPUTE***") {
8078 dbgs() << "SCEVValidator: SCEV for loop '"
8079 << OldI->first->getHeader()->getName()
8080 << "' changed from '" << OldI->second
8081 << "' to '" << NewI->second << "'!\n";
8086 // TODO: Verify more things.