1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #define DEBUG_TYPE "scalar-evolution"
62 #include "llvm/Analysis/ScalarEvolution.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/ConstantFolding.h"
67 #include "llvm/Analysis/InstructionSimplify.h"
68 #include "llvm/Analysis/LoopInfo.h"
69 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
70 #include "llvm/Analysis/ValueTracking.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/GlobalAlias.h"
76 #include "llvm/IR/GlobalVariable.h"
77 #include "llvm/IR/InstIterator.h"
78 #include "llvm/IR/Instructions.h"
79 #include "llvm/IR/LLVMContext.h"
80 #include "llvm/IR/Operator.h"
81 #include "llvm/Support/CommandLine.h"
82 #include "llvm/Support/ConstantRange.h"
83 #include "llvm/Support/Debug.h"
84 #include "llvm/Support/ErrorHandling.h"
85 #include "llvm/Support/GetElementPtrTypeIterator.h"
86 #include "llvm/Support/MathExtras.h"
87 #include "llvm/Support/raw_ostream.h"
88 #include "llvm/Target/TargetLibraryInfo.h"
92 STATISTIC(NumArrayLenItCounts,
93 "Number of trip counts computed with array length");
94 STATISTIC(NumTripCountsComputed,
95 "Number of loops with predictable loop counts");
96 STATISTIC(NumTripCountsNotComputed,
97 "Number of loops without predictable loop counts");
98 STATISTIC(NumBruteForceTripCountsComputed,
99 "Number of loops with trip counts computed by force");
101 static cl::opt<unsigned>
102 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
103 cl::desc("Maximum number of iterations SCEV will "
104 "symbolically execute a constant "
108 // FIXME: Enable this with XDEBUG when the test suite is clean.
110 VerifySCEV("verify-scev",
111 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
113 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
114 "Scalar Evolution Analysis", false, true)
115 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
116 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
117 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
118 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
119 "Scalar Evolution Analysis", false, true)
120 char ScalarEvolution::ID = 0;
122 //===----------------------------------------------------------------------===//
123 // SCEV class definitions
124 //===----------------------------------------------------------------------===//
126 //===----------------------------------------------------------------------===//
127 // Implementation of the SCEV class.
130 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
131 void SCEV::dump() const {
137 void SCEV::print(raw_ostream &OS) const {
138 switch (static_cast<SCEVTypes>(getSCEVType())) {
140 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
143 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
144 const SCEV *Op = Trunc->getOperand();
145 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
146 << *Trunc->getType() << ")";
150 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
151 const SCEV *Op = ZExt->getOperand();
152 OS << "(zext " << *Op->getType() << " " << *Op << " to "
153 << *ZExt->getType() << ")";
157 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
158 const SCEV *Op = SExt->getOperand();
159 OS << "(sext " << *Op->getType() << " " << *Op << " to "
160 << *SExt->getType() << ")";
164 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
165 OS << "{" << *AR->getOperand(0);
166 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
167 OS << ",+," << *AR->getOperand(i);
169 if (AR->getNoWrapFlags(FlagNUW))
171 if (AR->getNoWrapFlags(FlagNSW))
173 if (AR->getNoWrapFlags(FlagNW) &&
174 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
176 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
184 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
185 const char *OpStr = 0;
186 switch (NAry->getSCEVType()) {
187 case scAddExpr: OpStr = " + "; break;
188 case scMulExpr: OpStr = " * "; break;
189 case scUMaxExpr: OpStr = " umax "; break;
190 case scSMaxExpr: OpStr = " smax "; break;
193 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
196 if (std::next(I) != E)
200 switch (NAry->getSCEVType()) {
203 if (NAry->getNoWrapFlags(FlagNUW))
205 if (NAry->getNoWrapFlags(FlagNSW))
211 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
212 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
216 const SCEVUnknown *U = cast<SCEVUnknown>(this);
218 if (U->isSizeOf(AllocTy)) {
219 OS << "sizeof(" << *AllocTy << ")";
222 if (U->isAlignOf(AllocTy)) {
223 OS << "alignof(" << *AllocTy << ")";
229 if (U->isOffsetOf(CTy, FieldNo)) {
230 OS << "offsetof(" << *CTy << ", ";
231 FieldNo->printAsOperand(OS, false);
236 // Otherwise just print it normally.
237 U->getValue()->printAsOperand(OS, false);
240 case scCouldNotCompute:
241 OS << "***COULDNOTCOMPUTE***";
244 llvm_unreachable("Unknown SCEV kind!");
247 Type *SCEV::getType() const {
248 switch (static_cast<SCEVTypes>(getSCEVType())) {
250 return cast<SCEVConstant>(this)->getType();
254 return cast<SCEVCastExpr>(this)->getType();
259 return cast<SCEVNAryExpr>(this)->getType();
261 return cast<SCEVAddExpr>(this)->getType();
263 return cast<SCEVUDivExpr>(this)->getType();
265 return cast<SCEVUnknown>(this)->getType();
266 case scCouldNotCompute:
267 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
269 llvm_unreachable("Unknown SCEV kind!");
272 bool SCEV::isZero() const {
273 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
274 return SC->getValue()->isZero();
278 bool SCEV::isOne() const {
279 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
280 return SC->getValue()->isOne();
284 bool SCEV::isAllOnesValue() const {
285 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
286 return SC->getValue()->isAllOnesValue();
290 /// isNonConstantNegative - Return true if the specified scev is negated, but
292 bool SCEV::isNonConstantNegative() const {
293 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
294 if (!Mul) return false;
296 // If there is a constant factor, it will be first.
297 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
298 if (!SC) return false;
300 // Return true if the value is negative, this matches things like (-42 * V).
301 return SC->getValue()->getValue().isNegative();
304 SCEVCouldNotCompute::SCEVCouldNotCompute() :
305 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
307 bool SCEVCouldNotCompute::classof(const SCEV *S) {
308 return S->getSCEVType() == scCouldNotCompute;
311 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
313 ID.AddInteger(scConstant);
316 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
317 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
318 UniqueSCEVs.InsertNode(S, IP);
322 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
323 return getConstant(ConstantInt::get(getContext(), Val));
327 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
328 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
329 return getConstant(ConstantInt::get(ITy, V, isSigned));
332 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
333 unsigned SCEVTy, const SCEV *op, Type *ty)
334 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
336 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
337 const SCEV *op, Type *ty)
338 : SCEVCastExpr(ID, scTruncate, op, ty) {
339 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
340 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
341 "Cannot truncate non-integer value!");
344 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
345 const SCEV *op, Type *ty)
346 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
347 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
348 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
349 "Cannot zero extend non-integer value!");
352 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
353 const SCEV *op, Type *ty)
354 : SCEVCastExpr(ID, scSignExtend, op, ty) {
355 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
356 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
357 "Cannot sign extend non-integer value!");
360 void SCEVUnknown::deleted() {
361 // Clear this SCEVUnknown from various maps.
362 SE->forgetMemoizedResults(this);
364 // Remove this SCEVUnknown from the uniquing map.
365 SE->UniqueSCEVs.RemoveNode(this);
367 // Release the value.
371 void SCEVUnknown::allUsesReplacedWith(Value *New) {
372 // Clear this SCEVUnknown from various maps.
373 SE->forgetMemoizedResults(this);
375 // Remove this SCEVUnknown from the uniquing map.
376 SE->UniqueSCEVs.RemoveNode(this);
378 // Update this SCEVUnknown to point to the new value. This is needed
379 // because there may still be outstanding SCEVs which still point to
384 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
385 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
386 if (VCE->getOpcode() == Instruction::PtrToInt)
387 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
388 if (CE->getOpcode() == Instruction::GetElementPtr &&
389 CE->getOperand(0)->isNullValue() &&
390 CE->getNumOperands() == 2)
391 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
393 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
401 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
402 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
403 if (VCE->getOpcode() == Instruction::PtrToInt)
404 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
405 if (CE->getOpcode() == Instruction::GetElementPtr &&
406 CE->getOperand(0)->isNullValue()) {
408 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
409 if (StructType *STy = dyn_cast<StructType>(Ty))
410 if (!STy->isPacked() &&
411 CE->getNumOperands() == 3 &&
412 CE->getOperand(1)->isNullValue()) {
413 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
415 STy->getNumElements() == 2 &&
416 STy->getElementType(0)->isIntegerTy(1)) {
417 AllocTy = STy->getElementType(1);
426 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
427 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
428 if (VCE->getOpcode() == Instruction::PtrToInt)
429 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
430 if (CE->getOpcode() == Instruction::GetElementPtr &&
431 CE->getNumOperands() == 3 &&
432 CE->getOperand(0)->isNullValue() &&
433 CE->getOperand(1)->isNullValue()) {
435 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
436 // Ignore vector types here so that ScalarEvolutionExpander doesn't
437 // emit getelementptrs that index into vectors.
438 if (Ty->isStructTy() || Ty->isArrayTy()) {
440 FieldNo = CE->getOperand(2);
448 //===----------------------------------------------------------------------===//
450 //===----------------------------------------------------------------------===//
453 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
454 /// than the complexity of the RHS. This comparator is used to canonicalize
456 class SCEVComplexityCompare {
457 const LoopInfo *const LI;
459 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
461 // Return true or false if LHS is less than, or at least RHS, respectively.
462 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
463 return compare(LHS, RHS) < 0;
466 // Return negative, zero, or positive, if LHS is less than, equal to, or
467 // greater than RHS, respectively. A three-way result allows recursive
468 // comparisons to be more efficient.
469 int compare(const SCEV *LHS, const SCEV *RHS) const {
470 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
474 // Primarily, sort the SCEVs by their getSCEVType().
475 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
477 return (int)LType - (int)RType;
479 // Aside from the getSCEVType() ordering, the particular ordering
480 // isn't very important except that it's beneficial to be consistent,
481 // so that (a + b) and (b + a) don't end up as different expressions.
482 switch (static_cast<SCEVTypes>(LType)) {
484 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
485 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
487 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
488 // not as complete as it could be.
489 const Value *LV = LU->getValue(), *RV = RU->getValue();
491 // Order pointer values after integer values. This helps SCEVExpander
493 bool LIsPointer = LV->getType()->isPointerTy(),
494 RIsPointer = RV->getType()->isPointerTy();
495 if (LIsPointer != RIsPointer)
496 return (int)LIsPointer - (int)RIsPointer;
498 // Compare getValueID values.
499 unsigned LID = LV->getValueID(),
500 RID = RV->getValueID();
502 return (int)LID - (int)RID;
504 // Sort arguments by their position.
505 if (const Argument *LA = dyn_cast<Argument>(LV)) {
506 const Argument *RA = cast<Argument>(RV);
507 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
508 return (int)LArgNo - (int)RArgNo;
511 // For instructions, compare their loop depth, and their operand
512 // count. This is pretty loose.
513 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
514 const Instruction *RInst = cast<Instruction>(RV);
516 // Compare loop depths.
517 const BasicBlock *LParent = LInst->getParent(),
518 *RParent = RInst->getParent();
519 if (LParent != RParent) {
520 unsigned LDepth = LI->getLoopDepth(LParent),
521 RDepth = LI->getLoopDepth(RParent);
522 if (LDepth != RDepth)
523 return (int)LDepth - (int)RDepth;
526 // Compare the number of operands.
527 unsigned LNumOps = LInst->getNumOperands(),
528 RNumOps = RInst->getNumOperands();
529 return (int)LNumOps - (int)RNumOps;
536 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
537 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
539 // Compare constant values.
540 const APInt &LA = LC->getValue()->getValue();
541 const APInt &RA = RC->getValue()->getValue();
542 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
543 if (LBitWidth != RBitWidth)
544 return (int)LBitWidth - (int)RBitWidth;
545 return LA.ult(RA) ? -1 : 1;
549 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
550 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
552 // Compare addrec loop depths.
553 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
554 if (LLoop != RLoop) {
555 unsigned LDepth = LLoop->getLoopDepth(),
556 RDepth = RLoop->getLoopDepth();
557 if (LDepth != RDepth)
558 return (int)LDepth - (int)RDepth;
561 // Addrec complexity grows with operand count.
562 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
563 if (LNumOps != RNumOps)
564 return (int)LNumOps - (int)RNumOps;
566 // Lexicographically compare.
567 for (unsigned i = 0; i != LNumOps; ++i) {
568 long X = compare(LA->getOperand(i), RA->getOperand(i));
580 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
581 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
583 // Lexicographically compare n-ary expressions.
584 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
585 if (LNumOps != RNumOps)
586 return (int)LNumOps - (int)RNumOps;
588 for (unsigned i = 0; i != LNumOps; ++i) {
591 long X = compare(LC->getOperand(i), RC->getOperand(i));
595 return (int)LNumOps - (int)RNumOps;
599 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
600 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
602 // Lexicographically compare udiv expressions.
603 long X = compare(LC->getLHS(), RC->getLHS());
606 return compare(LC->getRHS(), RC->getRHS());
612 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
613 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
615 // Compare cast expressions by operand.
616 return compare(LC->getOperand(), RC->getOperand());
619 case scCouldNotCompute:
620 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
622 llvm_unreachable("Unknown SCEV kind!");
627 /// GroupByComplexity - Given a list of SCEV objects, order them by their
628 /// complexity, and group objects of the same complexity together by value.
629 /// When this routine is finished, we know that any duplicates in the vector are
630 /// consecutive and that complexity is monotonically increasing.
632 /// Note that we go take special precautions to ensure that we get deterministic
633 /// results from this routine. In other words, we don't want the results of
634 /// this to depend on where the addresses of various SCEV objects happened to
637 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
639 if (Ops.size() < 2) return; // Noop
640 if (Ops.size() == 2) {
641 // This is the common case, which also happens to be trivially simple.
643 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
644 if (SCEVComplexityCompare(LI)(RHS, LHS))
649 // Do the rough sort by complexity.
650 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
652 // Now that we are sorted by complexity, group elements of the same
653 // complexity. Note that this is, at worst, N^2, but the vector is likely to
654 // be extremely short in practice. Note that we take this approach because we
655 // do not want to depend on the addresses of the objects we are grouping.
656 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
657 const SCEV *S = Ops[i];
658 unsigned Complexity = S->getSCEVType();
660 // If there are any objects of the same complexity and same value as this
662 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
663 if (Ops[j] == S) { // Found a duplicate.
664 // Move it to immediately after i'th element.
665 std::swap(Ops[i+1], Ops[j]);
666 ++i; // no need to rescan it.
667 if (i == e-2) return; // Done!
675 //===----------------------------------------------------------------------===//
676 // Simple SCEV method implementations
677 //===----------------------------------------------------------------------===//
679 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
681 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
684 // Handle the simplest case efficiently.
686 return SE.getTruncateOrZeroExtend(It, ResultTy);
688 // We are using the following formula for BC(It, K):
690 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
692 // Suppose, W is the bitwidth of the return value. We must be prepared for
693 // overflow. Hence, we must assure that the result of our computation is
694 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
695 // safe in modular arithmetic.
697 // However, this code doesn't use exactly that formula; the formula it uses
698 // is something like the following, where T is the number of factors of 2 in
699 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
702 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
704 // This formula is trivially equivalent to the previous formula. However,
705 // this formula can be implemented much more efficiently. The trick is that
706 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
707 // arithmetic. To do exact division in modular arithmetic, all we have
708 // to do is multiply by the inverse. Therefore, this step can be done at
711 // The next issue is how to safely do the division by 2^T. The way this
712 // is done is by doing the multiplication step at a width of at least W + T
713 // bits. This way, the bottom W+T bits of the product are accurate. Then,
714 // when we perform the division by 2^T (which is equivalent to a right shift
715 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
716 // truncated out after the division by 2^T.
718 // In comparison to just directly using the first formula, this technique
719 // is much more efficient; using the first formula requires W * K bits,
720 // but this formula less than W + K bits. Also, the first formula requires
721 // a division step, whereas this formula only requires multiplies and shifts.
723 // It doesn't matter whether the subtraction step is done in the calculation
724 // width or the input iteration count's width; if the subtraction overflows,
725 // the result must be zero anyway. We prefer here to do it in the width of
726 // the induction variable because it helps a lot for certain cases; CodeGen
727 // isn't smart enough to ignore the overflow, which leads to much less
728 // efficient code if the width of the subtraction is wider than the native
731 // (It's possible to not widen at all by pulling out factors of 2 before
732 // the multiplication; for example, K=2 can be calculated as
733 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
734 // extra arithmetic, so it's not an obvious win, and it gets
735 // much more complicated for K > 3.)
737 // Protection from insane SCEVs; this bound is conservative,
738 // but it probably doesn't matter.
740 return SE.getCouldNotCompute();
742 unsigned W = SE.getTypeSizeInBits(ResultTy);
744 // Calculate K! / 2^T and T; we divide out the factors of two before
745 // multiplying for calculating K! / 2^T to avoid overflow.
746 // Other overflow doesn't matter because we only care about the bottom
747 // W bits of the result.
748 APInt OddFactorial(W, 1);
750 for (unsigned i = 3; i <= K; ++i) {
752 unsigned TwoFactors = Mult.countTrailingZeros();
754 Mult = Mult.lshr(TwoFactors);
755 OddFactorial *= Mult;
758 // We need at least W + T bits for the multiplication step
759 unsigned CalculationBits = W + T;
761 // Calculate 2^T, at width T+W.
762 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
764 // Calculate the multiplicative inverse of K! / 2^T;
765 // this multiplication factor will perform the exact division by
767 APInt Mod = APInt::getSignedMinValue(W+1);
768 APInt MultiplyFactor = OddFactorial.zext(W+1);
769 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
770 MultiplyFactor = MultiplyFactor.trunc(W);
772 // Calculate the product, at width T+W
773 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
775 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
776 for (unsigned i = 1; i != K; ++i) {
777 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
778 Dividend = SE.getMulExpr(Dividend,
779 SE.getTruncateOrZeroExtend(S, CalculationTy));
783 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
785 // Truncate the result, and divide by K! / 2^T.
787 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
788 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
791 /// evaluateAtIteration - Return the value of this chain of recurrences at
792 /// the specified iteration number. We can evaluate this recurrence by
793 /// multiplying each element in the chain by the binomial coefficient
794 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
796 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
798 /// where BC(It, k) stands for binomial coefficient.
800 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
801 ScalarEvolution &SE) const {
802 const SCEV *Result = getStart();
803 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
804 // The computation is correct in the face of overflow provided that the
805 // multiplication is performed _after_ the evaluation of the binomial
807 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
808 if (isa<SCEVCouldNotCompute>(Coeff))
811 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
816 //===----------------------------------------------------------------------===//
817 // SCEV Expression folder implementations
818 //===----------------------------------------------------------------------===//
820 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
822 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
823 "This is not a truncating conversion!");
824 assert(isSCEVable(Ty) &&
825 "This is not a conversion to a SCEVable type!");
826 Ty = getEffectiveSCEVType(Ty);
829 ID.AddInteger(scTruncate);
833 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
835 // Fold if the operand is constant.
836 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
838 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
840 // trunc(trunc(x)) --> trunc(x)
841 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
842 return getTruncateExpr(ST->getOperand(), Ty);
844 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
845 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
846 return getTruncateOrSignExtend(SS->getOperand(), Ty);
848 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
849 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
850 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
852 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
853 // eliminate all the truncates.
854 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
855 SmallVector<const SCEV *, 4> Operands;
856 bool hasTrunc = false;
857 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
858 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
859 hasTrunc = isa<SCEVTruncateExpr>(S);
860 Operands.push_back(S);
863 return getAddExpr(Operands);
864 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
867 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
868 // eliminate all the truncates.
869 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
870 SmallVector<const SCEV *, 4> Operands;
871 bool hasTrunc = false;
872 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
873 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
874 hasTrunc = isa<SCEVTruncateExpr>(S);
875 Operands.push_back(S);
878 return getMulExpr(Operands);
879 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
882 // If the input value is a chrec scev, truncate the chrec's operands.
883 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
884 SmallVector<const SCEV *, 4> Operands;
885 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
886 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
887 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
890 // The cast wasn't folded; create an explicit cast node. We can reuse
891 // the existing insert position since if we get here, we won't have
892 // made any changes which would invalidate it.
893 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
895 UniqueSCEVs.InsertNode(S, IP);
899 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
901 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
902 "This is not an extending conversion!");
903 assert(isSCEVable(Ty) &&
904 "This is not a conversion to a SCEVable type!");
905 Ty = getEffectiveSCEVType(Ty);
907 // Fold if the operand is constant.
908 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
910 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
912 // zext(zext(x)) --> zext(x)
913 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
914 return getZeroExtendExpr(SZ->getOperand(), Ty);
916 // Before doing any expensive analysis, check to see if we've already
917 // computed a SCEV for this Op and Ty.
919 ID.AddInteger(scZeroExtend);
923 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
925 // zext(trunc(x)) --> zext(x) or x or trunc(x)
926 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
927 // It's possible the bits taken off by the truncate were all zero bits. If
928 // so, we should be able to simplify this further.
929 const SCEV *X = ST->getOperand();
930 ConstantRange CR = getUnsignedRange(X);
931 unsigned TruncBits = getTypeSizeInBits(ST->getType());
932 unsigned NewBits = getTypeSizeInBits(Ty);
933 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
934 CR.zextOrTrunc(NewBits)))
935 return getTruncateOrZeroExtend(X, Ty);
938 // If the input value is a chrec scev, and we can prove that the value
939 // did not overflow the old, smaller, value, we can zero extend all of the
940 // operands (often constants). This allows analysis of something like
941 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
942 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
943 if (AR->isAffine()) {
944 const SCEV *Start = AR->getStart();
945 const SCEV *Step = AR->getStepRecurrence(*this);
946 unsigned BitWidth = getTypeSizeInBits(AR->getType());
947 const Loop *L = AR->getLoop();
949 // If we have special knowledge that this addrec won't overflow,
950 // we don't need to do any further analysis.
951 if (AR->getNoWrapFlags(SCEV::FlagNUW))
952 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
953 getZeroExtendExpr(Step, Ty),
954 L, AR->getNoWrapFlags());
956 // Check whether the backedge-taken count is SCEVCouldNotCompute.
957 // Note that this serves two purposes: It filters out loops that are
958 // simply not analyzable, and it covers the case where this code is
959 // being called from within backedge-taken count analysis, such that
960 // attempting to ask for the backedge-taken count would likely result
961 // in infinite recursion. In the later case, the analysis code will
962 // cope with a conservative value, and it will take care to purge
963 // that value once it has finished.
964 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
965 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
966 // Manually compute the final value for AR, checking for
969 // Check whether the backedge-taken count can be losslessly casted to
970 // the addrec's type. The count is always unsigned.
971 const SCEV *CastedMaxBECount =
972 getTruncateOrZeroExtend(MaxBECount, Start->getType());
973 const SCEV *RecastedMaxBECount =
974 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
975 if (MaxBECount == RecastedMaxBECount) {
976 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
977 // Check whether Start+Step*MaxBECount has no unsigned overflow.
978 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
979 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
980 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
981 const SCEV *WideMaxBECount =
982 getZeroExtendExpr(CastedMaxBECount, WideTy);
983 const SCEV *OperandExtendedAdd =
984 getAddExpr(WideStart,
985 getMulExpr(WideMaxBECount,
986 getZeroExtendExpr(Step, WideTy)));
987 if (ZAdd == OperandExtendedAdd) {
988 // Cache knowledge of AR NUW, which is propagated to this AddRec.
989 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
990 // Return the expression with the addrec on the outside.
991 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
992 getZeroExtendExpr(Step, Ty),
993 L, AR->getNoWrapFlags());
995 // Similar to above, only this time treat the step value as signed.
996 // This covers loops that count down.
998 getAddExpr(WideStart,
999 getMulExpr(WideMaxBECount,
1000 getSignExtendExpr(Step, WideTy)));
1001 if (ZAdd == OperandExtendedAdd) {
1002 // Cache knowledge of AR NW, which is propagated to this AddRec.
1003 // Negative step causes unsigned wrap, but it still can't self-wrap.
1004 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1005 // Return the expression with the addrec on the outside.
1006 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1007 getSignExtendExpr(Step, Ty),
1008 L, AR->getNoWrapFlags());
1012 // If the backedge is guarded by a comparison with the pre-inc value
1013 // the addrec is safe. Also, if the entry is guarded by a comparison
1014 // with the start value and the backedge is guarded by a comparison
1015 // with the post-inc value, the addrec is safe.
1016 if (isKnownPositive(Step)) {
1017 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1018 getUnsignedRange(Step).getUnsignedMax());
1019 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1020 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1021 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1022 AR->getPostIncExpr(*this), N))) {
1023 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1024 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1025 // Return the expression with the addrec on the outside.
1026 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1027 getZeroExtendExpr(Step, Ty),
1028 L, AR->getNoWrapFlags());
1030 } else if (isKnownNegative(Step)) {
1031 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1032 getSignedRange(Step).getSignedMin());
1033 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1034 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1035 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1036 AR->getPostIncExpr(*this), N))) {
1037 // Cache knowledge of AR NW, which is propagated to this AddRec.
1038 // Negative step causes unsigned wrap, but it still can't self-wrap.
1039 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1040 // Return the expression with the addrec on the outside.
1041 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1042 getSignExtendExpr(Step, Ty),
1043 L, AR->getNoWrapFlags());
1049 // The cast wasn't folded; create an explicit cast node.
1050 // Recompute the insert position, as it may have been invalidated.
1051 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1052 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1054 UniqueSCEVs.InsertNode(S, IP);
1058 // Get the limit of a recurrence such that incrementing by Step cannot cause
1059 // signed overflow as long as the value of the recurrence within the loop does
1060 // not exceed this limit before incrementing.
1061 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1062 ICmpInst::Predicate *Pred,
1063 ScalarEvolution *SE) {
1064 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1065 if (SE->isKnownPositive(Step)) {
1066 *Pred = ICmpInst::ICMP_SLT;
1067 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1068 SE->getSignedRange(Step).getSignedMax());
1070 if (SE->isKnownNegative(Step)) {
1071 *Pred = ICmpInst::ICMP_SGT;
1072 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1073 SE->getSignedRange(Step).getSignedMin());
1078 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1079 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1080 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1081 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1082 // result, the expression "Step + sext(PreIncAR)" is congruent with
1083 // "sext(PostIncAR)"
1084 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1086 ScalarEvolution *SE) {
1087 const Loop *L = AR->getLoop();
1088 const SCEV *Start = AR->getStart();
1089 const SCEV *Step = AR->getStepRecurrence(*SE);
1091 // Check for a simple looking step prior to loop entry.
1092 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1096 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1097 // subtraction is expensive. For this purpose, perform a quick and dirty
1098 // difference, by checking for Step in the operand list.
1099 SmallVector<const SCEV *, 4> DiffOps;
1100 for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end();
1103 DiffOps.push_back(*I);
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 // If the input value is a chrec scev, and we can prove that the value
1205 // did not overflow the old, smaller, value, we can sign extend all of the
1206 // operands (often constants). This allows analysis of something like
1207 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1208 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1209 if (AR->isAffine()) {
1210 const SCEV *Start = AR->getStart();
1211 const SCEV *Step = AR->getStepRecurrence(*this);
1212 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1213 const Loop *L = AR->getLoop();
1215 // If we have special knowledge that this addrec won't overflow,
1216 // we don't need to do any further analysis.
1217 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1218 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1219 getSignExtendExpr(Step, Ty),
1222 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1223 // Note that this serves two purposes: It filters out loops that are
1224 // simply not analyzable, and it covers the case where this code is
1225 // being called from within backedge-taken count analysis, such that
1226 // attempting to ask for the backedge-taken count would likely result
1227 // in infinite recursion. In the later case, the analysis code will
1228 // cope with a conservative value, and it will take care to purge
1229 // that value once it has finished.
1230 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1231 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1232 // Manually compute the final value for AR, checking for
1235 // Check whether the backedge-taken count can be losslessly casted to
1236 // the addrec's type. The count is always unsigned.
1237 const SCEV *CastedMaxBECount =
1238 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1239 const SCEV *RecastedMaxBECount =
1240 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1241 if (MaxBECount == RecastedMaxBECount) {
1242 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1243 // Check whether Start+Step*MaxBECount has no signed overflow.
1244 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1245 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1246 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1247 const SCEV *WideMaxBECount =
1248 getZeroExtendExpr(CastedMaxBECount, WideTy);
1249 const SCEV *OperandExtendedAdd =
1250 getAddExpr(WideStart,
1251 getMulExpr(WideMaxBECount,
1252 getSignExtendExpr(Step, WideTy)));
1253 if (SAdd == OperandExtendedAdd) {
1254 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1255 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1256 // Return the expression with the addrec on the outside.
1257 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1258 getSignExtendExpr(Step, Ty),
1259 L, AR->getNoWrapFlags());
1261 // Similar to above, only this time treat the step value as unsigned.
1262 // This covers loops that count up with an unsigned step.
1263 OperandExtendedAdd =
1264 getAddExpr(WideStart,
1265 getMulExpr(WideMaxBECount,
1266 getZeroExtendExpr(Step, WideTy)));
1267 if (SAdd == OperandExtendedAdd) {
1268 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1269 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1270 // Return the expression with the addrec on the outside.
1271 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1272 getZeroExtendExpr(Step, Ty),
1273 L, AR->getNoWrapFlags());
1277 // If the backedge is guarded by a comparison with the pre-inc value
1278 // the addrec is safe. Also, if the entry is guarded by a comparison
1279 // with the start value and the backedge is guarded by a comparison
1280 // with the post-inc value, the addrec is safe.
1281 ICmpInst::Predicate Pred;
1282 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1283 if (OverflowLimit &&
1284 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1285 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1286 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1288 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1289 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1290 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1291 getSignExtendExpr(Step, Ty),
1292 L, AR->getNoWrapFlags());
1297 // The cast wasn't folded; create an explicit cast node.
1298 // Recompute the insert position, as it may have been invalidated.
1299 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1300 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1302 UniqueSCEVs.InsertNode(S, IP);
1306 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1307 /// unspecified bits out to the given type.
1309 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1311 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1312 "This is not an extending conversion!");
1313 assert(isSCEVable(Ty) &&
1314 "This is not a conversion to a SCEVable type!");
1315 Ty = getEffectiveSCEVType(Ty);
1317 // Sign-extend negative constants.
1318 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1319 if (SC->getValue()->getValue().isNegative())
1320 return getSignExtendExpr(Op, Ty);
1322 // Peel off a truncate cast.
1323 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1324 const SCEV *NewOp = T->getOperand();
1325 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1326 return getAnyExtendExpr(NewOp, Ty);
1327 return getTruncateOrNoop(NewOp, Ty);
1330 // Next try a zext cast. If the cast is folded, use it.
1331 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1332 if (!isa<SCEVZeroExtendExpr>(ZExt))
1335 // Next try a sext cast. If the cast is folded, use it.
1336 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1337 if (!isa<SCEVSignExtendExpr>(SExt))
1340 // Force the cast to be folded into the operands of an addrec.
1341 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1342 SmallVector<const SCEV *, 4> Ops;
1343 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1345 Ops.push_back(getAnyExtendExpr(*I, Ty));
1346 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1349 // If the expression is obviously signed, use the sext cast value.
1350 if (isa<SCEVSMaxExpr>(Op))
1353 // Absent any other information, use the zext cast value.
1357 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1358 /// a list of operands to be added under the given scale, update the given
1359 /// map. This is a helper function for getAddRecExpr. As an example of
1360 /// what it does, given a sequence of operands that would form an add
1361 /// expression like this:
1363 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1365 /// where A and B are constants, update the map with these values:
1367 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1369 /// and add 13 + A*B*29 to AccumulatedConstant.
1370 /// This will allow getAddRecExpr to produce this:
1372 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1374 /// This form often exposes folding opportunities that are hidden in
1375 /// the original operand list.
1377 /// Return true iff it appears that any interesting folding opportunities
1378 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1379 /// the common case where no interesting opportunities are present, and
1380 /// is also used as a check to avoid infinite recursion.
1383 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1384 SmallVectorImpl<const SCEV *> &NewOps,
1385 APInt &AccumulatedConstant,
1386 const SCEV *const *Ops, size_t NumOperands,
1388 ScalarEvolution &SE) {
1389 bool Interesting = false;
1391 // Iterate over the add operands. They are sorted, with constants first.
1393 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1395 // Pull a buried constant out to the outside.
1396 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1398 AccumulatedConstant += Scale * C->getValue()->getValue();
1401 // Next comes everything else. We're especially interested in multiplies
1402 // here, but they're in the middle, so just visit the rest with one loop.
1403 for (; i != NumOperands; ++i) {
1404 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1405 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1407 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1408 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1409 // A multiplication of a constant with another add; recurse.
1410 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1412 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1413 Add->op_begin(), Add->getNumOperands(),
1416 // A multiplication of a constant with some other value. Update
1418 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1419 const SCEV *Key = SE.getMulExpr(MulOps);
1420 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1421 M.insert(std::make_pair(Key, NewScale));
1423 NewOps.push_back(Pair.first->first);
1425 Pair.first->second += NewScale;
1426 // The map already had an entry for this value, which may indicate
1427 // a folding opportunity.
1432 // An ordinary operand. Update the map.
1433 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1434 M.insert(std::make_pair(Ops[i], Scale));
1436 NewOps.push_back(Pair.first->first);
1438 Pair.first->second += Scale;
1439 // The map already had an entry for this value, which may indicate
1440 // a folding opportunity.
1450 struct APIntCompare {
1451 bool operator()(const APInt &LHS, const APInt &RHS) const {
1452 return LHS.ult(RHS);
1457 /// getAddExpr - Get a canonical add expression, or something simpler if
1459 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1460 SCEV::NoWrapFlags Flags) {
1461 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1462 "only nuw or nsw allowed");
1463 assert(!Ops.empty() && "Cannot get empty add!");
1464 if (Ops.size() == 1) return Ops[0];
1466 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1467 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1468 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1469 "SCEVAddExpr operand types don't match!");
1472 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1474 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1475 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1476 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1478 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1479 E = Ops.end(); I != E; ++I)
1480 if (!isKnownNonNegative(*I)) {
1484 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1487 // Sort by complexity, this groups all similar expression types together.
1488 GroupByComplexity(Ops, LI);
1490 // If there are any constants, fold them together.
1492 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1494 assert(Idx < Ops.size());
1495 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1496 // We found two constants, fold them together!
1497 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1498 RHSC->getValue()->getValue());
1499 if (Ops.size() == 2) return Ops[0];
1500 Ops.erase(Ops.begin()+1); // Erase the folded element
1501 LHSC = cast<SCEVConstant>(Ops[0]);
1504 // If we are left with a constant zero being added, strip it off.
1505 if (LHSC->getValue()->isZero()) {
1506 Ops.erase(Ops.begin());
1510 if (Ops.size() == 1) return Ops[0];
1513 // Okay, check to see if the same value occurs in the operand list more than
1514 // once. If so, merge them together into an multiply expression. Since we
1515 // sorted the list, these values are required to be adjacent.
1516 Type *Ty = Ops[0]->getType();
1517 bool FoundMatch = false;
1518 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1519 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1520 // Scan ahead to count how many equal operands there are.
1522 while (i+Count != e && Ops[i+Count] == Ops[i])
1524 // Merge the values into a multiply.
1525 const SCEV *Scale = getConstant(Ty, Count);
1526 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1527 if (Ops.size() == Count)
1530 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1531 --i; e -= Count - 1;
1535 return getAddExpr(Ops, Flags);
1537 // Check for truncates. If all the operands are truncated from the same
1538 // type, see if factoring out the truncate would permit the result to be
1539 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1540 // if the contents of the resulting outer trunc fold to something simple.
1541 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1542 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1543 Type *DstType = Trunc->getType();
1544 Type *SrcType = Trunc->getOperand()->getType();
1545 SmallVector<const SCEV *, 8> LargeOps;
1547 // Check all the operands to see if they can be represented in the
1548 // source type of the truncate.
1549 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1550 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1551 if (T->getOperand()->getType() != SrcType) {
1555 LargeOps.push_back(T->getOperand());
1556 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1557 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1558 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1559 SmallVector<const SCEV *, 8> LargeMulOps;
1560 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1561 if (const SCEVTruncateExpr *T =
1562 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1563 if (T->getOperand()->getType() != SrcType) {
1567 LargeMulOps.push_back(T->getOperand());
1568 } else if (const SCEVConstant *C =
1569 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1570 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1577 LargeOps.push_back(getMulExpr(LargeMulOps));
1584 // Evaluate the expression in the larger type.
1585 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1586 // If it folds to something simple, use it. Otherwise, don't.
1587 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1588 return getTruncateExpr(Fold, DstType);
1592 // Skip past any other cast SCEVs.
1593 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1596 // If there are add operands they would be next.
1597 if (Idx < Ops.size()) {
1598 bool DeletedAdd = false;
1599 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1600 // If we have an add, expand the add operands onto the end of the operands
1602 Ops.erase(Ops.begin()+Idx);
1603 Ops.append(Add->op_begin(), Add->op_end());
1607 // If we deleted at least one add, we added operands to the end of the list,
1608 // and they are not necessarily sorted. Recurse to resort and resimplify
1609 // any operands we just acquired.
1611 return getAddExpr(Ops);
1614 // Skip over the add expression until we get to a multiply.
1615 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1618 // Check to see if there are any folding opportunities present with
1619 // operands multiplied by constant values.
1620 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1621 uint64_t BitWidth = getTypeSizeInBits(Ty);
1622 DenseMap<const SCEV *, APInt> M;
1623 SmallVector<const SCEV *, 8> NewOps;
1624 APInt AccumulatedConstant(BitWidth, 0);
1625 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1626 Ops.data(), Ops.size(),
1627 APInt(BitWidth, 1), *this)) {
1628 // Some interesting folding opportunity is present, so its worthwhile to
1629 // re-generate the operands list. Group the operands by constant scale,
1630 // to avoid multiplying by the same constant scale multiple times.
1631 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1632 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1633 E = NewOps.end(); I != E; ++I)
1634 MulOpLists[M.find(*I)->second].push_back(*I);
1635 // Re-generate the operands list.
1637 if (AccumulatedConstant != 0)
1638 Ops.push_back(getConstant(AccumulatedConstant));
1639 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1640 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1642 Ops.push_back(getMulExpr(getConstant(I->first),
1643 getAddExpr(I->second)));
1645 return getConstant(Ty, 0);
1646 if (Ops.size() == 1)
1648 return getAddExpr(Ops);
1652 // If we are adding something to a multiply expression, make sure the
1653 // something is not already an operand of the multiply. If so, merge it into
1655 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1656 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1657 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1658 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1659 if (isa<SCEVConstant>(MulOpSCEV))
1661 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1662 if (MulOpSCEV == Ops[AddOp]) {
1663 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1664 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1665 if (Mul->getNumOperands() != 2) {
1666 // If the multiply has more than two operands, we must get the
1668 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1669 Mul->op_begin()+MulOp);
1670 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1671 InnerMul = getMulExpr(MulOps);
1673 const SCEV *One = getConstant(Ty, 1);
1674 const SCEV *AddOne = getAddExpr(One, InnerMul);
1675 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1676 if (Ops.size() == 2) return OuterMul;
1678 Ops.erase(Ops.begin()+AddOp);
1679 Ops.erase(Ops.begin()+Idx-1);
1681 Ops.erase(Ops.begin()+Idx);
1682 Ops.erase(Ops.begin()+AddOp-1);
1684 Ops.push_back(OuterMul);
1685 return getAddExpr(Ops);
1688 // Check this multiply against other multiplies being added together.
1689 for (unsigned OtherMulIdx = Idx+1;
1690 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1692 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1693 // If MulOp occurs in OtherMul, we can fold the two multiplies
1695 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1696 OMulOp != e; ++OMulOp)
1697 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1698 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1699 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1700 if (Mul->getNumOperands() != 2) {
1701 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1702 Mul->op_begin()+MulOp);
1703 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1704 InnerMul1 = getMulExpr(MulOps);
1706 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1707 if (OtherMul->getNumOperands() != 2) {
1708 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1709 OtherMul->op_begin()+OMulOp);
1710 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1711 InnerMul2 = getMulExpr(MulOps);
1713 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1714 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1715 if (Ops.size() == 2) return OuterMul;
1716 Ops.erase(Ops.begin()+Idx);
1717 Ops.erase(Ops.begin()+OtherMulIdx-1);
1718 Ops.push_back(OuterMul);
1719 return getAddExpr(Ops);
1725 // If there are any add recurrences in the operands list, see if any other
1726 // added values are loop invariant. If so, we can fold them into the
1728 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1731 // Scan over all recurrences, trying to fold loop invariants into them.
1732 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1733 // Scan all of the other operands to this add and add them to the vector if
1734 // they are loop invariant w.r.t. the recurrence.
1735 SmallVector<const SCEV *, 8> LIOps;
1736 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1737 const Loop *AddRecLoop = AddRec->getLoop();
1738 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1739 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1740 LIOps.push_back(Ops[i]);
1741 Ops.erase(Ops.begin()+i);
1745 // If we found some loop invariants, fold them into the recurrence.
1746 if (!LIOps.empty()) {
1747 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1748 LIOps.push_back(AddRec->getStart());
1750 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1752 AddRecOps[0] = getAddExpr(LIOps);
1754 // Build the new addrec. Propagate the NUW and NSW flags if both the
1755 // outer add and the inner addrec are guaranteed to have no overflow.
1756 // Always propagate NW.
1757 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1758 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1760 // If all of the other operands were loop invariant, we are done.
1761 if (Ops.size() == 1) return NewRec;
1763 // Otherwise, add the folded AddRec by the non-invariant parts.
1764 for (unsigned i = 0;; ++i)
1765 if (Ops[i] == AddRec) {
1769 return getAddExpr(Ops);
1772 // Okay, if there weren't any loop invariants to be folded, check to see if
1773 // there are multiple AddRec's with the same loop induction variable being
1774 // added together. If so, we can fold them.
1775 for (unsigned OtherIdx = Idx+1;
1776 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1778 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1779 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1780 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1782 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1784 if (const SCEVAddRecExpr *OtherAddRec =
1785 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1786 if (OtherAddRec->getLoop() == AddRecLoop) {
1787 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1789 if (i >= AddRecOps.size()) {
1790 AddRecOps.append(OtherAddRec->op_begin()+i,
1791 OtherAddRec->op_end());
1794 AddRecOps[i] = getAddExpr(AddRecOps[i],
1795 OtherAddRec->getOperand(i));
1797 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1799 // Step size has changed, so we cannot guarantee no self-wraparound.
1800 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1801 return getAddExpr(Ops);
1804 // Otherwise couldn't fold anything into this recurrence. Move onto the
1808 // Okay, it looks like we really DO need an add expr. Check to see if we
1809 // already have one, otherwise create a new one.
1810 FoldingSetNodeID ID;
1811 ID.AddInteger(scAddExpr);
1812 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1813 ID.AddPointer(Ops[i]);
1816 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1818 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1819 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1820 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1822 UniqueSCEVs.InsertNode(S, IP);
1824 S->setNoWrapFlags(Flags);
1828 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1830 if (j > 1 && k / j != i) Overflow = true;
1834 /// Compute the result of "n choose k", the binomial coefficient. If an
1835 /// intermediate computation overflows, Overflow will be set and the return will
1836 /// be garbage. Overflow is not cleared on absence of overflow.
1837 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1838 // We use the multiplicative formula:
1839 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1840 // At each iteration, we take the n-th term of the numeral and divide by the
1841 // (k-n)th term of the denominator. This division will always produce an
1842 // integral result, and helps reduce the chance of overflow in the
1843 // intermediate computations. However, we can still overflow even when the
1844 // final result would fit.
1846 if (n == 0 || n == k) return 1;
1847 if (k > n) return 0;
1853 for (uint64_t i = 1; i <= k; ++i) {
1854 r = umul_ov(r, n-(i-1), Overflow);
1860 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1862 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1863 SCEV::NoWrapFlags Flags) {
1864 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1865 "only nuw or nsw allowed");
1866 assert(!Ops.empty() && "Cannot get empty mul!");
1867 if (Ops.size() == 1) return Ops[0];
1869 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1870 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1871 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1872 "SCEVMulExpr operand types don't match!");
1875 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1877 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1878 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1879 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1881 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1882 E = Ops.end(); I != E; ++I)
1883 if (!isKnownNonNegative(*I)) {
1887 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1890 // Sort by complexity, this groups all similar expression types together.
1891 GroupByComplexity(Ops, LI);
1893 // If there are any constants, fold them together.
1895 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1897 // C1*(C2+V) -> C1*C2 + C1*V
1898 if (Ops.size() == 2)
1899 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1900 if (Add->getNumOperands() == 2 &&
1901 isa<SCEVConstant>(Add->getOperand(0)))
1902 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1903 getMulExpr(LHSC, Add->getOperand(1)));
1906 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1907 // We found two constants, fold them together!
1908 ConstantInt *Fold = ConstantInt::get(getContext(),
1909 LHSC->getValue()->getValue() *
1910 RHSC->getValue()->getValue());
1911 Ops[0] = getConstant(Fold);
1912 Ops.erase(Ops.begin()+1); // Erase the folded element
1913 if (Ops.size() == 1) return Ops[0];
1914 LHSC = cast<SCEVConstant>(Ops[0]);
1917 // If we are left with a constant one being multiplied, strip it off.
1918 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1919 Ops.erase(Ops.begin());
1921 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1922 // If we have a multiply of zero, it will always be zero.
1924 } else if (Ops[0]->isAllOnesValue()) {
1925 // If we have a mul by -1 of an add, try distributing the -1 among the
1927 if (Ops.size() == 2) {
1928 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1929 SmallVector<const SCEV *, 4> NewOps;
1930 bool AnyFolded = false;
1931 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1932 E = Add->op_end(); I != E; ++I) {
1933 const SCEV *Mul = getMulExpr(Ops[0], *I);
1934 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1935 NewOps.push_back(Mul);
1938 return getAddExpr(NewOps);
1940 else if (const SCEVAddRecExpr *
1941 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1942 // Negation preserves a recurrence's no self-wrap property.
1943 SmallVector<const SCEV *, 4> Operands;
1944 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1945 E = AddRec->op_end(); I != E; ++I) {
1946 Operands.push_back(getMulExpr(Ops[0], *I));
1948 return getAddRecExpr(Operands, AddRec->getLoop(),
1949 AddRec->getNoWrapFlags(SCEV::FlagNW));
1954 if (Ops.size() == 1)
1958 // Skip over the add expression until we get to a multiply.
1959 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1962 // If there are mul operands inline them all into this expression.
1963 if (Idx < Ops.size()) {
1964 bool DeletedMul = false;
1965 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1966 // If we have an mul, expand the mul operands onto the end of the operands
1968 Ops.erase(Ops.begin()+Idx);
1969 Ops.append(Mul->op_begin(), Mul->op_end());
1973 // If we deleted at least one mul, we added operands to the end of the list,
1974 // and they are not necessarily sorted. Recurse to resort and resimplify
1975 // any operands we just acquired.
1977 return getMulExpr(Ops);
1980 // If there are any add recurrences in the operands list, see if any other
1981 // added values are loop invariant. If so, we can fold them into the
1983 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1986 // Scan over all recurrences, trying to fold loop invariants into them.
1987 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1988 // Scan all of the other operands to this mul and add them to the vector if
1989 // they are loop invariant w.r.t. the recurrence.
1990 SmallVector<const SCEV *, 8> LIOps;
1991 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1992 const Loop *AddRecLoop = AddRec->getLoop();
1993 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1994 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1995 LIOps.push_back(Ops[i]);
1996 Ops.erase(Ops.begin()+i);
2000 // If we found some loop invariants, fold them into the recurrence.
2001 if (!LIOps.empty()) {
2002 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2003 SmallVector<const SCEV *, 4> NewOps;
2004 NewOps.reserve(AddRec->getNumOperands());
2005 const SCEV *Scale = getMulExpr(LIOps);
2006 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2007 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2009 // Build the new addrec. Propagate the NUW and NSW flags if both the
2010 // outer mul and the inner addrec are guaranteed to have no overflow.
2012 // No self-wrap cannot be guaranteed after changing the step size, but
2013 // will be inferred if either NUW or NSW is true.
2014 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2015 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2017 // If all of the other operands were loop invariant, we are done.
2018 if (Ops.size() == 1) return NewRec;
2020 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2021 for (unsigned i = 0;; ++i)
2022 if (Ops[i] == AddRec) {
2026 return getMulExpr(Ops);
2029 // Okay, if there weren't any loop invariants to be folded, check to see if
2030 // there are multiple AddRec's with the same loop induction variable being
2031 // multiplied together. If so, we can fold them.
2032 for (unsigned OtherIdx = Idx+1;
2033 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2035 if (AddRecLoop != cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop())
2038 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2039 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2040 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2041 // ]]],+,...up to x=2n}.
2042 // Note that the arguments to choose() are always integers with values
2043 // known at compile time, never SCEV objects.
2045 // The implementation avoids pointless extra computations when the two
2046 // addrec's are of different length (mathematically, it's equivalent to
2047 // an infinite stream of zeros on the right).
2048 bool OpsModified = false;
2049 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2051 const SCEVAddRecExpr *OtherAddRec =
2052 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2053 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2056 bool Overflow = false;
2057 Type *Ty = AddRec->getType();
2058 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2059 SmallVector<const SCEV*, 7> AddRecOps;
2060 for (int x = 0, xe = AddRec->getNumOperands() +
2061 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2062 const SCEV *Term = getConstant(Ty, 0);
2063 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2064 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2065 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2066 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2067 z < ze && !Overflow; ++z) {
2068 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2070 if (LargerThan64Bits)
2071 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2073 Coeff = Coeff1*Coeff2;
2074 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2075 const SCEV *Term1 = AddRec->getOperand(y-z);
2076 const SCEV *Term2 = OtherAddRec->getOperand(z);
2077 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2080 AddRecOps.push_back(Term);
2083 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2085 if (Ops.size() == 2) return NewAddRec;
2086 Ops[Idx] = NewAddRec;
2087 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2089 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2095 return getMulExpr(Ops);
2098 // Otherwise couldn't fold anything into this recurrence. Move onto the
2102 // Okay, it looks like we really DO need an mul expr. Check to see if we
2103 // already have one, otherwise create a new one.
2104 FoldingSetNodeID ID;
2105 ID.AddInteger(scMulExpr);
2106 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2107 ID.AddPointer(Ops[i]);
2110 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2112 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2113 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2114 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2116 UniqueSCEVs.InsertNode(S, IP);
2118 S->setNoWrapFlags(Flags);
2122 /// getUDivExpr - Get a canonical unsigned division expression, or something
2123 /// simpler if possible.
2124 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2126 assert(getEffectiveSCEVType(LHS->getType()) ==
2127 getEffectiveSCEVType(RHS->getType()) &&
2128 "SCEVUDivExpr operand types don't match!");
2130 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2131 if (RHSC->getValue()->equalsInt(1))
2132 return LHS; // X udiv 1 --> x
2133 // If the denominator is zero, the result of the udiv is undefined. Don't
2134 // try to analyze it, because the resolution chosen here may differ from
2135 // the resolution chosen in other parts of the compiler.
2136 if (!RHSC->getValue()->isZero()) {
2137 // Determine if the division can be folded into the operands of
2139 // TODO: Generalize this to non-constants by using known-bits information.
2140 Type *Ty = LHS->getType();
2141 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2142 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2143 // For non-power-of-two values, effectively round the value up to the
2144 // nearest power of two.
2145 if (!RHSC->getValue()->getValue().isPowerOf2())
2147 IntegerType *ExtTy =
2148 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2149 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2150 if (const SCEVConstant *Step =
2151 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2152 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2153 const APInt &StepInt = Step->getValue()->getValue();
2154 const APInt &DivInt = RHSC->getValue()->getValue();
2155 if (!StepInt.urem(DivInt) &&
2156 getZeroExtendExpr(AR, ExtTy) ==
2157 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2158 getZeroExtendExpr(Step, ExtTy),
2159 AR->getLoop(), SCEV::FlagAnyWrap)) {
2160 SmallVector<const SCEV *, 4> Operands;
2161 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2162 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2163 return getAddRecExpr(Operands, AR->getLoop(),
2166 /// Get a canonical UDivExpr for a recurrence.
2167 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2168 // We can currently only fold X%N if X is constant.
2169 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2170 if (StartC && !DivInt.urem(StepInt) &&
2171 getZeroExtendExpr(AR, ExtTy) ==
2172 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2173 getZeroExtendExpr(Step, ExtTy),
2174 AR->getLoop(), SCEV::FlagAnyWrap)) {
2175 const APInt &StartInt = StartC->getValue()->getValue();
2176 const APInt &StartRem = StartInt.urem(StepInt);
2178 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2179 AR->getLoop(), SCEV::FlagNW);
2182 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2183 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2184 SmallVector<const SCEV *, 4> Operands;
2185 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2186 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2187 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2188 // Find an operand that's safely divisible.
2189 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2190 const SCEV *Op = M->getOperand(i);
2191 const SCEV *Div = getUDivExpr(Op, RHSC);
2192 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2193 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2196 return getMulExpr(Operands);
2200 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2201 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2202 SmallVector<const SCEV *, 4> Operands;
2203 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2204 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2205 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2207 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2208 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2209 if (isa<SCEVUDivExpr>(Op) ||
2210 getMulExpr(Op, RHS) != A->getOperand(i))
2212 Operands.push_back(Op);
2214 if (Operands.size() == A->getNumOperands())
2215 return getAddExpr(Operands);
2219 // Fold if both operands are constant.
2220 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2221 Constant *LHSCV = LHSC->getValue();
2222 Constant *RHSCV = RHSC->getValue();
2223 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2229 FoldingSetNodeID ID;
2230 ID.AddInteger(scUDivExpr);
2234 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2235 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2237 UniqueSCEVs.InsertNode(S, IP);
2241 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2242 APInt A = C1->getValue()->getValue().abs();
2243 APInt B = C2->getValue()->getValue().abs();
2244 uint32_t ABW = A.getBitWidth();
2245 uint32_t BBW = B.getBitWidth();
2252 return APIntOps::GreatestCommonDivisor(A, B);
2255 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2256 /// something simpler if possible. There is no representation for an exact udiv
2257 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2258 /// We can't do this when it's not exact because the udiv may be clearing bits.
2259 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2261 // TODO: we could try to find factors in all sorts of things, but for now we
2262 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2263 // end of this file for inspiration.
2265 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2267 return getUDivExpr(LHS, RHS);
2269 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2270 // If the mulexpr multiplies by a constant, then that constant must be the
2271 // first element of the mulexpr.
2272 if (const SCEVConstant *LHSCst =
2273 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2274 if (LHSCst == RHSCst) {
2275 SmallVector<const SCEV *, 2> Operands;
2276 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2277 return getMulExpr(Operands);
2280 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2281 // that there's a factor provided by one of the other terms. We need to
2283 APInt Factor = gcd(LHSCst, RHSCst);
2284 if (!Factor.isIntN(1)) {
2285 LHSCst = cast<SCEVConstant>(
2286 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2287 RHSCst = cast<SCEVConstant>(
2288 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2289 SmallVector<const SCEV *, 2> Operands;
2290 Operands.push_back(LHSCst);
2291 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2292 LHS = getMulExpr(Operands);
2294 Mul = dyn_cast<SCEVMulExpr>(LHS);
2296 return getUDivExactExpr(LHS, RHS);
2301 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2302 if (Mul->getOperand(i) == RHS) {
2303 SmallVector<const SCEV *, 2> Operands;
2304 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2305 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2306 return getMulExpr(Operands);
2310 return getUDivExpr(LHS, RHS);
2313 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2314 /// Simplify the expression as much as possible.
2315 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2317 SCEV::NoWrapFlags Flags) {
2318 SmallVector<const SCEV *, 4> Operands;
2319 Operands.push_back(Start);
2320 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2321 if (StepChrec->getLoop() == L) {
2322 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2323 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2326 Operands.push_back(Step);
2327 return getAddRecExpr(Operands, L, Flags);
2330 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2331 /// Simplify the expression as much as possible.
2333 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2334 const Loop *L, SCEV::NoWrapFlags Flags) {
2335 if (Operands.size() == 1) return Operands[0];
2337 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2338 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2339 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2340 "SCEVAddRecExpr operand types don't match!");
2341 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2342 assert(isLoopInvariant(Operands[i], L) &&
2343 "SCEVAddRecExpr operand is not loop-invariant!");
2346 if (Operands.back()->isZero()) {
2347 Operands.pop_back();
2348 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2351 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2352 // use that information to infer NUW and NSW flags. However, computing a
2353 // BE count requires calling getAddRecExpr, so we may not yet have a
2354 // meaningful BE count at this point (and if we don't, we'd be stuck
2355 // with a SCEVCouldNotCompute as the cached BE count).
2357 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2359 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2360 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2361 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2363 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2364 E = Operands.end(); I != E; ++I)
2365 if (!isKnownNonNegative(*I)) {
2369 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2372 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2373 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2374 const Loop *NestedLoop = NestedAR->getLoop();
2375 if (L->contains(NestedLoop) ?
2376 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2377 (!NestedLoop->contains(L) &&
2378 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2379 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2380 NestedAR->op_end());
2381 Operands[0] = NestedAR->getStart();
2382 // AddRecs require their operands be loop-invariant with respect to their
2383 // loops. Don't perform this transformation if it would break this
2385 bool AllInvariant = true;
2386 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2387 if (!isLoopInvariant(Operands[i], L)) {
2388 AllInvariant = false;
2392 // Create a recurrence for the outer loop with the same step size.
2394 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2395 // inner recurrence has the same property.
2396 SCEV::NoWrapFlags OuterFlags =
2397 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2399 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2400 AllInvariant = true;
2401 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2402 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2403 AllInvariant = false;
2407 // Ok, both add recurrences are valid after the transformation.
2409 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2410 // the outer recurrence has the same property.
2411 SCEV::NoWrapFlags InnerFlags =
2412 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2413 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2416 // Reset Operands to its original state.
2417 Operands[0] = NestedAR;
2421 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2422 // already have one, otherwise create a new one.
2423 FoldingSetNodeID ID;
2424 ID.AddInteger(scAddRecExpr);
2425 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2426 ID.AddPointer(Operands[i]);
2430 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2432 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2433 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2434 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2435 O, Operands.size(), L);
2436 UniqueSCEVs.InsertNode(S, IP);
2438 S->setNoWrapFlags(Flags);
2442 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2444 SmallVector<const SCEV *, 2> Ops;
2447 return getSMaxExpr(Ops);
2451 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2452 assert(!Ops.empty() && "Cannot get empty smax!");
2453 if (Ops.size() == 1) return Ops[0];
2455 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2456 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2457 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2458 "SCEVSMaxExpr operand types don't match!");
2461 // Sort by complexity, this groups all similar expression types together.
2462 GroupByComplexity(Ops, LI);
2464 // If there are any constants, fold them together.
2466 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2468 assert(Idx < Ops.size());
2469 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2470 // We found two constants, fold them together!
2471 ConstantInt *Fold = ConstantInt::get(getContext(),
2472 APIntOps::smax(LHSC->getValue()->getValue(),
2473 RHSC->getValue()->getValue()));
2474 Ops[0] = getConstant(Fold);
2475 Ops.erase(Ops.begin()+1); // Erase the folded element
2476 if (Ops.size() == 1) return Ops[0];
2477 LHSC = cast<SCEVConstant>(Ops[0]);
2480 // If we are left with a constant minimum-int, strip it off.
2481 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2482 Ops.erase(Ops.begin());
2484 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2485 // If we have an smax with a constant maximum-int, it will always be
2490 if (Ops.size() == 1) return Ops[0];
2493 // Find the first SMax
2494 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2497 // Check to see if one of the operands is an SMax. If so, expand its operands
2498 // onto our operand list, and recurse to simplify.
2499 if (Idx < Ops.size()) {
2500 bool DeletedSMax = false;
2501 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2502 Ops.erase(Ops.begin()+Idx);
2503 Ops.append(SMax->op_begin(), SMax->op_end());
2508 return getSMaxExpr(Ops);
2511 // Okay, check to see if the same value occurs in the operand list twice. If
2512 // so, delete one. Since we sorted the list, these values are required to
2514 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2515 // X smax Y smax Y --> X smax Y
2516 // X smax Y --> X, if X is always greater than Y
2517 if (Ops[i] == Ops[i+1] ||
2518 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2519 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2521 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2522 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2526 if (Ops.size() == 1) return Ops[0];
2528 assert(!Ops.empty() && "Reduced smax down to nothing!");
2530 // Okay, it looks like we really DO need an smax expr. Check to see if we
2531 // already have one, otherwise create a new one.
2532 FoldingSetNodeID ID;
2533 ID.AddInteger(scSMaxExpr);
2534 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2535 ID.AddPointer(Ops[i]);
2537 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2538 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2539 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2540 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2542 UniqueSCEVs.InsertNode(S, IP);
2546 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2548 SmallVector<const SCEV *, 2> Ops;
2551 return getUMaxExpr(Ops);
2555 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2556 assert(!Ops.empty() && "Cannot get empty umax!");
2557 if (Ops.size() == 1) return Ops[0];
2559 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2560 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2561 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2562 "SCEVUMaxExpr operand types don't match!");
2565 // Sort by complexity, this groups all similar expression types together.
2566 GroupByComplexity(Ops, LI);
2568 // If there are any constants, fold them together.
2570 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2572 assert(Idx < Ops.size());
2573 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2574 // We found two constants, fold them together!
2575 ConstantInt *Fold = ConstantInt::get(getContext(),
2576 APIntOps::umax(LHSC->getValue()->getValue(),
2577 RHSC->getValue()->getValue()));
2578 Ops[0] = getConstant(Fold);
2579 Ops.erase(Ops.begin()+1); // Erase the folded element
2580 if (Ops.size() == 1) return Ops[0];
2581 LHSC = cast<SCEVConstant>(Ops[0]);
2584 // If we are left with a constant minimum-int, strip it off.
2585 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2586 Ops.erase(Ops.begin());
2588 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2589 // If we have an umax with a constant maximum-int, it will always be
2594 if (Ops.size() == 1) return Ops[0];
2597 // Find the first UMax
2598 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2601 // Check to see if one of the operands is a UMax. If so, expand its operands
2602 // onto our operand list, and recurse to simplify.
2603 if (Idx < Ops.size()) {
2604 bool DeletedUMax = false;
2605 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2606 Ops.erase(Ops.begin()+Idx);
2607 Ops.append(UMax->op_begin(), UMax->op_end());
2612 return getUMaxExpr(Ops);
2615 // Okay, check to see if the same value occurs in the operand list twice. If
2616 // so, delete one. Since we sorted the list, these values are required to
2618 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2619 // X umax Y umax Y --> X umax Y
2620 // X umax Y --> X, if X is always greater than Y
2621 if (Ops[i] == Ops[i+1] ||
2622 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2623 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2625 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2626 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2630 if (Ops.size() == 1) return Ops[0];
2632 assert(!Ops.empty() && "Reduced umax down to nothing!");
2634 // Okay, it looks like we really DO need a umax expr. Check to see if we
2635 // already have one, otherwise create a new one.
2636 FoldingSetNodeID ID;
2637 ID.AddInteger(scUMaxExpr);
2638 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2639 ID.AddPointer(Ops[i]);
2641 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2642 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2643 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2644 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2646 UniqueSCEVs.InsertNode(S, IP);
2650 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2652 // ~smax(~x, ~y) == smin(x, y).
2653 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2656 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2658 // ~umax(~x, ~y) == umin(x, y)
2659 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2662 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2663 // If we have DataLayout, we can bypass creating a target-independent
2664 // constant expression and then folding it back into a ConstantInt.
2665 // This is just a compile-time optimization.
2667 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
2669 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2670 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2671 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2673 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2674 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2675 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2678 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2681 // If we have DataLayout, we can bypass creating a target-independent
2682 // constant expression and then folding it back into a ConstantInt.
2683 // This is just a compile-time optimization.
2685 return getConstant(IntTy,
2686 DL->getStructLayout(STy)->getElementOffset(FieldNo));
2689 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2690 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2691 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2694 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2695 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2698 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2699 // Don't attempt to do anything other than create a SCEVUnknown object
2700 // here. createSCEV only calls getUnknown after checking for all other
2701 // interesting possibilities, and any other code that calls getUnknown
2702 // is doing so in order to hide a value from SCEV canonicalization.
2704 FoldingSetNodeID ID;
2705 ID.AddInteger(scUnknown);
2708 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2709 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2710 "Stale SCEVUnknown in uniquing map!");
2713 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2715 FirstUnknown = cast<SCEVUnknown>(S);
2716 UniqueSCEVs.InsertNode(S, IP);
2720 //===----------------------------------------------------------------------===//
2721 // Basic SCEV Analysis and PHI Idiom Recognition Code
2724 /// isSCEVable - Test if values of the given type are analyzable within
2725 /// the SCEV framework. This primarily includes integer types, and it
2726 /// can optionally include pointer types if the ScalarEvolution class
2727 /// has access to target-specific information.
2728 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2729 // Integers and pointers are always SCEVable.
2730 return Ty->isIntegerTy() || Ty->isPointerTy();
2733 /// getTypeSizeInBits - Return the size in bits of the specified type,
2734 /// for which isSCEVable must return true.
2735 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2736 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2738 // If we have a DataLayout, use it!
2740 return DL->getTypeSizeInBits(Ty);
2742 // Integer types have fixed sizes.
2743 if (Ty->isIntegerTy())
2744 return Ty->getPrimitiveSizeInBits();
2746 // The only other support type is pointer. Without DataLayout, conservatively
2747 // assume pointers are 64-bit.
2748 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2752 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2753 /// the given type and which represents how SCEV will treat the given
2754 /// type, for which isSCEVable must return true. For pointer types,
2755 /// this is the pointer-sized integer type.
2756 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2757 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2759 if (Ty->isIntegerTy()) {
2763 // The only other support type is pointer.
2764 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2767 return DL->getIntPtrType(Ty);
2769 // Without DataLayout, conservatively assume pointers are 64-bit.
2770 return Type::getInt64Ty(getContext());
2773 const SCEV *ScalarEvolution::getCouldNotCompute() {
2774 return &CouldNotCompute;
2778 // Helper class working with SCEVTraversal to figure out if a SCEV contains
2779 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
2780 // is set iff if find such SCEVUnknown.
2782 struct FindInvalidSCEVUnknown {
2784 FindInvalidSCEVUnknown() { FindOne = false; }
2785 bool follow(const SCEV *S) {
2786 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
2790 if (!cast<SCEVUnknown>(S)->getValue())
2797 bool isDone() const { return FindOne; }
2801 bool ScalarEvolution::checkValidity(const SCEV *S) const {
2802 FindInvalidSCEVUnknown F;
2803 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
2809 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2810 /// expression and create a new one.
2811 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2812 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2814 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
2815 if (I != ValueExprMap.end()) {
2816 const SCEV *S = I->second;
2817 if (checkValidity(S))
2820 ValueExprMap.erase(I);
2822 const SCEV *S = createSCEV(V);
2824 // The process of creating a SCEV for V may have caused other SCEVs
2825 // to have been created, so it's necessary to insert the new entry
2826 // from scratch, rather than trying to remember the insert position
2828 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2832 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2834 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2835 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2837 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2839 Type *Ty = V->getType();
2840 Ty = getEffectiveSCEVType(Ty);
2841 return getMulExpr(V,
2842 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2845 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2846 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2847 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2849 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2851 Type *Ty = V->getType();
2852 Ty = getEffectiveSCEVType(Ty);
2853 const SCEV *AllOnes =
2854 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2855 return getMinusSCEV(AllOnes, V);
2858 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2859 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2860 SCEV::NoWrapFlags Flags) {
2861 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2863 // Fast path: X - X --> 0.
2865 return getConstant(LHS->getType(), 0);
2868 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2871 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2872 /// input value to the specified type. If the type must be extended, it is zero
2875 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2876 Type *SrcTy = V->getType();
2877 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2878 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2879 "Cannot truncate or zero extend with non-integer arguments!");
2880 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2881 return V; // No conversion
2882 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2883 return getTruncateExpr(V, Ty);
2884 return getZeroExtendExpr(V, Ty);
2887 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2888 /// input value to the specified type. If the type must be extended, it is sign
2891 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2893 Type *SrcTy = V->getType();
2894 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2895 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2896 "Cannot truncate or zero extend with non-integer arguments!");
2897 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2898 return V; // No conversion
2899 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2900 return getTruncateExpr(V, Ty);
2901 return getSignExtendExpr(V, Ty);
2904 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2905 /// input value to the specified type. If the type must be extended, it is zero
2906 /// extended. The conversion must not be narrowing.
2908 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2909 Type *SrcTy = V->getType();
2910 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2911 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2912 "Cannot noop or zero extend with non-integer arguments!");
2913 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2914 "getNoopOrZeroExtend cannot truncate!");
2915 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2916 return V; // No conversion
2917 return getZeroExtendExpr(V, Ty);
2920 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2921 /// input value to the specified type. If the type must be extended, it is sign
2922 /// extended. The conversion must not be narrowing.
2924 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2925 Type *SrcTy = V->getType();
2926 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2927 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2928 "Cannot noop or sign extend with non-integer arguments!");
2929 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2930 "getNoopOrSignExtend cannot truncate!");
2931 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2932 return V; // No conversion
2933 return getSignExtendExpr(V, Ty);
2936 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2937 /// the input value to the specified type. If the type must be extended,
2938 /// it is extended with unspecified bits. The conversion must not be
2941 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2942 Type *SrcTy = V->getType();
2943 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2944 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2945 "Cannot noop or any extend with non-integer arguments!");
2946 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2947 "getNoopOrAnyExtend cannot truncate!");
2948 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2949 return V; // No conversion
2950 return getAnyExtendExpr(V, Ty);
2953 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2954 /// input value to the specified type. The conversion must not be widening.
2956 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2957 Type *SrcTy = V->getType();
2958 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2959 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2960 "Cannot truncate or noop with non-integer arguments!");
2961 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2962 "getTruncateOrNoop cannot extend!");
2963 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2964 return V; // No conversion
2965 return getTruncateExpr(V, Ty);
2968 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2969 /// the types using zero-extension, and then perform a umax operation
2971 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2973 const SCEV *PromotedLHS = LHS;
2974 const SCEV *PromotedRHS = RHS;
2976 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2977 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2979 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2981 return getUMaxExpr(PromotedLHS, PromotedRHS);
2984 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2985 /// the types using zero-extension, and then perform a umin operation
2987 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2989 const SCEV *PromotedLHS = LHS;
2990 const SCEV *PromotedRHS = RHS;
2992 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2993 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2995 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2997 return getUMinExpr(PromotedLHS, PromotedRHS);
3000 /// getPointerBase - Transitively follow the chain of pointer-type operands
3001 /// until reaching a SCEV that does not have a single pointer operand. This
3002 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3003 /// but corner cases do exist.
3004 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3005 // A pointer operand may evaluate to a nonpointer expression, such as null.
3006 if (!V->getType()->isPointerTy())
3009 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3010 return getPointerBase(Cast->getOperand());
3012 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3013 const SCEV *PtrOp = 0;
3014 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3016 if ((*I)->getType()->isPointerTy()) {
3017 // Cannot find the base of an expression with multiple pointer operands.
3025 return getPointerBase(PtrOp);
3030 /// PushDefUseChildren - Push users of the given Instruction
3031 /// onto the given Worklist.
3033 PushDefUseChildren(Instruction *I,
3034 SmallVectorImpl<Instruction *> &Worklist) {
3035 // Push the def-use children onto the Worklist stack.
3036 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
3038 Worklist.push_back(cast<Instruction>(*UI));
3041 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3042 /// instructions that depend on the given instruction and removes them from
3043 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3046 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3047 SmallVector<Instruction *, 16> Worklist;
3048 PushDefUseChildren(PN, Worklist);
3050 SmallPtrSet<Instruction *, 8> Visited;
3052 while (!Worklist.empty()) {
3053 Instruction *I = Worklist.pop_back_val();
3054 if (!Visited.insert(I)) continue;
3056 ValueExprMapType::iterator It =
3057 ValueExprMap.find_as(static_cast<Value *>(I));
3058 if (It != ValueExprMap.end()) {
3059 const SCEV *Old = It->second;
3061 // Short-circuit the def-use traversal if the symbolic name
3062 // ceases to appear in expressions.
3063 if (Old != SymName && !hasOperand(Old, SymName))
3066 // SCEVUnknown for a PHI either means that it has an unrecognized
3067 // structure, it's a PHI that's in the progress of being computed
3068 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3069 // additional loop trip count information isn't going to change anything.
3070 // In the second case, createNodeForPHI will perform the necessary
3071 // updates on its own when it gets to that point. In the third, we do
3072 // want to forget the SCEVUnknown.
3073 if (!isa<PHINode>(I) ||
3074 !isa<SCEVUnknown>(Old) ||
3075 (I != PN && Old == SymName)) {
3076 forgetMemoizedResults(Old);
3077 ValueExprMap.erase(It);
3081 PushDefUseChildren(I, Worklist);
3085 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3086 /// a loop header, making it a potential recurrence, or it doesn't.
3088 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3089 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3090 if (L->getHeader() == PN->getParent()) {
3091 // The loop may have multiple entrances or multiple exits; we can analyze
3092 // this phi as an addrec if it has a unique entry value and a unique
3094 Value *BEValueV = 0, *StartValueV = 0;
3095 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3096 Value *V = PN->getIncomingValue(i);
3097 if (L->contains(PN->getIncomingBlock(i))) {
3100 } else if (BEValueV != V) {
3104 } else if (!StartValueV) {
3106 } else if (StartValueV != V) {
3111 if (BEValueV && StartValueV) {
3112 // While we are analyzing this PHI node, handle its value symbolically.
3113 const SCEV *SymbolicName = getUnknown(PN);
3114 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3115 "PHI node already processed?");
3116 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3118 // Using this symbolic name for the PHI, analyze the value coming around
3120 const SCEV *BEValue = getSCEV(BEValueV);
3122 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3123 // has a special value for the first iteration of the loop.
3125 // If the value coming around the backedge is an add with the symbolic
3126 // value we just inserted, then we found a simple induction variable!
3127 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3128 // If there is a single occurrence of the symbolic value, replace it
3129 // with a recurrence.
3130 unsigned FoundIndex = Add->getNumOperands();
3131 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3132 if (Add->getOperand(i) == SymbolicName)
3133 if (FoundIndex == e) {
3138 if (FoundIndex != Add->getNumOperands()) {
3139 // Create an add with everything but the specified operand.
3140 SmallVector<const SCEV *, 8> Ops;
3141 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3142 if (i != FoundIndex)
3143 Ops.push_back(Add->getOperand(i));
3144 const SCEV *Accum = getAddExpr(Ops);
3146 // This is not a valid addrec if the step amount is varying each
3147 // loop iteration, but is not itself an addrec in this loop.
3148 if (isLoopInvariant(Accum, L) ||
3149 (isa<SCEVAddRecExpr>(Accum) &&
3150 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3151 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3153 // If the increment doesn't overflow, then neither the addrec nor
3154 // the post-increment will overflow.
3155 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3156 if (OBO->hasNoUnsignedWrap())
3157 Flags = setFlags(Flags, SCEV::FlagNUW);
3158 if (OBO->hasNoSignedWrap())
3159 Flags = setFlags(Flags, SCEV::FlagNSW);
3160 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3161 // If the increment is an inbounds GEP, then we know the address
3162 // space cannot be wrapped around. We cannot make any guarantee
3163 // about signed or unsigned overflow because pointers are
3164 // unsigned but we may have a negative index from the base
3165 // pointer. We can guarantee that no unsigned wrap occurs if the
3166 // indices form a positive value.
3167 if (GEP->isInBounds()) {
3168 Flags = setFlags(Flags, SCEV::FlagNW);
3170 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3171 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3172 Flags = setFlags(Flags, SCEV::FlagNUW);
3174 } else if (const SubOperator *OBO =
3175 dyn_cast<SubOperator>(BEValueV)) {
3176 if (OBO->hasNoUnsignedWrap())
3177 Flags = setFlags(Flags, SCEV::FlagNUW);
3178 if (OBO->hasNoSignedWrap())
3179 Flags = setFlags(Flags, SCEV::FlagNSW);
3182 const SCEV *StartVal = getSCEV(StartValueV);
3183 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3185 // Since the no-wrap flags are on the increment, they apply to the
3186 // post-incremented value as well.
3187 if (isLoopInvariant(Accum, L))
3188 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3191 // Okay, for the entire analysis of this edge we assumed the PHI
3192 // to be symbolic. We now need to go back and purge all of the
3193 // entries for the scalars that use the symbolic expression.
3194 ForgetSymbolicName(PN, SymbolicName);
3195 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3199 } else if (const SCEVAddRecExpr *AddRec =
3200 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3201 // Otherwise, this could be a loop like this:
3202 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3203 // In this case, j = {1,+,1} and BEValue is j.
3204 // Because the other in-value of i (0) fits the evolution of BEValue
3205 // i really is an addrec evolution.
3206 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3207 const SCEV *StartVal = getSCEV(StartValueV);
3209 // If StartVal = j.start - j.stride, we can use StartVal as the
3210 // initial step of the addrec evolution.
3211 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3212 AddRec->getOperand(1))) {
3213 // FIXME: For constant StartVal, we should be able to infer
3215 const SCEV *PHISCEV =
3216 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3219 // Okay, for the entire analysis of this edge we assumed the PHI
3220 // to be symbolic. We now need to go back and purge all of the
3221 // entries for the scalars that use the symbolic expression.
3222 ForgetSymbolicName(PN, SymbolicName);
3223 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3231 // If the PHI has a single incoming value, follow that value, unless the
3232 // PHI's incoming blocks are in a different loop, in which case doing so
3233 // risks breaking LCSSA form. Instcombine would normally zap these, but
3234 // it doesn't have DominatorTree information, so it may miss cases.
3235 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT))
3236 if (LI->replacementPreservesLCSSAForm(PN, V))
3239 // If it's not a loop phi, we can't handle it yet.
3240 return getUnknown(PN);
3243 /// createNodeForGEP - Expand GEP instructions into add and multiply
3244 /// operations. This allows them to be analyzed by regular SCEV code.
3246 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3247 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3248 Value *Base = GEP->getOperand(0);
3249 // Don't attempt to analyze GEPs over unsized objects.
3250 if (!Base->getType()->getPointerElementType()->isSized())
3251 return getUnknown(GEP);
3253 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3254 // Add expression, because the Instruction may be guarded by control flow
3255 // and the no-overflow bits may not be valid for the expression in any
3257 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3259 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3260 gep_type_iterator GTI = gep_type_begin(GEP);
3261 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3265 // Compute the (potentially symbolic) offset in bytes for this index.
3266 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3267 // For a struct, add the member offset.
3268 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3269 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3271 // Add the field offset to the running total offset.
3272 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3274 // For an array, add the element offset, explicitly scaled.
3275 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3276 const SCEV *IndexS = getSCEV(Index);
3277 // Getelementptr indices are signed.
3278 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3280 // Multiply the index by the element size to compute the element offset.
3281 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3283 // Add the element offset to the running total offset.
3284 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3288 // Get the SCEV for the GEP base.
3289 const SCEV *BaseS = getSCEV(Base);
3291 // Add the total offset from all the GEP indices to the base.
3292 return getAddExpr(BaseS, TotalOffset, Wrap);
3295 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3296 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3297 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3298 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3300 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3301 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3302 return C->getValue()->getValue().countTrailingZeros();
3304 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3305 return std::min(GetMinTrailingZeros(T->getOperand()),
3306 (uint32_t)getTypeSizeInBits(T->getType()));
3308 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3309 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3310 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3311 getTypeSizeInBits(E->getType()) : OpRes;
3314 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3315 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3316 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3317 getTypeSizeInBits(E->getType()) : OpRes;
3320 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3321 // The result is the min of all operands results.
3322 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3323 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3324 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3328 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3329 // The result is the sum of all operands results.
3330 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3331 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3332 for (unsigned i = 1, e = M->getNumOperands();
3333 SumOpRes != BitWidth && i != e; ++i)
3334 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3339 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3340 // The result is the min of all operands results.
3341 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3342 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3343 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3347 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3348 // The result is the min of all operands results.
3349 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3350 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3351 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3355 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3356 // The result is the min of all operands results.
3357 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3358 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3359 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3363 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3364 // For a SCEVUnknown, ask ValueTracking.
3365 unsigned BitWidth = getTypeSizeInBits(U->getType());
3366 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3367 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3368 return Zeros.countTrailingOnes();
3375 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3378 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3379 // See if we've computed this range already.
3380 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3381 if (I != UnsignedRanges.end())
3384 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3385 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3387 unsigned BitWidth = getTypeSizeInBits(S->getType());
3388 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3390 // If the value has known zeros, the maximum unsigned value will have those
3391 // known zeros as well.
3392 uint32_t TZ = GetMinTrailingZeros(S);
3394 ConservativeResult =
3395 ConstantRange(APInt::getMinValue(BitWidth),
3396 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3398 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3399 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3400 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3401 X = X.add(getUnsignedRange(Add->getOperand(i)));
3402 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3405 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3406 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3407 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3408 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3409 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3412 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3413 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3414 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3415 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3416 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3419 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3420 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3421 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3422 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3423 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3426 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3427 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3428 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3429 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3432 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3433 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3434 return setUnsignedRange(ZExt,
3435 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3438 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3439 ConstantRange X = getUnsignedRange(SExt->getOperand());
3440 return setUnsignedRange(SExt,
3441 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3444 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3445 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3446 return setUnsignedRange(Trunc,
3447 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3450 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3451 // If there's no unsigned wrap, the value will never be less than its
3453 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3454 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3455 if (!C->getValue()->isZero())
3456 ConservativeResult =
3457 ConservativeResult.intersectWith(
3458 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3460 // TODO: non-affine addrec
3461 if (AddRec->isAffine()) {
3462 Type *Ty = AddRec->getType();
3463 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3464 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3465 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3466 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3468 const SCEV *Start = AddRec->getStart();
3469 const SCEV *Step = AddRec->getStepRecurrence(*this);
3471 ConstantRange StartRange = getUnsignedRange(Start);
3472 ConstantRange StepRange = getSignedRange(Step);
3473 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3474 ConstantRange EndRange =
3475 StartRange.add(MaxBECountRange.multiply(StepRange));
3477 // Check for overflow. This must be done with ConstantRange arithmetic
3478 // because we could be called from within the ScalarEvolution overflow
3480 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3481 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3482 ConstantRange ExtMaxBECountRange =
3483 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3484 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3485 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3487 return setUnsignedRange(AddRec, ConservativeResult);
3489 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3490 EndRange.getUnsignedMin());
3491 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3492 EndRange.getUnsignedMax());
3493 if (Min.isMinValue() && Max.isMaxValue())
3494 return setUnsignedRange(AddRec, ConservativeResult);
3495 return setUnsignedRange(AddRec,
3496 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3500 return setUnsignedRange(AddRec, ConservativeResult);
3503 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3504 // For a SCEVUnknown, ask ValueTracking.
3505 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3506 ComputeMaskedBits(U->getValue(), Zeros, Ones, DL);
3507 if (Ones == ~Zeros + 1)
3508 return setUnsignedRange(U, ConservativeResult);
3509 return setUnsignedRange(U,
3510 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3513 return setUnsignedRange(S, ConservativeResult);
3516 /// getSignedRange - Determine the signed range for a particular SCEV.
3519 ScalarEvolution::getSignedRange(const SCEV *S) {
3520 // See if we've computed this range already.
3521 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3522 if (I != SignedRanges.end())
3525 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3526 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3528 unsigned BitWidth = getTypeSizeInBits(S->getType());
3529 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3531 // If the value has known zeros, the maximum signed value will have those
3532 // known zeros as well.
3533 uint32_t TZ = GetMinTrailingZeros(S);
3535 ConservativeResult =
3536 ConstantRange(APInt::getSignedMinValue(BitWidth),
3537 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3539 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3540 ConstantRange X = getSignedRange(Add->getOperand(0));
3541 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3542 X = X.add(getSignedRange(Add->getOperand(i)));
3543 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3546 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3547 ConstantRange X = getSignedRange(Mul->getOperand(0));
3548 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3549 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3550 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3553 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3554 ConstantRange X = getSignedRange(SMax->getOperand(0));
3555 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3556 X = X.smax(getSignedRange(SMax->getOperand(i)));
3557 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3560 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3561 ConstantRange X = getSignedRange(UMax->getOperand(0));
3562 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3563 X = X.umax(getSignedRange(UMax->getOperand(i)));
3564 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3567 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3568 ConstantRange X = getSignedRange(UDiv->getLHS());
3569 ConstantRange Y = getSignedRange(UDiv->getRHS());
3570 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3573 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3574 ConstantRange X = getSignedRange(ZExt->getOperand());
3575 return setSignedRange(ZExt,
3576 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3579 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3580 ConstantRange X = getSignedRange(SExt->getOperand());
3581 return setSignedRange(SExt,
3582 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3585 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3586 ConstantRange X = getSignedRange(Trunc->getOperand());
3587 return setSignedRange(Trunc,
3588 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3591 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3592 // If there's no signed wrap, and all the operands have the same sign or
3593 // zero, the value won't ever change sign.
3594 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3595 bool AllNonNeg = true;
3596 bool AllNonPos = true;
3597 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3598 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3599 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3602 ConservativeResult = ConservativeResult.intersectWith(
3603 ConstantRange(APInt(BitWidth, 0),
3604 APInt::getSignedMinValue(BitWidth)));
3606 ConservativeResult = ConservativeResult.intersectWith(
3607 ConstantRange(APInt::getSignedMinValue(BitWidth),
3608 APInt(BitWidth, 1)));
3611 // TODO: non-affine addrec
3612 if (AddRec->isAffine()) {
3613 Type *Ty = AddRec->getType();
3614 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3615 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3616 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3617 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3619 const SCEV *Start = AddRec->getStart();
3620 const SCEV *Step = AddRec->getStepRecurrence(*this);
3622 ConstantRange StartRange = getSignedRange(Start);
3623 ConstantRange StepRange = getSignedRange(Step);
3624 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3625 ConstantRange EndRange =
3626 StartRange.add(MaxBECountRange.multiply(StepRange));
3628 // Check for overflow. This must be done with ConstantRange arithmetic
3629 // because we could be called from within the ScalarEvolution overflow
3631 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3632 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3633 ConstantRange ExtMaxBECountRange =
3634 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3635 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3636 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3638 return setSignedRange(AddRec, ConservativeResult);
3640 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3641 EndRange.getSignedMin());
3642 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3643 EndRange.getSignedMax());
3644 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3645 return setSignedRange(AddRec, ConservativeResult);
3646 return setSignedRange(AddRec,
3647 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3651 return setSignedRange(AddRec, ConservativeResult);
3654 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3655 // For a SCEVUnknown, ask ValueTracking.
3656 if (!U->getValue()->getType()->isIntegerTy() && !DL)
3657 return setSignedRange(U, ConservativeResult);
3658 unsigned NS = ComputeNumSignBits(U->getValue(), DL);
3660 return setSignedRange(U, ConservativeResult);
3661 return setSignedRange(U, ConservativeResult.intersectWith(
3662 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3663 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3666 return setSignedRange(S, ConservativeResult);
3669 /// createSCEV - We know that there is no SCEV for the specified value.
3670 /// Analyze the expression.
3672 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3673 if (!isSCEVable(V->getType()))
3674 return getUnknown(V);
3676 unsigned Opcode = Instruction::UserOp1;
3677 if (Instruction *I = dyn_cast<Instruction>(V)) {
3678 Opcode = I->getOpcode();
3680 // Don't attempt to analyze instructions in blocks that aren't
3681 // reachable. Such instructions don't matter, and they aren't required
3682 // to obey basic rules for definitions dominating uses which this
3683 // analysis depends on.
3684 if (!DT->isReachableFromEntry(I->getParent()))
3685 return getUnknown(V);
3686 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3687 Opcode = CE->getOpcode();
3688 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3689 return getConstant(CI);
3690 else if (isa<ConstantPointerNull>(V))
3691 return getConstant(V->getType(), 0);
3692 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3693 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3695 return getUnknown(V);
3697 Operator *U = cast<Operator>(V);
3699 case Instruction::Add: {
3700 // The simple thing to do would be to just call getSCEV on both operands
3701 // and call getAddExpr with the result. However if we're looking at a
3702 // bunch of things all added together, this can be quite inefficient,
3703 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3704 // Instead, gather up all the operands and make a single getAddExpr call.
3705 // LLVM IR canonical form means we need only traverse the left operands.
3707 // Don't apply this instruction's NSW or NUW flags to the new
3708 // expression. The instruction may be guarded by control flow that the
3709 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3710 // mapped to the same SCEV expression, and it would be incorrect to transfer
3711 // NSW/NUW semantics to those operations.
3712 SmallVector<const SCEV *, 4> AddOps;
3713 AddOps.push_back(getSCEV(U->getOperand(1)));
3714 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3715 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3716 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3718 U = cast<Operator>(Op);
3719 const SCEV *Op1 = getSCEV(U->getOperand(1));
3720 if (Opcode == Instruction::Sub)
3721 AddOps.push_back(getNegativeSCEV(Op1));
3723 AddOps.push_back(Op1);
3725 AddOps.push_back(getSCEV(U->getOperand(0)));
3726 return getAddExpr(AddOps);
3728 case Instruction::Mul: {
3729 // Don't transfer NSW/NUW for the same reason as AddExpr.
3730 SmallVector<const SCEV *, 4> MulOps;
3731 MulOps.push_back(getSCEV(U->getOperand(1)));
3732 for (Value *Op = U->getOperand(0);
3733 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3734 Op = U->getOperand(0)) {
3735 U = cast<Operator>(Op);
3736 MulOps.push_back(getSCEV(U->getOperand(1)));
3738 MulOps.push_back(getSCEV(U->getOperand(0)));
3739 return getMulExpr(MulOps);
3741 case Instruction::UDiv:
3742 return getUDivExpr(getSCEV(U->getOperand(0)),
3743 getSCEV(U->getOperand(1)));
3744 case Instruction::Sub:
3745 return getMinusSCEV(getSCEV(U->getOperand(0)),
3746 getSCEV(U->getOperand(1)));
3747 case Instruction::And:
3748 // For an expression like x&255 that merely masks off the high bits,
3749 // use zext(trunc(x)) as the SCEV expression.
3750 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3751 if (CI->isNullValue())
3752 return getSCEV(U->getOperand(1));
3753 if (CI->isAllOnesValue())
3754 return getSCEV(U->getOperand(0));
3755 const APInt &A = CI->getValue();
3757 // Instcombine's ShrinkDemandedConstant may strip bits out of
3758 // constants, obscuring what would otherwise be a low-bits mask.
3759 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3760 // knew about to reconstruct a low-bits mask value.
3761 unsigned LZ = A.countLeadingZeros();
3762 unsigned TZ = A.countTrailingZeros();
3763 unsigned BitWidth = A.getBitWidth();
3764 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3765 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, DL);
3767 APInt EffectiveMask =
3768 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
3769 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
3770 const SCEV *MulCount = getConstant(
3771 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
3775 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
3776 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
3783 case Instruction::Or:
3784 // If the RHS of the Or is a constant, we may have something like:
3785 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3786 // optimizations will transparently handle this case.
3788 // In order for this transformation to be safe, the LHS must be of the
3789 // form X*(2^n) and the Or constant must be less than 2^n.
3790 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3791 const SCEV *LHS = getSCEV(U->getOperand(0));
3792 const APInt &CIVal = CI->getValue();
3793 if (GetMinTrailingZeros(LHS) >=
3794 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3795 // Build a plain add SCEV.
3796 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3797 // If the LHS of the add was an addrec and it has no-wrap flags,
3798 // transfer the no-wrap flags, since an or won't introduce a wrap.
3799 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3800 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3801 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3802 OldAR->getNoWrapFlags());
3808 case Instruction::Xor:
3809 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3810 // If the RHS of the xor is a signbit, then this is just an add.
3811 // Instcombine turns add of signbit into xor as a strength reduction step.
3812 if (CI->getValue().isSignBit())
3813 return getAddExpr(getSCEV(U->getOperand(0)),
3814 getSCEV(U->getOperand(1)));
3816 // If the RHS of xor is -1, then this is a not operation.
3817 if (CI->isAllOnesValue())
3818 return getNotSCEV(getSCEV(U->getOperand(0)));
3820 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3821 // This is a variant of the check for xor with -1, and it handles
3822 // the case where instcombine has trimmed non-demanded bits out
3823 // of an xor with -1.
3824 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3825 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3826 if (BO->getOpcode() == Instruction::And &&
3827 LCI->getValue() == CI->getValue())
3828 if (const SCEVZeroExtendExpr *Z =
3829 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3830 Type *UTy = U->getType();
3831 const SCEV *Z0 = Z->getOperand();
3832 Type *Z0Ty = Z0->getType();
3833 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3835 // If C is a low-bits mask, the zero extend is serving to
3836 // mask off the high bits. Complement the operand and
3837 // re-apply the zext.
3838 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3839 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3841 // If C is a single bit, it may be in the sign-bit position
3842 // before the zero-extend. In this case, represent the xor
3843 // using an add, which is equivalent, and re-apply the zext.
3844 APInt Trunc = CI->getValue().trunc(Z0TySize);
3845 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3847 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3853 case Instruction::Shl:
3854 // Turn shift left of a constant amount into a multiply.
3855 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3856 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3858 // If the shift count is not less than the bitwidth, the result of
3859 // the shift is undefined. Don't try to analyze it, because the
3860 // resolution chosen here may differ from the resolution chosen in
3861 // other parts of the compiler.
3862 if (SA->getValue().uge(BitWidth))
3865 Constant *X = ConstantInt::get(getContext(),
3866 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3867 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3871 case Instruction::LShr:
3872 // Turn logical shift right of a constant into a unsigned divide.
3873 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3874 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3876 // If the shift count is not less than the bitwidth, the result of
3877 // the shift is undefined. Don't try to analyze it, because the
3878 // resolution chosen here may differ from the resolution chosen in
3879 // other parts of the compiler.
3880 if (SA->getValue().uge(BitWidth))
3883 Constant *X = ConstantInt::get(getContext(),
3884 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3885 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3889 case Instruction::AShr:
3890 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3891 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3892 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3893 if (L->getOpcode() == Instruction::Shl &&
3894 L->getOperand(1) == U->getOperand(1)) {
3895 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3897 // If the shift count is not less than the bitwidth, the result of
3898 // the shift is undefined. Don't try to analyze it, because the
3899 // resolution chosen here may differ from the resolution chosen in
3900 // other parts of the compiler.
3901 if (CI->getValue().uge(BitWidth))
3904 uint64_t Amt = BitWidth - CI->getZExtValue();
3905 if (Amt == BitWidth)
3906 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3908 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3909 IntegerType::get(getContext(),
3915 case Instruction::Trunc:
3916 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3918 case Instruction::ZExt:
3919 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3921 case Instruction::SExt:
3922 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3924 case Instruction::BitCast:
3925 // BitCasts are no-op casts so we just eliminate the cast.
3926 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3927 return getSCEV(U->getOperand(0));
3930 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3931 // lead to pointer expressions which cannot safely be expanded to GEPs,
3932 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3933 // simplifying integer expressions.
3935 case Instruction::GetElementPtr:
3936 return createNodeForGEP(cast<GEPOperator>(U));
3938 case Instruction::PHI:
3939 return createNodeForPHI(cast<PHINode>(U));
3941 case Instruction::Select:
3942 // This could be a smax or umax that was lowered earlier.
3943 // Try to recover it.
3944 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3945 Value *LHS = ICI->getOperand(0);
3946 Value *RHS = ICI->getOperand(1);
3947 switch (ICI->getPredicate()) {
3948 case ICmpInst::ICMP_SLT:
3949 case ICmpInst::ICMP_SLE:
3950 std::swap(LHS, RHS);
3952 case ICmpInst::ICMP_SGT:
3953 case ICmpInst::ICMP_SGE:
3954 // a >s b ? a+x : b+x -> smax(a, b)+x
3955 // a >s b ? b+x : a+x -> smin(a, b)+x
3956 if (LHS->getType() == U->getType()) {
3957 const SCEV *LS = getSCEV(LHS);
3958 const SCEV *RS = getSCEV(RHS);
3959 const SCEV *LA = getSCEV(U->getOperand(1));
3960 const SCEV *RA = getSCEV(U->getOperand(2));
3961 const SCEV *LDiff = getMinusSCEV(LA, LS);
3962 const SCEV *RDiff = getMinusSCEV(RA, RS);
3964 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3965 LDiff = getMinusSCEV(LA, RS);
3966 RDiff = getMinusSCEV(RA, LS);
3968 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3971 case ICmpInst::ICMP_ULT:
3972 case ICmpInst::ICMP_ULE:
3973 std::swap(LHS, RHS);
3975 case ICmpInst::ICMP_UGT:
3976 case ICmpInst::ICMP_UGE:
3977 // a >u b ? a+x : b+x -> umax(a, b)+x
3978 // a >u b ? b+x : a+x -> umin(a, b)+x
3979 if (LHS->getType() == U->getType()) {
3980 const SCEV *LS = getSCEV(LHS);
3981 const SCEV *RS = getSCEV(RHS);
3982 const SCEV *LA = getSCEV(U->getOperand(1));
3983 const SCEV *RA = getSCEV(U->getOperand(2));
3984 const SCEV *LDiff = getMinusSCEV(LA, LS);
3985 const SCEV *RDiff = getMinusSCEV(RA, RS);
3987 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3988 LDiff = getMinusSCEV(LA, RS);
3989 RDiff = getMinusSCEV(RA, LS);
3991 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3994 case ICmpInst::ICMP_NE:
3995 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3996 if (LHS->getType() == U->getType() &&
3997 isa<ConstantInt>(RHS) &&
3998 cast<ConstantInt>(RHS)->isZero()) {
3999 const SCEV *One = getConstant(LHS->getType(), 1);
4000 const SCEV *LS = getSCEV(LHS);
4001 const SCEV *LA = getSCEV(U->getOperand(1));
4002 const SCEV *RA = getSCEV(U->getOperand(2));
4003 const SCEV *LDiff = getMinusSCEV(LA, LS);
4004 const SCEV *RDiff = getMinusSCEV(RA, One);
4006 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4009 case ICmpInst::ICMP_EQ:
4010 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4011 if (LHS->getType() == U->getType() &&
4012 isa<ConstantInt>(RHS) &&
4013 cast<ConstantInt>(RHS)->isZero()) {
4014 const SCEV *One = getConstant(LHS->getType(), 1);
4015 const SCEV *LS = getSCEV(LHS);
4016 const SCEV *LA = getSCEV(U->getOperand(1));
4017 const SCEV *RA = getSCEV(U->getOperand(2));
4018 const SCEV *LDiff = getMinusSCEV(LA, One);
4019 const SCEV *RDiff = getMinusSCEV(RA, LS);
4021 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4029 default: // We cannot analyze this expression.
4033 return getUnknown(V);
4038 //===----------------------------------------------------------------------===//
4039 // Iteration Count Computation Code
4042 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4043 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4044 /// constant. Will also return 0 if the maximum trip count is very large (>=
4047 /// This "trip count" assumes that control exits via ExitingBlock. More
4048 /// precisely, it is the number of times that control may reach ExitingBlock
4049 /// before taking the branch. For loops with multiple exits, it may not be the
4050 /// number times that the loop header executes because the loop may exit
4051 /// prematurely via another branch.
4053 /// FIXME: We conservatively call getBackedgeTakenCount(L) instead of
4054 /// getExitCount(L, ExitingBlock) to compute a safe trip count considering all
4055 /// loop exits. getExitCount() may return an exact count for this branch
4056 /// assuming no-signed-wrap. The number of well-defined iterations may actually
4057 /// be higher than this trip count if this exit test is skipped and the loop
4058 /// exits via a different branch. Ideally, getExitCount() would know whether it
4059 /// depends on a NSW assumption, and we would only fall back to a conservative
4060 /// trip count in that case.
4061 unsigned ScalarEvolution::
4062 getSmallConstantTripCount(Loop *L, BasicBlock * /*ExitingBlock*/) {
4063 const SCEVConstant *ExitCount =
4064 dyn_cast<SCEVConstant>(getBackedgeTakenCount(L));
4068 ConstantInt *ExitConst = ExitCount->getValue();
4070 // Guard against huge trip counts.
4071 if (ExitConst->getValue().getActiveBits() > 32)
4074 // In case of integer overflow, this returns 0, which is correct.
4075 return ((unsigned)ExitConst->getZExtValue()) + 1;
4078 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4079 /// trip count of this loop as a normal unsigned value, if possible. This
4080 /// means that the actual trip count is always a multiple of the returned
4081 /// value (don't forget the trip count could very well be zero as well!).
4083 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4084 /// multiple of a constant (which is also the case if the trip count is simply
4085 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4086 /// if the trip count is very large (>= 2^32).
4088 /// As explained in the comments for getSmallConstantTripCount, this assumes
4089 /// that control exits the loop via ExitingBlock.
4090 unsigned ScalarEvolution::
4091 getSmallConstantTripMultiple(Loop *L, BasicBlock * /*ExitingBlock*/) {
4092 const SCEV *ExitCount = getBackedgeTakenCount(L);
4093 if (ExitCount == getCouldNotCompute())
4096 // Get the trip count from the BE count by adding 1.
4097 const SCEV *TCMul = getAddExpr(ExitCount,
4098 getConstant(ExitCount->getType(), 1));
4099 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4100 // to factor simple cases.
4101 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4102 TCMul = Mul->getOperand(0);
4104 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4108 ConstantInt *Result = MulC->getValue();
4110 // Guard against huge trip counts (this requires checking
4111 // for zero to handle the case where the trip count == -1 and the
4113 if (!Result || Result->getValue().getActiveBits() > 32 ||
4114 Result->getValue().getActiveBits() == 0)
4117 return (unsigned)Result->getZExtValue();
4120 // getExitCount - Get the expression for the number of loop iterations for which
4121 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4122 // SCEVCouldNotCompute.
4123 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4124 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4127 /// getBackedgeTakenCount - If the specified loop has a predictable
4128 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4129 /// object. The backedge-taken count is the number of times the loop header
4130 /// will be branched to from within the loop. This is one less than the
4131 /// trip count of the loop, since it doesn't count the first iteration,
4132 /// when the header is branched to from outside the loop.
4134 /// Note that it is not valid to call this method on a loop without a
4135 /// loop-invariant backedge-taken count (see
4136 /// hasLoopInvariantBackedgeTakenCount).
4138 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4139 return getBackedgeTakenInfo(L).getExact(this);
4142 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4143 /// return the least SCEV value that is known never to be less than the
4144 /// actual backedge taken count.
4145 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4146 return getBackedgeTakenInfo(L).getMax(this);
4149 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4150 /// onto the given Worklist.
4152 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4153 BasicBlock *Header = L->getHeader();
4155 // Push all Loop-header PHIs onto the Worklist stack.
4156 for (BasicBlock::iterator I = Header->begin();
4157 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4158 Worklist.push_back(PN);
4161 const ScalarEvolution::BackedgeTakenInfo &
4162 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4163 // Initially insert an invalid entry for this loop. If the insertion
4164 // succeeds, proceed to actually compute a backedge-taken count and
4165 // update the value. The temporary CouldNotCompute value tells SCEV
4166 // code elsewhere that it shouldn't attempt to request a new
4167 // backedge-taken count, which could result in infinite recursion.
4168 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4169 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4171 return Pair.first->second;
4173 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4174 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4175 // must be cleared in this scope.
4176 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4178 if (Result.getExact(this) != getCouldNotCompute()) {
4179 assert(isLoopInvariant(Result.getExact(this), L) &&
4180 isLoopInvariant(Result.getMax(this), L) &&
4181 "Computed backedge-taken count isn't loop invariant for loop!");
4182 ++NumTripCountsComputed;
4184 else if (Result.getMax(this) == getCouldNotCompute() &&
4185 isa<PHINode>(L->getHeader()->begin())) {
4186 // Only count loops that have phi nodes as not being computable.
4187 ++NumTripCountsNotComputed;
4190 // Now that we know more about the trip count for this loop, forget any
4191 // existing SCEV values for PHI nodes in this loop since they are only
4192 // conservative estimates made without the benefit of trip count
4193 // information. This is similar to the code in forgetLoop, except that
4194 // it handles SCEVUnknown PHI nodes specially.
4195 if (Result.hasAnyInfo()) {
4196 SmallVector<Instruction *, 16> Worklist;
4197 PushLoopPHIs(L, Worklist);
4199 SmallPtrSet<Instruction *, 8> Visited;
4200 while (!Worklist.empty()) {
4201 Instruction *I = Worklist.pop_back_val();
4202 if (!Visited.insert(I)) continue;
4204 ValueExprMapType::iterator It =
4205 ValueExprMap.find_as(static_cast<Value *>(I));
4206 if (It != ValueExprMap.end()) {
4207 const SCEV *Old = It->second;
4209 // SCEVUnknown for a PHI either means that it has an unrecognized
4210 // structure, or it's a PHI that's in the progress of being computed
4211 // by createNodeForPHI. In the former case, additional loop trip
4212 // count information isn't going to change anything. In the later
4213 // case, createNodeForPHI will perform the necessary updates on its
4214 // own when it gets to that point.
4215 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4216 forgetMemoizedResults(Old);
4217 ValueExprMap.erase(It);
4219 if (PHINode *PN = dyn_cast<PHINode>(I))
4220 ConstantEvolutionLoopExitValue.erase(PN);
4223 PushDefUseChildren(I, Worklist);
4227 // Re-lookup the insert position, since the call to
4228 // ComputeBackedgeTakenCount above could result in a
4229 // recusive call to getBackedgeTakenInfo (on a different
4230 // loop), which would invalidate the iterator computed
4232 return BackedgeTakenCounts.find(L)->second = Result;
4235 /// forgetLoop - This method should be called by the client when it has
4236 /// changed a loop in a way that may effect ScalarEvolution's ability to
4237 /// compute a trip count, or if the loop is deleted.
4238 void ScalarEvolution::forgetLoop(const Loop *L) {
4239 // Drop any stored trip count value.
4240 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4241 BackedgeTakenCounts.find(L);
4242 if (BTCPos != BackedgeTakenCounts.end()) {
4243 BTCPos->second.clear();
4244 BackedgeTakenCounts.erase(BTCPos);
4247 // Drop information about expressions based on loop-header PHIs.
4248 SmallVector<Instruction *, 16> Worklist;
4249 PushLoopPHIs(L, Worklist);
4251 SmallPtrSet<Instruction *, 8> Visited;
4252 while (!Worklist.empty()) {
4253 Instruction *I = Worklist.pop_back_val();
4254 if (!Visited.insert(I)) continue;
4256 ValueExprMapType::iterator It =
4257 ValueExprMap.find_as(static_cast<Value *>(I));
4258 if (It != ValueExprMap.end()) {
4259 forgetMemoizedResults(It->second);
4260 ValueExprMap.erase(It);
4261 if (PHINode *PN = dyn_cast<PHINode>(I))
4262 ConstantEvolutionLoopExitValue.erase(PN);
4265 PushDefUseChildren(I, Worklist);
4268 // Forget all contained loops too, to avoid dangling entries in the
4269 // ValuesAtScopes map.
4270 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4274 /// forgetValue - This method should be called by the client when it has
4275 /// changed a value in a way that may effect its value, or which may
4276 /// disconnect it from a def-use chain linking it to a loop.
4277 void ScalarEvolution::forgetValue(Value *V) {
4278 Instruction *I = dyn_cast<Instruction>(V);
4281 // Drop information about expressions based on loop-header PHIs.
4282 SmallVector<Instruction *, 16> Worklist;
4283 Worklist.push_back(I);
4285 SmallPtrSet<Instruction *, 8> Visited;
4286 while (!Worklist.empty()) {
4287 I = Worklist.pop_back_val();
4288 if (!Visited.insert(I)) continue;
4290 ValueExprMapType::iterator It =
4291 ValueExprMap.find_as(static_cast<Value *>(I));
4292 if (It != ValueExprMap.end()) {
4293 forgetMemoizedResults(It->second);
4294 ValueExprMap.erase(It);
4295 if (PHINode *PN = dyn_cast<PHINode>(I))
4296 ConstantEvolutionLoopExitValue.erase(PN);
4299 PushDefUseChildren(I, Worklist);
4303 /// getExact - Get the exact loop backedge taken count considering all loop
4304 /// exits. A computable result can only be return for loops with a single exit.
4305 /// Returning the minimum taken count among all exits is incorrect because one
4306 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4307 /// the limit of each loop test is never skipped. This is a valid assumption as
4308 /// long as the loop exits via that test. For precise results, it is the
4309 /// caller's responsibility to specify the relevant loop exit using
4310 /// getExact(ExitingBlock, SE).
4312 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4313 // If any exits were not computable, the loop is not computable.
4314 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4316 // We need exactly one computable exit.
4317 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4318 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4320 const SCEV *BECount = 0;
4321 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4322 ENT != 0; ENT = ENT->getNextExit()) {
4324 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4327 BECount = ENT->ExactNotTaken;
4328 else if (BECount != ENT->ExactNotTaken)
4329 return SE->getCouldNotCompute();
4331 assert(BECount && "Invalid not taken count for loop exit");
4335 /// getExact - Get the exact not taken count for this loop exit.
4337 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4338 ScalarEvolution *SE) const {
4339 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4340 ENT != 0; ENT = ENT->getNextExit()) {
4342 if (ENT->ExitingBlock == ExitingBlock)
4343 return ENT->ExactNotTaken;
4345 return SE->getCouldNotCompute();
4348 /// getMax - Get the max backedge taken count for the loop.
4350 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4351 return Max ? Max : SE->getCouldNotCompute();
4354 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4355 ScalarEvolution *SE) const {
4356 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4359 if (!ExitNotTaken.ExitingBlock)
4362 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4363 ENT != 0; ENT = ENT->getNextExit()) {
4365 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4366 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4373 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4374 /// computable exit into a persistent ExitNotTakenInfo array.
4375 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4376 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4377 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4380 ExitNotTaken.setIncomplete();
4382 unsigned NumExits = ExitCounts.size();
4383 if (NumExits == 0) return;
4385 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4386 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4387 if (NumExits == 1) return;
4389 // Handle the rare case of multiple computable exits.
4390 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4392 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4393 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4394 PrevENT->setNextExit(ENT);
4395 ENT->ExitingBlock = ExitCounts[i].first;
4396 ENT->ExactNotTaken = ExitCounts[i].second;
4400 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4401 void ScalarEvolution::BackedgeTakenInfo::clear() {
4402 ExitNotTaken.ExitingBlock = 0;
4403 ExitNotTaken.ExactNotTaken = 0;
4404 delete[] ExitNotTaken.getNextExit();
4407 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4408 /// of the specified loop will execute.
4409 ScalarEvolution::BackedgeTakenInfo
4410 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4411 SmallVector<BasicBlock *, 8> ExitingBlocks;
4412 L->getExitingBlocks(ExitingBlocks);
4414 // Examine all exits and pick the most conservative values.
4415 const SCEV *MaxBECount = getCouldNotCompute();
4416 bool CouldComputeBECount = true;
4417 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4418 const SCEV *LatchMaxCount = 0;
4419 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4420 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4421 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4422 if (EL.Exact == getCouldNotCompute())
4423 // We couldn't compute an exact value for this exit, so
4424 // we won't be able to compute an exact value for the loop.
4425 CouldComputeBECount = false;
4427 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4429 if (MaxBECount == getCouldNotCompute())
4430 MaxBECount = EL.Max;
4431 else if (EL.Max != getCouldNotCompute()) {
4432 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4433 // skip some loop tests. Taking the max over the exits is sufficiently
4434 // conservative. TODO: We could do better taking into consideration
4435 // non-latch exits that dominate the latch.
4436 if (EL.MustExit && ExitingBlocks[i] == Latch)
4437 LatchMaxCount = EL.Max;
4439 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4442 // Be more precise in the easy case of a loop latch that must exit.
4443 if (LatchMaxCount) {
4444 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, LatchMaxCount);
4446 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4449 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4450 /// loop will execute if it exits via the specified block.
4451 ScalarEvolution::ExitLimit
4452 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4454 // Okay, we've chosen an exiting block. See what condition causes us to
4455 // exit at this block and remember the exit block and whether all other targets
4456 // lead to the loop header.
4457 bool MustExecuteLoopHeader = true;
4458 BasicBlock *Exit = 0;
4459 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4461 if (!L->contains(*SI)) {
4462 if (Exit) // Multiple exit successors.
4463 return getCouldNotCompute();
4465 } else if (*SI != L->getHeader()) {
4466 MustExecuteLoopHeader = false;
4469 // At this point, we know we have a conditional branch that determines whether
4470 // the loop is exited. However, we don't know if the branch is executed each
4471 // time through the loop. If not, then the execution count of the branch will
4472 // not be equal to the trip count of the loop.
4474 // Currently we check for this by checking to see if the Exit branch goes to
4475 // the loop header. If so, we know it will always execute the same number of
4476 // times as the loop. We also handle the case where the exit block *is* the
4477 // loop header. This is common for un-rotated loops.
4479 // If both of those tests fail, walk up the unique predecessor chain to the
4480 // header, stopping if there is an edge that doesn't exit the loop. If the
4481 // header is reached, the execution count of the branch will be equal to the
4482 // trip count of the loop.
4484 // More extensive analysis could be done to handle more cases here.
4486 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4487 // The simple checks failed, try climbing the unique predecessor chain
4488 // up to the header.
4490 for (BasicBlock *BB = ExitingBlock; BB; ) {
4491 BasicBlock *Pred = BB->getUniquePredecessor();
4493 return getCouldNotCompute();
4494 TerminatorInst *PredTerm = Pred->getTerminator();
4495 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4496 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4499 // If the predecessor has a successor that isn't BB and isn't
4500 // outside the loop, assume the worst.
4501 if (L->contains(PredSucc))
4502 return getCouldNotCompute();
4504 if (Pred == L->getHeader()) {
4511 return getCouldNotCompute();
4514 TerminatorInst *Term = ExitingBlock->getTerminator();
4515 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4516 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4517 // Proceed to the next level to examine the exit condition expression.
4518 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4519 BI->getSuccessor(1),
4520 /*IsSubExpr=*/false);
4523 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4524 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4525 /*IsSubExpr=*/false);
4527 return getCouldNotCompute();
4530 /// ComputeExitLimitFromCond - Compute the number of times the
4531 /// backedge of the specified loop will execute if its exit condition
4532 /// were a conditional branch of ExitCond, TBB, and FBB.
4534 /// @param IsSubExpr is true if ExitCond does not directly control the exit
4535 /// branch. In this case, we cannot assume that the loop only exits when the
4536 /// condition is true and cannot infer that failing to meet the condition prior
4537 /// to integer wraparound results in undefined behavior.
4538 ScalarEvolution::ExitLimit
4539 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4544 // Check if the controlling expression for this loop is an And or Or.
4545 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4546 if (BO->getOpcode() == Instruction::And) {
4547 // Recurse on the operands of the and.
4548 bool EitherMayExit = L->contains(TBB);
4549 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4550 IsSubExpr || EitherMayExit);
4551 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4552 IsSubExpr || EitherMayExit);
4553 const SCEV *BECount = getCouldNotCompute();
4554 const SCEV *MaxBECount = getCouldNotCompute();
4555 bool MustExit = false;
4556 if (EitherMayExit) {
4557 // Both conditions must be true for the loop to continue executing.
4558 // Choose the less conservative count.
4559 if (EL0.Exact == getCouldNotCompute() ||
4560 EL1.Exact == getCouldNotCompute())
4561 BECount = getCouldNotCompute();
4563 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4564 if (EL0.Max == getCouldNotCompute())
4565 MaxBECount = EL1.Max;
4566 else if (EL1.Max == getCouldNotCompute())
4567 MaxBECount = EL0.Max;
4569 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4570 MustExit = EL0.MustExit || EL1.MustExit;
4572 // Both conditions must be true at the same time for the loop to exit.
4573 // For now, be conservative.
4574 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4575 if (EL0.Max == EL1.Max)
4576 MaxBECount = EL0.Max;
4577 if (EL0.Exact == EL1.Exact)
4578 BECount = EL0.Exact;
4579 MustExit = EL0.MustExit && EL1.MustExit;
4582 return ExitLimit(BECount, MaxBECount, MustExit);
4584 if (BO->getOpcode() == Instruction::Or) {
4585 // Recurse on the operands of the or.
4586 bool EitherMayExit = L->contains(FBB);
4587 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4588 IsSubExpr || EitherMayExit);
4589 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4590 IsSubExpr || EitherMayExit);
4591 const SCEV *BECount = getCouldNotCompute();
4592 const SCEV *MaxBECount = getCouldNotCompute();
4593 bool MustExit = false;
4594 if (EitherMayExit) {
4595 // Both conditions must be false for the loop to continue executing.
4596 // Choose the less conservative count.
4597 if (EL0.Exact == getCouldNotCompute() ||
4598 EL1.Exact == getCouldNotCompute())
4599 BECount = getCouldNotCompute();
4601 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4602 if (EL0.Max == getCouldNotCompute())
4603 MaxBECount = EL1.Max;
4604 else if (EL1.Max == getCouldNotCompute())
4605 MaxBECount = EL0.Max;
4607 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4608 MustExit = EL0.MustExit || EL1.MustExit;
4610 // Both conditions must be false at the same time for the loop to exit.
4611 // For now, be conservative.
4612 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4613 if (EL0.Max == EL1.Max)
4614 MaxBECount = EL0.Max;
4615 if (EL0.Exact == EL1.Exact)
4616 BECount = EL0.Exact;
4617 MustExit = EL0.MustExit && EL1.MustExit;
4620 return ExitLimit(BECount, MaxBECount, MustExit);
4624 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4625 // Proceed to the next level to examine the icmp.
4626 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4627 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, IsSubExpr);
4629 // Check for a constant condition. These are normally stripped out by
4630 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4631 // preserve the CFG and is temporarily leaving constant conditions
4633 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4634 if (L->contains(FBB) == !CI->getZExtValue())
4635 // The backedge is always taken.
4636 return getCouldNotCompute();
4638 // The backedge is never taken.
4639 return getConstant(CI->getType(), 0);
4642 // If it's not an integer or pointer comparison then compute it the hard way.
4643 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4646 /// ComputeExitLimitFromICmp - Compute the number of times the
4647 /// backedge of the specified loop will execute if its exit condition
4648 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4649 ScalarEvolution::ExitLimit
4650 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4656 // If the condition was exit on true, convert the condition to exit on false
4657 ICmpInst::Predicate Cond;
4658 if (!L->contains(FBB))
4659 Cond = ExitCond->getPredicate();
4661 Cond = ExitCond->getInversePredicate();
4663 // Handle common loops like: for (X = "string"; *X; ++X)
4664 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4665 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4667 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4668 if (ItCnt.hasAnyInfo())
4672 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4673 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4675 // Try to evaluate any dependencies out of the loop.
4676 LHS = getSCEVAtScope(LHS, L);
4677 RHS = getSCEVAtScope(RHS, L);
4679 // At this point, we would like to compute how many iterations of the
4680 // loop the predicate will return true for these inputs.
4681 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4682 // If there is a loop-invariant, force it into the RHS.
4683 std::swap(LHS, RHS);
4684 Cond = ICmpInst::getSwappedPredicate(Cond);
4687 // Simplify the operands before analyzing them.
4688 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4690 // If we have a comparison of a chrec against a constant, try to use value
4691 // ranges to answer this query.
4692 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4693 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4694 if (AddRec->getLoop() == L) {
4695 // Form the constant range.
4696 ConstantRange CompRange(
4697 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4699 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4700 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4704 case ICmpInst::ICMP_NE: { // while (X != Y)
4705 // Convert to: while (X-Y != 0)
4706 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4707 if (EL.hasAnyInfo()) return EL;
4710 case ICmpInst::ICMP_EQ: { // while (X == Y)
4711 // Convert to: while (X-Y == 0)
4712 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4713 if (EL.hasAnyInfo()) return EL;
4716 case ICmpInst::ICMP_SLT:
4717 case ICmpInst::ICMP_ULT: { // while (X < Y)
4718 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
4719 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, IsSubExpr);
4720 if (EL.hasAnyInfo()) return EL;
4723 case ICmpInst::ICMP_SGT:
4724 case ICmpInst::ICMP_UGT: { // while (X > Y)
4725 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
4726 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, IsSubExpr);
4727 if (EL.hasAnyInfo()) return EL;
4732 dbgs() << "ComputeBackedgeTakenCount ";
4733 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4734 dbgs() << "[unsigned] ";
4735 dbgs() << *LHS << " "
4736 << Instruction::getOpcodeName(Instruction::ICmp)
4737 << " " << *RHS << "\n";
4741 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4744 ScalarEvolution::ExitLimit
4745 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
4747 BasicBlock *ExitingBlock,
4749 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
4751 // Give up if the exit is the default dest of a switch.
4752 if (Switch->getDefaultDest() == ExitingBlock)
4753 return getCouldNotCompute();
4755 assert(L->contains(Switch->getDefaultDest()) &&
4756 "Default case must not exit the loop!");
4757 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
4758 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
4760 // while (X != Y) --> while (X-Y != 0)
4761 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4762 if (EL.hasAnyInfo())
4765 return getCouldNotCompute();
4768 static ConstantInt *
4769 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4770 ScalarEvolution &SE) {
4771 const SCEV *InVal = SE.getConstant(C);
4772 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4773 assert(isa<SCEVConstant>(Val) &&
4774 "Evaluation of SCEV at constant didn't fold correctly?");
4775 return cast<SCEVConstant>(Val)->getValue();
4778 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4779 /// 'icmp op load X, cst', try to see if we can compute the backedge
4780 /// execution count.
4781 ScalarEvolution::ExitLimit
4782 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4786 ICmpInst::Predicate predicate) {
4788 if (LI->isVolatile()) return getCouldNotCompute();
4790 // Check to see if the loaded pointer is a getelementptr of a global.
4791 // TODO: Use SCEV instead of manually grubbing with GEPs.
4792 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4793 if (!GEP) return getCouldNotCompute();
4795 // Make sure that it is really a constant global we are gepping, with an
4796 // initializer, and make sure the first IDX is really 0.
4797 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4798 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4799 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4800 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4801 return getCouldNotCompute();
4803 // Okay, we allow one non-constant index into the GEP instruction.
4805 std::vector<Constant*> Indexes;
4806 unsigned VarIdxNum = 0;
4807 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4808 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4809 Indexes.push_back(CI);
4810 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4811 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4812 VarIdx = GEP->getOperand(i);
4814 Indexes.push_back(0);
4817 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4819 return getCouldNotCompute();
4821 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4822 // Check to see if X is a loop variant variable value now.
4823 const SCEV *Idx = getSCEV(VarIdx);
4824 Idx = getSCEVAtScope(Idx, L);
4826 // We can only recognize very limited forms of loop index expressions, in
4827 // particular, only affine AddRec's like {C1,+,C2}.
4828 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4829 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4830 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4831 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4832 return getCouldNotCompute();
4834 unsigned MaxSteps = MaxBruteForceIterations;
4835 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4836 ConstantInt *ItCst = ConstantInt::get(
4837 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4838 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4840 // Form the GEP offset.
4841 Indexes[VarIdxNum] = Val;
4843 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4845 if (Result == 0) break; // Cannot compute!
4847 // Evaluate the condition for this iteration.
4848 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4849 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4850 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4852 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4853 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4856 ++NumArrayLenItCounts;
4857 return getConstant(ItCst); // Found terminating iteration!
4860 return getCouldNotCompute();
4864 /// CanConstantFold - Return true if we can constant fold an instruction of the
4865 /// specified type, assuming that all operands were constants.
4866 static bool CanConstantFold(const Instruction *I) {
4867 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4868 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4872 if (const CallInst *CI = dyn_cast<CallInst>(I))
4873 if (const Function *F = CI->getCalledFunction())
4874 return canConstantFoldCallTo(F);
4878 /// Determine whether this instruction can constant evolve within this loop
4879 /// assuming its operands can all constant evolve.
4880 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4881 // An instruction outside of the loop can't be derived from a loop PHI.
4882 if (!L->contains(I)) return false;
4884 if (isa<PHINode>(I)) {
4885 if (L->getHeader() == I->getParent())
4888 // We don't currently keep track of the control flow needed to evaluate
4889 // PHIs, so we cannot handle PHIs inside of loops.
4893 // If we won't be able to constant fold this expression even if the operands
4894 // are constants, bail early.
4895 return CanConstantFold(I);
4898 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4899 /// recursing through each instruction operand until reaching a loop header phi.
4901 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4902 DenseMap<Instruction *, PHINode *> &PHIMap) {
4904 // Otherwise, we can evaluate this instruction if all of its operands are
4905 // constant or derived from a PHI node themselves.
4907 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4908 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4910 if (isa<Constant>(*OpI)) continue;
4912 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4913 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4915 PHINode *P = dyn_cast<PHINode>(OpInst);
4917 // If this operand is already visited, reuse the prior result.
4918 // We may have P != PHI if this is the deepest point at which the
4919 // inconsistent paths meet.
4920 P = PHIMap.lookup(OpInst);
4922 // Recurse and memoize the results, whether a phi is found or not.
4923 // This recursive call invalidates pointers into PHIMap.
4924 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4927 if (P == 0) return 0; // Not evolving from PHI
4928 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4931 // This is a expression evolving from a constant PHI!
4935 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4936 /// in the loop that V is derived from. We allow arbitrary operations along the
4937 /// way, but the operands of an operation must either be constants or a value
4938 /// derived from a constant PHI. If this expression does not fit with these
4939 /// constraints, return null.
4940 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4941 Instruction *I = dyn_cast<Instruction>(V);
4942 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4944 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4948 // Record non-constant instructions contained by the loop.
4949 DenseMap<Instruction *, PHINode *> PHIMap;
4950 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4953 /// EvaluateExpression - Given an expression that passes the
4954 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4955 /// in the loop has the value PHIVal. If we can't fold this expression for some
4956 /// reason, return null.
4957 static Constant *EvaluateExpression(Value *V, const Loop *L,
4958 DenseMap<Instruction *, Constant *> &Vals,
4959 const DataLayout *DL,
4960 const TargetLibraryInfo *TLI) {
4961 // Convenient constant check, but redundant for recursive calls.
4962 if (Constant *C = dyn_cast<Constant>(V)) return C;
4963 Instruction *I = dyn_cast<Instruction>(V);
4966 if (Constant *C = Vals.lookup(I)) return C;
4968 // An instruction inside the loop depends on a value outside the loop that we
4969 // weren't given a mapping for, or a value such as a call inside the loop.
4970 if (!canConstantEvolve(I, L)) return 0;
4972 // An unmapped PHI can be due to a branch or another loop inside this loop,
4973 // or due to this not being the initial iteration through a loop where we
4974 // couldn't compute the evolution of this particular PHI last time.
4975 if (isa<PHINode>(I)) return 0;
4977 std::vector<Constant*> Operands(I->getNumOperands());
4979 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4980 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4982 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4983 if (!Operands[i]) return 0;
4986 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
4992 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4993 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4994 Operands[1], DL, TLI);
4995 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4996 if (!LI->isVolatile())
4997 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
4999 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5003 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5004 /// in the header of its containing loop, we know the loop executes a
5005 /// constant number of times, and the PHI node is just a recurrence
5006 /// involving constants, fold it.
5008 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5011 DenseMap<PHINode*, Constant*>::const_iterator I =
5012 ConstantEvolutionLoopExitValue.find(PN);
5013 if (I != ConstantEvolutionLoopExitValue.end())
5016 if (BEs.ugt(MaxBruteForceIterations))
5017 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
5019 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5021 DenseMap<Instruction *, Constant *> CurrentIterVals;
5022 BasicBlock *Header = L->getHeader();
5023 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5025 // Since the loop is canonicalized, the PHI node must have two entries. One
5026 // entry must be a constant (coming in from outside of the loop), and the
5027 // second must be derived from the same PHI.
5028 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5030 for (BasicBlock::iterator I = Header->begin();
5031 (PHI = dyn_cast<PHINode>(I)); ++I) {
5032 Constant *StartCST =
5033 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5034 if (StartCST == 0) continue;
5035 CurrentIterVals[PHI] = StartCST;
5037 if (!CurrentIterVals.count(PN))
5040 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5042 // Execute the loop symbolically to determine the exit value.
5043 if (BEs.getActiveBits() >= 32)
5044 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
5046 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5047 unsigned IterationNum = 0;
5048 for (; ; ++IterationNum) {
5049 if (IterationNum == NumIterations)
5050 return RetVal = CurrentIterVals[PN]; // Got exit value!
5052 // Compute the value of the PHIs for the next iteration.
5053 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5054 DenseMap<Instruction *, Constant *> NextIterVals;
5055 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5058 return 0; // Couldn't evaluate!
5059 NextIterVals[PN] = NextPHI;
5061 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5063 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5064 // cease to be able to evaluate one of them or if they stop evolving,
5065 // because that doesn't necessarily prevent us from computing PN.
5066 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5067 for (DenseMap<Instruction *, Constant *>::const_iterator
5068 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5069 PHINode *PHI = dyn_cast<PHINode>(I->first);
5070 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5071 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5073 // We use two distinct loops because EvaluateExpression may invalidate any
5074 // iterators into CurrentIterVals.
5075 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5076 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5077 PHINode *PHI = I->first;
5078 Constant *&NextPHI = NextIterVals[PHI];
5079 if (!NextPHI) { // Not already computed.
5080 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5081 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5083 if (NextPHI != I->second)
5084 StoppedEvolving = false;
5087 // If all entries in CurrentIterVals == NextIterVals then we can stop
5088 // iterating, the loop can't continue to change.
5089 if (StoppedEvolving)
5090 return RetVal = CurrentIterVals[PN];
5092 CurrentIterVals.swap(NextIterVals);
5096 /// ComputeExitCountExhaustively - If the loop is known to execute a
5097 /// constant number of times (the condition evolves only from constants),
5098 /// try to evaluate a few iterations of the loop until we get the exit
5099 /// condition gets a value of ExitWhen (true or false). If we cannot
5100 /// evaluate the trip count of the loop, return getCouldNotCompute().
5101 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5104 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5105 if (PN == 0) return getCouldNotCompute();
5107 // If the loop is canonicalized, the PHI will have exactly two entries.
5108 // That's the only form we support here.
5109 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5111 DenseMap<Instruction *, Constant *> CurrentIterVals;
5112 BasicBlock *Header = L->getHeader();
5113 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5115 // One entry must be a constant (coming in from outside of the loop), and the
5116 // second must be derived from the same PHI.
5117 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5119 for (BasicBlock::iterator I = Header->begin();
5120 (PHI = dyn_cast<PHINode>(I)); ++I) {
5121 Constant *StartCST =
5122 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5123 if (StartCST == 0) continue;
5124 CurrentIterVals[PHI] = StartCST;
5126 if (!CurrentIterVals.count(PN))
5127 return getCouldNotCompute();
5129 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5130 // the loop symbolically to determine when the condition gets a value of
5133 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5134 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5135 ConstantInt *CondVal =
5136 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5139 // Couldn't symbolically evaluate.
5140 if (!CondVal) return getCouldNotCompute();
5142 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5143 ++NumBruteForceTripCountsComputed;
5144 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5147 // Update all the PHI nodes for the next iteration.
5148 DenseMap<Instruction *, Constant *> NextIterVals;
5150 // Create a list of which PHIs we need to compute. We want to do this before
5151 // calling EvaluateExpression on them because that may invalidate iterators
5152 // into CurrentIterVals.
5153 SmallVector<PHINode *, 8> PHIsToCompute;
5154 for (DenseMap<Instruction *, Constant *>::const_iterator
5155 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5156 PHINode *PHI = dyn_cast<PHINode>(I->first);
5157 if (!PHI || PHI->getParent() != Header) continue;
5158 PHIsToCompute.push_back(PHI);
5160 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5161 E = PHIsToCompute.end(); I != E; ++I) {
5163 Constant *&NextPHI = NextIterVals[PHI];
5164 if (NextPHI) continue; // Already computed!
5166 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5167 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5169 CurrentIterVals.swap(NextIterVals);
5172 // Too many iterations were needed to evaluate.
5173 return getCouldNotCompute();
5176 /// getSCEVAtScope - Return a SCEV expression for the specified value
5177 /// at the specified scope in the program. The L value specifies a loop
5178 /// nest to evaluate the expression at, where null is the top-level or a
5179 /// specified loop is immediately inside of the loop.
5181 /// This method can be used to compute the exit value for a variable defined
5182 /// in a loop by querying what the value will hold in the parent loop.
5184 /// In the case that a relevant loop exit value cannot be computed, the
5185 /// original value V is returned.
5186 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5187 // Check to see if we've folded this expression at this loop before.
5188 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5189 for (unsigned u = 0; u < Values.size(); u++) {
5190 if (Values[u].first == L)
5191 return Values[u].second ? Values[u].second : V;
5193 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(0)));
5194 // Otherwise compute it.
5195 const SCEV *C = computeSCEVAtScope(V, L);
5196 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5197 for (unsigned u = Values2.size(); u > 0; u--) {
5198 if (Values2[u - 1].first == L) {
5199 Values2[u - 1].second = C;
5206 /// This builds up a Constant using the ConstantExpr interface. That way, we
5207 /// will return Constants for objects which aren't represented by a
5208 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5209 /// Returns NULL if the SCEV isn't representable as a Constant.
5210 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5211 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5212 case scCouldNotCompute:
5216 return cast<SCEVConstant>(V)->getValue();
5218 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5219 case scSignExtend: {
5220 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5221 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5222 return ConstantExpr::getSExt(CastOp, SS->getType());
5225 case scZeroExtend: {
5226 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5227 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5228 return ConstantExpr::getZExt(CastOp, SZ->getType());
5232 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5233 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5234 return ConstantExpr::getTrunc(CastOp, ST->getType());
5238 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5239 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5240 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5241 unsigned AS = PTy->getAddressSpace();
5242 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5243 C = ConstantExpr::getBitCast(C, DestPtrTy);
5245 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5246 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5250 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5251 unsigned AS = C2->getType()->getPointerAddressSpace();
5253 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5254 // The offsets have been converted to bytes. We can add bytes to an
5255 // i8* by GEP with the byte count in the first index.
5256 C = ConstantExpr::getBitCast(C, DestPtrTy);
5259 // Don't bother trying to sum two pointers. We probably can't
5260 // statically compute a load that results from it anyway.
5261 if (C2->getType()->isPointerTy())
5264 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5265 if (PTy->getElementType()->isStructTy())
5266 C2 = ConstantExpr::getIntegerCast(
5267 C2, Type::getInt32Ty(C->getContext()), true);
5268 C = ConstantExpr::getGetElementPtr(C, C2);
5270 C = ConstantExpr::getAdd(C, C2);
5277 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5278 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5279 // Don't bother with pointers at all.
5280 if (C->getType()->isPointerTy()) return 0;
5281 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5282 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5283 if (!C2 || C2->getType()->isPointerTy()) return 0;
5284 C = ConstantExpr::getMul(C, C2);
5291 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5292 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5293 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5294 if (LHS->getType() == RHS->getType())
5295 return ConstantExpr::getUDiv(LHS, RHS);
5300 break; // TODO: smax, umax.
5305 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5306 if (isa<SCEVConstant>(V)) return V;
5308 // If this instruction is evolved from a constant-evolving PHI, compute the
5309 // exit value from the loop without using SCEVs.
5310 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5311 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5312 const Loop *LI = (*this->LI)[I->getParent()];
5313 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5314 if (PHINode *PN = dyn_cast<PHINode>(I))
5315 if (PN->getParent() == LI->getHeader()) {
5316 // Okay, there is no closed form solution for the PHI node. Check
5317 // to see if the loop that contains it has a known backedge-taken
5318 // count. If so, we may be able to force computation of the exit
5320 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5321 if (const SCEVConstant *BTCC =
5322 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5323 // Okay, we know how many times the containing loop executes. If
5324 // this is a constant evolving PHI node, get the final value at
5325 // the specified iteration number.
5326 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5327 BTCC->getValue()->getValue(),
5329 if (RV) return getSCEV(RV);
5333 // Okay, this is an expression that we cannot symbolically evaluate
5334 // into a SCEV. Check to see if it's possible to symbolically evaluate
5335 // the arguments into constants, and if so, try to constant propagate the
5336 // result. This is particularly useful for computing loop exit values.
5337 if (CanConstantFold(I)) {
5338 SmallVector<Constant *, 4> Operands;
5339 bool MadeImprovement = false;
5340 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5341 Value *Op = I->getOperand(i);
5342 if (Constant *C = dyn_cast<Constant>(Op)) {
5343 Operands.push_back(C);
5347 // If any of the operands is non-constant and if they are
5348 // non-integer and non-pointer, don't even try to analyze them
5349 // with scev techniques.
5350 if (!isSCEVable(Op->getType()))
5353 const SCEV *OrigV = getSCEV(Op);
5354 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5355 MadeImprovement |= OrigV != OpV;
5357 Constant *C = BuildConstantFromSCEV(OpV);
5359 if (C->getType() != Op->getType())
5360 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5364 Operands.push_back(C);
5367 // Check to see if getSCEVAtScope actually made an improvement.
5368 if (MadeImprovement) {
5370 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5371 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5372 Operands[0], Operands[1], DL,
5374 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5375 if (!LI->isVolatile())
5376 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5378 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5386 // This is some other type of SCEVUnknown, just return it.
5390 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5391 // Avoid performing the look-up in the common case where the specified
5392 // expression has no loop-variant portions.
5393 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5394 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5395 if (OpAtScope != Comm->getOperand(i)) {
5396 // Okay, at least one of these operands is loop variant but might be
5397 // foldable. Build a new instance of the folded commutative expression.
5398 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5399 Comm->op_begin()+i);
5400 NewOps.push_back(OpAtScope);
5402 for (++i; i != e; ++i) {
5403 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5404 NewOps.push_back(OpAtScope);
5406 if (isa<SCEVAddExpr>(Comm))
5407 return getAddExpr(NewOps);
5408 if (isa<SCEVMulExpr>(Comm))
5409 return getMulExpr(NewOps);
5410 if (isa<SCEVSMaxExpr>(Comm))
5411 return getSMaxExpr(NewOps);
5412 if (isa<SCEVUMaxExpr>(Comm))
5413 return getUMaxExpr(NewOps);
5414 llvm_unreachable("Unknown commutative SCEV type!");
5417 // If we got here, all operands are loop invariant.
5421 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5422 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5423 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5424 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5425 return Div; // must be loop invariant
5426 return getUDivExpr(LHS, RHS);
5429 // If this is a loop recurrence for a loop that does not contain L, then we
5430 // are dealing with the final value computed by the loop.
5431 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5432 // First, attempt to evaluate each operand.
5433 // Avoid performing the look-up in the common case where the specified
5434 // expression has no loop-variant portions.
5435 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5436 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5437 if (OpAtScope == AddRec->getOperand(i))
5440 // Okay, at least one of these operands is loop variant but might be
5441 // foldable. Build a new instance of the folded commutative expression.
5442 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5443 AddRec->op_begin()+i);
5444 NewOps.push_back(OpAtScope);
5445 for (++i; i != e; ++i)
5446 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5448 const SCEV *FoldedRec =
5449 getAddRecExpr(NewOps, AddRec->getLoop(),
5450 AddRec->getNoWrapFlags(SCEV::FlagNW));
5451 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5452 // The addrec may be folded to a nonrecurrence, for example, if the
5453 // induction variable is multiplied by zero after constant folding. Go
5454 // ahead and return the folded value.
5460 // If the scope is outside the addrec's loop, evaluate it by using the
5461 // loop exit value of the addrec.
5462 if (!AddRec->getLoop()->contains(L)) {
5463 // To evaluate this recurrence, we need to know how many times the AddRec
5464 // loop iterates. Compute this now.
5465 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5466 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5468 // Then, evaluate the AddRec.
5469 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5475 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5476 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5477 if (Op == Cast->getOperand())
5478 return Cast; // must be loop invariant
5479 return getZeroExtendExpr(Op, Cast->getType());
5482 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5483 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5484 if (Op == Cast->getOperand())
5485 return Cast; // must be loop invariant
5486 return getSignExtendExpr(Op, Cast->getType());
5489 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5490 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5491 if (Op == Cast->getOperand())
5492 return Cast; // must be loop invariant
5493 return getTruncateExpr(Op, Cast->getType());
5496 llvm_unreachable("Unknown SCEV type!");
5499 /// getSCEVAtScope - This is a convenience function which does
5500 /// getSCEVAtScope(getSCEV(V), L).
5501 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5502 return getSCEVAtScope(getSCEV(V), L);
5505 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5506 /// following equation:
5508 /// A * X = B (mod N)
5510 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5511 /// A and B isn't important.
5513 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5514 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5515 ScalarEvolution &SE) {
5516 uint32_t BW = A.getBitWidth();
5517 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5518 assert(A != 0 && "A must be non-zero.");
5522 // The gcd of A and N may have only one prime factor: 2. The number of
5523 // trailing zeros in A is its multiplicity
5524 uint32_t Mult2 = A.countTrailingZeros();
5527 // 2. Check if B is divisible by D.
5529 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5530 // is not less than multiplicity of this prime factor for D.
5531 if (B.countTrailingZeros() < Mult2)
5532 return SE.getCouldNotCompute();
5534 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5537 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5538 // bit width during computations.
5539 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5540 APInt Mod(BW + 1, 0);
5541 Mod.setBit(BW - Mult2); // Mod = N / D
5542 APInt I = AD.multiplicativeInverse(Mod);
5544 // 4. Compute the minimum unsigned root of the equation:
5545 // I * (B / D) mod (N / D)
5546 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5548 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5550 return SE.getConstant(Result.trunc(BW));
5553 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5554 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5555 /// might be the same) or two SCEVCouldNotCompute objects.
5557 static std::pair<const SCEV *,const SCEV *>
5558 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5559 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5560 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5561 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5562 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5564 // We currently can only solve this if the coefficients are constants.
5565 if (!LC || !MC || !NC) {
5566 const SCEV *CNC = SE.getCouldNotCompute();
5567 return std::make_pair(CNC, CNC);
5570 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5571 const APInt &L = LC->getValue()->getValue();
5572 const APInt &M = MC->getValue()->getValue();
5573 const APInt &N = NC->getValue()->getValue();
5574 APInt Two(BitWidth, 2);
5575 APInt Four(BitWidth, 4);
5578 using namespace APIntOps;
5580 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5581 // The B coefficient is M-N/2
5585 // The A coefficient is N/2
5586 APInt A(N.sdiv(Two));
5588 // Compute the B^2-4ac term.
5591 SqrtTerm -= Four * (A * C);
5593 if (SqrtTerm.isNegative()) {
5594 // The loop is provably infinite.
5595 const SCEV *CNC = SE.getCouldNotCompute();
5596 return std::make_pair(CNC, CNC);
5599 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5600 // integer value or else APInt::sqrt() will assert.
5601 APInt SqrtVal(SqrtTerm.sqrt());
5603 // Compute the two solutions for the quadratic formula.
5604 // The divisions must be performed as signed divisions.
5607 if (TwoA.isMinValue()) {
5608 const SCEV *CNC = SE.getCouldNotCompute();
5609 return std::make_pair(CNC, CNC);
5612 LLVMContext &Context = SE.getContext();
5614 ConstantInt *Solution1 =
5615 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5616 ConstantInt *Solution2 =
5617 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5619 return std::make_pair(SE.getConstant(Solution1),
5620 SE.getConstant(Solution2));
5621 } // end APIntOps namespace
5624 /// HowFarToZero - Return the number of times a backedge comparing the specified
5625 /// value to zero will execute. If not computable, return CouldNotCompute.
5627 /// This is only used for loops with a "x != y" exit test. The exit condition is
5628 /// now expressed as a single expression, V = x-y. So the exit test is
5629 /// effectively V != 0. We know and take advantage of the fact that this
5630 /// expression only being used in a comparison by zero context.
5631 ScalarEvolution::ExitLimit
5632 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
5633 // If the value is a constant
5634 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5635 // If the value is already zero, the branch will execute zero times.
5636 if (C->getValue()->isZero()) return C;
5637 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5640 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5641 if (!AddRec || AddRec->getLoop() != L)
5642 return getCouldNotCompute();
5644 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5645 // the quadratic equation to solve it.
5646 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5647 std::pair<const SCEV *,const SCEV *> Roots =
5648 SolveQuadraticEquation(AddRec, *this);
5649 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5650 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5653 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5654 << " sol#2: " << *R2 << "\n";
5656 // Pick the smallest positive root value.
5657 if (ConstantInt *CB =
5658 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5661 if (CB->getZExtValue() == false)
5662 std::swap(R1, R2); // R1 is the minimum root now.
5664 // We can only use this value if the chrec ends up with an exact zero
5665 // value at this index. When solving for "X*X != 5", for example, we
5666 // should not accept a root of 2.
5667 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5669 return R1; // We found a quadratic root!
5672 return getCouldNotCompute();
5675 // Otherwise we can only handle this if it is affine.
5676 if (!AddRec->isAffine())
5677 return getCouldNotCompute();
5679 // If this is an affine expression, the execution count of this branch is
5680 // the minimum unsigned root of the following equation:
5682 // Start + Step*N = 0 (mod 2^BW)
5686 // Step*N = -Start (mod 2^BW)
5688 // where BW is the common bit width of Start and Step.
5690 // Get the initial value for the loop.
5691 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5692 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5694 // For now we handle only constant steps.
5696 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5697 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5698 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5699 // We have not yet seen any such cases.
5700 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5701 if (StepC == 0 || StepC->getValue()->equalsInt(0))
5702 return getCouldNotCompute();
5704 // For positive steps (counting up until unsigned overflow):
5705 // N = -Start/Step (as unsigned)
5706 // For negative steps (counting down to zero):
5708 // First compute the unsigned distance from zero in the direction of Step.
5709 bool CountDown = StepC->getValue()->getValue().isNegative();
5710 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5712 // Handle unitary steps, which cannot wraparound.
5713 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5714 // N = Distance (as unsigned)
5715 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5716 ConstantRange CR = getUnsignedRange(Start);
5717 const SCEV *MaxBECount;
5718 if (!CountDown && CR.getUnsignedMin().isMinValue())
5719 // When counting up, the worst starting value is 1, not 0.
5720 MaxBECount = CR.getUnsignedMax().isMinValue()
5721 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5722 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5724 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5725 : -CR.getUnsignedMin());
5726 return ExitLimit(Distance, MaxBECount, /*MustExit=*/true);
5729 // If the recurrence is known not to wraparound, unsigned divide computes the
5730 // back edge count. (Ideally we would have an "isexact" bit for udiv). We know
5731 // that the value will either become zero (and thus the loop terminates), that
5732 // the loop will terminate through some other exit condition first, or that
5733 // the loop has undefined behavior. This means we can't "miss" the exit
5734 // value, even with nonunit stride, and exit later via the same branch. Note
5735 // that we can skip this exit if loop later exits via a different
5736 // branch. Hence MustExit=false.
5738 // This is only valid for expressions that directly compute the loop exit. It
5739 // is invalid for subexpressions in which the loop may exit through this
5740 // branch even if this subexpression is false. In that case, the trip count
5741 // computed by this udiv could be smaller than the number of well-defined
5743 if (!IsSubExpr && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5745 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5746 return ExitLimit(Exact, Exact, /*MustExit=*/false);
5748 // Then, try to solve the above equation provided that Start is constant.
5749 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5750 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5751 -StartC->getValue()->getValue(),
5753 return getCouldNotCompute();
5756 /// HowFarToNonZero - Return the number of times a backedge checking the
5757 /// specified value for nonzero will execute. If not computable, return
5759 ScalarEvolution::ExitLimit
5760 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5761 // Loops that look like: while (X == 0) are very strange indeed. We don't
5762 // handle them yet except for the trivial case. This could be expanded in the
5763 // future as needed.
5765 // If the value is a constant, check to see if it is known to be non-zero
5766 // already. If so, the backedge will execute zero times.
5767 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5768 if (!C->getValue()->isNullValue())
5769 return getConstant(C->getType(), 0);
5770 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5773 // We could implement others, but I really doubt anyone writes loops like
5774 // this, and if they did, they would already be constant folded.
5775 return getCouldNotCompute();
5778 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5779 /// (which may not be an immediate predecessor) which has exactly one
5780 /// successor from which BB is reachable, or null if no such block is
5783 std::pair<BasicBlock *, BasicBlock *>
5784 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5785 // If the block has a unique predecessor, then there is no path from the
5786 // predecessor to the block that does not go through the direct edge
5787 // from the predecessor to the block.
5788 if (BasicBlock *Pred = BB->getSinglePredecessor())
5789 return std::make_pair(Pred, BB);
5791 // A loop's header is defined to be a block that dominates the loop.
5792 // If the header has a unique predecessor outside the loop, it must be
5793 // a block that has exactly one successor that can reach the loop.
5794 if (Loop *L = LI->getLoopFor(BB))
5795 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5797 return std::pair<BasicBlock *, BasicBlock *>();
5800 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5801 /// testing whether two expressions are equal, however for the purposes of
5802 /// looking for a condition guarding a loop, it can be useful to be a little
5803 /// more general, since a front-end may have replicated the controlling
5806 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5807 // Quick check to see if they are the same SCEV.
5808 if (A == B) return true;
5810 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5811 // two different instructions with the same value. Check for this case.
5812 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5813 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5814 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5815 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5816 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5819 // Otherwise assume they may have a different value.
5823 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5824 /// predicate Pred. Return true iff any changes were made.
5826 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5827 const SCEV *&LHS, const SCEV *&RHS,
5829 bool Changed = false;
5831 // If we hit the max recursion limit bail out.
5835 // Canonicalize a constant to the right side.
5836 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5837 // Check for both operands constant.
5838 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5839 if (ConstantExpr::getICmp(Pred,
5841 RHSC->getValue())->isNullValue())
5842 goto trivially_false;
5844 goto trivially_true;
5846 // Otherwise swap the operands to put the constant on the right.
5847 std::swap(LHS, RHS);
5848 Pred = ICmpInst::getSwappedPredicate(Pred);
5852 // If we're comparing an addrec with a value which is loop-invariant in the
5853 // addrec's loop, put the addrec on the left. Also make a dominance check,
5854 // as both operands could be addrecs loop-invariant in each other's loop.
5855 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5856 const Loop *L = AR->getLoop();
5857 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5858 std::swap(LHS, RHS);
5859 Pred = ICmpInst::getSwappedPredicate(Pred);
5864 // If there's a constant operand, canonicalize comparisons with boundary
5865 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5866 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5867 const APInt &RA = RC->getValue()->getValue();
5869 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5870 case ICmpInst::ICMP_EQ:
5871 case ICmpInst::ICMP_NE:
5872 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5874 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5875 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5876 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5877 ME->getOperand(0)->isAllOnesValue()) {
5878 RHS = AE->getOperand(1);
5879 LHS = ME->getOperand(1);
5883 case ICmpInst::ICMP_UGE:
5884 if ((RA - 1).isMinValue()) {
5885 Pred = ICmpInst::ICMP_NE;
5886 RHS = getConstant(RA - 1);
5890 if (RA.isMaxValue()) {
5891 Pred = ICmpInst::ICMP_EQ;
5895 if (RA.isMinValue()) goto trivially_true;
5897 Pred = ICmpInst::ICMP_UGT;
5898 RHS = getConstant(RA - 1);
5901 case ICmpInst::ICMP_ULE:
5902 if ((RA + 1).isMaxValue()) {
5903 Pred = ICmpInst::ICMP_NE;
5904 RHS = getConstant(RA + 1);
5908 if (RA.isMinValue()) {
5909 Pred = ICmpInst::ICMP_EQ;
5913 if (RA.isMaxValue()) goto trivially_true;
5915 Pred = ICmpInst::ICMP_ULT;
5916 RHS = getConstant(RA + 1);
5919 case ICmpInst::ICMP_SGE:
5920 if ((RA - 1).isMinSignedValue()) {
5921 Pred = ICmpInst::ICMP_NE;
5922 RHS = getConstant(RA - 1);
5926 if (RA.isMaxSignedValue()) {
5927 Pred = ICmpInst::ICMP_EQ;
5931 if (RA.isMinSignedValue()) goto trivially_true;
5933 Pred = ICmpInst::ICMP_SGT;
5934 RHS = getConstant(RA - 1);
5937 case ICmpInst::ICMP_SLE:
5938 if ((RA + 1).isMaxSignedValue()) {
5939 Pred = ICmpInst::ICMP_NE;
5940 RHS = getConstant(RA + 1);
5944 if (RA.isMinSignedValue()) {
5945 Pred = ICmpInst::ICMP_EQ;
5949 if (RA.isMaxSignedValue()) goto trivially_true;
5951 Pred = ICmpInst::ICMP_SLT;
5952 RHS = getConstant(RA + 1);
5955 case ICmpInst::ICMP_UGT:
5956 if (RA.isMinValue()) {
5957 Pred = ICmpInst::ICMP_NE;
5961 if ((RA + 1).isMaxValue()) {
5962 Pred = ICmpInst::ICMP_EQ;
5963 RHS = getConstant(RA + 1);
5967 if (RA.isMaxValue()) goto trivially_false;
5969 case ICmpInst::ICMP_ULT:
5970 if (RA.isMaxValue()) {
5971 Pred = ICmpInst::ICMP_NE;
5975 if ((RA - 1).isMinValue()) {
5976 Pred = ICmpInst::ICMP_EQ;
5977 RHS = getConstant(RA - 1);
5981 if (RA.isMinValue()) goto trivially_false;
5983 case ICmpInst::ICMP_SGT:
5984 if (RA.isMinSignedValue()) {
5985 Pred = ICmpInst::ICMP_NE;
5989 if ((RA + 1).isMaxSignedValue()) {
5990 Pred = ICmpInst::ICMP_EQ;
5991 RHS = getConstant(RA + 1);
5995 if (RA.isMaxSignedValue()) goto trivially_false;
5997 case ICmpInst::ICMP_SLT:
5998 if (RA.isMaxSignedValue()) {
5999 Pred = ICmpInst::ICMP_NE;
6003 if ((RA - 1).isMinSignedValue()) {
6004 Pred = ICmpInst::ICMP_EQ;
6005 RHS = getConstant(RA - 1);
6009 if (RA.isMinSignedValue()) goto trivially_false;
6014 // Check for obvious equality.
6015 if (HasSameValue(LHS, RHS)) {
6016 if (ICmpInst::isTrueWhenEqual(Pred))
6017 goto trivially_true;
6018 if (ICmpInst::isFalseWhenEqual(Pred))
6019 goto trivially_false;
6022 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6023 // adding or subtracting 1 from one of the operands.
6025 case ICmpInst::ICMP_SLE:
6026 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6027 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6029 Pred = ICmpInst::ICMP_SLT;
6031 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6032 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6034 Pred = ICmpInst::ICMP_SLT;
6038 case ICmpInst::ICMP_SGE:
6039 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6040 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6042 Pred = ICmpInst::ICMP_SGT;
6044 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6045 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6047 Pred = ICmpInst::ICMP_SGT;
6051 case ICmpInst::ICMP_ULE:
6052 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6053 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6055 Pred = ICmpInst::ICMP_ULT;
6057 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6058 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6060 Pred = ICmpInst::ICMP_ULT;
6064 case ICmpInst::ICMP_UGE:
6065 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6066 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6068 Pred = ICmpInst::ICMP_UGT;
6070 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6071 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6073 Pred = ICmpInst::ICMP_UGT;
6081 // TODO: More simplifications are possible here.
6083 // Recursively simplify until we either hit a recursion limit or nothing
6086 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6092 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6093 Pred = ICmpInst::ICMP_EQ;
6098 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6099 Pred = ICmpInst::ICMP_NE;
6103 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6104 return getSignedRange(S).getSignedMax().isNegative();
6107 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6108 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6111 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6112 return !getSignedRange(S).getSignedMin().isNegative();
6115 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6116 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6119 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6120 return isKnownNegative(S) || isKnownPositive(S);
6123 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6124 const SCEV *LHS, const SCEV *RHS) {
6125 // Canonicalize the inputs first.
6126 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6128 // If LHS or RHS is an addrec, check to see if the condition is true in
6129 // every iteration of the loop.
6130 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
6131 if (isLoopEntryGuardedByCond(
6132 AR->getLoop(), Pred, AR->getStart(), RHS) &&
6133 isLoopBackedgeGuardedByCond(
6134 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
6136 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
6137 if (isLoopEntryGuardedByCond(
6138 AR->getLoop(), Pred, LHS, AR->getStart()) &&
6139 isLoopBackedgeGuardedByCond(
6140 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
6143 // Otherwise see what can be done with known constant ranges.
6144 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6148 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6149 const SCEV *LHS, const SCEV *RHS) {
6150 if (HasSameValue(LHS, RHS))
6151 return ICmpInst::isTrueWhenEqual(Pred);
6153 // This code is split out from isKnownPredicate because it is called from
6154 // within isLoopEntryGuardedByCond.
6157 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6158 case ICmpInst::ICMP_SGT:
6159 Pred = ICmpInst::ICMP_SLT;
6160 std::swap(LHS, RHS);
6161 case ICmpInst::ICMP_SLT: {
6162 ConstantRange LHSRange = getSignedRange(LHS);
6163 ConstantRange RHSRange = getSignedRange(RHS);
6164 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6166 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6170 case ICmpInst::ICMP_SGE:
6171 Pred = ICmpInst::ICMP_SLE;
6172 std::swap(LHS, RHS);
6173 case ICmpInst::ICMP_SLE: {
6174 ConstantRange LHSRange = getSignedRange(LHS);
6175 ConstantRange RHSRange = getSignedRange(RHS);
6176 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6178 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6182 case ICmpInst::ICMP_UGT:
6183 Pred = ICmpInst::ICMP_ULT;
6184 std::swap(LHS, RHS);
6185 case ICmpInst::ICMP_ULT: {
6186 ConstantRange LHSRange = getUnsignedRange(LHS);
6187 ConstantRange RHSRange = getUnsignedRange(RHS);
6188 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6190 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6194 case ICmpInst::ICMP_UGE:
6195 Pred = ICmpInst::ICMP_ULE;
6196 std::swap(LHS, RHS);
6197 case ICmpInst::ICMP_ULE: {
6198 ConstantRange LHSRange = getUnsignedRange(LHS);
6199 ConstantRange RHSRange = getUnsignedRange(RHS);
6200 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6202 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6206 case ICmpInst::ICMP_NE: {
6207 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6209 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6212 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6213 if (isKnownNonZero(Diff))
6217 case ICmpInst::ICMP_EQ:
6218 // The check at the top of the function catches the case where
6219 // the values are known to be equal.
6225 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6226 /// protected by a conditional between LHS and RHS. This is used to
6227 /// to eliminate casts.
6229 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6230 ICmpInst::Predicate Pred,
6231 const SCEV *LHS, const SCEV *RHS) {
6232 // Interpret a null as meaning no loop, where there is obviously no guard
6233 // (interprocedural conditions notwithstanding).
6234 if (!L) return true;
6236 BasicBlock *Latch = L->getLoopLatch();
6240 BranchInst *LoopContinuePredicate =
6241 dyn_cast<BranchInst>(Latch->getTerminator());
6242 if (!LoopContinuePredicate ||
6243 LoopContinuePredicate->isUnconditional())
6246 return isImpliedCond(Pred, LHS, RHS,
6247 LoopContinuePredicate->getCondition(),
6248 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6251 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6252 /// by a conditional between LHS and RHS. This is used to help avoid max
6253 /// expressions in loop trip counts, and to eliminate casts.
6255 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6256 ICmpInst::Predicate Pred,
6257 const SCEV *LHS, const SCEV *RHS) {
6258 // Interpret a null as meaning no loop, where there is obviously no guard
6259 // (interprocedural conditions notwithstanding).
6260 if (!L) return false;
6262 // Starting at the loop predecessor, climb up the predecessor chain, as long
6263 // as there are predecessors that can be found that have unique successors
6264 // leading to the original header.
6265 for (std::pair<BasicBlock *, BasicBlock *>
6266 Pair(L->getLoopPredecessor(), L->getHeader());
6268 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6270 BranchInst *LoopEntryPredicate =
6271 dyn_cast<BranchInst>(Pair.first->getTerminator());
6272 if (!LoopEntryPredicate ||
6273 LoopEntryPredicate->isUnconditional())
6276 if (isImpliedCond(Pred, LHS, RHS,
6277 LoopEntryPredicate->getCondition(),
6278 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6285 /// RAII wrapper to prevent recursive application of isImpliedCond.
6286 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6287 /// currently evaluating isImpliedCond.
6288 struct MarkPendingLoopPredicate {
6290 DenseSet<Value*> &LoopPreds;
6293 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6294 : Cond(C), LoopPreds(LP) {
6295 Pending = !LoopPreds.insert(Cond).second;
6297 ~MarkPendingLoopPredicate() {
6299 LoopPreds.erase(Cond);
6303 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6304 /// and RHS is true whenever the given Cond value evaluates to true.
6305 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6306 const SCEV *LHS, const SCEV *RHS,
6307 Value *FoundCondValue,
6309 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6313 // Recursively handle And and Or conditions.
6314 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6315 if (BO->getOpcode() == Instruction::And) {
6317 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6318 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6319 } else if (BO->getOpcode() == Instruction::Or) {
6321 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6322 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6326 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6327 if (!ICI) return false;
6329 // Bail if the ICmp's operands' types are wider than the needed type
6330 // before attempting to call getSCEV on them. This avoids infinite
6331 // recursion, since the analysis of widening casts can require loop
6332 // exit condition information for overflow checking, which would
6334 if (getTypeSizeInBits(LHS->getType()) <
6335 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6338 // Now that we found a conditional branch that dominates the loop or controls
6339 // the loop latch. Check to see if it is the comparison we are looking for.
6340 ICmpInst::Predicate FoundPred;
6342 FoundPred = ICI->getInversePredicate();
6344 FoundPred = ICI->getPredicate();
6346 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6347 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6349 // Balance the types. The case where FoundLHS' type is wider than
6350 // LHS' type is checked for above.
6351 if (getTypeSizeInBits(LHS->getType()) >
6352 getTypeSizeInBits(FoundLHS->getType())) {
6353 if (CmpInst::isSigned(FoundPred)) {
6354 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6355 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6357 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6358 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6362 // Canonicalize the query to match the way instcombine will have
6363 // canonicalized the comparison.
6364 if (SimplifyICmpOperands(Pred, LHS, RHS))
6366 return CmpInst::isTrueWhenEqual(Pred);
6367 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6368 if (FoundLHS == FoundRHS)
6369 return CmpInst::isFalseWhenEqual(FoundPred);
6371 // Check to see if we can make the LHS or RHS match.
6372 if (LHS == FoundRHS || RHS == FoundLHS) {
6373 if (isa<SCEVConstant>(RHS)) {
6374 std::swap(FoundLHS, FoundRHS);
6375 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6377 std::swap(LHS, RHS);
6378 Pred = ICmpInst::getSwappedPredicate(Pred);
6382 // Check whether the found predicate is the same as the desired predicate.
6383 if (FoundPred == Pred)
6384 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6386 // Check whether swapping the found predicate makes it the same as the
6387 // desired predicate.
6388 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6389 if (isa<SCEVConstant>(RHS))
6390 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6392 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6393 RHS, LHS, FoundLHS, FoundRHS);
6396 // Check whether the actual condition is beyond sufficient.
6397 if (FoundPred == ICmpInst::ICMP_EQ)
6398 if (ICmpInst::isTrueWhenEqual(Pred))
6399 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6401 if (Pred == ICmpInst::ICMP_NE)
6402 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6403 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6406 // Otherwise assume the worst.
6410 /// isImpliedCondOperands - Test whether the condition described by Pred,
6411 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6412 /// and FoundRHS is true.
6413 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6414 const SCEV *LHS, const SCEV *RHS,
6415 const SCEV *FoundLHS,
6416 const SCEV *FoundRHS) {
6417 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6418 FoundLHS, FoundRHS) ||
6419 // ~x < ~y --> x > y
6420 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6421 getNotSCEV(FoundRHS),
6422 getNotSCEV(FoundLHS));
6425 /// isImpliedCondOperandsHelper - Test whether the condition described by
6426 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6427 /// FoundLHS, and FoundRHS is true.
6429 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6430 const SCEV *LHS, const SCEV *RHS,
6431 const SCEV *FoundLHS,
6432 const SCEV *FoundRHS) {
6434 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6435 case ICmpInst::ICMP_EQ:
6436 case ICmpInst::ICMP_NE:
6437 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6440 case ICmpInst::ICMP_SLT:
6441 case ICmpInst::ICMP_SLE:
6442 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6443 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6446 case ICmpInst::ICMP_SGT:
6447 case ICmpInst::ICMP_SGE:
6448 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6449 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6452 case ICmpInst::ICMP_ULT:
6453 case ICmpInst::ICMP_ULE:
6454 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6455 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6458 case ICmpInst::ICMP_UGT:
6459 case ICmpInst::ICMP_UGE:
6460 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6461 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6469 // Verify if an linear IV with positive stride can overflow when in a
6470 // less-than comparison, knowing the invariant term of the comparison, the
6471 // stride and the knowledge of NSW/NUW flags on the recurrence.
6472 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
6473 bool IsSigned, bool NoWrap) {
6474 if (NoWrap) return false;
6476 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6477 const SCEV *One = getConstant(Stride->getType(), 1);
6480 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
6481 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
6482 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6485 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
6486 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
6489 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
6490 APInt MaxValue = APInt::getMaxValue(BitWidth);
6491 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6494 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
6495 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
6498 // Verify if an linear IV with negative stride can overflow when in a
6499 // greater-than comparison, knowing the invariant term of the comparison,
6500 // the stride and the knowledge of NSW/NUW flags on the recurrence.
6501 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
6502 bool IsSigned, bool NoWrap) {
6503 if (NoWrap) return false;
6505 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6506 const SCEV *One = getConstant(Stride->getType(), 1);
6509 APInt MinRHS = getSignedRange(RHS).getSignedMin();
6510 APInt MinValue = APInt::getSignedMinValue(BitWidth);
6511 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6514 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
6515 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
6518 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
6519 APInt MinValue = APInt::getMinValue(BitWidth);
6520 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6523 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
6524 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
6527 // Compute the backedge taken count knowing the interval difference, the
6528 // stride and presence of the equality in the comparison.
6529 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
6531 const SCEV *One = getConstant(Step->getType(), 1);
6532 Delta = Equality ? getAddExpr(Delta, Step)
6533 : getAddExpr(Delta, getMinusSCEV(Step, One));
6534 return getUDivExpr(Delta, Step);
6537 /// HowManyLessThans - Return the number of times a backedge containing the
6538 /// specified less-than comparison will execute. If not computable, return
6539 /// CouldNotCompute.
6541 /// @param IsSubExpr is true when the LHS < RHS condition does not directly
6542 /// control the branch. In this case, we can only compute an iteration count for
6543 /// a subexpression that cannot overflow before evaluating true.
6544 ScalarEvolution::ExitLimit
6545 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6546 const Loop *L, bool IsSigned,
6548 // We handle only IV < Invariant
6549 if (!isLoopInvariant(RHS, L))
6550 return getCouldNotCompute();
6552 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6554 // Avoid weird loops
6555 if (!IV || IV->getLoop() != L || !IV->isAffine())
6556 return getCouldNotCompute();
6558 bool NoWrap = !IsSubExpr &&
6559 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6561 const SCEV *Stride = IV->getStepRecurrence(*this);
6563 // Avoid negative or zero stride values
6564 if (!isKnownPositive(Stride))
6565 return getCouldNotCompute();
6567 // Avoid proven overflow cases: this will ensure that the backedge taken count
6568 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6569 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6570 // behaviors like the case of C language.
6571 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
6572 return getCouldNotCompute();
6574 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
6575 : ICmpInst::ICMP_ULT;
6576 const SCEV *Start = IV->getStart();
6577 const SCEV *End = RHS;
6578 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
6579 End = IsSigned ? getSMaxExpr(RHS, Start)
6580 : getUMaxExpr(RHS, Start);
6582 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
6584 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
6585 : getUnsignedRange(Start).getUnsignedMin();
6587 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6588 : getUnsignedRange(Stride).getUnsignedMin();
6590 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6591 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
6592 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
6594 // Although End can be a MAX expression we estimate MaxEnd considering only
6595 // the case End = RHS. This is safe because in the other case (End - Start)
6596 // is zero, leading to a zero maximum backedge taken count.
6598 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
6599 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
6601 const SCEV *MaxBECount = getCouldNotCompute();
6602 if (isa<SCEVConstant>(BECount))
6603 MaxBECount = BECount;
6605 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
6606 getConstant(MinStride), false);
6608 if (isa<SCEVCouldNotCompute>(MaxBECount))
6609 MaxBECount = BECount;
6611 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6614 ScalarEvolution::ExitLimit
6615 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
6616 const Loop *L, bool IsSigned,
6618 // We handle only IV > Invariant
6619 if (!isLoopInvariant(RHS, L))
6620 return getCouldNotCompute();
6622 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6624 // Avoid weird loops
6625 if (!IV || IV->getLoop() != L || !IV->isAffine())
6626 return getCouldNotCompute();
6628 bool NoWrap = !IsSubExpr &&
6629 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6631 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
6633 // Avoid negative or zero stride values
6634 if (!isKnownPositive(Stride))
6635 return getCouldNotCompute();
6637 // Avoid proven overflow cases: this will ensure that the backedge taken count
6638 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6639 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6640 // behaviors like the case of C language.
6641 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
6642 return getCouldNotCompute();
6644 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
6645 : ICmpInst::ICMP_UGT;
6647 const SCEV *Start = IV->getStart();
6648 const SCEV *End = RHS;
6649 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
6650 End = IsSigned ? getSMinExpr(RHS, Start)
6651 : getUMinExpr(RHS, Start);
6653 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
6655 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
6656 : getUnsignedRange(Start).getUnsignedMax();
6658 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6659 : getUnsignedRange(Stride).getUnsignedMin();
6661 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6662 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
6663 : APInt::getMinValue(BitWidth) + (MinStride - 1);
6665 // Although End can be a MIN expression we estimate MinEnd considering only
6666 // the case End = RHS. This is safe because in the other case (Start - End)
6667 // is zero, leading to a zero maximum backedge taken count.
6669 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
6670 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
6673 const SCEV *MaxBECount = getCouldNotCompute();
6674 if (isa<SCEVConstant>(BECount))
6675 MaxBECount = BECount;
6677 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
6678 getConstant(MinStride), false);
6680 if (isa<SCEVCouldNotCompute>(MaxBECount))
6681 MaxBECount = BECount;
6683 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6686 /// getNumIterationsInRange - Return the number of iterations of this loop that
6687 /// produce values in the specified constant range. Another way of looking at
6688 /// this is that it returns the first iteration number where the value is not in
6689 /// the condition, thus computing the exit count. If the iteration count can't
6690 /// be computed, an instance of SCEVCouldNotCompute is returned.
6691 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6692 ScalarEvolution &SE) const {
6693 if (Range.isFullSet()) // Infinite loop.
6694 return SE.getCouldNotCompute();
6696 // If the start is a non-zero constant, shift the range to simplify things.
6697 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6698 if (!SC->getValue()->isZero()) {
6699 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6700 Operands[0] = SE.getConstant(SC->getType(), 0);
6701 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6702 getNoWrapFlags(FlagNW));
6703 if (const SCEVAddRecExpr *ShiftedAddRec =
6704 dyn_cast<SCEVAddRecExpr>(Shifted))
6705 return ShiftedAddRec->getNumIterationsInRange(
6706 Range.subtract(SC->getValue()->getValue()), SE);
6707 // This is strange and shouldn't happen.
6708 return SE.getCouldNotCompute();
6711 // The only time we can solve this is when we have all constant indices.
6712 // Otherwise, we cannot determine the overflow conditions.
6713 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6714 if (!isa<SCEVConstant>(getOperand(i)))
6715 return SE.getCouldNotCompute();
6718 // Okay at this point we know that all elements of the chrec are constants and
6719 // that the start element is zero.
6721 // First check to see if the range contains zero. If not, the first
6723 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6724 if (!Range.contains(APInt(BitWidth, 0)))
6725 return SE.getConstant(getType(), 0);
6728 // If this is an affine expression then we have this situation:
6729 // Solve {0,+,A} in Range === Ax in Range
6731 // We know that zero is in the range. If A is positive then we know that
6732 // the upper value of the range must be the first possible exit value.
6733 // If A is negative then the lower of the range is the last possible loop
6734 // value. Also note that we already checked for a full range.
6735 APInt One(BitWidth,1);
6736 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6737 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6739 // The exit value should be (End+A)/A.
6740 APInt ExitVal = (End + A).udiv(A);
6741 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6743 // Evaluate at the exit value. If we really did fall out of the valid
6744 // range, then we computed our trip count, otherwise wrap around or other
6745 // things must have happened.
6746 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6747 if (Range.contains(Val->getValue()))
6748 return SE.getCouldNotCompute(); // Something strange happened
6750 // Ensure that the previous value is in the range. This is a sanity check.
6751 assert(Range.contains(
6752 EvaluateConstantChrecAtConstant(this,
6753 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6754 "Linear scev computation is off in a bad way!");
6755 return SE.getConstant(ExitValue);
6756 } else if (isQuadratic()) {
6757 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6758 // quadratic equation to solve it. To do this, we must frame our problem in
6759 // terms of figuring out when zero is crossed, instead of when
6760 // Range.getUpper() is crossed.
6761 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6762 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6763 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6764 // getNoWrapFlags(FlagNW)
6767 // Next, solve the constructed addrec
6768 std::pair<const SCEV *,const SCEV *> Roots =
6769 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6770 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6771 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6773 // Pick the smallest positive root value.
6774 if (ConstantInt *CB =
6775 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6776 R1->getValue(), R2->getValue()))) {
6777 if (CB->getZExtValue() == false)
6778 std::swap(R1, R2); // R1 is the minimum root now.
6780 // Make sure the root is not off by one. The returned iteration should
6781 // not be in the range, but the previous one should be. When solving
6782 // for "X*X < 5", for example, we should not return a root of 2.
6783 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6786 if (Range.contains(R1Val->getValue())) {
6787 // The next iteration must be out of the range...
6788 ConstantInt *NextVal =
6789 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6791 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6792 if (!Range.contains(R1Val->getValue()))
6793 return SE.getConstant(NextVal);
6794 return SE.getCouldNotCompute(); // Something strange happened
6797 // If R1 was not in the range, then it is a good return value. Make
6798 // sure that R1-1 WAS in the range though, just in case.
6799 ConstantInt *NextVal =
6800 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6801 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6802 if (Range.contains(R1Val->getValue()))
6804 return SE.getCouldNotCompute(); // Something strange happened
6809 return SE.getCouldNotCompute();
6812 static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
6813 APInt A = C1->getValue()->getValue();
6814 APInt B = C2->getValue()->getValue();
6815 uint32_t ABW = A.getBitWidth();
6816 uint32_t BBW = B.getBitWidth();
6823 return APIntOps::srem(A, B);
6826 static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
6827 APInt A = C1->getValue()->getValue();
6828 APInt B = C2->getValue()->getValue();
6829 uint32_t ABW = A.getBitWidth();
6830 uint32_t BBW = B.getBitWidth();
6837 return APIntOps::sdiv(A, B);
6841 struct SCEVGCD : public SCEVVisitor<SCEVGCD, const SCEV *> {
6843 // Pattern match Step into Start. When Step is a multiply expression, find
6844 // the largest subexpression of Step that appears in Start. When Start is an
6845 // add expression, try to match Step in the subexpressions of Start, non
6846 // matching subexpressions are returned under Remainder.
6847 static const SCEV *findGCD(ScalarEvolution &SE, const SCEV *Start,
6848 const SCEV *Step, const SCEV **Remainder) {
6849 assert(Remainder && "Remainder should not be NULL");
6850 SCEVGCD R(SE, Step, SE.getConstant(Step->getType(), 0));
6851 const SCEV *Res = R.visit(Start);
6852 *Remainder = R.Remainder;
6856 SCEVGCD(ScalarEvolution &S, const SCEV *G, const SCEV *R)
6857 : SE(S), GCD(G), Remainder(R) {
6858 Zero = SE.getConstant(GCD->getType(), 0);
6859 One = SE.getConstant(GCD->getType(), 1);
6862 const SCEV *visitConstant(const SCEVConstant *Constant) {
6863 if (GCD == Constant || Constant == Zero)
6866 if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD)) {
6867 const SCEV *Res = SE.getConstant(gcd(Constant, CGCD));
6871 Remainder = SE.getConstant(srem(Constant, CGCD));
6872 Constant = cast<SCEVConstant>(SE.getMinusSCEV(Constant, Remainder));
6873 Res = SE.getConstant(gcd(Constant, CGCD));
6877 // When GCD is not a constant, it could be that the GCD is an Add, Mul,
6878 // AddRec, etc., in which case we want to find out how many times the
6879 // Constant divides the GCD: we then return that as the new GCD.
6880 const SCEV *Rem = Zero;
6881 const SCEV *Res = findGCD(SE, GCD, Constant, &Rem);
6883 if (Res == One || Rem != Zero) {
6884 Remainder = Constant;
6888 assert(isa<SCEVConstant>(Res) && "Res should be a constant");
6889 Remainder = SE.getConstant(srem(Constant, cast<SCEVConstant>(Res)));
6893 const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
6899 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
6905 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
6911 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
6915 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6916 const SCEV *Rem = Zero;
6917 const SCEV *Res = findGCD(SE, Expr->getOperand(e - 1 - i), GCD, &Rem);
6919 // FIXME: There may be ambiguous situations: for instance,
6920 // GCD(-4 + (3 * %m), 2 * %m) where 2 divides -4 and %m divides (3 * %m).
6921 // The order in which the AddExpr is traversed computes a different GCD
6926 Remainder = SE.getAddExpr(Remainder, Rem);
6932 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
6936 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6937 if (Expr->getOperand(i) == GCD)
6941 // If we have not returned yet, it means that GCD is not part of Expr.
6942 const SCEV *PartialGCD = One;
6943 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6944 const SCEV *Rem = Zero;
6945 const SCEV *Res = findGCD(SE, Expr->getOperand(i), GCD, &Rem);
6947 // GCD does not divide Expr->getOperand(i).
6952 PartialGCD = SE.getMulExpr(PartialGCD, Res);
6953 if (PartialGCD == GCD)
6957 if (PartialGCD != One)
6961 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(GCD);
6965 // When the GCD is a multiply expression, try to decompose it:
6966 // this occurs when Step does not divide the Start expression
6967 // as in: {(-4 + (3 * %m)),+,(2 * %m)}
6968 for (int i = 0, e = Mul->getNumOperands(); i < e; ++i) {
6969 const SCEV *Rem = Zero;
6970 const SCEV *Res = findGCD(SE, Expr, Mul->getOperand(i), &Rem);
6980 const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
6986 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
6990 if (!Expr->isAffine()) {
6995 const SCEV *Rem = Zero;
6996 const SCEV *Res = findGCD(SE, Expr->getOperand(0), GCD, &Rem);
6998 Remainder = SE.getAddExpr(Remainder, Rem);
7001 Res = findGCD(SE, Expr->getOperand(1), Res, &Rem);
7010 const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
7016 const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
7022 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
7028 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
7033 ScalarEvolution &SE;
7034 const SCEV *GCD, *Remainder, *Zero, *One;
7037 struct SCEVDivision : public SCEVVisitor<SCEVDivision, const SCEV *> {
7039 // Remove from Start all multiples of Step.
7040 static const SCEV *divide(ScalarEvolution &SE, const SCEV *Start,
7042 SCEVDivision D(SE, Step);
7043 const SCEV *Rem = D.Zero;
7045 // The division is guaranteed to succeed: Step should divide Start with no
7047 assert(Step == SCEVGCD::findGCD(SE, Start, Step, &Rem) && Rem == D.Zero &&
7048 "Step should divide Start with no remainder.");
7049 return D.visit(Start);
7052 SCEVDivision(ScalarEvolution &S, const SCEV *G) : SE(S), GCD(G) {
7053 Zero = SE.getConstant(GCD->getType(), 0);
7054 One = SE.getConstant(GCD->getType(), 1);
7057 const SCEV *visitConstant(const SCEVConstant *Constant) {
7058 if (GCD == Constant)
7061 if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD))
7062 return SE.getConstant(sdiv(Constant, CGCD));
7066 const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
7072 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
7078 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
7084 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
7088 SmallVector<const SCEV *, 2> Operands;
7089 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
7090 Operands.push_back(divide(SE, Expr->getOperand(i), GCD));
7092 if (Operands.size() == 1)
7094 return SE.getAddExpr(Operands);
7097 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
7101 bool FoundGCDTerm = false;
7102 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
7103 if (Expr->getOperand(i) == GCD)
7104 FoundGCDTerm = true;
7106 SmallVector<const SCEV *, 2> Operands;
7108 FoundGCDTerm = false;
7109 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
7111 Operands.push_back(Expr->getOperand(i));
7112 else if (Expr->getOperand(i) == GCD)
7113 FoundGCDTerm = true;
7115 Operands.push_back(Expr->getOperand(i));
7118 FoundGCDTerm = false;
7119 const SCEV *PartialGCD = One;
7120 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
7121 if (PartialGCD == GCD) {
7122 Operands.push_back(Expr->getOperand(i));
7126 const SCEV *Rem = Zero;
7127 const SCEV *Res = SCEVGCD::findGCD(SE, Expr->getOperand(i), GCD, &Rem);
7129 PartialGCD = SE.getMulExpr(PartialGCD, Res);
7130 Operands.push_back(divide(SE, Expr->getOperand(i), GCD));
7132 Operands.push_back(Expr->getOperand(i));
7137 if (Operands.size() == 1)
7139 return SE.getMulExpr(Operands);
7142 const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
7148 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
7152 assert(Expr->isAffine() && "Expr should be affine");
7154 const SCEV *Start = divide(SE, Expr->getStart(), GCD);
7155 const SCEV *Step = divide(SE, Expr->getStepRecurrence(SE), GCD);
7157 return SE.getAddRecExpr(Start, Step, Expr->getLoop(),
7158 Expr->getNoWrapFlags());
7161 const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
7167 const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
7173 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
7179 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
7184 ScalarEvolution &SE;
7185 const SCEV *GCD, *Zero, *One;
7189 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7190 /// sizes of an array access. Returns the remainder of the delinearization that
7191 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7192 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7193 /// expressions in the stride and base of a SCEV corresponding to the
7194 /// computation of a GCD (greatest common divisor) of base and stride. When
7195 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7197 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7199 /// void foo(long n, long m, long o, double A[n][m][o]) {
7201 /// for (long i = 0; i < n; i++)
7202 /// for (long j = 0; j < m; j++)
7203 /// for (long k = 0; k < o; k++)
7204 /// A[i][j][k] = 1.0;
7207 /// the delinearization input is the following AddRec SCEV:
7209 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7211 /// From this SCEV, we are able to say that the base offset of the access is %A
7212 /// because it appears as an offset that does not divide any of the strides in
7215 /// CHECK: Base offset: %A
7217 /// and then SCEV->delinearize determines the size of some of the dimensions of
7218 /// the array as these are the multiples by which the strides are happening:
7220 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7222 /// Note that the outermost dimension remains of UnknownSize because there are
7223 /// no strides that would help identifying the size of the last dimension: when
7224 /// the array has been statically allocated, one could compute the size of that
7225 /// dimension by dividing the overall size of the array by the size of the known
7226 /// dimensions: %m * %o * 8.
7228 /// Finally delinearize provides the access functions for the array reference
7229 /// that does correspond to A[i][j][k] of the above C testcase:
7231 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7233 /// The testcases are checking the output of a function pass:
7234 /// DelinearizationPass that walks through all loads and stores of a function
7235 /// asking for the SCEV of the memory access with respect to all enclosing
7236 /// loops, calling SCEV->delinearize on that and printing the results.
7239 SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7240 SmallVectorImpl<const SCEV *> &Subscripts,
7241 SmallVectorImpl<const SCEV *> &Sizes) const {
7242 // Early exit in case this SCEV is not an affine multivariate function.
7243 if (!this->isAffine())
7246 const SCEV *Start = this->getStart();
7247 const SCEV *Step = this->getStepRecurrence(SE);
7249 // Build the SCEV representation of the canonical induction variable in the
7250 // loop of this SCEV.
7251 const SCEV *Zero = SE.getConstant(this->getType(), 0);
7252 const SCEV *One = SE.getConstant(this->getType(), 1);
7254 SE.getAddRecExpr(Zero, One, this->getLoop(), this->getNoWrapFlags());
7256 DEBUG(dbgs() << "(delinearize: " << *this << "\n");
7258 // When the stride of this SCEV is 1, do not compute the GCD: the size of this
7259 // subscript is 1, and this same SCEV for the access function.
7260 const SCEV *Remainder = Zero;
7261 const SCEV *GCD = One;
7263 // Find the GCD and Remainder of the Start and Step coefficients of this SCEV.
7264 if (Step != One && !Step->isAllOnesValue())
7265 GCD = SCEVGCD::findGCD(SE, Start, Step, &Remainder);
7267 DEBUG(dbgs() << "GCD: " << *GCD << "\n");
7268 DEBUG(dbgs() << "Remainder: " << *Remainder << "\n");
7270 const SCEV *Quotient = Start;
7271 if (GCD != One && !GCD->isAllOnesValue())
7272 // As findGCD computed Remainder, GCD divides "Start - Remainder." The
7273 // Quotient is then this SCEV without Remainder, scaled down by the GCD. The
7274 // Quotient is what will be used in the next subscript delinearization.
7275 Quotient = SCEVDivision::divide(SE, SE.getMinusSCEV(Start, Remainder), GCD);
7277 DEBUG(dbgs() << "Quotient: " << *Quotient << "\n");
7279 const SCEV *Rem = Quotient;
7280 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Quotient))
7281 // Recursively call delinearize on the Quotient until there are no more
7282 // multiples that can be recognized.
7283 Rem = AR->delinearize(SE, Subscripts, Sizes);
7285 // Scale up the canonical induction variable IV by whatever remains from the
7286 // Step after division by the GCD: the GCD is the size of all the sub-array.
7287 if (Step != One && !Step->isAllOnesValue() && GCD != One &&
7288 !GCD->isAllOnesValue() && Step != GCD) {
7289 Step = SCEVDivision::divide(SE, Step, GCD);
7290 IV = SE.getMulExpr(IV, Step);
7292 // The access function in the current subscript is computed as the canonical
7293 // induction variable IV (potentially scaled up by the step) and offset by
7294 // Rem, the offset of delinearization in the sub-array.
7295 const SCEV *Index = SE.getAddExpr(IV, Rem);
7297 // Record the access function and the size of the current subscript.
7298 Subscripts.push_back(Index);
7299 Sizes.push_back(GCD);
7302 int Size = Sizes.size();
7303 DEBUG(dbgs() << "succeeded to delinearize " << *this << "\n");
7304 DEBUG(dbgs() << "ArrayDecl[UnknownSize]");
7305 for (int i = 0; i < Size - 1; i++)
7306 DEBUG(dbgs() << "[" << *Sizes[i] << "]");
7307 DEBUG(dbgs() << " with elements of " << *Sizes[Size - 1] << " bytes.\n");
7309 DEBUG(dbgs() << "ArrayRef");
7310 for (int i = 0; i < Size; i++)
7311 DEBUG(dbgs() << "[" << *Subscripts[i] << "]");
7312 DEBUG(dbgs() << "\n)\n");
7318 //===----------------------------------------------------------------------===//
7319 // SCEVCallbackVH Class Implementation
7320 //===----------------------------------------------------------------------===//
7322 void ScalarEvolution::SCEVCallbackVH::deleted() {
7323 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7324 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7325 SE->ConstantEvolutionLoopExitValue.erase(PN);
7326 SE->ValueExprMap.erase(getValPtr());
7327 // this now dangles!
7330 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7331 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7333 // Forget all the expressions associated with users of the old value,
7334 // so that future queries will recompute the expressions using the new
7336 Value *Old = getValPtr();
7337 SmallVector<User *, 16> Worklist;
7338 SmallPtrSet<User *, 8> Visited;
7339 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
7341 Worklist.push_back(*UI);
7342 while (!Worklist.empty()) {
7343 User *U = Worklist.pop_back_val();
7344 // Deleting the Old value will cause this to dangle. Postpone
7345 // that until everything else is done.
7348 if (!Visited.insert(U))
7350 if (PHINode *PN = dyn_cast<PHINode>(U))
7351 SE->ConstantEvolutionLoopExitValue.erase(PN);
7352 SE->ValueExprMap.erase(U);
7353 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
7355 Worklist.push_back(*UI);
7357 // Delete the Old value.
7358 if (PHINode *PN = dyn_cast<PHINode>(Old))
7359 SE->ConstantEvolutionLoopExitValue.erase(PN);
7360 SE->ValueExprMap.erase(Old);
7361 // this now dangles!
7364 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7365 : CallbackVH(V), SE(se) {}
7367 //===----------------------------------------------------------------------===//
7368 // ScalarEvolution Class Implementation
7369 //===----------------------------------------------------------------------===//
7371 ScalarEvolution::ScalarEvolution()
7372 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64), FirstUnknown(0) {
7373 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7376 bool ScalarEvolution::runOnFunction(Function &F) {
7378 LI = &getAnalysis<LoopInfo>();
7379 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7380 DL = DLP ? &DLP->getDataLayout() : 0;
7381 TLI = &getAnalysis<TargetLibraryInfo>();
7382 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7386 void ScalarEvolution::releaseMemory() {
7387 // Iterate through all the SCEVUnknown instances and call their
7388 // destructors, so that they release their references to their values.
7389 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7393 ValueExprMap.clear();
7395 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7396 // that a loop had multiple computable exits.
7397 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7398 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7403 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7405 BackedgeTakenCounts.clear();
7406 ConstantEvolutionLoopExitValue.clear();
7407 ValuesAtScopes.clear();
7408 LoopDispositions.clear();
7409 BlockDispositions.clear();
7410 UnsignedRanges.clear();
7411 SignedRanges.clear();
7412 UniqueSCEVs.clear();
7413 SCEVAllocator.Reset();
7416 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7417 AU.setPreservesAll();
7418 AU.addRequiredTransitive<LoopInfo>();
7419 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7420 AU.addRequired<TargetLibraryInfo>();
7423 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7424 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7427 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7429 // Print all inner loops first
7430 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7431 PrintLoopInfo(OS, SE, *I);
7434 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7437 SmallVector<BasicBlock *, 8> ExitBlocks;
7438 L->getExitBlocks(ExitBlocks);
7439 if (ExitBlocks.size() != 1)
7440 OS << "<multiple exits> ";
7442 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7443 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7445 OS << "Unpredictable backedge-taken count. ";
7450 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7453 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7454 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7456 OS << "Unpredictable max backedge-taken count. ";
7462 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7463 // ScalarEvolution's implementation of the print method is to print
7464 // out SCEV values of all instructions that are interesting. Doing
7465 // this potentially causes it to create new SCEV objects though,
7466 // which technically conflicts with the const qualifier. This isn't
7467 // observable from outside the class though, so casting away the
7468 // const isn't dangerous.
7469 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7471 OS << "Classifying expressions for: ";
7472 F->printAsOperand(OS, /*PrintType=*/false);
7474 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7475 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7478 const SCEV *SV = SE.getSCEV(&*I);
7481 const Loop *L = LI->getLoopFor((*I).getParent());
7483 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
7490 OS << "\t\t" "Exits: ";
7491 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
7492 if (!SE.isLoopInvariant(ExitValue, L)) {
7493 OS << "<<Unknown>>";
7502 OS << "Determining loop execution counts for: ";
7503 F->printAsOperand(OS, /*PrintType=*/false);
7505 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
7506 PrintLoopInfo(OS, &SE, *I);
7509 ScalarEvolution::LoopDisposition
7510 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
7511 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
7512 for (unsigned u = 0; u < Values.size(); u++) {
7513 if (Values[u].first == L)
7514 return Values[u].second;
7516 Values.push_back(std::make_pair(L, LoopVariant));
7517 LoopDisposition D = computeLoopDisposition(S, L);
7518 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
7519 for (unsigned u = Values2.size(); u > 0; u--) {
7520 if (Values2[u - 1].first == L) {
7521 Values2[u - 1].second = D;
7528 ScalarEvolution::LoopDisposition
7529 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
7530 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7532 return LoopInvariant;
7536 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
7537 case scAddRecExpr: {
7538 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7540 // If L is the addrec's loop, it's computable.
7541 if (AR->getLoop() == L)
7542 return LoopComputable;
7544 // Add recurrences are never invariant in the function-body (null loop).
7548 // This recurrence is variant w.r.t. L if L contains AR's loop.
7549 if (L->contains(AR->getLoop()))
7552 // This recurrence is invariant w.r.t. L if AR's loop contains L.
7553 if (AR->getLoop()->contains(L))
7554 return LoopInvariant;
7556 // This recurrence is variant w.r.t. L if any of its operands
7558 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
7560 if (!isLoopInvariant(*I, L))
7563 // Otherwise it's loop-invariant.
7564 return LoopInvariant;
7570 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7571 bool HasVarying = false;
7572 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7574 LoopDisposition D = getLoopDisposition(*I, L);
7575 if (D == LoopVariant)
7577 if (D == LoopComputable)
7580 return HasVarying ? LoopComputable : LoopInvariant;
7583 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7584 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
7585 if (LD == LoopVariant)
7587 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
7588 if (RD == LoopVariant)
7590 return (LD == LoopInvariant && RD == LoopInvariant) ?
7591 LoopInvariant : LoopComputable;
7594 // All non-instruction values are loop invariant. All instructions are loop
7595 // invariant if they are not contained in the specified loop.
7596 // Instructions are never considered invariant in the function body
7597 // (null loop) because they are defined within the "loop".
7598 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
7599 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
7600 return LoopInvariant;
7601 case scCouldNotCompute:
7602 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7604 llvm_unreachable("Unknown SCEV kind!");
7607 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
7608 return getLoopDisposition(S, L) == LoopInvariant;
7611 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
7612 return getLoopDisposition(S, L) == LoopComputable;
7615 ScalarEvolution::BlockDisposition
7616 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7617 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
7618 for (unsigned u = 0; u < Values.size(); u++) {
7619 if (Values[u].first == BB)
7620 return Values[u].second;
7622 Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
7623 BlockDisposition D = computeBlockDisposition(S, BB);
7624 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
7625 for (unsigned u = Values2.size(); u > 0; u--) {
7626 if (Values2[u - 1].first == BB) {
7627 Values2[u - 1].second = D;
7634 ScalarEvolution::BlockDisposition
7635 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7636 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7638 return ProperlyDominatesBlock;
7642 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
7643 case scAddRecExpr: {
7644 // This uses a "dominates" query instead of "properly dominates" query
7645 // to test for proper dominance too, because the instruction which
7646 // produces the addrec's value is a PHI, and a PHI effectively properly
7647 // dominates its entire containing block.
7648 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7649 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
7650 return DoesNotDominateBlock;
7652 // FALL THROUGH into SCEVNAryExpr handling.
7657 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7659 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7661 BlockDisposition D = getBlockDisposition(*I, BB);
7662 if (D == DoesNotDominateBlock)
7663 return DoesNotDominateBlock;
7664 if (D == DominatesBlock)
7667 return Proper ? ProperlyDominatesBlock : DominatesBlock;
7670 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7671 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
7672 BlockDisposition LD = getBlockDisposition(LHS, BB);
7673 if (LD == DoesNotDominateBlock)
7674 return DoesNotDominateBlock;
7675 BlockDisposition RD = getBlockDisposition(RHS, BB);
7676 if (RD == DoesNotDominateBlock)
7677 return DoesNotDominateBlock;
7678 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
7679 ProperlyDominatesBlock : DominatesBlock;
7682 if (Instruction *I =
7683 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
7684 if (I->getParent() == BB)
7685 return DominatesBlock;
7686 if (DT->properlyDominates(I->getParent(), BB))
7687 return ProperlyDominatesBlock;
7688 return DoesNotDominateBlock;
7690 return ProperlyDominatesBlock;
7691 case scCouldNotCompute:
7692 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7694 llvm_unreachable("Unknown SCEV kind!");
7697 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
7698 return getBlockDisposition(S, BB) >= DominatesBlock;
7701 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
7702 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
7706 // Search for a SCEV expression node within an expression tree.
7707 // Implements SCEVTraversal::Visitor.
7712 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
7714 bool follow(const SCEV *S) {
7715 IsFound |= (S == Node);
7718 bool isDone() const { return IsFound; }
7722 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
7723 SCEVSearch Search(Op);
7724 visitAll(S, Search);
7725 return Search.IsFound;
7728 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
7729 ValuesAtScopes.erase(S);
7730 LoopDispositions.erase(S);
7731 BlockDispositions.erase(S);
7732 UnsignedRanges.erase(S);
7733 SignedRanges.erase(S);
7735 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7736 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
7737 BackedgeTakenInfo &BEInfo = I->second;
7738 if (BEInfo.hasOperand(S, this)) {
7740 BackedgeTakenCounts.erase(I++);
7747 typedef DenseMap<const Loop *, std::string> VerifyMap;
7749 /// replaceSubString - Replaces all occurrences of From in Str with To.
7750 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
7752 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
7753 Str.replace(Pos, From.size(), To.data(), To.size());
7758 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
7760 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
7761 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
7762 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
7764 std::string &S = Map[L];
7766 raw_string_ostream OS(S);
7767 SE.getBackedgeTakenCount(L)->print(OS);
7769 // false and 0 are semantically equivalent. This can happen in dead loops.
7770 replaceSubString(OS.str(), "false", "0");
7771 // Remove wrap flags, their use in SCEV is highly fragile.
7772 // FIXME: Remove this when SCEV gets smarter about them.
7773 replaceSubString(OS.str(), "<nw>", "");
7774 replaceSubString(OS.str(), "<nsw>", "");
7775 replaceSubString(OS.str(), "<nuw>", "");
7780 void ScalarEvolution::verifyAnalysis() const {
7784 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7786 // Gather stringified backedge taken counts for all loops using SCEV's caches.
7787 // FIXME: It would be much better to store actual values instead of strings,
7788 // but SCEV pointers will change if we drop the caches.
7789 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
7790 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7791 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
7793 // Gather stringified backedge taken counts for all loops without using
7796 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7797 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
7799 // Now compare whether they're the same with and without caches. This allows
7800 // verifying that no pass changed the cache.
7801 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
7802 "New loops suddenly appeared!");
7804 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
7805 OldE = BackedgeDumpsOld.end(),
7806 NewI = BackedgeDumpsNew.begin();
7807 OldI != OldE; ++OldI, ++NewI) {
7808 assert(OldI->first == NewI->first && "Loop order changed!");
7810 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
7812 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
7813 // means that a pass is buggy or SCEV has to learn a new pattern but is
7814 // usually not harmful.
7815 if (OldI->second != NewI->second &&
7816 OldI->second.find("undef") == std::string::npos &&
7817 NewI->second.find("undef") == std::string::npos &&
7818 OldI->second != "***COULDNOTCOMPUTE***" &&
7819 NewI->second != "***COULDNOTCOMPUTE***") {
7820 dbgs() << "SCEVValidator: SCEV for loop '"
7821 << OldI->first->getHeader()->getName()
7822 << "' changed from '" << OldI->second
7823 << "' to '" << NewI->second << "'!\n";
7828 // TODO: Verify more things.