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/ConstantRange.h"
72 #include "llvm/IR/Constants.h"
73 #include "llvm/IR/DataLayout.h"
74 #include "llvm/IR/DerivedTypes.h"
75 #include "llvm/IR/Dominators.h"
76 #include "llvm/IR/GetElementPtrTypeIterator.h"
77 #include "llvm/IR/GlobalAlias.h"
78 #include "llvm/IR/GlobalVariable.h"
79 #include "llvm/IR/InstIterator.h"
80 #include "llvm/IR/Instructions.h"
81 #include "llvm/IR/LLVMContext.h"
82 #include "llvm/IR/Operator.h"
83 #include "llvm/Support/CommandLine.h"
84 #include "llvm/Support/Debug.h"
85 #include "llvm/Support/ErrorHandling.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 (User *U : I->users())
3037 Worklist.push_back(cast<Instruction>(U));
3040 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3041 /// instructions that depend on the given instruction and removes them from
3042 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3045 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3046 SmallVector<Instruction *, 16> Worklist;
3047 PushDefUseChildren(PN, Worklist);
3049 SmallPtrSet<Instruction *, 8> Visited;
3051 while (!Worklist.empty()) {
3052 Instruction *I = Worklist.pop_back_val();
3053 if (!Visited.insert(I)) continue;
3055 ValueExprMapType::iterator It =
3056 ValueExprMap.find_as(static_cast<Value *>(I));
3057 if (It != ValueExprMap.end()) {
3058 const SCEV *Old = It->second;
3060 // Short-circuit the def-use traversal if the symbolic name
3061 // ceases to appear in expressions.
3062 if (Old != SymName && !hasOperand(Old, SymName))
3065 // SCEVUnknown for a PHI either means that it has an unrecognized
3066 // structure, it's a PHI that's in the progress of being computed
3067 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3068 // additional loop trip count information isn't going to change anything.
3069 // In the second case, createNodeForPHI will perform the necessary
3070 // updates on its own when it gets to that point. In the third, we do
3071 // want to forget the SCEVUnknown.
3072 if (!isa<PHINode>(I) ||
3073 !isa<SCEVUnknown>(Old) ||
3074 (I != PN && Old == SymName)) {
3075 forgetMemoizedResults(Old);
3076 ValueExprMap.erase(It);
3080 PushDefUseChildren(I, Worklist);
3084 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3085 /// a loop header, making it a potential recurrence, or it doesn't.
3087 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3088 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3089 if (L->getHeader() == PN->getParent()) {
3090 // The loop may have multiple entrances or multiple exits; we can analyze
3091 // this phi as an addrec if it has a unique entry value and a unique
3093 Value *BEValueV = 0, *StartValueV = 0;
3094 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3095 Value *V = PN->getIncomingValue(i);
3096 if (L->contains(PN->getIncomingBlock(i))) {
3099 } else if (BEValueV != V) {
3103 } else if (!StartValueV) {
3105 } else if (StartValueV != V) {
3110 if (BEValueV && StartValueV) {
3111 // While we are analyzing this PHI node, handle its value symbolically.
3112 const SCEV *SymbolicName = getUnknown(PN);
3113 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3114 "PHI node already processed?");
3115 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3117 // Using this symbolic name for the PHI, analyze the value coming around
3119 const SCEV *BEValue = getSCEV(BEValueV);
3121 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3122 // has a special value for the first iteration of the loop.
3124 // If the value coming around the backedge is an add with the symbolic
3125 // value we just inserted, then we found a simple induction variable!
3126 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3127 // If there is a single occurrence of the symbolic value, replace it
3128 // with a recurrence.
3129 unsigned FoundIndex = Add->getNumOperands();
3130 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3131 if (Add->getOperand(i) == SymbolicName)
3132 if (FoundIndex == e) {
3137 if (FoundIndex != Add->getNumOperands()) {
3138 // Create an add with everything but the specified operand.
3139 SmallVector<const SCEV *, 8> Ops;
3140 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3141 if (i != FoundIndex)
3142 Ops.push_back(Add->getOperand(i));
3143 const SCEV *Accum = getAddExpr(Ops);
3145 // This is not a valid addrec if the step amount is varying each
3146 // loop iteration, but is not itself an addrec in this loop.
3147 if (isLoopInvariant(Accum, L) ||
3148 (isa<SCEVAddRecExpr>(Accum) &&
3149 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3150 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3152 // If the increment doesn't overflow, then neither the addrec nor
3153 // the post-increment will overflow.
3154 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3155 if (OBO->hasNoUnsignedWrap())
3156 Flags = setFlags(Flags, SCEV::FlagNUW);
3157 if (OBO->hasNoSignedWrap())
3158 Flags = setFlags(Flags, SCEV::FlagNSW);
3159 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3160 // If the increment is an inbounds GEP, then we know the address
3161 // space cannot be wrapped around. We cannot make any guarantee
3162 // about signed or unsigned overflow because pointers are
3163 // unsigned but we may have a negative index from the base
3164 // pointer. We can guarantee that no unsigned wrap occurs if the
3165 // indices form a positive value.
3166 if (GEP->isInBounds()) {
3167 Flags = setFlags(Flags, SCEV::FlagNW);
3169 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3170 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3171 Flags = setFlags(Flags, SCEV::FlagNUW);
3173 } else if (const SubOperator *OBO =
3174 dyn_cast<SubOperator>(BEValueV)) {
3175 if (OBO->hasNoUnsignedWrap())
3176 Flags = setFlags(Flags, SCEV::FlagNUW);
3177 if (OBO->hasNoSignedWrap())
3178 Flags = setFlags(Flags, SCEV::FlagNSW);
3181 const SCEV *StartVal = getSCEV(StartValueV);
3182 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3184 // Since the no-wrap flags are on the increment, they apply to the
3185 // post-incremented value as well.
3186 if (isLoopInvariant(Accum, L))
3187 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3190 // Okay, for the entire analysis of this edge we assumed the PHI
3191 // to be symbolic. We now need to go back and purge all of the
3192 // entries for the scalars that use the symbolic expression.
3193 ForgetSymbolicName(PN, SymbolicName);
3194 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3198 } else if (const SCEVAddRecExpr *AddRec =
3199 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3200 // Otherwise, this could be a loop like this:
3201 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3202 // In this case, j = {1,+,1} and BEValue is j.
3203 // Because the other in-value of i (0) fits the evolution of BEValue
3204 // i really is an addrec evolution.
3205 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3206 const SCEV *StartVal = getSCEV(StartValueV);
3208 // If StartVal = j.start - j.stride, we can use StartVal as the
3209 // initial step of the addrec evolution.
3210 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3211 AddRec->getOperand(1))) {
3212 // FIXME: For constant StartVal, we should be able to infer
3214 const SCEV *PHISCEV =
3215 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3218 // Okay, for the entire analysis of this edge we assumed the PHI
3219 // to be symbolic. We now need to go back and purge all of the
3220 // entries for the scalars that use the symbolic expression.
3221 ForgetSymbolicName(PN, SymbolicName);
3222 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3230 // If the PHI has a single incoming value, follow that value, unless the
3231 // PHI's incoming blocks are in a different loop, in which case doing so
3232 // risks breaking LCSSA form. Instcombine would normally zap these, but
3233 // it doesn't have DominatorTree information, so it may miss cases.
3234 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT))
3235 if (LI->replacementPreservesLCSSAForm(PN, V))
3238 // If it's not a loop phi, we can't handle it yet.
3239 return getUnknown(PN);
3242 /// createNodeForGEP - Expand GEP instructions into add and multiply
3243 /// operations. This allows them to be analyzed by regular SCEV code.
3245 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3246 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3247 Value *Base = GEP->getOperand(0);
3248 // Don't attempt to analyze GEPs over unsized objects.
3249 if (!Base->getType()->getPointerElementType()->isSized())
3250 return getUnknown(GEP);
3252 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3253 // Add expression, because the Instruction may be guarded by control flow
3254 // and the no-overflow bits may not be valid for the expression in any
3256 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3258 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3259 gep_type_iterator GTI = gep_type_begin(GEP);
3260 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3264 // Compute the (potentially symbolic) offset in bytes for this index.
3265 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3266 // For a struct, add the member offset.
3267 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3268 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3270 // Add the field offset to the running total offset.
3271 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3273 // For an array, add the element offset, explicitly scaled.
3274 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3275 const SCEV *IndexS = getSCEV(Index);
3276 // Getelementptr indices are signed.
3277 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3279 // Multiply the index by the element size to compute the element offset.
3280 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3282 // Add the element offset to the running total offset.
3283 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3287 // Get the SCEV for the GEP base.
3288 const SCEV *BaseS = getSCEV(Base);
3290 // Add the total offset from all the GEP indices to the base.
3291 return getAddExpr(BaseS, TotalOffset, Wrap);
3294 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3295 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3296 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3297 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3299 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3300 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3301 return C->getValue()->getValue().countTrailingZeros();
3303 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3304 return std::min(GetMinTrailingZeros(T->getOperand()),
3305 (uint32_t)getTypeSizeInBits(T->getType()));
3307 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3308 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3309 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3310 getTypeSizeInBits(E->getType()) : OpRes;
3313 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3314 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3315 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3316 getTypeSizeInBits(E->getType()) : OpRes;
3319 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3320 // The result is the min of all operands results.
3321 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3322 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3323 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3327 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3328 // The result is the sum of all operands results.
3329 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3330 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3331 for (unsigned i = 1, e = M->getNumOperands();
3332 SumOpRes != BitWidth && i != e; ++i)
3333 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3338 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3339 // The result is the min of all operands results.
3340 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3341 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3342 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3346 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3347 // The result is the min of all operands results.
3348 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3349 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3350 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3354 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3355 // The result is the min of all operands results.
3356 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3357 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3358 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3362 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3363 // For a SCEVUnknown, ask ValueTracking.
3364 unsigned BitWidth = getTypeSizeInBits(U->getType());
3365 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3366 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3367 return Zeros.countTrailingOnes();
3374 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3377 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3378 // See if we've computed this range already.
3379 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3380 if (I != UnsignedRanges.end())
3383 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3384 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3386 unsigned BitWidth = getTypeSizeInBits(S->getType());
3387 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3389 // If the value has known zeros, the maximum unsigned value will have those
3390 // known zeros as well.
3391 uint32_t TZ = GetMinTrailingZeros(S);
3393 ConservativeResult =
3394 ConstantRange(APInt::getMinValue(BitWidth),
3395 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3397 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3398 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3399 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3400 X = X.add(getUnsignedRange(Add->getOperand(i)));
3401 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3404 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3405 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3406 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3407 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3408 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3411 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3412 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3413 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3414 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3415 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3418 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3419 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3420 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3421 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3422 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3425 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3426 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3427 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3428 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3431 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3432 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3433 return setUnsignedRange(ZExt,
3434 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3437 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3438 ConstantRange X = getUnsignedRange(SExt->getOperand());
3439 return setUnsignedRange(SExt,
3440 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3443 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3444 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3445 return setUnsignedRange(Trunc,
3446 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3449 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3450 // If there's no unsigned wrap, the value will never be less than its
3452 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3453 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3454 if (!C->getValue()->isZero())
3455 ConservativeResult =
3456 ConservativeResult.intersectWith(
3457 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3459 // TODO: non-affine addrec
3460 if (AddRec->isAffine()) {
3461 Type *Ty = AddRec->getType();
3462 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3463 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3464 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3465 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3467 const SCEV *Start = AddRec->getStart();
3468 const SCEV *Step = AddRec->getStepRecurrence(*this);
3470 ConstantRange StartRange = getUnsignedRange(Start);
3471 ConstantRange StepRange = getSignedRange(Step);
3472 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3473 ConstantRange EndRange =
3474 StartRange.add(MaxBECountRange.multiply(StepRange));
3476 // Check for overflow. This must be done with ConstantRange arithmetic
3477 // because we could be called from within the ScalarEvolution overflow
3479 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3480 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3481 ConstantRange ExtMaxBECountRange =
3482 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3483 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3484 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3486 return setUnsignedRange(AddRec, ConservativeResult);
3488 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3489 EndRange.getUnsignedMin());
3490 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3491 EndRange.getUnsignedMax());
3492 if (Min.isMinValue() && Max.isMaxValue())
3493 return setUnsignedRange(AddRec, ConservativeResult);
3494 return setUnsignedRange(AddRec,
3495 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3499 return setUnsignedRange(AddRec, ConservativeResult);
3502 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3503 // For a SCEVUnknown, ask ValueTracking.
3504 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3505 ComputeMaskedBits(U->getValue(), Zeros, Ones, DL);
3506 if (Ones == ~Zeros + 1)
3507 return setUnsignedRange(U, ConservativeResult);
3508 return setUnsignedRange(U,
3509 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3512 return setUnsignedRange(S, ConservativeResult);
3515 /// getSignedRange - Determine the signed range for a particular SCEV.
3518 ScalarEvolution::getSignedRange(const SCEV *S) {
3519 // See if we've computed this range already.
3520 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3521 if (I != SignedRanges.end())
3524 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3525 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3527 unsigned BitWidth = getTypeSizeInBits(S->getType());
3528 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3530 // If the value has known zeros, the maximum signed value will have those
3531 // known zeros as well.
3532 uint32_t TZ = GetMinTrailingZeros(S);
3534 ConservativeResult =
3535 ConstantRange(APInt::getSignedMinValue(BitWidth),
3536 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3538 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3539 ConstantRange X = getSignedRange(Add->getOperand(0));
3540 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3541 X = X.add(getSignedRange(Add->getOperand(i)));
3542 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3545 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3546 ConstantRange X = getSignedRange(Mul->getOperand(0));
3547 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3548 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3549 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3552 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3553 ConstantRange X = getSignedRange(SMax->getOperand(0));
3554 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3555 X = X.smax(getSignedRange(SMax->getOperand(i)));
3556 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3559 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3560 ConstantRange X = getSignedRange(UMax->getOperand(0));
3561 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3562 X = X.umax(getSignedRange(UMax->getOperand(i)));
3563 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3566 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3567 ConstantRange X = getSignedRange(UDiv->getLHS());
3568 ConstantRange Y = getSignedRange(UDiv->getRHS());
3569 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3572 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3573 ConstantRange X = getSignedRange(ZExt->getOperand());
3574 return setSignedRange(ZExt,
3575 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3578 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3579 ConstantRange X = getSignedRange(SExt->getOperand());
3580 return setSignedRange(SExt,
3581 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3584 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3585 ConstantRange X = getSignedRange(Trunc->getOperand());
3586 return setSignedRange(Trunc,
3587 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3590 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3591 // If there's no signed wrap, and all the operands have the same sign or
3592 // zero, the value won't ever change sign.
3593 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3594 bool AllNonNeg = true;
3595 bool AllNonPos = true;
3596 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3597 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3598 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3601 ConservativeResult = ConservativeResult.intersectWith(
3602 ConstantRange(APInt(BitWidth, 0),
3603 APInt::getSignedMinValue(BitWidth)));
3605 ConservativeResult = ConservativeResult.intersectWith(
3606 ConstantRange(APInt::getSignedMinValue(BitWidth),
3607 APInt(BitWidth, 1)));
3610 // TODO: non-affine addrec
3611 if (AddRec->isAffine()) {
3612 Type *Ty = AddRec->getType();
3613 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3614 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3615 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3616 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3618 const SCEV *Start = AddRec->getStart();
3619 const SCEV *Step = AddRec->getStepRecurrence(*this);
3621 ConstantRange StartRange = getSignedRange(Start);
3622 ConstantRange StepRange = getSignedRange(Step);
3623 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3624 ConstantRange EndRange =
3625 StartRange.add(MaxBECountRange.multiply(StepRange));
3627 // Check for overflow. This must be done with ConstantRange arithmetic
3628 // because we could be called from within the ScalarEvolution overflow
3630 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3631 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3632 ConstantRange ExtMaxBECountRange =
3633 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3634 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3635 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3637 return setSignedRange(AddRec, ConservativeResult);
3639 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3640 EndRange.getSignedMin());
3641 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3642 EndRange.getSignedMax());
3643 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3644 return setSignedRange(AddRec, ConservativeResult);
3645 return setSignedRange(AddRec,
3646 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3650 return setSignedRange(AddRec, ConservativeResult);
3653 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3654 // For a SCEVUnknown, ask ValueTracking.
3655 if (!U->getValue()->getType()->isIntegerTy() && !DL)
3656 return setSignedRange(U, ConservativeResult);
3657 unsigned NS = ComputeNumSignBits(U->getValue(), DL);
3659 return setSignedRange(U, ConservativeResult);
3660 return setSignedRange(U, ConservativeResult.intersectWith(
3661 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3662 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3665 return setSignedRange(S, ConservativeResult);
3668 /// createSCEV - We know that there is no SCEV for the specified value.
3669 /// Analyze the expression.
3671 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3672 if (!isSCEVable(V->getType()))
3673 return getUnknown(V);
3675 unsigned Opcode = Instruction::UserOp1;
3676 if (Instruction *I = dyn_cast<Instruction>(V)) {
3677 Opcode = I->getOpcode();
3679 // Don't attempt to analyze instructions in blocks that aren't
3680 // reachable. Such instructions don't matter, and they aren't required
3681 // to obey basic rules for definitions dominating uses which this
3682 // analysis depends on.
3683 if (!DT->isReachableFromEntry(I->getParent()))
3684 return getUnknown(V);
3685 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3686 Opcode = CE->getOpcode();
3687 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3688 return getConstant(CI);
3689 else if (isa<ConstantPointerNull>(V))
3690 return getConstant(V->getType(), 0);
3691 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3692 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3694 return getUnknown(V);
3696 Operator *U = cast<Operator>(V);
3698 case Instruction::Add: {
3699 // The simple thing to do would be to just call getSCEV on both operands
3700 // and call getAddExpr with the result. However if we're looking at a
3701 // bunch of things all added together, this can be quite inefficient,
3702 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3703 // Instead, gather up all the operands and make a single getAddExpr call.
3704 // LLVM IR canonical form means we need only traverse the left operands.
3706 // Don't apply this instruction's NSW or NUW flags to the new
3707 // expression. The instruction may be guarded by control flow that the
3708 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3709 // mapped to the same SCEV expression, and it would be incorrect to transfer
3710 // NSW/NUW semantics to those operations.
3711 SmallVector<const SCEV *, 4> AddOps;
3712 AddOps.push_back(getSCEV(U->getOperand(1)));
3713 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3714 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3715 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3717 U = cast<Operator>(Op);
3718 const SCEV *Op1 = getSCEV(U->getOperand(1));
3719 if (Opcode == Instruction::Sub)
3720 AddOps.push_back(getNegativeSCEV(Op1));
3722 AddOps.push_back(Op1);
3724 AddOps.push_back(getSCEV(U->getOperand(0)));
3725 return getAddExpr(AddOps);
3727 case Instruction::Mul: {
3728 // Don't transfer NSW/NUW for the same reason as AddExpr.
3729 SmallVector<const SCEV *, 4> MulOps;
3730 MulOps.push_back(getSCEV(U->getOperand(1)));
3731 for (Value *Op = U->getOperand(0);
3732 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3733 Op = U->getOperand(0)) {
3734 U = cast<Operator>(Op);
3735 MulOps.push_back(getSCEV(U->getOperand(1)));
3737 MulOps.push_back(getSCEV(U->getOperand(0)));
3738 return getMulExpr(MulOps);
3740 case Instruction::UDiv:
3741 return getUDivExpr(getSCEV(U->getOperand(0)),
3742 getSCEV(U->getOperand(1)));
3743 case Instruction::Sub:
3744 return getMinusSCEV(getSCEV(U->getOperand(0)),
3745 getSCEV(U->getOperand(1)));
3746 case Instruction::And:
3747 // For an expression like x&255 that merely masks off the high bits,
3748 // use zext(trunc(x)) as the SCEV expression.
3749 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3750 if (CI->isNullValue())
3751 return getSCEV(U->getOperand(1));
3752 if (CI->isAllOnesValue())
3753 return getSCEV(U->getOperand(0));
3754 const APInt &A = CI->getValue();
3756 // Instcombine's ShrinkDemandedConstant may strip bits out of
3757 // constants, obscuring what would otherwise be a low-bits mask.
3758 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3759 // knew about to reconstruct a low-bits mask value.
3760 unsigned LZ = A.countLeadingZeros();
3761 unsigned TZ = A.countTrailingZeros();
3762 unsigned BitWidth = A.getBitWidth();
3763 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3764 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, DL);
3766 APInt EffectiveMask =
3767 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
3768 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
3769 const SCEV *MulCount = getConstant(
3770 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
3774 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
3775 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
3782 case Instruction::Or:
3783 // If the RHS of the Or is a constant, we may have something like:
3784 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3785 // optimizations will transparently handle this case.
3787 // In order for this transformation to be safe, the LHS must be of the
3788 // form X*(2^n) and the Or constant must be less than 2^n.
3789 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3790 const SCEV *LHS = getSCEV(U->getOperand(0));
3791 const APInt &CIVal = CI->getValue();
3792 if (GetMinTrailingZeros(LHS) >=
3793 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3794 // Build a plain add SCEV.
3795 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3796 // If the LHS of the add was an addrec and it has no-wrap flags,
3797 // transfer the no-wrap flags, since an or won't introduce a wrap.
3798 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3799 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3800 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3801 OldAR->getNoWrapFlags());
3807 case Instruction::Xor:
3808 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3809 // If the RHS of the xor is a signbit, then this is just an add.
3810 // Instcombine turns add of signbit into xor as a strength reduction step.
3811 if (CI->getValue().isSignBit())
3812 return getAddExpr(getSCEV(U->getOperand(0)),
3813 getSCEV(U->getOperand(1)));
3815 // If the RHS of xor is -1, then this is a not operation.
3816 if (CI->isAllOnesValue())
3817 return getNotSCEV(getSCEV(U->getOperand(0)));
3819 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3820 // This is a variant of the check for xor with -1, and it handles
3821 // the case where instcombine has trimmed non-demanded bits out
3822 // of an xor with -1.
3823 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3824 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3825 if (BO->getOpcode() == Instruction::And &&
3826 LCI->getValue() == CI->getValue())
3827 if (const SCEVZeroExtendExpr *Z =
3828 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3829 Type *UTy = U->getType();
3830 const SCEV *Z0 = Z->getOperand();
3831 Type *Z0Ty = Z0->getType();
3832 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3834 // If C is a low-bits mask, the zero extend is serving to
3835 // mask off the high bits. Complement the operand and
3836 // re-apply the zext.
3837 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3838 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3840 // If C is a single bit, it may be in the sign-bit position
3841 // before the zero-extend. In this case, represent the xor
3842 // using an add, which is equivalent, and re-apply the zext.
3843 APInt Trunc = CI->getValue().trunc(Z0TySize);
3844 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3846 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3852 case Instruction::Shl:
3853 // Turn shift left of a constant amount into a multiply.
3854 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3855 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3857 // If the shift count is not less than the bitwidth, the result of
3858 // the shift is undefined. Don't try to analyze it, because the
3859 // resolution chosen here may differ from the resolution chosen in
3860 // other parts of the compiler.
3861 if (SA->getValue().uge(BitWidth))
3864 Constant *X = ConstantInt::get(getContext(),
3865 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3866 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3870 case Instruction::LShr:
3871 // Turn logical shift right of a constant into a unsigned divide.
3872 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3873 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3875 // If the shift count is not less than the bitwidth, the result of
3876 // the shift is undefined. Don't try to analyze it, because the
3877 // resolution chosen here may differ from the resolution chosen in
3878 // other parts of the compiler.
3879 if (SA->getValue().uge(BitWidth))
3882 Constant *X = ConstantInt::get(getContext(),
3883 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3884 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3888 case Instruction::AShr:
3889 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3890 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3891 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3892 if (L->getOpcode() == Instruction::Shl &&
3893 L->getOperand(1) == U->getOperand(1)) {
3894 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3896 // If the shift count is not less than the bitwidth, the result of
3897 // the shift is undefined. Don't try to analyze it, because the
3898 // resolution chosen here may differ from the resolution chosen in
3899 // other parts of the compiler.
3900 if (CI->getValue().uge(BitWidth))
3903 uint64_t Amt = BitWidth - CI->getZExtValue();
3904 if (Amt == BitWidth)
3905 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3907 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3908 IntegerType::get(getContext(),
3914 case Instruction::Trunc:
3915 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3917 case Instruction::ZExt:
3918 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3920 case Instruction::SExt:
3921 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3923 case Instruction::BitCast:
3924 // BitCasts are no-op casts so we just eliminate the cast.
3925 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3926 return getSCEV(U->getOperand(0));
3929 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3930 // lead to pointer expressions which cannot safely be expanded to GEPs,
3931 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3932 // simplifying integer expressions.
3934 case Instruction::GetElementPtr:
3935 return createNodeForGEP(cast<GEPOperator>(U));
3937 case Instruction::PHI:
3938 return createNodeForPHI(cast<PHINode>(U));
3940 case Instruction::Select:
3941 // This could be a smax or umax that was lowered earlier.
3942 // Try to recover it.
3943 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3944 Value *LHS = ICI->getOperand(0);
3945 Value *RHS = ICI->getOperand(1);
3946 switch (ICI->getPredicate()) {
3947 case ICmpInst::ICMP_SLT:
3948 case ICmpInst::ICMP_SLE:
3949 std::swap(LHS, RHS);
3951 case ICmpInst::ICMP_SGT:
3952 case ICmpInst::ICMP_SGE:
3953 // a >s b ? a+x : b+x -> smax(a, b)+x
3954 // a >s b ? b+x : a+x -> smin(a, b)+x
3955 if (LHS->getType() == U->getType()) {
3956 const SCEV *LS = getSCEV(LHS);
3957 const SCEV *RS = getSCEV(RHS);
3958 const SCEV *LA = getSCEV(U->getOperand(1));
3959 const SCEV *RA = getSCEV(U->getOperand(2));
3960 const SCEV *LDiff = getMinusSCEV(LA, LS);
3961 const SCEV *RDiff = getMinusSCEV(RA, RS);
3963 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3964 LDiff = getMinusSCEV(LA, RS);
3965 RDiff = getMinusSCEV(RA, LS);
3967 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3970 case ICmpInst::ICMP_ULT:
3971 case ICmpInst::ICMP_ULE:
3972 std::swap(LHS, RHS);
3974 case ICmpInst::ICMP_UGT:
3975 case ICmpInst::ICMP_UGE:
3976 // a >u b ? a+x : b+x -> umax(a, b)+x
3977 // a >u b ? b+x : a+x -> umin(a, b)+x
3978 if (LHS->getType() == U->getType()) {
3979 const SCEV *LS = getSCEV(LHS);
3980 const SCEV *RS = getSCEV(RHS);
3981 const SCEV *LA = getSCEV(U->getOperand(1));
3982 const SCEV *RA = getSCEV(U->getOperand(2));
3983 const SCEV *LDiff = getMinusSCEV(LA, LS);
3984 const SCEV *RDiff = getMinusSCEV(RA, RS);
3986 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3987 LDiff = getMinusSCEV(LA, RS);
3988 RDiff = getMinusSCEV(RA, LS);
3990 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3993 case ICmpInst::ICMP_NE:
3994 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3995 if (LHS->getType() == U->getType() &&
3996 isa<ConstantInt>(RHS) &&
3997 cast<ConstantInt>(RHS)->isZero()) {
3998 const SCEV *One = getConstant(LHS->getType(), 1);
3999 const SCEV *LS = getSCEV(LHS);
4000 const SCEV *LA = getSCEV(U->getOperand(1));
4001 const SCEV *RA = getSCEV(U->getOperand(2));
4002 const SCEV *LDiff = getMinusSCEV(LA, LS);
4003 const SCEV *RDiff = getMinusSCEV(RA, One);
4005 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4008 case ICmpInst::ICMP_EQ:
4009 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4010 if (LHS->getType() == U->getType() &&
4011 isa<ConstantInt>(RHS) &&
4012 cast<ConstantInt>(RHS)->isZero()) {
4013 const SCEV *One = getConstant(LHS->getType(), 1);
4014 const SCEV *LS = getSCEV(LHS);
4015 const SCEV *LA = getSCEV(U->getOperand(1));
4016 const SCEV *RA = getSCEV(U->getOperand(2));
4017 const SCEV *LDiff = getMinusSCEV(LA, One);
4018 const SCEV *RDiff = getMinusSCEV(RA, LS);
4020 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4028 default: // We cannot analyze this expression.
4032 return getUnknown(V);
4037 //===----------------------------------------------------------------------===//
4038 // Iteration Count Computation Code
4041 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4042 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4043 /// constant. Will also return 0 if the maximum trip count is very large (>=
4046 /// This "trip count" assumes that control exits via ExitingBlock. More
4047 /// precisely, it is the number of times that control may reach ExitingBlock
4048 /// before taking the branch. For loops with multiple exits, it may not be the
4049 /// number times that the loop header executes because the loop may exit
4050 /// prematurely via another branch.
4052 /// FIXME: We conservatively call getBackedgeTakenCount(L) instead of
4053 /// getExitCount(L, ExitingBlock) to compute a safe trip count considering all
4054 /// loop exits. getExitCount() may return an exact count for this branch
4055 /// assuming no-signed-wrap. The number of well-defined iterations may actually
4056 /// be higher than this trip count if this exit test is skipped and the loop
4057 /// exits via a different branch. Ideally, getExitCount() would know whether it
4058 /// depends on a NSW assumption, and we would only fall back to a conservative
4059 /// trip count in that case.
4060 unsigned ScalarEvolution::
4061 getSmallConstantTripCount(Loop *L, BasicBlock * /*ExitingBlock*/) {
4062 const SCEVConstant *ExitCount =
4063 dyn_cast<SCEVConstant>(getBackedgeTakenCount(L));
4067 ConstantInt *ExitConst = ExitCount->getValue();
4069 // Guard against huge trip counts.
4070 if (ExitConst->getValue().getActiveBits() > 32)
4073 // In case of integer overflow, this returns 0, which is correct.
4074 return ((unsigned)ExitConst->getZExtValue()) + 1;
4077 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4078 /// trip count of this loop as a normal unsigned value, if possible. This
4079 /// means that the actual trip count is always a multiple of the returned
4080 /// value (don't forget the trip count could very well be zero as well!).
4082 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4083 /// multiple of a constant (which is also the case if the trip count is simply
4084 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4085 /// if the trip count is very large (>= 2^32).
4087 /// As explained in the comments for getSmallConstantTripCount, this assumes
4088 /// that control exits the loop via ExitingBlock.
4089 unsigned ScalarEvolution::
4090 getSmallConstantTripMultiple(Loop *L, BasicBlock * /*ExitingBlock*/) {
4091 const SCEV *ExitCount = getBackedgeTakenCount(L);
4092 if (ExitCount == getCouldNotCompute())
4095 // Get the trip count from the BE count by adding 1.
4096 const SCEV *TCMul = getAddExpr(ExitCount,
4097 getConstant(ExitCount->getType(), 1));
4098 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4099 // to factor simple cases.
4100 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4101 TCMul = Mul->getOperand(0);
4103 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4107 ConstantInt *Result = MulC->getValue();
4109 // Guard against huge trip counts (this requires checking
4110 // for zero to handle the case where the trip count == -1 and the
4112 if (!Result || Result->getValue().getActiveBits() > 32 ||
4113 Result->getValue().getActiveBits() == 0)
4116 return (unsigned)Result->getZExtValue();
4119 // getExitCount - Get the expression for the number of loop iterations for which
4120 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4121 // SCEVCouldNotCompute.
4122 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4123 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4126 /// getBackedgeTakenCount - If the specified loop has a predictable
4127 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4128 /// object. The backedge-taken count is the number of times the loop header
4129 /// will be branched to from within the loop. This is one less than the
4130 /// trip count of the loop, since it doesn't count the first iteration,
4131 /// when the header is branched to from outside the loop.
4133 /// Note that it is not valid to call this method on a loop without a
4134 /// loop-invariant backedge-taken count (see
4135 /// hasLoopInvariantBackedgeTakenCount).
4137 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4138 return getBackedgeTakenInfo(L).getExact(this);
4141 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4142 /// return the least SCEV value that is known never to be less than the
4143 /// actual backedge taken count.
4144 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4145 return getBackedgeTakenInfo(L).getMax(this);
4148 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4149 /// onto the given Worklist.
4151 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4152 BasicBlock *Header = L->getHeader();
4154 // Push all Loop-header PHIs onto the Worklist stack.
4155 for (BasicBlock::iterator I = Header->begin();
4156 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4157 Worklist.push_back(PN);
4160 const ScalarEvolution::BackedgeTakenInfo &
4161 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4162 // Initially insert an invalid entry for this loop. If the insertion
4163 // succeeds, proceed to actually compute a backedge-taken count and
4164 // update the value. The temporary CouldNotCompute value tells SCEV
4165 // code elsewhere that it shouldn't attempt to request a new
4166 // backedge-taken count, which could result in infinite recursion.
4167 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4168 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4170 return Pair.first->second;
4172 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4173 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4174 // must be cleared in this scope.
4175 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4177 if (Result.getExact(this) != getCouldNotCompute()) {
4178 assert(isLoopInvariant(Result.getExact(this), L) &&
4179 isLoopInvariant(Result.getMax(this), L) &&
4180 "Computed backedge-taken count isn't loop invariant for loop!");
4181 ++NumTripCountsComputed;
4183 else if (Result.getMax(this) == getCouldNotCompute() &&
4184 isa<PHINode>(L->getHeader()->begin())) {
4185 // Only count loops that have phi nodes as not being computable.
4186 ++NumTripCountsNotComputed;
4189 // Now that we know more about the trip count for this loop, forget any
4190 // existing SCEV values for PHI nodes in this loop since they are only
4191 // conservative estimates made without the benefit of trip count
4192 // information. This is similar to the code in forgetLoop, except that
4193 // it handles SCEVUnknown PHI nodes specially.
4194 if (Result.hasAnyInfo()) {
4195 SmallVector<Instruction *, 16> Worklist;
4196 PushLoopPHIs(L, Worklist);
4198 SmallPtrSet<Instruction *, 8> Visited;
4199 while (!Worklist.empty()) {
4200 Instruction *I = Worklist.pop_back_val();
4201 if (!Visited.insert(I)) continue;
4203 ValueExprMapType::iterator It =
4204 ValueExprMap.find_as(static_cast<Value *>(I));
4205 if (It != ValueExprMap.end()) {
4206 const SCEV *Old = It->second;
4208 // SCEVUnknown for a PHI either means that it has an unrecognized
4209 // structure, or it's a PHI that's in the progress of being computed
4210 // by createNodeForPHI. In the former case, additional loop trip
4211 // count information isn't going to change anything. In the later
4212 // case, createNodeForPHI will perform the necessary updates on its
4213 // own when it gets to that point.
4214 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4215 forgetMemoizedResults(Old);
4216 ValueExprMap.erase(It);
4218 if (PHINode *PN = dyn_cast<PHINode>(I))
4219 ConstantEvolutionLoopExitValue.erase(PN);
4222 PushDefUseChildren(I, Worklist);
4226 // Re-lookup the insert position, since the call to
4227 // ComputeBackedgeTakenCount above could result in a
4228 // recusive call to getBackedgeTakenInfo (on a different
4229 // loop), which would invalidate the iterator computed
4231 return BackedgeTakenCounts.find(L)->second = Result;
4234 /// forgetLoop - This method should be called by the client when it has
4235 /// changed a loop in a way that may effect ScalarEvolution's ability to
4236 /// compute a trip count, or if the loop is deleted.
4237 void ScalarEvolution::forgetLoop(const Loop *L) {
4238 // Drop any stored trip count value.
4239 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4240 BackedgeTakenCounts.find(L);
4241 if (BTCPos != BackedgeTakenCounts.end()) {
4242 BTCPos->second.clear();
4243 BackedgeTakenCounts.erase(BTCPos);
4246 // Drop information about expressions based on loop-header PHIs.
4247 SmallVector<Instruction *, 16> Worklist;
4248 PushLoopPHIs(L, Worklist);
4250 SmallPtrSet<Instruction *, 8> Visited;
4251 while (!Worklist.empty()) {
4252 Instruction *I = Worklist.pop_back_val();
4253 if (!Visited.insert(I)) continue;
4255 ValueExprMapType::iterator It =
4256 ValueExprMap.find_as(static_cast<Value *>(I));
4257 if (It != ValueExprMap.end()) {
4258 forgetMemoizedResults(It->second);
4259 ValueExprMap.erase(It);
4260 if (PHINode *PN = dyn_cast<PHINode>(I))
4261 ConstantEvolutionLoopExitValue.erase(PN);
4264 PushDefUseChildren(I, Worklist);
4267 // Forget all contained loops too, to avoid dangling entries in the
4268 // ValuesAtScopes map.
4269 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4273 /// forgetValue - This method should be called by the client when it has
4274 /// changed a value in a way that may effect its value, or which may
4275 /// disconnect it from a def-use chain linking it to a loop.
4276 void ScalarEvolution::forgetValue(Value *V) {
4277 Instruction *I = dyn_cast<Instruction>(V);
4280 // Drop information about expressions based on loop-header PHIs.
4281 SmallVector<Instruction *, 16> Worklist;
4282 Worklist.push_back(I);
4284 SmallPtrSet<Instruction *, 8> Visited;
4285 while (!Worklist.empty()) {
4286 I = Worklist.pop_back_val();
4287 if (!Visited.insert(I)) continue;
4289 ValueExprMapType::iterator It =
4290 ValueExprMap.find_as(static_cast<Value *>(I));
4291 if (It != ValueExprMap.end()) {
4292 forgetMemoizedResults(It->second);
4293 ValueExprMap.erase(It);
4294 if (PHINode *PN = dyn_cast<PHINode>(I))
4295 ConstantEvolutionLoopExitValue.erase(PN);
4298 PushDefUseChildren(I, Worklist);
4302 /// getExact - Get the exact loop backedge taken count considering all loop
4303 /// exits. A computable result can only be return for loops with a single exit.
4304 /// Returning the minimum taken count among all exits is incorrect because one
4305 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4306 /// the limit of each loop test is never skipped. This is a valid assumption as
4307 /// long as the loop exits via that test. For precise results, it is the
4308 /// caller's responsibility to specify the relevant loop exit using
4309 /// getExact(ExitingBlock, SE).
4311 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4312 // If any exits were not computable, the loop is not computable.
4313 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4315 // We need exactly one computable exit.
4316 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4317 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4319 const SCEV *BECount = 0;
4320 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4321 ENT != 0; ENT = ENT->getNextExit()) {
4323 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4326 BECount = ENT->ExactNotTaken;
4327 else if (BECount != ENT->ExactNotTaken)
4328 return SE->getCouldNotCompute();
4330 assert(BECount && "Invalid not taken count for loop exit");
4334 /// getExact - Get the exact not taken count for this loop exit.
4336 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4337 ScalarEvolution *SE) const {
4338 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4339 ENT != 0; ENT = ENT->getNextExit()) {
4341 if (ENT->ExitingBlock == ExitingBlock)
4342 return ENT->ExactNotTaken;
4344 return SE->getCouldNotCompute();
4347 /// getMax - Get the max backedge taken count for the loop.
4349 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4350 return Max ? Max : SE->getCouldNotCompute();
4353 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4354 ScalarEvolution *SE) const {
4355 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4358 if (!ExitNotTaken.ExitingBlock)
4361 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4362 ENT != 0; ENT = ENT->getNextExit()) {
4364 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4365 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4372 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4373 /// computable exit into a persistent ExitNotTakenInfo array.
4374 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4375 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4376 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4379 ExitNotTaken.setIncomplete();
4381 unsigned NumExits = ExitCounts.size();
4382 if (NumExits == 0) return;
4384 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4385 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4386 if (NumExits == 1) return;
4388 // Handle the rare case of multiple computable exits.
4389 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4391 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4392 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4393 PrevENT->setNextExit(ENT);
4394 ENT->ExitingBlock = ExitCounts[i].first;
4395 ENT->ExactNotTaken = ExitCounts[i].second;
4399 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4400 void ScalarEvolution::BackedgeTakenInfo::clear() {
4401 ExitNotTaken.ExitingBlock = 0;
4402 ExitNotTaken.ExactNotTaken = 0;
4403 delete[] ExitNotTaken.getNextExit();
4406 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4407 /// of the specified loop will execute.
4408 ScalarEvolution::BackedgeTakenInfo
4409 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4410 SmallVector<BasicBlock *, 8> ExitingBlocks;
4411 L->getExitingBlocks(ExitingBlocks);
4413 // Examine all exits and pick the most conservative values.
4414 const SCEV *MaxBECount = getCouldNotCompute();
4415 bool CouldComputeBECount = true;
4416 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4417 const SCEV *LatchMaxCount = 0;
4418 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4419 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4420 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4421 if (EL.Exact == getCouldNotCompute())
4422 // We couldn't compute an exact value for this exit, so
4423 // we won't be able to compute an exact value for the loop.
4424 CouldComputeBECount = false;
4426 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4428 if (MaxBECount == getCouldNotCompute())
4429 MaxBECount = EL.Max;
4430 else if (EL.Max != getCouldNotCompute()) {
4431 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4432 // skip some loop tests. Taking the max over the exits is sufficiently
4433 // conservative. TODO: We could do better taking into consideration
4434 // non-latch exits that dominate the latch.
4435 if (EL.MustExit && ExitingBlocks[i] == Latch)
4436 LatchMaxCount = EL.Max;
4438 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4441 // Be more precise in the easy case of a loop latch that must exit.
4442 if (LatchMaxCount) {
4443 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, LatchMaxCount);
4445 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4448 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4449 /// loop will execute if it exits via the specified block.
4450 ScalarEvolution::ExitLimit
4451 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4453 // Okay, we've chosen an exiting block. See what condition causes us to
4454 // exit at this block and remember the exit block and whether all other targets
4455 // lead to the loop header.
4456 bool MustExecuteLoopHeader = true;
4457 BasicBlock *Exit = 0;
4458 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4460 if (!L->contains(*SI)) {
4461 if (Exit) // Multiple exit successors.
4462 return getCouldNotCompute();
4464 } else if (*SI != L->getHeader()) {
4465 MustExecuteLoopHeader = false;
4468 // At this point, we know we have a conditional branch that determines whether
4469 // the loop is exited. However, we don't know if the branch is executed each
4470 // time through the loop. If not, then the execution count of the branch will
4471 // not be equal to the trip count of the loop.
4473 // Currently we check for this by checking to see if the Exit branch goes to
4474 // the loop header. If so, we know it will always execute the same number of
4475 // times as the loop. We also handle the case where the exit block *is* the
4476 // loop header. This is common for un-rotated loops.
4478 // If both of those tests fail, walk up the unique predecessor chain to the
4479 // header, stopping if there is an edge that doesn't exit the loop. If the
4480 // header is reached, the execution count of the branch will be equal to the
4481 // trip count of the loop.
4483 // More extensive analysis could be done to handle more cases here.
4485 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4486 // The simple checks failed, try climbing the unique predecessor chain
4487 // up to the header.
4489 for (BasicBlock *BB = ExitingBlock; BB; ) {
4490 BasicBlock *Pred = BB->getUniquePredecessor();
4492 return getCouldNotCompute();
4493 TerminatorInst *PredTerm = Pred->getTerminator();
4494 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4495 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4498 // If the predecessor has a successor that isn't BB and isn't
4499 // outside the loop, assume the worst.
4500 if (L->contains(PredSucc))
4501 return getCouldNotCompute();
4503 if (Pred == L->getHeader()) {
4510 return getCouldNotCompute();
4513 TerminatorInst *Term = ExitingBlock->getTerminator();
4514 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4515 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4516 // Proceed to the next level to examine the exit condition expression.
4517 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4518 BI->getSuccessor(1),
4519 /*IsSubExpr=*/false);
4522 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4523 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4524 /*IsSubExpr=*/false);
4526 return getCouldNotCompute();
4529 /// ComputeExitLimitFromCond - Compute the number of times the
4530 /// backedge of the specified loop will execute if its exit condition
4531 /// were a conditional branch of ExitCond, TBB, and FBB.
4533 /// @param IsSubExpr is true if ExitCond does not directly control the exit
4534 /// branch. In this case, we cannot assume that the loop only exits when the
4535 /// condition is true and cannot infer that failing to meet the condition prior
4536 /// to integer wraparound results in undefined behavior.
4537 ScalarEvolution::ExitLimit
4538 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4543 // Check if the controlling expression for this loop is an And or Or.
4544 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4545 if (BO->getOpcode() == Instruction::And) {
4546 // Recurse on the operands of the and.
4547 bool EitherMayExit = L->contains(TBB);
4548 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4549 IsSubExpr || EitherMayExit);
4550 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4551 IsSubExpr || EitherMayExit);
4552 const SCEV *BECount = getCouldNotCompute();
4553 const SCEV *MaxBECount = getCouldNotCompute();
4554 bool MustExit = false;
4555 if (EitherMayExit) {
4556 // Both conditions must be true for the loop to continue executing.
4557 // Choose the less conservative count.
4558 if (EL0.Exact == getCouldNotCompute() ||
4559 EL1.Exact == getCouldNotCompute())
4560 BECount = getCouldNotCompute();
4562 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4563 if (EL0.Max == getCouldNotCompute())
4564 MaxBECount = EL1.Max;
4565 else if (EL1.Max == getCouldNotCompute())
4566 MaxBECount = EL0.Max;
4568 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4569 MustExit = EL0.MustExit || EL1.MustExit;
4571 // Both conditions must be true at the same time for the loop to exit.
4572 // For now, be conservative.
4573 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4574 if (EL0.Max == EL1.Max)
4575 MaxBECount = EL0.Max;
4576 if (EL0.Exact == EL1.Exact)
4577 BECount = EL0.Exact;
4578 MustExit = EL0.MustExit && EL1.MustExit;
4581 return ExitLimit(BECount, MaxBECount, MustExit);
4583 if (BO->getOpcode() == Instruction::Or) {
4584 // Recurse on the operands of the or.
4585 bool EitherMayExit = L->contains(FBB);
4586 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4587 IsSubExpr || EitherMayExit);
4588 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4589 IsSubExpr || EitherMayExit);
4590 const SCEV *BECount = getCouldNotCompute();
4591 const SCEV *MaxBECount = getCouldNotCompute();
4592 bool MustExit = false;
4593 if (EitherMayExit) {
4594 // Both conditions must be false for the loop to continue executing.
4595 // Choose the less conservative count.
4596 if (EL0.Exact == getCouldNotCompute() ||
4597 EL1.Exact == getCouldNotCompute())
4598 BECount = getCouldNotCompute();
4600 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4601 if (EL0.Max == getCouldNotCompute())
4602 MaxBECount = EL1.Max;
4603 else if (EL1.Max == getCouldNotCompute())
4604 MaxBECount = EL0.Max;
4606 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4607 MustExit = EL0.MustExit || EL1.MustExit;
4609 // Both conditions must be false at the same time for the loop to exit.
4610 // For now, be conservative.
4611 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4612 if (EL0.Max == EL1.Max)
4613 MaxBECount = EL0.Max;
4614 if (EL0.Exact == EL1.Exact)
4615 BECount = EL0.Exact;
4616 MustExit = EL0.MustExit && EL1.MustExit;
4619 return ExitLimit(BECount, MaxBECount, MustExit);
4623 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4624 // Proceed to the next level to examine the icmp.
4625 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4626 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, IsSubExpr);
4628 // Check for a constant condition. These are normally stripped out by
4629 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4630 // preserve the CFG and is temporarily leaving constant conditions
4632 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4633 if (L->contains(FBB) == !CI->getZExtValue())
4634 // The backedge is always taken.
4635 return getCouldNotCompute();
4637 // The backedge is never taken.
4638 return getConstant(CI->getType(), 0);
4641 // If it's not an integer or pointer comparison then compute it the hard way.
4642 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4645 /// ComputeExitLimitFromICmp - Compute the number of times the
4646 /// backedge of the specified loop will execute if its exit condition
4647 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4648 ScalarEvolution::ExitLimit
4649 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4655 // If the condition was exit on true, convert the condition to exit on false
4656 ICmpInst::Predicate Cond;
4657 if (!L->contains(FBB))
4658 Cond = ExitCond->getPredicate();
4660 Cond = ExitCond->getInversePredicate();
4662 // Handle common loops like: for (X = "string"; *X; ++X)
4663 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4664 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4666 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4667 if (ItCnt.hasAnyInfo())
4671 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4672 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4674 // Try to evaluate any dependencies out of the loop.
4675 LHS = getSCEVAtScope(LHS, L);
4676 RHS = getSCEVAtScope(RHS, L);
4678 // At this point, we would like to compute how many iterations of the
4679 // loop the predicate will return true for these inputs.
4680 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4681 // If there is a loop-invariant, force it into the RHS.
4682 std::swap(LHS, RHS);
4683 Cond = ICmpInst::getSwappedPredicate(Cond);
4686 // Simplify the operands before analyzing them.
4687 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4689 // If we have a comparison of a chrec against a constant, try to use value
4690 // ranges to answer this query.
4691 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4692 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4693 if (AddRec->getLoop() == L) {
4694 // Form the constant range.
4695 ConstantRange CompRange(
4696 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4698 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4699 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4703 case ICmpInst::ICMP_NE: { // while (X != Y)
4704 // Convert to: while (X-Y != 0)
4705 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4706 if (EL.hasAnyInfo()) return EL;
4709 case ICmpInst::ICMP_EQ: { // while (X == Y)
4710 // Convert to: while (X-Y == 0)
4711 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4712 if (EL.hasAnyInfo()) return EL;
4715 case ICmpInst::ICMP_SLT:
4716 case ICmpInst::ICMP_ULT: { // while (X < Y)
4717 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
4718 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, IsSubExpr);
4719 if (EL.hasAnyInfo()) return EL;
4722 case ICmpInst::ICMP_SGT:
4723 case ICmpInst::ICMP_UGT: { // while (X > Y)
4724 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
4725 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, IsSubExpr);
4726 if (EL.hasAnyInfo()) return EL;
4731 dbgs() << "ComputeBackedgeTakenCount ";
4732 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4733 dbgs() << "[unsigned] ";
4734 dbgs() << *LHS << " "
4735 << Instruction::getOpcodeName(Instruction::ICmp)
4736 << " " << *RHS << "\n";
4740 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4743 ScalarEvolution::ExitLimit
4744 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
4746 BasicBlock *ExitingBlock,
4748 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
4750 // Give up if the exit is the default dest of a switch.
4751 if (Switch->getDefaultDest() == ExitingBlock)
4752 return getCouldNotCompute();
4754 assert(L->contains(Switch->getDefaultDest()) &&
4755 "Default case must not exit the loop!");
4756 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
4757 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
4759 // while (X != Y) --> while (X-Y != 0)
4760 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4761 if (EL.hasAnyInfo())
4764 return getCouldNotCompute();
4767 static ConstantInt *
4768 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4769 ScalarEvolution &SE) {
4770 const SCEV *InVal = SE.getConstant(C);
4771 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4772 assert(isa<SCEVConstant>(Val) &&
4773 "Evaluation of SCEV at constant didn't fold correctly?");
4774 return cast<SCEVConstant>(Val)->getValue();
4777 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4778 /// 'icmp op load X, cst', try to see if we can compute the backedge
4779 /// execution count.
4780 ScalarEvolution::ExitLimit
4781 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4785 ICmpInst::Predicate predicate) {
4787 if (LI->isVolatile()) return getCouldNotCompute();
4789 // Check to see if the loaded pointer is a getelementptr of a global.
4790 // TODO: Use SCEV instead of manually grubbing with GEPs.
4791 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4792 if (!GEP) return getCouldNotCompute();
4794 // Make sure that it is really a constant global we are gepping, with an
4795 // initializer, and make sure the first IDX is really 0.
4796 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4797 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4798 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4799 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4800 return getCouldNotCompute();
4802 // Okay, we allow one non-constant index into the GEP instruction.
4804 std::vector<Constant*> Indexes;
4805 unsigned VarIdxNum = 0;
4806 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4807 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4808 Indexes.push_back(CI);
4809 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4810 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4811 VarIdx = GEP->getOperand(i);
4813 Indexes.push_back(0);
4816 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4818 return getCouldNotCompute();
4820 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4821 // Check to see if X is a loop variant variable value now.
4822 const SCEV *Idx = getSCEV(VarIdx);
4823 Idx = getSCEVAtScope(Idx, L);
4825 // We can only recognize very limited forms of loop index expressions, in
4826 // particular, only affine AddRec's like {C1,+,C2}.
4827 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4828 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4829 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4830 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4831 return getCouldNotCompute();
4833 unsigned MaxSteps = MaxBruteForceIterations;
4834 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4835 ConstantInt *ItCst = ConstantInt::get(
4836 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4837 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4839 // Form the GEP offset.
4840 Indexes[VarIdxNum] = Val;
4842 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4844 if (Result == 0) break; // Cannot compute!
4846 // Evaluate the condition for this iteration.
4847 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4848 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4849 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4851 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4852 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4855 ++NumArrayLenItCounts;
4856 return getConstant(ItCst); // Found terminating iteration!
4859 return getCouldNotCompute();
4863 /// CanConstantFold - Return true if we can constant fold an instruction of the
4864 /// specified type, assuming that all operands were constants.
4865 static bool CanConstantFold(const Instruction *I) {
4866 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4867 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4871 if (const CallInst *CI = dyn_cast<CallInst>(I))
4872 if (const Function *F = CI->getCalledFunction())
4873 return canConstantFoldCallTo(F);
4877 /// Determine whether this instruction can constant evolve within this loop
4878 /// assuming its operands can all constant evolve.
4879 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4880 // An instruction outside of the loop can't be derived from a loop PHI.
4881 if (!L->contains(I)) return false;
4883 if (isa<PHINode>(I)) {
4884 if (L->getHeader() == I->getParent())
4887 // We don't currently keep track of the control flow needed to evaluate
4888 // PHIs, so we cannot handle PHIs inside of loops.
4892 // If we won't be able to constant fold this expression even if the operands
4893 // are constants, bail early.
4894 return CanConstantFold(I);
4897 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4898 /// recursing through each instruction operand until reaching a loop header phi.
4900 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4901 DenseMap<Instruction *, PHINode *> &PHIMap) {
4903 // Otherwise, we can evaluate this instruction if all of its operands are
4904 // constant or derived from a PHI node themselves.
4906 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4907 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4909 if (isa<Constant>(*OpI)) continue;
4911 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4912 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4914 PHINode *P = dyn_cast<PHINode>(OpInst);
4916 // If this operand is already visited, reuse the prior result.
4917 // We may have P != PHI if this is the deepest point at which the
4918 // inconsistent paths meet.
4919 P = PHIMap.lookup(OpInst);
4921 // Recurse and memoize the results, whether a phi is found or not.
4922 // This recursive call invalidates pointers into PHIMap.
4923 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4926 if (P == 0) return 0; // Not evolving from PHI
4927 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4930 // This is a expression evolving from a constant PHI!
4934 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4935 /// in the loop that V is derived from. We allow arbitrary operations along the
4936 /// way, but the operands of an operation must either be constants or a value
4937 /// derived from a constant PHI. If this expression does not fit with these
4938 /// constraints, return null.
4939 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4940 Instruction *I = dyn_cast<Instruction>(V);
4941 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4943 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4947 // Record non-constant instructions contained by the loop.
4948 DenseMap<Instruction *, PHINode *> PHIMap;
4949 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4952 /// EvaluateExpression - Given an expression that passes the
4953 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4954 /// in the loop has the value PHIVal. If we can't fold this expression for some
4955 /// reason, return null.
4956 static Constant *EvaluateExpression(Value *V, const Loop *L,
4957 DenseMap<Instruction *, Constant *> &Vals,
4958 const DataLayout *DL,
4959 const TargetLibraryInfo *TLI) {
4960 // Convenient constant check, but redundant for recursive calls.
4961 if (Constant *C = dyn_cast<Constant>(V)) return C;
4962 Instruction *I = dyn_cast<Instruction>(V);
4965 if (Constant *C = Vals.lookup(I)) return C;
4967 // An instruction inside the loop depends on a value outside the loop that we
4968 // weren't given a mapping for, or a value such as a call inside the loop.
4969 if (!canConstantEvolve(I, L)) return 0;
4971 // An unmapped PHI can be due to a branch or another loop inside this loop,
4972 // or due to this not being the initial iteration through a loop where we
4973 // couldn't compute the evolution of this particular PHI last time.
4974 if (isa<PHINode>(I)) return 0;
4976 std::vector<Constant*> Operands(I->getNumOperands());
4978 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4979 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4981 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4982 if (!Operands[i]) return 0;
4985 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
4991 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4992 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4993 Operands[1], DL, TLI);
4994 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4995 if (!LI->isVolatile())
4996 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
4998 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5002 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5003 /// in the header of its containing loop, we know the loop executes a
5004 /// constant number of times, and the PHI node is just a recurrence
5005 /// involving constants, fold it.
5007 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5010 DenseMap<PHINode*, Constant*>::const_iterator I =
5011 ConstantEvolutionLoopExitValue.find(PN);
5012 if (I != ConstantEvolutionLoopExitValue.end())
5015 if (BEs.ugt(MaxBruteForceIterations))
5016 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
5018 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5020 DenseMap<Instruction *, Constant *> CurrentIterVals;
5021 BasicBlock *Header = L->getHeader();
5022 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5024 // Since the loop is canonicalized, the PHI node must have two entries. One
5025 // entry must be a constant (coming in from outside of the loop), and the
5026 // second must be derived from the same PHI.
5027 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5029 for (BasicBlock::iterator I = Header->begin();
5030 (PHI = dyn_cast<PHINode>(I)); ++I) {
5031 Constant *StartCST =
5032 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5033 if (StartCST == 0) continue;
5034 CurrentIterVals[PHI] = StartCST;
5036 if (!CurrentIterVals.count(PN))
5039 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5041 // Execute the loop symbolically to determine the exit value.
5042 if (BEs.getActiveBits() >= 32)
5043 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
5045 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5046 unsigned IterationNum = 0;
5047 for (; ; ++IterationNum) {
5048 if (IterationNum == NumIterations)
5049 return RetVal = CurrentIterVals[PN]; // Got exit value!
5051 // Compute the value of the PHIs for the next iteration.
5052 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5053 DenseMap<Instruction *, Constant *> NextIterVals;
5054 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5057 return 0; // Couldn't evaluate!
5058 NextIterVals[PN] = NextPHI;
5060 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5062 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5063 // cease to be able to evaluate one of them or if they stop evolving,
5064 // because that doesn't necessarily prevent us from computing PN.
5065 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5066 for (DenseMap<Instruction *, Constant *>::const_iterator
5067 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5068 PHINode *PHI = dyn_cast<PHINode>(I->first);
5069 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5070 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5072 // We use two distinct loops because EvaluateExpression may invalidate any
5073 // iterators into CurrentIterVals.
5074 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5075 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5076 PHINode *PHI = I->first;
5077 Constant *&NextPHI = NextIterVals[PHI];
5078 if (!NextPHI) { // Not already computed.
5079 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5080 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5082 if (NextPHI != I->second)
5083 StoppedEvolving = false;
5086 // If all entries in CurrentIterVals == NextIterVals then we can stop
5087 // iterating, the loop can't continue to change.
5088 if (StoppedEvolving)
5089 return RetVal = CurrentIterVals[PN];
5091 CurrentIterVals.swap(NextIterVals);
5095 /// ComputeExitCountExhaustively - If the loop is known to execute a
5096 /// constant number of times (the condition evolves only from constants),
5097 /// try to evaluate a few iterations of the loop until we get the exit
5098 /// condition gets a value of ExitWhen (true or false). If we cannot
5099 /// evaluate the trip count of the loop, return getCouldNotCompute().
5100 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5103 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5104 if (PN == 0) return getCouldNotCompute();
5106 // If the loop is canonicalized, the PHI will have exactly two entries.
5107 // That's the only form we support here.
5108 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5110 DenseMap<Instruction *, Constant *> CurrentIterVals;
5111 BasicBlock *Header = L->getHeader();
5112 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5114 // One entry must be a constant (coming in from outside of the loop), and the
5115 // second must be derived from the same PHI.
5116 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5118 for (BasicBlock::iterator I = Header->begin();
5119 (PHI = dyn_cast<PHINode>(I)); ++I) {
5120 Constant *StartCST =
5121 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5122 if (StartCST == 0) continue;
5123 CurrentIterVals[PHI] = StartCST;
5125 if (!CurrentIterVals.count(PN))
5126 return getCouldNotCompute();
5128 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5129 // the loop symbolically to determine when the condition gets a value of
5132 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5133 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5134 ConstantInt *CondVal =
5135 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5138 // Couldn't symbolically evaluate.
5139 if (!CondVal) return getCouldNotCompute();
5141 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5142 ++NumBruteForceTripCountsComputed;
5143 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5146 // Update all the PHI nodes for the next iteration.
5147 DenseMap<Instruction *, Constant *> NextIterVals;
5149 // Create a list of which PHIs we need to compute. We want to do this before
5150 // calling EvaluateExpression on them because that may invalidate iterators
5151 // into CurrentIterVals.
5152 SmallVector<PHINode *, 8> PHIsToCompute;
5153 for (DenseMap<Instruction *, Constant *>::const_iterator
5154 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5155 PHINode *PHI = dyn_cast<PHINode>(I->first);
5156 if (!PHI || PHI->getParent() != Header) continue;
5157 PHIsToCompute.push_back(PHI);
5159 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5160 E = PHIsToCompute.end(); I != E; ++I) {
5162 Constant *&NextPHI = NextIterVals[PHI];
5163 if (NextPHI) continue; // Already computed!
5165 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5166 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5168 CurrentIterVals.swap(NextIterVals);
5171 // Too many iterations were needed to evaluate.
5172 return getCouldNotCompute();
5175 /// getSCEVAtScope - Return a SCEV expression for the specified value
5176 /// at the specified scope in the program. The L value specifies a loop
5177 /// nest to evaluate the expression at, where null is the top-level or a
5178 /// specified loop is immediately inside of the loop.
5180 /// This method can be used to compute the exit value for a variable defined
5181 /// in a loop by querying what the value will hold in the parent loop.
5183 /// In the case that a relevant loop exit value cannot be computed, the
5184 /// original value V is returned.
5185 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5186 // Check to see if we've folded this expression at this loop before.
5187 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5188 for (unsigned u = 0; u < Values.size(); u++) {
5189 if (Values[u].first == L)
5190 return Values[u].second ? Values[u].second : V;
5192 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(0)));
5193 // Otherwise compute it.
5194 const SCEV *C = computeSCEVAtScope(V, L);
5195 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5196 for (unsigned u = Values2.size(); u > 0; u--) {
5197 if (Values2[u - 1].first == L) {
5198 Values2[u - 1].second = C;
5205 /// This builds up a Constant using the ConstantExpr interface. That way, we
5206 /// will return Constants for objects which aren't represented by a
5207 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5208 /// Returns NULL if the SCEV isn't representable as a Constant.
5209 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5210 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5211 case scCouldNotCompute:
5215 return cast<SCEVConstant>(V)->getValue();
5217 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5218 case scSignExtend: {
5219 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5220 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5221 return ConstantExpr::getSExt(CastOp, SS->getType());
5224 case scZeroExtend: {
5225 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5226 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5227 return ConstantExpr::getZExt(CastOp, SZ->getType());
5231 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5232 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5233 return ConstantExpr::getTrunc(CastOp, ST->getType());
5237 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5238 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5239 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5240 unsigned AS = PTy->getAddressSpace();
5241 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5242 C = ConstantExpr::getBitCast(C, DestPtrTy);
5244 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5245 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5249 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5250 unsigned AS = C2->getType()->getPointerAddressSpace();
5252 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5253 // The offsets have been converted to bytes. We can add bytes to an
5254 // i8* by GEP with the byte count in the first index.
5255 C = ConstantExpr::getBitCast(C, DestPtrTy);
5258 // Don't bother trying to sum two pointers. We probably can't
5259 // statically compute a load that results from it anyway.
5260 if (C2->getType()->isPointerTy())
5263 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5264 if (PTy->getElementType()->isStructTy())
5265 C2 = ConstantExpr::getIntegerCast(
5266 C2, Type::getInt32Ty(C->getContext()), true);
5267 C = ConstantExpr::getGetElementPtr(C, C2);
5269 C = ConstantExpr::getAdd(C, C2);
5276 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5277 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5278 // Don't bother with pointers at all.
5279 if (C->getType()->isPointerTy()) return 0;
5280 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5281 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5282 if (!C2 || C2->getType()->isPointerTy()) return 0;
5283 C = ConstantExpr::getMul(C, C2);
5290 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5291 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5292 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5293 if (LHS->getType() == RHS->getType())
5294 return ConstantExpr::getUDiv(LHS, RHS);
5299 break; // TODO: smax, umax.
5304 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5305 if (isa<SCEVConstant>(V)) return V;
5307 // If this instruction is evolved from a constant-evolving PHI, compute the
5308 // exit value from the loop without using SCEVs.
5309 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5310 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5311 const Loop *LI = (*this->LI)[I->getParent()];
5312 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5313 if (PHINode *PN = dyn_cast<PHINode>(I))
5314 if (PN->getParent() == LI->getHeader()) {
5315 // Okay, there is no closed form solution for the PHI node. Check
5316 // to see if the loop that contains it has a known backedge-taken
5317 // count. If so, we may be able to force computation of the exit
5319 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5320 if (const SCEVConstant *BTCC =
5321 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5322 // Okay, we know how many times the containing loop executes. If
5323 // this is a constant evolving PHI node, get the final value at
5324 // the specified iteration number.
5325 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5326 BTCC->getValue()->getValue(),
5328 if (RV) return getSCEV(RV);
5332 // Okay, this is an expression that we cannot symbolically evaluate
5333 // into a SCEV. Check to see if it's possible to symbolically evaluate
5334 // the arguments into constants, and if so, try to constant propagate the
5335 // result. This is particularly useful for computing loop exit values.
5336 if (CanConstantFold(I)) {
5337 SmallVector<Constant *, 4> Operands;
5338 bool MadeImprovement = false;
5339 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5340 Value *Op = I->getOperand(i);
5341 if (Constant *C = dyn_cast<Constant>(Op)) {
5342 Operands.push_back(C);
5346 // If any of the operands is non-constant and if they are
5347 // non-integer and non-pointer, don't even try to analyze them
5348 // with scev techniques.
5349 if (!isSCEVable(Op->getType()))
5352 const SCEV *OrigV = getSCEV(Op);
5353 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5354 MadeImprovement |= OrigV != OpV;
5356 Constant *C = BuildConstantFromSCEV(OpV);
5358 if (C->getType() != Op->getType())
5359 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5363 Operands.push_back(C);
5366 // Check to see if getSCEVAtScope actually made an improvement.
5367 if (MadeImprovement) {
5369 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5370 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5371 Operands[0], Operands[1], DL,
5373 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5374 if (!LI->isVolatile())
5375 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5377 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5385 // This is some other type of SCEVUnknown, just return it.
5389 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5390 // Avoid performing the look-up in the common case where the specified
5391 // expression has no loop-variant portions.
5392 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5393 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5394 if (OpAtScope != Comm->getOperand(i)) {
5395 // Okay, at least one of these operands is loop variant but might be
5396 // foldable. Build a new instance of the folded commutative expression.
5397 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5398 Comm->op_begin()+i);
5399 NewOps.push_back(OpAtScope);
5401 for (++i; i != e; ++i) {
5402 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5403 NewOps.push_back(OpAtScope);
5405 if (isa<SCEVAddExpr>(Comm))
5406 return getAddExpr(NewOps);
5407 if (isa<SCEVMulExpr>(Comm))
5408 return getMulExpr(NewOps);
5409 if (isa<SCEVSMaxExpr>(Comm))
5410 return getSMaxExpr(NewOps);
5411 if (isa<SCEVUMaxExpr>(Comm))
5412 return getUMaxExpr(NewOps);
5413 llvm_unreachable("Unknown commutative SCEV type!");
5416 // If we got here, all operands are loop invariant.
5420 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5421 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5422 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5423 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5424 return Div; // must be loop invariant
5425 return getUDivExpr(LHS, RHS);
5428 // If this is a loop recurrence for a loop that does not contain L, then we
5429 // are dealing with the final value computed by the loop.
5430 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5431 // First, attempt to evaluate each operand.
5432 // Avoid performing the look-up in the common case where the specified
5433 // expression has no loop-variant portions.
5434 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5435 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5436 if (OpAtScope == AddRec->getOperand(i))
5439 // Okay, at least one of these operands is loop variant but might be
5440 // foldable. Build a new instance of the folded commutative expression.
5441 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5442 AddRec->op_begin()+i);
5443 NewOps.push_back(OpAtScope);
5444 for (++i; i != e; ++i)
5445 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5447 const SCEV *FoldedRec =
5448 getAddRecExpr(NewOps, AddRec->getLoop(),
5449 AddRec->getNoWrapFlags(SCEV::FlagNW));
5450 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5451 // The addrec may be folded to a nonrecurrence, for example, if the
5452 // induction variable is multiplied by zero after constant folding. Go
5453 // ahead and return the folded value.
5459 // If the scope is outside the addrec's loop, evaluate it by using the
5460 // loop exit value of the addrec.
5461 if (!AddRec->getLoop()->contains(L)) {
5462 // To evaluate this recurrence, we need to know how many times the AddRec
5463 // loop iterates. Compute this now.
5464 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5465 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5467 // Then, evaluate the AddRec.
5468 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5474 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5475 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5476 if (Op == Cast->getOperand())
5477 return Cast; // must be loop invariant
5478 return getZeroExtendExpr(Op, Cast->getType());
5481 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5482 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5483 if (Op == Cast->getOperand())
5484 return Cast; // must be loop invariant
5485 return getSignExtendExpr(Op, Cast->getType());
5488 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5489 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5490 if (Op == Cast->getOperand())
5491 return Cast; // must be loop invariant
5492 return getTruncateExpr(Op, Cast->getType());
5495 llvm_unreachable("Unknown SCEV type!");
5498 /// getSCEVAtScope - This is a convenience function which does
5499 /// getSCEVAtScope(getSCEV(V), L).
5500 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5501 return getSCEVAtScope(getSCEV(V), L);
5504 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5505 /// following equation:
5507 /// A * X = B (mod N)
5509 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5510 /// A and B isn't important.
5512 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5513 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5514 ScalarEvolution &SE) {
5515 uint32_t BW = A.getBitWidth();
5516 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5517 assert(A != 0 && "A must be non-zero.");
5521 // The gcd of A and N may have only one prime factor: 2. The number of
5522 // trailing zeros in A is its multiplicity
5523 uint32_t Mult2 = A.countTrailingZeros();
5526 // 2. Check if B is divisible by D.
5528 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5529 // is not less than multiplicity of this prime factor for D.
5530 if (B.countTrailingZeros() < Mult2)
5531 return SE.getCouldNotCompute();
5533 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5536 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5537 // bit width during computations.
5538 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5539 APInt Mod(BW + 1, 0);
5540 Mod.setBit(BW - Mult2); // Mod = N / D
5541 APInt I = AD.multiplicativeInverse(Mod);
5543 // 4. Compute the minimum unsigned root of the equation:
5544 // I * (B / D) mod (N / D)
5545 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5547 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5549 return SE.getConstant(Result.trunc(BW));
5552 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5553 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5554 /// might be the same) or two SCEVCouldNotCompute objects.
5556 static std::pair<const SCEV *,const SCEV *>
5557 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5558 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5559 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5560 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5561 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5563 // We currently can only solve this if the coefficients are constants.
5564 if (!LC || !MC || !NC) {
5565 const SCEV *CNC = SE.getCouldNotCompute();
5566 return std::make_pair(CNC, CNC);
5569 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5570 const APInt &L = LC->getValue()->getValue();
5571 const APInt &M = MC->getValue()->getValue();
5572 const APInt &N = NC->getValue()->getValue();
5573 APInt Two(BitWidth, 2);
5574 APInt Four(BitWidth, 4);
5577 using namespace APIntOps;
5579 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5580 // The B coefficient is M-N/2
5584 // The A coefficient is N/2
5585 APInt A(N.sdiv(Two));
5587 // Compute the B^2-4ac term.
5590 SqrtTerm -= Four * (A * C);
5592 if (SqrtTerm.isNegative()) {
5593 // The loop is provably infinite.
5594 const SCEV *CNC = SE.getCouldNotCompute();
5595 return std::make_pair(CNC, CNC);
5598 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5599 // integer value or else APInt::sqrt() will assert.
5600 APInt SqrtVal(SqrtTerm.sqrt());
5602 // Compute the two solutions for the quadratic formula.
5603 // The divisions must be performed as signed divisions.
5606 if (TwoA.isMinValue()) {
5607 const SCEV *CNC = SE.getCouldNotCompute();
5608 return std::make_pair(CNC, CNC);
5611 LLVMContext &Context = SE.getContext();
5613 ConstantInt *Solution1 =
5614 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5615 ConstantInt *Solution2 =
5616 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5618 return std::make_pair(SE.getConstant(Solution1),
5619 SE.getConstant(Solution2));
5620 } // end APIntOps namespace
5623 /// HowFarToZero - Return the number of times a backedge comparing the specified
5624 /// value to zero will execute. If not computable, return CouldNotCompute.
5626 /// This is only used for loops with a "x != y" exit test. The exit condition is
5627 /// now expressed as a single expression, V = x-y. So the exit test is
5628 /// effectively V != 0. We know and take advantage of the fact that this
5629 /// expression only being used in a comparison by zero context.
5630 ScalarEvolution::ExitLimit
5631 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
5632 // If the value is a constant
5633 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5634 // If the value is already zero, the branch will execute zero times.
5635 if (C->getValue()->isZero()) return C;
5636 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5639 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5640 if (!AddRec || AddRec->getLoop() != L)
5641 return getCouldNotCompute();
5643 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5644 // the quadratic equation to solve it.
5645 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5646 std::pair<const SCEV *,const SCEV *> Roots =
5647 SolveQuadraticEquation(AddRec, *this);
5648 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5649 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5652 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5653 << " sol#2: " << *R2 << "\n";
5655 // Pick the smallest positive root value.
5656 if (ConstantInt *CB =
5657 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5660 if (CB->getZExtValue() == false)
5661 std::swap(R1, R2); // R1 is the minimum root now.
5663 // We can only use this value if the chrec ends up with an exact zero
5664 // value at this index. When solving for "X*X != 5", for example, we
5665 // should not accept a root of 2.
5666 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5668 return R1; // We found a quadratic root!
5671 return getCouldNotCompute();
5674 // Otherwise we can only handle this if it is affine.
5675 if (!AddRec->isAffine())
5676 return getCouldNotCompute();
5678 // If this is an affine expression, the execution count of this branch is
5679 // the minimum unsigned root of the following equation:
5681 // Start + Step*N = 0 (mod 2^BW)
5685 // Step*N = -Start (mod 2^BW)
5687 // where BW is the common bit width of Start and Step.
5689 // Get the initial value for the loop.
5690 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5691 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5693 // For now we handle only constant steps.
5695 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5696 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5697 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5698 // We have not yet seen any such cases.
5699 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5700 if (StepC == 0 || StepC->getValue()->equalsInt(0))
5701 return getCouldNotCompute();
5703 // For positive steps (counting up until unsigned overflow):
5704 // N = -Start/Step (as unsigned)
5705 // For negative steps (counting down to zero):
5707 // First compute the unsigned distance from zero in the direction of Step.
5708 bool CountDown = StepC->getValue()->getValue().isNegative();
5709 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5711 // Handle unitary steps, which cannot wraparound.
5712 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5713 // N = Distance (as unsigned)
5714 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5715 ConstantRange CR = getUnsignedRange(Start);
5716 const SCEV *MaxBECount;
5717 if (!CountDown && CR.getUnsignedMin().isMinValue())
5718 // When counting up, the worst starting value is 1, not 0.
5719 MaxBECount = CR.getUnsignedMax().isMinValue()
5720 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5721 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5723 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5724 : -CR.getUnsignedMin());
5725 return ExitLimit(Distance, MaxBECount, /*MustExit=*/true);
5728 // If the recurrence is known not to wraparound, unsigned divide computes the
5729 // back edge count. (Ideally we would have an "isexact" bit for udiv). We know
5730 // that the value will either become zero (and thus the loop terminates), that
5731 // the loop will terminate through some other exit condition first, or that
5732 // the loop has undefined behavior. This means we can't "miss" the exit
5733 // value, even with nonunit stride, and exit later via the same branch. Note
5734 // that we can skip this exit if loop later exits via a different
5735 // branch. Hence MustExit=false.
5737 // This is only valid for expressions that directly compute the loop exit. It
5738 // is invalid for subexpressions in which the loop may exit through this
5739 // branch even if this subexpression is false. In that case, the trip count
5740 // computed by this udiv could be smaller than the number of well-defined
5742 if (!IsSubExpr && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5744 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5745 return ExitLimit(Exact, Exact, /*MustExit=*/false);
5748 // If Step is a power of two that evenly divides Start we know that the loop
5749 // will always terminate. Start may not be a constant so we just have the
5750 // number of trailing zeros available. This is safe even in presence of
5751 // overflow as the recurrence will overflow to exactly 0.
5752 const APInt &StepV = StepC->getValue()->getValue();
5753 if (StepV.isPowerOf2() &&
5754 GetMinTrailingZeros(getNegativeSCEV(Start)) >= StepV.countTrailingZeros())
5755 return getUDivExactExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5757 // Then, try to solve the above equation provided that Start is constant.
5758 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5759 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5760 -StartC->getValue()->getValue(),
5762 return getCouldNotCompute();
5765 /// HowFarToNonZero - Return the number of times a backedge checking the
5766 /// specified value for nonzero will execute. If not computable, return
5768 ScalarEvolution::ExitLimit
5769 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5770 // Loops that look like: while (X == 0) are very strange indeed. We don't
5771 // handle them yet except for the trivial case. This could be expanded in the
5772 // future as needed.
5774 // If the value is a constant, check to see if it is known to be non-zero
5775 // already. If so, the backedge will execute zero times.
5776 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5777 if (!C->getValue()->isNullValue())
5778 return getConstant(C->getType(), 0);
5779 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5782 // We could implement others, but I really doubt anyone writes loops like
5783 // this, and if they did, they would already be constant folded.
5784 return getCouldNotCompute();
5787 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5788 /// (which may not be an immediate predecessor) which has exactly one
5789 /// successor from which BB is reachable, or null if no such block is
5792 std::pair<BasicBlock *, BasicBlock *>
5793 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5794 // If the block has a unique predecessor, then there is no path from the
5795 // predecessor to the block that does not go through the direct edge
5796 // from the predecessor to the block.
5797 if (BasicBlock *Pred = BB->getSinglePredecessor())
5798 return std::make_pair(Pred, BB);
5800 // A loop's header is defined to be a block that dominates the loop.
5801 // If the header has a unique predecessor outside the loop, it must be
5802 // a block that has exactly one successor that can reach the loop.
5803 if (Loop *L = LI->getLoopFor(BB))
5804 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5806 return std::pair<BasicBlock *, BasicBlock *>();
5809 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5810 /// testing whether two expressions are equal, however for the purposes of
5811 /// looking for a condition guarding a loop, it can be useful to be a little
5812 /// more general, since a front-end may have replicated the controlling
5815 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5816 // Quick check to see if they are the same SCEV.
5817 if (A == B) return true;
5819 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5820 // two different instructions with the same value. Check for this case.
5821 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5822 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5823 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5824 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5825 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5828 // Otherwise assume they may have a different value.
5832 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5833 /// predicate Pred. Return true iff any changes were made.
5835 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5836 const SCEV *&LHS, const SCEV *&RHS,
5838 bool Changed = false;
5840 // If we hit the max recursion limit bail out.
5844 // Canonicalize a constant to the right side.
5845 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5846 // Check for both operands constant.
5847 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5848 if (ConstantExpr::getICmp(Pred,
5850 RHSC->getValue())->isNullValue())
5851 goto trivially_false;
5853 goto trivially_true;
5855 // Otherwise swap the operands to put the constant on the right.
5856 std::swap(LHS, RHS);
5857 Pred = ICmpInst::getSwappedPredicate(Pred);
5861 // If we're comparing an addrec with a value which is loop-invariant in the
5862 // addrec's loop, put the addrec on the left. Also make a dominance check,
5863 // as both operands could be addrecs loop-invariant in each other's loop.
5864 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5865 const Loop *L = AR->getLoop();
5866 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5867 std::swap(LHS, RHS);
5868 Pred = ICmpInst::getSwappedPredicate(Pred);
5873 // If there's a constant operand, canonicalize comparisons with boundary
5874 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5875 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5876 const APInt &RA = RC->getValue()->getValue();
5878 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5879 case ICmpInst::ICMP_EQ:
5880 case ICmpInst::ICMP_NE:
5881 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5883 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5884 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5885 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5886 ME->getOperand(0)->isAllOnesValue()) {
5887 RHS = AE->getOperand(1);
5888 LHS = ME->getOperand(1);
5892 case ICmpInst::ICMP_UGE:
5893 if ((RA - 1).isMinValue()) {
5894 Pred = ICmpInst::ICMP_NE;
5895 RHS = getConstant(RA - 1);
5899 if (RA.isMaxValue()) {
5900 Pred = ICmpInst::ICMP_EQ;
5904 if (RA.isMinValue()) goto trivially_true;
5906 Pred = ICmpInst::ICMP_UGT;
5907 RHS = getConstant(RA - 1);
5910 case ICmpInst::ICMP_ULE:
5911 if ((RA + 1).isMaxValue()) {
5912 Pred = ICmpInst::ICMP_NE;
5913 RHS = getConstant(RA + 1);
5917 if (RA.isMinValue()) {
5918 Pred = ICmpInst::ICMP_EQ;
5922 if (RA.isMaxValue()) goto trivially_true;
5924 Pred = ICmpInst::ICMP_ULT;
5925 RHS = getConstant(RA + 1);
5928 case ICmpInst::ICMP_SGE:
5929 if ((RA - 1).isMinSignedValue()) {
5930 Pred = ICmpInst::ICMP_NE;
5931 RHS = getConstant(RA - 1);
5935 if (RA.isMaxSignedValue()) {
5936 Pred = ICmpInst::ICMP_EQ;
5940 if (RA.isMinSignedValue()) goto trivially_true;
5942 Pred = ICmpInst::ICMP_SGT;
5943 RHS = getConstant(RA - 1);
5946 case ICmpInst::ICMP_SLE:
5947 if ((RA + 1).isMaxSignedValue()) {
5948 Pred = ICmpInst::ICMP_NE;
5949 RHS = getConstant(RA + 1);
5953 if (RA.isMinSignedValue()) {
5954 Pred = ICmpInst::ICMP_EQ;
5958 if (RA.isMaxSignedValue()) goto trivially_true;
5960 Pred = ICmpInst::ICMP_SLT;
5961 RHS = getConstant(RA + 1);
5964 case ICmpInst::ICMP_UGT:
5965 if (RA.isMinValue()) {
5966 Pred = ICmpInst::ICMP_NE;
5970 if ((RA + 1).isMaxValue()) {
5971 Pred = ICmpInst::ICMP_EQ;
5972 RHS = getConstant(RA + 1);
5976 if (RA.isMaxValue()) goto trivially_false;
5978 case ICmpInst::ICMP_ULT:
5979 if (RA.isMaxValue()) {
5980 Pred = ICmpInst::ICMP_NE;
5984 if ((RA - 1).isMinValue()) {
5985 Pred = ICmpInst::ICMP_EQ;
5986 RHS = getConstant(RA - 1);
5990 if (RA.isMinValue()) goto trivially_false;
5992 case ICmpInst::ICMP_SGT:
5993 if (RA.isMinSignedValue()) {
5994 Pred = ICmpInst::ICMP_NE;
5998 if ((RA + 1).isMaxSignedValue()) {
5999 Pred = ICmpInst::ICMP_EQ;
6000 RHS = getConstant(RA + 1);
6004 if (RA.isMaxSignedValue()) goto trivially_false;
6006 case ICmpInst::ICMP_SLT:
6007 if (RA.isMaxSignedValue()) {
6008 Pred = ICmpInst::ICMP_NE;
6012 if ((RA - 1).isMinSignedValue()) {
6013 Pred = ICmpInst::ICMP_EQ;
6014 RHS = getConstant(RA - 1);
6018 if (RA.isMinSignedValue()) goto trivially_false;
6023 // Check for obvious equality.
6024 if (HasSameValue(LHS, RHS)) {
6025 if (ICmpInst::isTrueWhenEqual(Pred))
6026 goto trivially_true;
6027 if (ICmpInst::isFalseWhenEqual(Pred))
6028 goto trivially_false;
6031 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6032 // adding or subtracting 1 from one of the operands.
6034 case ICmpInst::ICMP_SLE:
6035 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6036 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6038 Pred = ICmpInst::ICMP_SLT;
6040 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6041 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6043 Pred = ICmpInst::ICMP_SLT;
6047 case ICmpInst::ICMP_SGE:
6048 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6049 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6051 Pred = ICmpInst::ICMP_SGT;
6053 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6054 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6056 Pred = ICmpInst::ICMP_SGT;
6060 case ICmpInst::ICMP_ULE:
6061 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6062 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6064 Pred = ICmpInst::ICMP_ULT;
6066 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6067 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6069 Pred = ICmpInst::ICMP_ULT;
6073 case ICmpInst::ICMP_UGE:
6074 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6075 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6077 Pred = ICmpInst::ICMP_UGT;
6079 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6080 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6082 Pred = ICmpInst::ICMP_UGT;
6090 // TODO: More simplifications are possible here.
6092 // Recursively simplify until we either hit a recursion limit or nothing
6095 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6101 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6102 Pred = ICmpInst::ICMP_EQ;
6107 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6108 Pred = ICmpInst::ICMP_NE;
6112 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6113 return getSignedRange(S).getSignedMax().isNegative();
6116 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6117 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6120 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6121 return !getSignedRange(S).getSignedMin().isNegative();
6124 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6125 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6128 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6129 return isKnownNegative(S) || isKnownPositive(S);
6132 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6133 const SCEV *LHS, const SCEV *RHS) {
6134 // Canonicalize the inputs first.
6135 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6137 // If LHS or RHS is an addrec, check to see if the condition is true in
6138 // every iteration of the loop.
6139 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
6140 if (isLoopEntryGuardedByCond(
6141 AR->getLoop(), Pred, AR->getStart(), RHS) &&
6142 isLoopBackedgeGuardedByCond(
6143 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
6145 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
6146 if (isLoopEntryGuardedByCond(
6147 AR->getLoop(), Pred, LHS, AR->getStart()) &&
6148 isLoopBackedgeGuardedByCond(
6149 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
6152 // Otherwise see what can be done with known constant ranges.
6153 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6157 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6158 const SCEV *LHS, const SCEV *RHS) {
6159 if (HasSameValue(LHS, RHS))
6160 return ICmpInst::isTrueWhenEqual(Pred);
6162 // This code is split out from isKnownPredicate because it is called from
6163 // within isLoopEntryGuardedByCond.
6166 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6167 case ICmpInst::ICMP_SGT:
6168 std::swap(LHS, RHS);
6169 case ICmpInst::ICMP_SLT: {
6170 ConstantRange LHSRange = getSignedRange(LHS);
6171 ConstantRange RHSRange = getSignedRange(RHS);
6172 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6174 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6178 case ICmpInst::ICMP_SGE:
6179 std::swap(LHS, RHS);
6180 case ICmpInst::ICMP_SLE: {
6181 ConstantRange LHSRange = getSignedRange(LHS);
6182 ConstantRange RHSRange = getSignedRange(RHS);
6183 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6185 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6189 case ICmpInst::ICMP_UGT:
6190 std::swap(LHS, RHS);
6191 case ICmpInst::ICMP_ULT: {
6192 ConstantRange LHSRange = getUnsignedRange(LHS);
6193 ConstantRange RHSRange = getUnsignedRange(RHS);
6194 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6196 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6200 case ICmpInst::ICMP_UGE:
6201 std::swap(LHS, RHS);
6202 case ICmpInst::ICMP_ULE: {
6203 ConstantRange LHSRange = getUnsignedRange(LHS);
6204 ConstantRange RHSRange = getUnsignedRange(RHS);
6205 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6207 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6211 case ICmpInst::ICMP_NE: {
6212 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6214 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6217 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6218 if (isKnownNonZero(Diff))
6222 case ICmpInst::ICMP_EQ:
6223 // The check at the top of the function catches the case where
6224 // the values are known to be equal.
6230 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6231 /// protected by a conditional between LHS and RHS. This is used to
6232 /// to eliminate casts.
6234 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6235 ICmpInst::Predicate Pred,
6236 const SCEV *LHS, const SCEV *RHS) {
6237 // Interpret a null as meaning no loop, where there is obviously no guard
6238 // (interprocedural conditions notwithstanding).
6239 if (!L) return true;
6241 BasicBlock *Latch = L->getLoopLatch();
6245 BranchInst *LoopContinuePredicate =
6246 dyn_cast<BranchInst>(Latch->getTerminator());
6247 if (!LoopContinuePredicate ||
6248 LoopContinuePredicate->isUnconditional())
6251 return isImpliedCond(Pred, LHS, RHS,
6252 LoopContinuePredicate->getCondition(),
6253 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6256 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6257 /// by a conditional between LHS and RHS. This is used to help avoid max
6258 /// expressions in loop trip counts, and to eliminate casts.
6260 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6261 ICmpInst::Predicate Pred,
6262 const SCEV *LHS, const SCEV *RHS) {
6263 // Interpret a null as meaning no loop, where there is obviously no guard
6264 // (interprocedural conditions notwithstanding).
6265 if (!L) return false;
6267 // Starting at the loop predecessor, climb up the predecessor chain, as long
6268 // as there are predecessors that can be found that have unique successors
6269 // leading to the original header.
6270 for (std::pair<BasicBlock *, BasicBlock *>
6271 Pair(L->getLoopPredecessor(), L->getHeader());
6273 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6275 BranchInst *LoopEntryPredicate =
6276 dyn_cast<BranchInst>(Pair.first->getTerminator());
6277 if (!LoopEntryPredicate ||
6278 LoopEntryPredicate->isUnconditional())
6281 if (isImpliedCond(Pred, LHS, RHS,
6282 LoopEntryPredicate->getCondition(),
6283 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6290 /// RAII wrapper to prevent recursive application of isImpliedCond.
6291 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6292 /// currently evaluating isImpliedCond.
6293 struct MarkPendingLoopPredicate {
6295 DenseSet<Value*> &LoopPreds;
6298 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6299 : Cond(C), LoopPreds(LP) {
6300 Pending = !LoopPreds.insert(Cond).second;
6302 ~MarkPendingLoopPredicate() {
6304 LoopPreds.erase(Cond);
6308 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6309 /// and RHS is true whenever the given Cond value evaluates to true.
6310 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6311 const SCEV *LHS, const SCEV *RHS,
6312 Value *FoundCondValue,
6314 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6318 // Recursively handle And and Or conditions.
6319 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6320 if (BO->getOpcode() == Instruction::And) {
6322 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6323 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6324 } else if (BO->getOpcode() == Instruction::Or) {
6326 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6327 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6331 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6332 if (!ICI) return false;
6334 // Bail if the ICmp's operands' types are wider than the needed type
6335 // before attempting to call getSCEV on them. This avoids infinite
6336 // recursion, since the analysis of widening casts can require loop
6337 // exit condition information for overflow checking, which would
6339 if (getTypeSizeInBits(LHS->getType()) <
6340 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6343 // Now that we found a conditional branch that dominates the loop or controls
6344 // the loop latch. Check to see if it is the comparison we are looking for.
6345 ICmpInst::Predicate FoundPred;
6347 FoundPred = ICI->getInversePredicate();
6349 FoundPred = ICI->getPredicate();
6351 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6352 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6354 // Balance the types. The case where FoundLHS' type is wider than
6355 // LHS' type is checked for above.
6356 if (getTypeSizeInBits(LHS->getType()) >
6357 getTypeSizeInBits(FoundLHS->getType())) {
6358 if (CmpInst::isSigned(FoundPred)) {
6359 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6360 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6362 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6363 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6367 // Canonicalize the query to match the way instcombine will have
6368 // canonicalized the comparison.
6369 if (SimplifyICmpOperands(Pred, LHS, RHS))
6371 return CmpInst::isTrueWhenEqual(Pred);
6372 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6373 if (FoundLHS == FoundRHS)
6374 return CmpInst::isFalseWhenEqual(FoundPred);
6376 // Check to see if we can make the LHS or RHS match.
6377 if (LHS == FoundRHS || RHS == FoundLHS) {
6378 if (isa<SCEVConstant>(RHS)) {
6379 std::swap(FoundLHS, FoundRHS);
6380 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6382 std::swap(LHS, RHS);
6383 Pred = ICmpInst::getSwappedPredicate(Pred);
6387 // Check whether the found predicate is the same as the desired predicate.
6388 if (FoundPred == Pred)
6389 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6391 // Check whether swapping the found predicate makes it the same as the
6392 // desired predicate.
6393 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6394 if (isa<SCEVConstant>(RHS))
6395 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6397 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6398 RHS, LHS, FoundLHS, FoundRHS);
6401 // Check whether the actual condition is beyond sufficient.
6402 if (FoundPred == ICmpInst::ICMP_EQ)
6403 if (ICmpInst::isTrueWhenEqual(Pred))
6404 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6406 if (Pred == ICmpInst::ICMP_NE)
6407 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6408 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6411 // Otherwise assume the worst.
6415 /// isImpliedCondOperands - Test whether the condition described by Pred,
6416 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6417 /// and FoundRHS is true.
6418 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6419 const SCEV *LHS, const SCEV *RHS,
6420 const SCEV *FoundLHS,
6421 const SCEV *FoundRHS) {
6422 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6423 FoundLHS, FoundRHS) ||
6424 // ~x < ~y --> x > y
6425 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6426 getNotSCEV(FoundRHS),
6427 getNotSCEV(FoundLHS));
6430 /// isImpliedCondOperandsHelper - Test whether the condition described by
6431 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6432 /// FoundLHS, and FoundRHS is true.
6434 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6435 const SCEV *LHS, const SCEV *RHS,
6436 const SCEV *FoundLHS,
6437 const SCEV *FoundRHS) {
6439 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6440 case ICmpInst::ICMP_EQ:
6441 case ICmpInst::ICMP_NE:
6442 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6445 case ICmpInst::ICMP_SLT:
6446 case ICmpInst::ICMP_SLE:
6447 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6448 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6451 case ICmpInst::ICMP_SGT:
6452 case ICmpInst::ICMP_SGE:
6453 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6454 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6457 case ICmpInst::ICMP_ULT:
6458 case ICmpInst::ICMP_ULE:
6459 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6460 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6463 case ICmpInst::ICMP_UGT:
6464 case ICmpInst::ICMP_UGE:
6465 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6466 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6474 // Verify if an linear IV with positive stride can overflow when in a
6475 // less-than comparison, knowing the invariant term of the comparison, the
6476 // stride and the knowledge of NSW/NUW flags on the recurrence.
6477 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
6478 bool IsSigned, bool NoWrap) {
6479 if (NoWrap) return false;
6481 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6482 const SCEV *One = getConstant(Stride->getType(), 1);
6485 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
6486 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
6487 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6490 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
6491 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
6494 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
6495 APInt MaxValue = APInt::getMaxValue(BitWidth);
6496 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6499 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
6500 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
6503 // Verify if an linear IV with negative stride can overflow when in a
6504 // greater-than comparison, knowing the invariant term of the comparison,
6505 // the stride and the knowledge of NSW/NUW flags on the recurrence.
6506 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
6507 bool IsSigned, bool NoWrap) {
6508 if (NoWrap) return false;
6510 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6511 const SCEV *One = getConstant(Stride->getType(), 1);
6514 APInt MinRHS = getSignedRange(RHS).getSignedMin();
6515 APInt MinValue = APInt::getSignedMinValue(BitWidth);
6516 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6519 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
6520 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
6523 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
6524 APInt MinValue = APInt::getMinValue(BitWidth);
6525 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6528 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
6529 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
6532 // Compute the backedge taken count knowing the interval difference, the
6533 // stride and presence of the equality in the comparison.
6534 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
6536 const SCEV *One = getConstant(Step->getType(), 1);
6537 Delta = Equality ? getAddExpr(Delta, Step)
6538 : getAddExpr(Delta, getMinusSCEV(Step, One));
6539 return getUDivExpr(Delta, Step);
6542 /// HowManyLessThans - Return the number of times a backedge containing the
6543 /// specified less-than comparison will execute. If not computable, return
6544 /// CouldNotCompute.
6546 /// @param IsSubExpr is true when the LHS < RHS condition does not directly
6547 /// control the branch. In this case, we can only compute an iteration count for
6548 /// a subexpression that cannot overflow before evaluating true.
6549 ScalarEvolution::ExitLimit
6550 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6551 const Loop *L, bool IsSigned,
6553 // We handle only IV < Invariant
6554 if (!isLoopInvariant(RHS, L))
6555 return getCouldNotCompute();
6557 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6559 // Avoid weird loops
6560 if (!IV || IV->getLoop() != L || !IV->isAffine())
6561 return getCouldNotCompute();
6563 bool NoWrap = !IsSubExpr &&
6564 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6566 const SCEV *Stride = IV->getStepRecurrence(*this);
6568 // Avoid negative or zero stride values
6569 if (!isKnownPositive(Stride))
6570 return getCouldNotCompute();
6572 // Avoid proven overflow cases: this will ensure that the backedge taken count
6573 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6574 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6575 // behaviors like the case of C language.
6576 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
6577 return getCouldNotCompute();
6579 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
6580 : ICmpInst::ICMP_ULT;
6581 const SCEV *Start = IV->getStart();
6582 const SCEV *End = RHS;
6583 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
6584 End = IsSigned ? getSMaxExpr(RHS, Start)
6585 : getUMaxExpr(RHS, Start);
6587 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
6589 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
6590 : getUnsignedRange(Start).getUnsignedMin();
6592 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6593 : getUnsignedRange(Stride).getUnsignedMin();
6595 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6596 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
6597 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
6599 // Although End can be a MAX expression we estimate MaxEnd considering only
6600 // the case End = RHS. This is safe because in the other case (End - Start)
6601 // is zero, leading to a zero maximum backedge taken count.
6603 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
6604 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
6606 const SCEV *MaxBECount;
6607 if (isa<SCEVConstant>(BECount))
6608 MaxBECount = BECount;
6610 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
6611 getConstant(MinStride), false);
6613 if (isa<SCEVCouldNotCompute>(MaxBECount))
6614 MaxBECount = BECount;
6616 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6619 ScalarEvolution::ExitLimit
6620 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
6621 const Loop *L, bool IsSigned,
6623 // We handle only IV > Invariant
6624 if (!isLoopInvariant(RHS, L))
6625 return getCouldNotCompute();
6627 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6629 // Avoid weird loops
6630 if (!IV || IV->getLoop() != L || !IV->isAffine())
6631 return getCouldNotCompute();
6633 bool NoWrap = !IsSubExpr &&
6634 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6636 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
6638 // Avoid negative or zero stride values
6639 if (!isKnownPositive(Stride))
6640 return getCouldNotCompute();
6642 // Avoid proven overflow cases: this will ensure that the backedge taken count
6643 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6644 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6645 // behaviors like the case of C language.
6646 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
6647 return getCouldNotCompute();
6649 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
6650 : ICmpInst::ICMP_UGT;
6652 const SCEV *Start = IV->getStart();
6653 const SCEV *End = RHS;
6654 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
6655 End = IsSigned ? getSMinExpr(RHS, Start)
6656 : getUMinExpr(RHS, Start);
6658 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
6660 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
6661 : getUnsignedRange(Start).getUnsignedMax();
6663 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6664 : getUnsignedRange(Stride).getUnsignedMin();
6666 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6667 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
6668 : APInt::getMinValue(BitWidth) + (MinStride - 1);
6670 // Although End can be a MIN expression we estimate MinEnd considering only
6671 // the case End = RHS. This is safe because in the other case (Start - End)
6672 // is zero, leading to a zero maximum backedge taken count.
6674 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
6675 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
6678 const SCEV *MaxBECount = getCouldNotCompute();
6679 if (isa<SCEVConstant>(BECount))
6680 MaxBECount = BECount;
6682 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
6683 getConstant(MinStride), false);
6685 if (isa<SCEVCouldNotCompute>(MaxBECount))
6686 MaxBECount = BECount;
6688 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6691 /// getNumIterationsInRange - Return the number of iterations of this loop that
6692 /// produce values in the specified constant range. Another way of looking at
6693 /// this is that it returns the first iteration number where the value is not in
6694 /// the condition, thus computing the exit count. If the iteration count can't
6695 /// be computed, an instance of SCEVCouldNotCompute is returned.
6696 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6697 ScalarEvolution &SE) const {
6698 if (Range.isFullSet()) // Infinite loop.
6699 return SE.getCouldNotCompute();
6701 // If the start is a non-zero constant, shift the range to simplify things.
6702 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6703 if (!SC->getValue()->isZero()) {
6704 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6705 Operands[0] = SE.getConstant(SC->getType(), 0);
6706 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6707 getNoWrapFlags(FlagNW));
6708 if (const SCEVAddRecExpr *ShiftedAddRec =
6709 dyn_cast<SCEVAddRecExpr>(Shifted))
6710 return ShiftedAddRec->getNumIterationsInRange(
6711 Range.subtract(SC->getValue()->getValue()), SE);
6712 // This is strange and shouldn't happen.
6713 return SE.getCouldNotCompute();
6716 // The only time we can solve this is when we have all constant indices.
6717 // Otherwise, we cannot determine the overflow conditions.
6718 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6719 if (!isa<SCEVConstant>(getOperand(i)))
6720 return SE.getCouldNotCompute();
6723 // Okay at this point we know that all elements of the chrec are constants and
6724 // that the start element is zero.
6726 // First check to see if the range contains zero. If not, the first
6728 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6729 if (!Range.contains(APInt(BitWidth, 0)))
6730 return SE.getConstant(getType(), 0);
6733 // If this is an affine expression then we have this situation:
6734 // Solve {0,+,A} in Range === Ax in Range
6736 // We know that zero is in the range. If A is positive then we know that
6737 // the upper value of the range must be the first possible exit value.
6738 // If A is negative then the lower of the range is the last possible loop
6739 // value. Also note that we already checked for a full range.
6740 APInt One(BitWidth,1);
6741 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6742 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6744 // The exit value should be (End+A)/A.
6745 APInt ExitVal = (End + A).udiv(A);
6746 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6748 // Evaluate at the exit value. If we really did fall out of the valid
6749 // range, then we computed our trip count, otherwise wrap around or other
6750 // things must have happened.
6751 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6752 if (Range.contains(Val->getValue()))
6753 return SE.getCouldNotCompute(); // Something strange happened
6755 // Ensure that the previous value is in the range. This is a sanity check.
6756 assert(Range.contains(
6757 EvaluateConstantChrecAtConstant(this,
6758 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6759 "Linear scev computation is off in a bad way!");
6760 return SE.getConstant(ExitValue);
6761 } else if (isQuadratic()) {
6762 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6763 // quadratic equation to solve it. To do this, we must frame our problem in
6764 // terms of figuring out when zero is crossed, instead of when
6765 // Range.getUpper() is crossed.
6766 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6767 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6768 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6769 // getNoWrapFlags(FlagNW)
6772 // Next, solve the constructed addrec
6773 std::pair<const SCEV *,const SCEV *> Roots =
6774 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6775 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6776 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6778 // Pick the smallest positive root value.
6779 if (ConstantInt *CB =
6780 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6781 R1->getValue(), R2->getValue()))) {
6782 if (CB->getZExtValue() == false)
6783 std::swap(R1, R2); // R1 is the minimum root now.
6785 // Make sure the root is not off by one. The returned iteration should
6786 // not be in the range, but the previous one should be. When solving
6787 // for "X*X < 5", for example, we should not return a root of 2.
6788 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6791 if (Range.contains(R1Val->getValue())) {
6792 // The next iteration must be out of the range...
6793 ConstantInt *NextVal =
6794 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6796 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6797 if (!Range.contains(R1Val->getValue()))
6798 return SE.getConstant(NextVal);
6799 return SE.getCouldNotCompute(); // Something strange happened
6802 // If R1 was not in the range, then it is a good return value. Make
6803 // sure that R1-1 WAS in the range though, just in case.
6804 ConstantInt *NextVal =
6805 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6806 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6807 if (Range.contains(R1Val->getValue()))
6809 return SE.getCouldNotCompute(); // Something strange happened
6814 return SE.getCouldNotCompute();
6817 static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
6818 APInt A = C1->getValue()->getValue();
6819 APInt B = C2->getValue()->getValue();
6820 uint32_t ABW = A.getBitWidth();
6821 uint32_t BBW = B.getBitWidth();
6828 return APIntOps::srem(A, B);
6831 static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
6832 APInt A = C1->getValue()->getValue();
6833 APInt B = C2->getValue()->getValue();
6834 uint32_t ABW = A.getBitWidth();
6835 uint32_t BBW = B.getBitWidth();
6842 return APIntOps::sdiv(A, B);
6846 struct SCEVGCD : public SCEVVisitor<SCEVGCD, const SCEV *> {
6848 // Pattern match Step into Start. When Step is a multiply expression, find
6849 // the largest subexpression of Step that appears in Start. When Start is an
6850 // add expression, try to match Step in the subexpressions of Start, non
6851 // matching subexpressions are returned under Remainder.
6852 static const SCEV *findGCD(ScalarEvolution &SE, const SCEV *Start,
6853 const SCEV *Step, const SCEV **Remainder) {
6854 assert(Remainder && "Remainder should not be NULL");
6855 SCEVGCD R(SE, Step, SE.getConstant(Step->getType(), 0));
6856 const SCEV *Res = R.visit(Start);
6857 *Remainder = R.Remainder;
6861 SCEVGCD(ScalarEvolution &S, const SCEV *G, const SCEV *R)
6862 : SE(S), GCD(G), Remainder(R) {
6863 Zero = SE.getConstant(GCD->getType(), 0);
6864 One = SE.getConstant(GCD->getType(), 1);
6867 const SCEV *visitConstant(const SCEVConstant *Constant) {
6868 if (GCD == Constant || Constant == Zero)
6871 if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD)) {
6872 const SCEV *Res = SE.getConstant(gcd(Constant, CGCD));
6876 Remainder = SE.getConstant(srem(Constant, CGCD));
6877 Constant = cast<SCEVConstant>(SE.getMinusSCEV(Constant, Remainder));
6878 Res = SE.getConstant(gcd(Constant, CGCD));
6882 // When GCD is not a constant, it could be that the GCD is an Add, Mul,
6883 // AddRec, etc., in which case we want to find out how many times the
6884 // Constant divides the GCD: we then return that as the new GCD.
6885 const SCEV *Rem = Zero;
6886 const SCEV *Res = findGCD(SE, GCD, Constant, &Rem);
6888 if (Res == One || Rem != Zero) {
6889 Remainder = Constant;
6893 assert(isa<SCEVConstant>(Res) && "Res should be a constant");
6894 Remainder = SE.getConstant(srem(Constant, cast<SCEVConstant>(Res)));
6898 const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
6904 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
6910 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
6916 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
6920 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6921 const SCEV *Rem = Zero;
6922 const SCEV *Res = findGCD(SE, Expr->getOperand(e - 1 - i), GCD, &Rem);
6924 // FIXME: There may be ambiguous situations: for instance,
6925 // GCD(-4 + (3 * %m), 2 * %m) where 2 divides -4 and %m divides (3 * %m).
6926 // The order in which the AddExpr is traversed computes a different GCD
6931 Remainder = SE.getAddExpr(Remainder, Rem);
6937 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
6941 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6942 if (Expr->getOperand(i) == GCD)
6946 // If we have not returned yet, it means that GCD is not part of Expr.
6947 const SCEV *PartialGCD = One;
6948 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6949 const SCEV *Rem = Zero;
6950 const SCEV *Res = findGCD(SE, Expr->getOperand(i), GCD, &Rem);
6952 // GCD does not divide Expr->getOperand(i).
6957 PartialGCD = SE.getMulExpr(PartialGCD, Res);
6958 if (PartialGCD == GCD)
6962 if (PartialGCD != One)
6966 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(GCD);
6970 // When the GCD is a multiply expression, try to decompose it:
6971 // this occurs when Step does not divide the Start expression
6972 // as in: {(-4 + (3 * %m)),+,(2 * %m)}
6973 for (int i = 0, e = Mul->getNumOperands(); i < e; ++i) {
6974 const SCEV *Rem = Zero;
6975 const SCEV *Res = findGCD(SE, Expr, Mul->getOperand(i), &Rem);
6985 const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
6991 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
6995 if (!Expr->isAffine()) {
7000 const SCEV *Rem = Zero;
7001 const SCEV *Res = findGCD(SE, Expr->getOperand(0), GCD, &Rem);
7003 Remainder = SE.getAddExpr(Remainder, Rem);
7006 Res = findGCD(SE, Expr->getOperand(1), Res, &Rem);
7015 const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
7021 const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
7027 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
7033 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
7038 ScalarEvolution &SE;
7039 const SCEV *GCD, *Remainder, *Zero, *One;
7042 struct SCEVDivision : public SCEVVisitor<SCEVDivision, const SCEV *> {
7044 // Remove from Start all multiples of Step.
7045 static const SCEV *divide(ScalarEvolution &SE, const SCEV *Start,
7047 SCEVDivision D(SE, Step);
7048 const SCEV *Rem = D.Zero;
7050 // The division is guaranteed to succeed: Step should divide Start with no
7052 assert(Step == SCEVGCD::findGCD(SE, Start, Step, &Rem) && Rem == D.Zero &&
7053 "Step should divide Start with no remainder.");
7054 return D.visit(Start);
7057 SCEVDivision(ScalarEvolution &S, const SCEV *G) : SE(S), GCD(G) {
7058 Zero = SE.getConstant(GCD->getType(), 0);
7059 One = SE.getConstant(GCD->getType(), 1);
7062 const SCEV *visitConstant(const SCEVConstant *Constant) {
7063 if (GCD == Constant)
7066 if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD))
7067 return SE.getConstant(sdiv(Constant, CGCD));
7071 const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
7077 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
7083 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
7089 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
7093 SmallVector<const SCEV *, 2> Operands;
7094 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
7095 Operands.push_back(divide(SE, Expr->getOperand(i), GCD));
7097 if (Operands.size() == 1)
7099 return SE.getAddExpr(Operands);
7102 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
7106 bool FoundGCDTerm = false;
7107 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
7108 if (Expr->getOperand(i) == GCD)
7109 FoundGCDTerm = true;
7111 SmallVector<const SCEV *, 2> Operands;
7113 FoundGCDTerm = false;
7114 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
7116 Operands.push_back(Expr->getOperand(i));
7117 else if (Expr->getOperand(i) == GCD)
7118 FoundGCDTerm = true;
7120 Operands.push_back(Expr->getOperand(i));
7123 const SCEV *PartialGCD = One;
7124 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
7125 if (PartialGCD == GCD) {
7126 Operands.push_back(Expr->getOperand(i));
7130 const SCEV *Rem = Zero;
7131 const SCEV *Res = SCEVGCD::findGCD(SE, Expr->getOperand(i), GCD, &Rem);
7133 PartialGCD = SE.getMulExpr(PartialGCD, Res);
7134 Operands.push_back(divide(SE, Expr->getOperand(i), GCD));
7136 Operands.push_back(Expr->getOperand(i));
7141 if (Operands.size() == 1)
7143 return SE.getMulExpr(Operands);
7146 const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
7152 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
7156 assert(Expr->isAffine() && "Expr should be affine");
7158 const SCEV *Start = divide(SE, Expr->getStart(), GCD);
7159 const SCEV *Step = divide(SE, Expr->getStepRecurrence(SE), GCD);
7161 return SE.getAddRecExpr(Start, Step, Expr->getLoop(),
7162 Expr->getNoWrapFlags());
7165 const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
7171 const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
7177 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
7183 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
7188 ScalarEvolution &SE;
7189 const SCEV *GCD, *Zero, *One;
7193 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7194 /// sizes of an array access. Returns the remainder of the delinearization that
7195 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7196 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7197 /// expressions in the stride and base of a SCEV corresponding to the
7198 /// computation of a GCD (greatest common divisor) of base and stride. When
7199 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7201 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7203 /// void foo(long n, long m, long o, double A[n][m][o]) {
7205 /// for (long i = 0; i < n; i++)
7206 /// for (long j = 0; j < m; j++)
7207 /// for (long k = 0; k < o; k++)
7208 /// A[i][j][k] = 1.0;
7211 /// the delinearization input is the following AddRec SCEV:
7213 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7215 /// From this SCEV, we are able to say that the base offset of the access is %A
7216 /// because it appears as an offset that does not divide any of the strides in
7219 /// CHECK: Base offset: %A
7221 /// and then SCEV->delinearize determines the size of some of the dimensions of
7222 /// the array as these are the multiples by which the strides are happening:
7224 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7226 /// Note that the outermost dimension remains of UnknownSize because there are
7227 /// no strides that would help identifying the size of the last dimension: when
7228 /// the array has been statically allocated, one could compute the size of that
7229 /// dimension by dividing the overall size of the array by the size of the known
7230 /// dimensions: %m * %o * 8.
7232 /// Finally delinearize provides the access functions for the array reference
7233 /// that does correspond to A[i][j][k] of the above C testcase:
7235 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7237 /// The testcases are checking the output of a function pass:
7238 /// DelinearizationPass that walks through all loads and stores of a function
7239 /// asking for the SCEV of the memory access with respect to all enclosing
7240 /// loops, calling SCEV->delinearize on that and printing the results.
7243 SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7244 SmallVectorImpl<const SCEV *> &Subscripts,
7245 SmallVectorImpl<const SCEV *> &Sizes) const {
7246 // Early exit in case this SCEV is not an affine multivariate function.
7247 if (!this->isAffine())
7250 const SCEV *Start = this->getStart();
7251 const SCEV *Step = this->getStepRecurrence(SE);
7253 // Build the SCEV representation of the canonical induction variable in the
7254 // loop of this SCEV.
7255 const SCEV *Zero = SE.getConstant(this->getType(), 0);
7256 const SCEV *One = SE.getConstant(this->getType(), 1);
7258 SE.getAddRecExpr(Zero, One, this->getLoop(), this->getNoWrapFlags());
7260 DEBUG(dbgs() << "(delinearize: " << *this << "\n");
7262 // When the stride of this SCEV is 1, do not compute the GCD: the size of this
7263 // subscript is 1, and this same SCEV for the access function.
7264 const SCEV *Remainder = Zero;
7265 const SCEV *GCD = One;
7267 // Find the GCD and Remainder of the Start and Step coefficients of this SCEV.
7268 if (Step != One && !Step->isAllOnesValue())
7269 GCD = SCEVGCD::findGCD(SE, Start, Step, &Remainder);
7271 DEBUG(dbgs() << "GCD: " << *GCD << "\n");
7272 DEBUG(dbgs() << "Remainder: " << *Remainder << "\n");
7274 const SCEV *Quotient = Start;
7275 if (GCD != One && !GCD->isAllOnesValue())
7276 // As findGCD computed Remainder, GCD divides "Start - Remainder." The
7277 // Quotient is then this SCEV without Remainder, scaled down by the GCD. The
7278 // Quotient is what will be used in the next subscript delinearization.
7279 Quotient = SCEVDivision::divide(SE, SE.getMinusSCEV(Start, Remainder), GCD);
7281 DEBUG(dbgs() << "Quotient: " << *Quotient << "\n");
7283 const SCEV *Rem = Quotient;
7284 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Quotient))
7285 // Recursively call delinearize on the Quotient until there are no more
7286 // multiples that can be recognized.
7287 Rem = AR->delinearize(SE, Subscripts, Sizes);
7289 // Scale up the canonical induction variable IV by whatever remains from the
7290 // Step after division by the GCD: the GCD is the size of all the sub-array.
7291 if (Step != One && !Step->isAllOnesValue() && GCD != One &&
7292 !GCD->isAllOnesValue() && Step != GCD) {
7293 Step = SCEVDivision::divide(SE, Step, GCD);
7294 IV = SE.getMulExpr(IV, Step);
7296 // The access function in the current subscript is computed as the canonical
7297 // induction variable IV (potentially scaled up by the step) and offset by
7298 // Rem, the offset of delinearization in the sub-array.
7299 const SCEV *Index = SE.getAddExpr(IV, Rem);
7301 // Record the access function and the size of the current subscript.
7302 Subscripts.push_back(Index);
7303 Sizes.push_back(GCD);
7306 int Size = Sizes.size();
7307 DEBUG(dbgs() << "succeeded to delinearize " << *this << "\n");
7308 DEBUG(dbgs() << "ArrayDecl[UnknownSize]");
7309 for (int i = 0; i < Size - 1; i++)
7310 DEBUG(dbgs() << "[" << *Sizes[i] << "]");
7311 DEBUG(dbgs() << " with elements of " << *Sizes[Size - 1] << " bytes.\n");
7313 DEBUG(dbgs() << "ArrayRef");
7314 for (int i = 0; i < Size; i++)
7315 DEBUG(dbgs() << "[" << *Subscripts[i] << "]");
7316 DEBUG(dbgs() << "\n)\n");
7322 //===----------------------------------------------------------------------===//
7323 // SCEVCallbackVH Class Implementation
7324 //===----------------------------------------------------------------------===//
7326 void ScalarEvolution::SCEVCallbackVH::deleted() {
7327 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7328 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7329 SE->ConstantEvolutionLoopExitValue.erase(PN);
7330 SE->ValueExprMap.erase(getValPtr());
7331 // this now dangles!
7334 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7335 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7337 // Forget all the expressions associated with users of the old value,
7338 // so that future queries will recompute the expressions using the new
7340 Value *Old = getValPtr();
7341 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7342 SmallPtrSet<User *, 8> Visited;
7343 while (!Worklist.empty()) {
7344 User *U = Worklist.pop_back_val();
7345 // Deleting the Old value will cause this to dangle. Postpone
7346 // that until everything else is done.
7349 if (!Visited.insert(U))
7351 if (PHINode *PN = dyn_cast<PHINode>(U))
7352 SE->ConstantEvolutionLoopExitValue.erase(PN);
7353 SE->ValueExprMap.erase(U);
7354 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7356 // Delete the Old value.
7357 if (PHINode *PN = dyn_cast<PHINode>(Old))
7358 SE->ConstantEvolutionLoopExitValue.erase(PN);
7359 SE->ValueExprMap.erase(Old);
7360 // this now dangles!
7363 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7364 : CallbackVH(V), SE(se) {}
7366 //===----------------------------------------------------------------------===//
7367 // ScalarEvolution Class Implementation
7368 //===----------------------------------------------------------------------===//
7370 ScalarEvolution::ScalarEvolution()
7371 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64), FirstUnknown(0) {
7372 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7375 bool ScalarEvolution::runOnFunction(Function &F) {
7377 LI = &getAnalysis<LoopInfo>();
7378 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7379 DL = DLP ? &DLP->getDataLayout() : 0;
7380 TLI = &getAnalysis<TargetLibraryInfo>();
7381 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7385 void ScalarEvolution::releaseMemory() {
7386 // Iterate through all the SCEVUnknown instances and call their
7387 // destructors, so that they release their references to their values.
7388 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7392 ValueExprMap.clear();
7394 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7395 // that a loop had multiple computable exits.
7396 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7397 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7402 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7404 BackedgeTakenCounts.clear();
7405 ConstantEvolutionLoopExitValue.clear();
7406 ValuesAtScopes.clear();
7407 LoopDispositions.clear();
7408 BlockDispositions.clear();
7409 UnsignedRanges.clear();
7410 SignedRanges.clear();
7411 UniqueSCEVs.clear();
7412 SCEVAllocator.Reset();
7415 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7416 AU.setPreservesAll();
7417 AU.addRequiredTransitive<LoopInfo>();
7418 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7419 AU.addRequired<TargetLibraryInfo>();
7422 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7423 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7426 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7428 // Print all inner loops first
7429 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7430 PrintLoopInfo(OS, SE, *I);
7433 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7436 SmallVector<BasicBlock *, 8> ExitBlocks;
7437 L->getExitBlocks(ExitBlocks);
7438 if (ExitBlocks.size() != 1)
7439 OS << "<multiple exits> ";
7441 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7442 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7444 OS << "Unpredictable backedge-taken count. ";
7449 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7452 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7453 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7455 OS << "Unpredictable max backedge-taken count. ";
7461 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7462 // ScalarEvolution's implementation of the print method is to print
7463 // out SCEV values of all instructions that are interesting. Doing
7464 // this potentially causes it to create new SCEV objects though,
7465 // which technically conflicts with the const qualifier. This isn't
7466 // observable from outside the class though, so casting away the
7467 // const isn't dangerous.
7468 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7470 OS << "Classifying expressions for: ";
7471 F->printAsOperand(OS, /*PrintType=*/false);
7473 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7474 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7477 const SCEV *SV = SE.getSCEV(&*I);
7480 const Loop *L = LI->getLoopFor((*I).getParent());
7482 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
7489 OS << "\t\t" "Exits: ";
7490 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
7491 if (!SE.isLoopInvariant(ExitValue, L)) {
7492 OS << "<<Unknown>>";
7501 OS << "Determining loop execution counts for: ";
7502 F->printAsOperand(OS, /*PrintType=*/false);
7504 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
7505 PrintLoopInfo(OS, &SE, *I);
7508 ScalarEvolution::LoopDisposition
7509 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
7510 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
7511 for (unsigned u = 0; u < Values.size(); u++) {
7512 if (Values[u].first == L)
7513 return Values[u].second;
7515 Values.push_back(std::make_pair(L, LoopVariant));
7516 LoopDisposition D = computeLoopDisposition(S, L);
7517 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
7518 for (unsigned u = Values2.size(); u > 0; u--) {
7519 if (Values2[u - 1].first == L) {
7520 Values2[u - 1].second = D;
7527 ScalarEvolution::LoopDisposition
7528 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
7529 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7531 return LoopInvariant;
7535 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
7536 case scAddRecExpr: {
7537 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7539 // If L is the addrec's loop, it's computable.
7540 if (AR->getLoop() == L)
7541 return LoopComputable;
7543 // Add recurrences are never invariant in the function-body (null loop).
7547 // This recurrence is variant w.r.t. L if L contains AR's loop.
7548 if (L->contains(AR->getLoop()))
7551 // This recurrence is invariant w.r.t. L if AR's loop contains L.
7552 if (AR->getLoop()->contains(L))
7553 return LoopInvariant;
7555 // This recurrence is variant w.r.t. L if any of its operands
7557 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
7559 if (!isLoopInvariant(*I, L))
7562 // Otherwise it's loop-invariant.
7563 return LoopInvariant;
7569 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7570 bool HasVarying = false;
7571 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7573 LoopDisposition D = getLoopDisposition(*I, L);
7574 if (D == LoopVariant)
7576 if (D == LoopComputable)
7579 return HasVarying ? LoopComputable : LoopInvariant;
7582 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7583 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
7584 if (LD == LoopVariant)
7586 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
7587 if (RD == LoopVariant)
7589 return (LD == LoopInvariant && RD == LoopInvariant) ?
7590 LoopInvariant : LoopComputable;
7593 // All non-instruction values are loop invariant. All instructions are loop
7594 // invariant if they are not contained in the specified loop.
7595 // Instructions are never considered invariant in the function body
7596 // (null loop) because they are defined within the "loop".
7597 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
7598 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
7599 return LoopInvariant;
7600 case scCouldNotCompute:
7601 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7603 llvm_unreachable("Unknown SCEV kind!");
7606 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
7607 return getLoopDisposition(S, L) == LoopInvariant;
7610 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
7611 return getLoopDisposition(S, L) == LoopComputable;
7614 ScalarEvolution::BlockDisposition
7615 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7616 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
7617 for (unsigned u = 0; u < Values.size(); u++) {
7618 if (Values[u].first == BB)
7619 return Values[u].second;
7621 Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
7622 BlockDisposition D = computeBlockDisposition(S, BB);
7623 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
7624 for (unsigned u = Values2.size(); u > 0; u--) {
7625 if (Values2[u - 1].first == BB) {
7626 Values2[u - 1].second = D;
7633 ScalarEvolution::BlockDisposition
7634 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7635 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7637 return ProperlyDominatesBlock;
7641 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
7642 case scAddRecExpr: {
7643 // This uses a "dominates" query instead of "properly dominates" query
7644 // to test for proper dominance too, because the instruction which
7645 // produces the addrec's value is a PHI, and a PHI effectively properly
7646 // dominates its entire containing block.
7647 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7648 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
7649 return DoesNotDominateBlock;
7651 // FALL THROUGH into SCEVNAryExpr handling.
7656 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7658 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7660 BlockDisposition D = getBlockDisposition(*I, BB);
7661 if (D == DoesNotDominateBlock)
7662 return DoesNotDominateBlock;
7663 if (D == DominatesBlock)
7666 return Proper ? ProperlyDominatesBlock : DominatesBlock;
7669 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7670 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
7671 BlockDisposition LD = getBlockDisposition(LHS, BB);
7672 if (LD == DoesNotDominateBlock)
7673 return DoesNotDominateBlock;
7674 BlockDisposition RD = getBlockDisposition(RHS, BB);
7675 if (RD == DoesNotDominateBlock)
7676 return DoesNotDominateBlock;
7677 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
7678 ProperlyDominatesBlock : DominatesBlock;
7681 if (Instruction *I =
7682 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
7683 if (I->getParent() == BB)
7684 return DominatesBlock;
7685 if (DT->properlyDominates(I->getParent(), BB))
7686 return ProperlyDominatesBlock;
7687 return DoesNotDominateBlock;
7689 return ProperlyDominatesBlock;
7690 case scCouldNotCompute:
7691 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7693 llvm_unreachable("Unknown SCEV kind!");
7696 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
7697 return getBlockDisposition(S, BB) >= DominatesBlock;
7700 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
7701 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
7705 // Search for a SCEV expression node within an expression tree.
7706 // Implements SCEVTraversal::Visitor.
7711 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
7713 bool follow(const SCEV *S) {
7714 IsFound |= (S == Node);
7717 bool isDone() const { return IsFound; }
7721 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
7722 SCEVSearch Search(Op);
7723 visitAll(S, Search);
7724 return Search.IsFound;
7727 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
7728 ValuesAtScopes.erase(S);
7729 LoopDispositions.erase(S);
7730 BlockDispositions.erase(S);
7731 UnsignedRanges.erase(S);
7732 SignedRanges.erase(S);
7734 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7735 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
7736 BackedgeTakenInfo &BEInfo = I->second;
7737 if (BEInfo.hasOperand(S, this)) {
7739 BackedgeTakenCounts.erase(I++);
7746 typedef DenseMap<const Loop *, std::string> VerifyMap;
7748 /// replaceSubString - Replaces all occurrences of From in Str with To.
7749 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
7751 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
7752 Str.replace(Pos, From.size(), To.data(), To.size());
7757 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
7759 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
7760 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
7761 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
7763 std::string &S = Map[L];
7765 raw_string_ostream OS(S);
7766 SE.getBackedgeTakenCount(L)->print(OS);
7768 // false and 0 are semantically equivalent. This can happen in dead loops.
7769 replaceSubString(OS.str(), "false", "0");
7770 // Remove wrap flags, their use in SCEV is highly fragile.
7771 // FIXME: Remove this when SCEV gets smarter about them.
7772 replaceSubString(OS.str(), "<nw>", "");
7773 replaceSubString(OS.str(), "<nsw>", "");
7774 replaceSubString(OS.str(), "<nuw>", "");
7779 void ScalarEvolution::verifyAnalysis() const {
7783 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7785 // Gather stringified backedge taken counts for all loops using SCEV's caches.
7786 // FIXME: It would be much better to store actual values instead of strings,
7787 // but SCEV pointers will change if we drop the caches.
7788 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
7789 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7790 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
7792 // Gather stringified backedge taken counts for all loops without using
7795 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7796 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
7798 // Now compare whether they're the same with and without caches. This allows
7799 // verifying that no pass changed the cache.
7800 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
7801 "New loops suddenly appeared!");
7803 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
7804 OldE = BackedgeDumpsOld.end(),
7805 NewI = BackedgeDumpsNew.begin();
7806 OldI != OldE; ++OldI, ++NewI) {
7807 assert(OldI->first == NewI->first && "Loop order changed!");
7809 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
7811 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
7812 // means that a pass is buggy or SCEV has to learn a new pattern but is
7813 // usually not harmful.
7814 if (OldI->second != NewI->second &&
7815 OldI->second.find("undef") == std::string::npos &&
7816 NewI->second.find("undef") == std::string::npos &&
7817 OldI->second != "***COULDNOTCOMPUTE***" &&
7818 NewI->second != "***COULDNOTCOMPUTE***") {
7819 dbgs() << "SCEVValidator: SCEV for loop '"
7820 << OldI->first->getHeader()->getName()
7821 << "' changed from '" << OldI->second
7822 << "' to '" << NewI->second << "'!\n";
7827 // TODO: Verify more things.