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/Dominators.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/ValueTracking.h"
72 #include "llvm/Assembly/Writer.h"
73 #include "llvm/IR/Constants.h"
74 #include "llvm/IR/DataLayout.h"
75 #include "llvm/IR/DerivedTypes.h"
76 #include "llvm/IR/GlobalAlias.h"
77 #include "llvm/IR/GlobalVariable.h"
78 #include "llvm/IR/Instructions.h"
79 #include "llvm/IR/LLVMContext.h"
80 #include "llvm/IR/Operator.h"
81 #include "llvm/Support/CommandLine.h"
82 #include "llvm/Support/ConstantRange.h"
83 #include "llvm/Support/Debug.h"
84 #include "llvm/Support/ErrorHandling.h"
85 #include "llvm/Support/GetElementPtrTypeIterator.h"
86 #include "llvm/Support/InstIterator.h"
87 #include "llvm/Support/MathExtras.h"
88 #include "llvm/Support/raw_ostream.h"
89 #include "llvm/Target/TargetLibraryInfo.h"
93 STATISTIC(NumArrayLenItCounts,
94 "Number of trip counts computed with array length");
95 STATISTIC(NumTripCountsComputed,
96 "Number of loops with predictable loop counts");
97 STATISTIC(NumTripCountsNotComputed,
98 "Number of loops without predictable loop counts");
99 STATISTIC(NumBruteForceTripCountsComputed,
100 "Number of loops with trip counts computed by force");
102 static cl::opt<unsigned>
103 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
104 cl::desc("Maximum number of iterations SCEV will "
105 "symbolically execute a constant "
109 // FIXME: Enable this with XDEBUG when the test suite is clean.
111 VerifySCEV("verify-scev",
112 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
114 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
115 "Scalar Evolution Analysis", false, true)
116 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
117 INITIALIZE_PASS_DEPENDENCY(DominatorTree)
118 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
119 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
120 "Scalar Evolution Analysis", false, true)
121 char ScalarEvolution::ID = 0;
123 //===----------------------------------------------------------------------===//
124 // SCEV class definitions
125 //===----------------------------------------------------------------------===//
127 //===----------------------------------------------------------------------===//
128 // Implementation of the SCEV class.
131 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
132 void SCEV::dump() const {
138 void SCEV::print(raw_ostream &OS) const {
139 switch (getSCEVType()) {
141 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false);
144 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
145 const SCEV *Op = Trunc->getOperand();
146 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
147 << *Trunc->getType() << ")";
151 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
152 const SCEV *Op = ZExt->getOperand();
153 OS << "(zext " << *Op->getType() << " " << *Op << " to "
154 << *ZExt->getType() << ")";
158 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
159 const SCEV *Op = SExt->getOperand();
160 OS << "(sext " << *Op->getType() << " " << *Op << " to "
161 << *SExt->getType() << ")";
165 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
166 OS << "{" << *AR->getOperand(0);
167 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
168 OS << ",+," << *AR->getOperand(i);
170 if (AR->getNoWrapFlags(FlagNUW))
172 if (AR->getNoWrapFlags(FlagNSW))
174 if (AR->getNoWrapFlags(FlagNW) &&
175 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
177 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false);
185 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
186 const char *OpStr = 0;
187 switch (NAry->getSCEVType()) {
188 case scAddExpr: OpStr = " + "; break;
189 case scMulExpr: OpStr = " * "; break;
190 case scUMaxExpr: OpStr = " umax "; break;
191 case scSMaxExpr: OpStr = " smax "; break;
194 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
197 if (llvm::next(I) != E)
201 switch (NAry->getSCEVType()) {
204 if (NAry->getNoWrapFlags(FlagNUW))
206 if (NAry->getNoWrapFlags(FlagNSW))
212 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
213 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
217 const SCEVUnknown *U = cast<SCEVUnknown>(this);
219 if (U->isSizeOf(AllocTy)) {
220 OS << "sizeof(" << *AllocTy << ")";
223 if (U->isAlignOf(AllocTy)) {
224 OS << "alignof(" << *AllocTy << ")";
230 if (U->isOffsetOf(CTy, FieldNo)) {
231 OS << "offsetof(" << *CTy << ", ";
232 WriteAsOperand(OS, FieldNo, false);
237 // Otherwise just print it normally.
238 WriteAsOperand(OS, U->getValue(), false);
241 case scCouldNotCompute:
242 OS << "***COULDNOTCOMPUTE***";
246 llvm_unreachable("Unknown SCEV kind!");
249 Type *SCEV::getType() const {
250 switch (getSCEVType()) {
252 return cast<SCEVConstant>(this)->getType();
256 return cast<SCEVCastExpr>(this)->getType();
261 return cast<SCEVNAryExpr>(this)->getType();
263 return cast<SCEVAddExpr>(this)->getType();
265 return cast<SCEVUDivExpr>(this)->getType();
267 return cast<SCEVUnknown>(this)->getType();
268 case scCouldNotCompute:
269 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
271 llvm_unreachable("Unknown SCEV kind!");
275 bool SCEV::isZero() const {
276 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
277 return SC->getValue()->isZero();
281 bool SCEV::isOne() const {
282 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
283 return SC->getValue()->isOne();
287 bool SCEV::isAllOnesValue() const {
288 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
289 return SC->getValue()->isAllOnesValue();
293 /// isNonConstantNegative - Return true if the specified scev is negated, but
295 bool SCEV::isNonConstantNegative() const {
296 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
297 if (!Mul) return false;
299 // If there is a constant factor, it will be first.
300 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
301 if (!SC) return false;
303 // Return true if the value is negative, this matches things like (-42 * V).
304 return SC->getValue()->getValue().isNegative();
307 SCEVCouldNotCompute::SCEVCouldNotCompute() :
308 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
310 bool SCEVCouldNotCompute::classof(const SCEV *S) {
311 return S->getSCEVType() == scCouldNotCompute;
314 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
316 ID.AddInteger(scConstant);
319 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
320 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
321 UniqueSCEVs.InsertNode(S, IP);
325 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
326 return getConstant(ConstantInt::get(getContext(), Val));
330 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
331 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
332 return getConstant(ConstantInt::get(ITy, V, isSigned));
335 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
336 unsigned SCEVTy, const SCEV *op, Type *ty)
337 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
339 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
340 const SCEV *op, Type *ty)
341 : SCEVCastExpr(ID, scTruncate, op, ty) {
342 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
343 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
344 "Cannot truncate non-integer value!");
347 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
348 const SCEV *op, Type *ty)
349 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
350 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
351 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
352 "Cannot zero extend non-integer value!");
355 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
356 const SCEV *op, Type *ty)
357 : SCEVCastExpr(ID, scSignExtend, op, ty) {
358 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
359 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
360 "Cannot sign extend non-integer value!");
363 void SCEVUnknown::deleted() {
364 // Clear this SCEVUnknown from various maps.
365 SE->forgetMemoizedResults(this);
367 // Remove this SCEVUnknown from the uniquing map.
368 SE->UniqueSCEVs.RemoveNode(this);
370 // Release the value.
374 void SCEVUnknown::allUsesReplacedWith(Value *New) {
375 // Clear this SCEVUnknown from various maps.
376 SE->forgetMemoizedResults(this);
378 // Remove this SCEVUnknown from the uniquing map.
379 SE->UniqueSCEVs.RemoveNode(this);
381 // Update this SCEVUnknown to point to the new value. This is needed
382 // because there may still be outstanding SCEVs which still point to
387 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
388 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
389 if (VCE->getOpcode() == Instruction::PtrToInt)
390 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
391 if (CE->getOpcode() == Instruction::GetElementPtr &&
392 CE->getOperand(0)->isNullValue() &&
393 CE->getNumOperands() == 2)
394 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
396 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
404 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
405 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
406 if (VCE->getOpcode() == Instruction::PtrToInt)
407 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
408 if (CE->getOpcode() == Instruction::GetElementPtr &&
409 CE->getOperand(0)->isNullValue()) {
411 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
412 if (StructType *STy = dyn_cast<StructType>(Ty))
413 if (!STy->isPacked() &&
414 CE->getNumOperands() == 3 &&
415 CE->getOperand(1)->isNullValue()) {
416 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
418 STy->getNumElements() == 2 &&
419 STy->getElementType(0)->isIntegerTy(1)) {
420 AllocTy = STy->getElementType(1);
429 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
430 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
431 if (VCE->getOpcode() == Instruction::PtrToInt)
432 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
433 if (CE->getOpcode() == Instruction::GetElementPtr &&
434 CE->getNumOperands() == 3 &&
435 CE->getOperand(0)->isNullValue() &&
436 CE->getOperand(1)->isNullValue()) {
438 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
439 // Ignore vector types here so that ScalarEvolutionExpander doesn't
440 // emit getelementptrs that index into vectors.
441 if (Ty->isStructTy() || Ty->isArrayTy()) {
443 FieldNo = CE->getOperand(2);
451 //===----------------------------------------------------------------------===//
453 //===----------------------------------------------------------------------===//
456 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
457 /// than the complexity of the RHS. This comparator is used to canonicalize
459 class SCEVComplexityCompare {
460 const LoopInfo *const LI;
462 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
464 // Return true or false if LHS is less than, or at least RHS, respectively.
465 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
466 return compare(LHS, RHS) < 0;
469 // Return negative, zero, or positive, if LHS is less than, equal to, or
470 // greater than RHS, respectively. A three-way result allows recursive
471 // comparisons to be more efficient.
472 int compare(const SCEV *LHS, const SCEV *RHS) const {
473 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
477 // Primarily, sort the SCEVs by their getSCEVType().
478 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
480 return (int)LType - (int)RType;
482 // Aside from the getSCEVType() ordering, the particular ordering
483 // isn't very important except that it's beneficial to be consistent,
484 // so that (a + b) and (b + a) don't end up as different expressions.
487 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
488 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
490 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
491 // not as complete as it could be.
492 const Value *LV = LU->getValue(), *RV = RU->getValue();
494 // Order pointer values after integer values. This helps SCEVExpander
496 bool LIsPointer = LV->getType()->isPointerTy(),
497 RIsPointer = RV->getType()->isPointerTy();
498 if (LIsPointer != RIsPointer)
499 return (int)LIsPointer - (int)RIsPointer;
501 // Compare getValueID values.
502 unsigned LID = LV->getValueID(),
503 RID = RV->getValueID();
505 return (int)LID - (int)RID;
507 // Sort arguments by their position.
508 if (const Argument *LA = dyn_cast<Argument>(LV)) {
509 const Argument *RA = cast<Argument>(RV);
510 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
511 return (int)LArgNo - (int)RArgNo;
514 // For instructions, compare their loop depth, and their operand
515 // count. This is pretty loose.
516 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
517 const Instruction *RInst = cast<Instruction>(RV);
519 // Compare loop depths.
520 const BasicBlock *LParent = LInst->getParent(),
521 *RParent = RInst->getParent();
522 if (LParent != RParent) {
523 unsigned LDepth = LI->getLoopDepth(LParent),
524 RDepth = LI->getLoopDepth(RParent);
525 if (LDepth != RDepth)
526 return (int)LDepth - (int)RDepth;
529 // Compare the number of operands.
530 unsigned LNumOps = LInst->getNumOperands(),
531 RNumOps = RInst->getNumOperands();
532 return (int)LNumOps - (int)RNumOps;
539 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
540 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
542 // Compare constant values.
543 const APInt &LA = LC->getValue()->getValue();
544 const APInt &RA = RC->getValue()->getValue();
545 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
546 if (LBitWidth != RBitWidth)
547 return (int)LBitWidth - (int)RBitWidth;
548 return LA.ult(RA) ? -1 : 1;
552 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
553 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
555 // Compare addrec loop depths.
556 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
557 if (LLoop != RLoop) {
558 unsigned LDepth = LLoop->getLoopDepth(),
559 RDepth = RLoop->getLoopDepth();
560 if (LDepth != RDepth)
561 return (int)LDepth - (int)RDepth;
564 // Addrec complexity grows with operand count.
565 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
566 if (LNumOps != RNumOps)
567 return (int)LNumOps - (int)RNumOps;
569 // Lexicographically compare.
570 for (unsigned i = 0; i != LNumOps; ++i) {
571 long X = compare(LA->getOperand(i), RA->getOperand(i));
583 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
584 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
586 // Lexicographically compare n-ary expressions.
587 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
588 if (LNumOps != RNumOps)
589 return (int)LNumOps - (int)RNumOps;
591 for (unsigned i = 0; i != LNumOps; ++i) {
594 long X = compare(LC->getOperand(i), RC->getOperand(i));
598 return (int)LNumOps - (int)RNumOps;
602 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
603 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
605 // Lexicographically compare udiv expressions.
606 long X = compare(LC->getLHS(), RC->getLHS());
609 return compare(LC->getRHS(), RC->getRHS());
615 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
616 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
618 // Compare cast expressions by operand.
619 return compare(LC->getOperand(), RC->getOperand());
623 llvm_unreachable("Unknown SCEV kind!");
629 /// GroupByComplexity - Given a list of SCEV objects, order them by their
630 /// complexity, and group objects of the same complexity together by value.
631 /// When this routine is finished, we know that any duplicates in the vector are
632 /// consecutive and that complexity is monotonically increasing.
634 /// Note that we go take special precautions to ensure that we get deterministic
635 /// results from this routine. In other words, we don't want the results of
636 /// this to depend on where the addresses of various SCEV objects happened to
639 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
641 if (Ops.size() < 2) return; // Noop
642 if (Ops.size() == 2) {
643 // This is the common case, which also happens to be trivially simple.
645 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
646 if (SCEVComplexityCompare(LI)(RHS, LHS))
651 // Do the rough sort by complexity.
652 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
654 // Now that we are sorted by complexity, group elements of the same
655 // complexity. Note that this is, at worst, N^2, but the vector is likely to
656 // be extremely short in practice. Note that we take this approach because we
657 // do not want to depend on the addresses of the objects we are grouping.
658 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
659 const SCEV *S = Ops[i];
660 unsigned Complexity = S->getSCEVType();
662 // If there are any objects of the same complexity and same value as this
664 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
665 if (Ops[j] == S) { // Found a duplicate.
666 // Move it to immediately after i'th element.
667 std::swap(Ops[i+1], Ops[j]);
668 ++i; // no need to rescan it.
669 if (i == e-2) return; // Done!
677 //===----------------------------------------------------------------------===//
678 // Simple SCEV method implementations
679 //===----------------------------------------------------------------------===//
681 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
683 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
686 // Handle the simplest case efficiently.
688 return SE.getTruncateOrZeroExtend(It, ResultTy);
690 // We are using the following formula for BC(It, K):
692 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
694 // Suppose, W is the bitwidth of the return value. We must be prepared for
695 // overflow. Hence, we must assure that the result of our computation is
696 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
697 // safe in modular arithmetic.
699 // However, this code doesn't use exactly that formula; the formula it uses
700 // is something like the following, where T is the number of factors of 2 in
701 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
704 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
706 // This formula is trivially equivalent to the previous formula. However,
707 // this formula can be implemented much more efficiently. The trick is that
708 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
709 // arithmetic. To do exact division in modular arithmetic, all we have
710 // to do is multiply by the inverse. Therefore, this step can be done at
713 // The next issue is how to safely do the division by 2^T. The way this
714 // is done is by doing the multiplication step at a width of at least W + T
715 // bits. This way, the bottom W+T bits of the product are accurate. Then,
716 // when we perform the division by 2^T (which is equivalent to a right shift
717 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
718 // truncated out after the division by 2^T.
720 // In comparison to just directly using the first formula, this technique
721 // is much more efficient; using the first formula requires W * K bits,
722 // but this formula less than W + K bits. Also, the first formula requires
723 // a division step, whereas this formula only requires multiplies and shifts.
725 // It doesn't matter whether the subtraction step is done in the calculation
726 // width or the input iteration count's width; if the subtraction overflows,
727 // the result must be zero anyway. We prefer here to do it in the width of
728 // the induction variable because it helps a lot for certain cases; CodeGen
729 // isn't smart enough to ignore the overflow, which leads to much less
730 // efficient code if the width of the subtraction is wider than the native
733 // (It's possible to not widen at all by pulling out factors of 2 before
734 // the multiplication; for example, K=2 can be calculated as
735 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
736 // extra arithmetic, so it's not an obvious win, and it gets
737 // much more complicated for K > 3.)
739 // Protection from insane SCEVs; this bound is conservative,
740 // but it probably doesn't matter.
742 return SE.getCouldNotCompute();
744 unsigned W = SE.getTypeSizeInBits(ResultTy);
746 // Calculate K! / 2^T and T; we divide out the factors of two before
747 // multiplying for calculating K! / 2^T to avoid overflow.
748 // Other overflow doesn't matter because we only care about the bottom
749 // W bits of the result.
750 APInt OddFactorial(W, 1);
752 for (unsigned i = 3; i <= K; ++i) {
754 unsigned TwoFactors = Mult.countTrailingZeros();
756 Mult = Mult.lshr(TwoFactors);
757 OddFactorial *= Mult;
760 // We need at least W + T bits for the multiplication step
761 unsigned CalculationBits = W + T;
763 // Calculate 2^T, at width T+W.
764 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
766 // Calculate the multiplicative inverse of K! / 2^T;
767 // this multiplication factor will perform the exact division by
769 APInt Mod = APInt::getSignedMinValue(W+1);
770 APInt MultiplyFactor = OddFactorial.zext(W+1);
771 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
772 MultiplyFactor = MultiplyFactor.trunc(W);
774 // Calculate the product, at width T+W
775 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
777 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
778 for (unsigned i = 1; i != K; ++i) {
779 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
780 Dividend = SE.getMulExpr(Dividend,
781 SE.getTruncateOrZeroExtend(S, CalculationTy));
785 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
787 // Truncate the result, and divide by K! / 2^T.
789 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
790 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
793 /// evaluateAtIteration - Return the value of this chain of recurrences at
794 /// the specified iteration number. We can evaluate this recurrence by
795 /// multiplying each element in the chain by the binomial coefficient
796 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
798 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
800 /// where BC(It, k) stands for binomial coefficient.
802 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
803 ScalarEvolution &SE) const {
804 const SCEV *Result = getStart();
805 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
806 // The computation is correct in the face of overflow provided that the
807 // multiplication is performed _after_ the evaluation of the binomial
809 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
810 if (isa<SCEVCouldNotCompute>(Coeff))
813 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
818 //===----------------------------------------------------------------------===//
819 // SCEV Expression folder implementations
820 //===----------------------------------------------------------------------===//
822 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
824 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
825 "This is not a truncating conversion!");
826 assert(isSCEVable(Ty) &&
827 "This is not a conversion to a SCEVable type!");
828 Ty = getEffectiveSCEVType(Ty);
831 ID.AddInteger(scTruncate);
835 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
837 // Fold if the operand is constant.
838 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
840 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
842 // trunc(trunc(x)) --> trunc(x)
843 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
844 return getTruncateExpr(ST->getOperand(), Ty);
846 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
847 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
848 return getTruncateOrSignExtend(SS->getOperand(), Ty);
850 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
851 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
852 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
854 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
855 // eliminate all the truncates.
856 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
857 SmallVector<const SCEV *, 4> Operands;
858 bool hasTrunc = false;
859 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
860 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
861 hasTrunc = isa<SCEVTruncateExpr>(S);
862 Operands.push_back(S);
865 return getAddExpr(Operands);
866 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
869 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
870 // eliminate all the truncates.
871 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
872 SmallVector<const SCEV *, 4> Operands;
873 bool hasTrunc = false;
874 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
875 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
876 hasTrunc = isa<SCEVTruncateExpr>(S);
877 Operands.push_back(S);
880 return getMulExpr(Operands);
881 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
884 // If the input value is a chrec scev, truncate the chrec's operands.
885 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
886 SmallVector<const SCEV *, 4> Operands;
887 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
888 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
889 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
892 // The cast wasn't folded; create an explicit cast node. We can reuse
893 // the existing insert position since if we get here, we won't have
894 // made any changes which would invalidate it.
895 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
897 UniqueSCEVs.InsertNode(S, IP);
901 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
903 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
904 "This is not an extending conversion!");
905 assert(isSCEVable(Ty) &&
906 "This is not a conversion to a SCEVable type!");
907 Ty = getEffectiveSCEVType(Ty);
909 // Fold if the operand is constant.
910 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
912 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
914 // zext(zext(x)) --> zext(x)
915 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
916 return getZeroExtendExpr(SZ->getOperand(), Ty);
918 // Before doing any expensive analysis, check to see if we've already
919 // computed a SCEV for this Op and Ty.
921 ID.AddInteger(scZeroExtend);
925 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
927 // zext(trunc(x)) --> zext(x) or x or trunc(x)
928 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
929 // It's possible the bits taken off by the truncate were all zero bits. If
930 // so, we should be able to simplify this further.
931 const SCEV *X = ST->getOperand();
932 ConstantRange CR = getUnsignedRange(X);
933 unsigned TruncBits = getTypeSizeInBits(ST->getType());
934 unsigned NewBits = getTypeSizeInBits(Ty);
935 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
936 CR.zextOrTrunc(NewBits)))
937 return getTruncateOrZeroExtend(X, Ty);
940 // If the input value is a chrec scev, and we can prove that the value
941 // did not overflow the old, smaller, value, we can zero extend all of the
942 // operands (often constants). This allows analysis of something like
943 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
944 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
945 if (AR->isAffine()) {
946 const SCEV *Start = AR->getStart();
947 const SCEV *Step = AR->getStepRecurrence(*this);
948 unsigned BitWidth = getTypeSizeInBits(AR->getType());
949 const Loop *L = AR->getLoop();
951 // If we have special knowledge that this addrec won't overflow,
952 // we don't need to do any further analysis.
953 if (AR->getNoWrapFlags(SCEV::FlagNUW))
954 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
955 getZeroExtendExpr(Step, Ty),
956 L, AR->getNoWrapFlags());
958 // Check whether the backedge-taken count is SCEVCouldNotCompute.
959 // Note that this serves two purposes: It filters out loops that are
960 // simply not analyzable, and it covers the case where this code is
961 // being called from within backedge-taken count analysis, such that
962 // attempting to ask for the backedge-taken count would likely result
963 // in infinite recursion. In the later case, the analysis code will
964 // cope with a conservative value, and it will take care to purge
965 // that value once it has finished.
966 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
967 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
968 // Manually compute the final value for AR, checking for
971 // Check whether the backedge-taken count can be losslessly casted to
972 // the addrec's type. The count is always unsigned.
973 const SCEV *CastedMaxBECount =
974 getTruncateOrZeroExtend(MaxBECount, Start->getType());
975 const SCEV *RecastedMaxBECount =
976 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
977 if (MaxBECount == RecastedMaxBECount) {
978 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
979 // Check whether Start+Step*MaxBECount has no unsigned overflow.
980 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
981 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
982 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
983 const SCEV *WideMaxBECount =
984 getZeroExtendExpr(CastedMaxBECount, WideTy);
985 const SCEV *OperandExtendedAdd =
986 getAddExpr(WideStart,
987 getMulExpr(WideMaxBECount,
988 getZeroExtendExpr(Step, WideTy)));
989 if (ZAdd == OperandExtendedAdd) {
990 // Cache knowledge of AR NUW, which is propagated to this AddRec.
991 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
992 // Return the expression with the addrec on the outside.
993 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
994 getZeroExtendExpr(Step, Ty),
995 L, AR->getNoWrapFlags());
997 // Similar to above, only this time treat the step value as signed.
998 // This covers loops that count down.
1000 getAddExpr(WideStart,
1001 getMulExpr(WideMaxBECount,
1002 getSignExtendExpr(Step, WideTy)));
1003 if (ZAdd == OperandExtendedAdd) {
1004 // Cache knowledge of AR NW, which is propagated to this AddRec.
1005 // Negative step causes unsigned wrap, but it still can't self-wrap.
1006 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1007 // Return the expression with the addrec on the outside.
1008 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1009 getSignExtendExpr(Step, Ty),
1010 L, AR->getNoWrapFlags());
1014 // If the backedge is guarded by a comparison with the pre-inc value
1015 // the addrec is safe. Also, if the entry is guarded by a comparison
1016 // with the start value and the backedge is guarded by a comparison
1017 // with the post-inc value, the addrec is safe.
1018 if (isKnownPositive(Step)) {
1019 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1020 getUnsignedRange(Step).getUnsignedMax());
1021 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1022 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1023 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1024 AR->getPostIncExpr(*this), N))) {
1025 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1026 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1027 // Return the expression with the addrec on the outside.
1028 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1029 getZeroExtendExpr(Step, Ty),
1030 L, AR->getNoWrapFlags());
1032 } else if (isKnownNegative(Step)) {
1033 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1034 getSignedRange(Step).getSignedMin());
1035 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1036 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1037 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1038 AR->getPostIncExpr(*this), N))) {
1039 // Cache knowledge of AR NW, which is propagated to this AddRec.
1040 // Negative step causes unsigned wrap, but it still can't self-wrap.
1041 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1042 // Return the expression with the addrec on the outside.
1043 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1044 getSignExtendExpr(Step, Ty),
1045 L, AR->getNoWrapFlags());
1051 // The cast wasn't folded; create an explicit cast node.
1052 // Recompute the insert position, as it may have been invalidated.
1053 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1054 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1056 UniqueSCEVs.InsertNode(S, IP);
1060 // Get the limit of a recurrence such that incrementing by Step cannot cause
1061 // signed overflow as long as the value of the recurrence within the loop does
1062 // not exceed this limit before incrementing.
1063 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1064 ICmpInst::Predicate *Pred,
1065 ScalarEvolution *SE) {
1066 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1067 if (SE->isKnownPositive(Step)) {
1068 *Pred = ICmpInst::ICMP_SLT;
1069 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1070 SE->getSignedRange(Step).getSignedMax());
1072 if (SE->isKnownNegative(Step)) {
1073 *Pred = ICmpInst::ICMP_SGT;
1074 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1075 SE->getSignedRange(Step).getSignedMin());
1080 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1081 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1082 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1083 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1084 // result, the expression "Step + sext(PreIncAR)" is congruent with
1085 // "sext(PostIncAR)"
1086 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1088 ScalarEvolution *SE) {
1089 const Loop *L = AR->getLoop();
1090 const SCEV *Start = AR->getStart();
1091 const SCEV *Step = AR->getStepRecurrence(*SE);
1093 // Check for a simple looking step prior to loop entry.
1094 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1098 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1099 // subtraction is expensive. For this purpose, perform a quick and dirty
1100 // difference, by checking for Step in the operand list.
1101 SmallVector<const SCEV *, 4> DiffOps;
1102 for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end();
1105 DiffOps.push_back(*I);
1107 if (DiffOps.size() == SA->getNumOperands())
1110 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1111 // same three conditions that getSignExtendedExpr checks.
1113 // 1. NSW flags on the step increment.
1114 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1115 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1116 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1118 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1121 // 2. Direct overflow check on the step operation's expression.
1122 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1123 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1124 const SCEV *OperandExtendedStart =
1125 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1126 SE->getSignExtendExpr(Step, WideTy));
1127 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1128 // Cache knowledge of PreAR NSW.
1130 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1131 // FIXME: this optimization needs a unit test
1132 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1136 // 3. Loop precondition.
1137 ICmpInst::Predicate Pred;
1138 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1140 if (OverflowLimit &&
1141 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1147 // Get the normalized sign-extended expression for this AddRec's Start.
1148 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1150 ScalarEvolution *SE) {
1151 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1153 return SE->getSignExtendExpr(AR->getStart(), Ty);
1155 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1156 SE->getSignExtendExpr(PreStart, Ty));
1159 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1161 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1162 "This is not an extending conversion!");
1163 assert(isSCEVable(Ty) &&
1164 "This is not a conversion to a SCEVable type!");
1165 Ty = getEffectiveSCEVType(Ty);
1167 // Fold if the operand is constant.
1168 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1170 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1172 // sext(sext(x)) --> sext(x)
1173 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1174 return getSignExtendExpr(SS->getOperand(), Ty);
1176 // sext(zext(x)) --> zext(x)
1177 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1178 return getZeroExtendExpr(SZ->getOperand(), Ty);
1180 // Before doing any expensive analysis, check to see if we've already
1181 // computed a SCEV for this Op and Ty.
1182 FoldingSetNodeID ID;
1183 ID.AddInteger(scSignExtend);
1187 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1189 // If the input value is provably positive, build a zext instead.
1190 if (isKnownNonNegative(Op))
1191 return getZeroExtendExpr(Op, Ty);
1193 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1194 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1195 // It's possible the bits taken off by the truncate were all sign bits. If
1196 // so, we should be able to simplify this further.
1197 const SCEV *X = ST->getOperand();
1198 ConstantRange CR = getSignedRange(X);
1199 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1200 unsigned NewBits = getTypeSizeInBits(Ty);
1201 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1202 CR.sextOrTrunc(NewBits)))
1203 return getTruncateOrSignExtend(X, Ty);
1206 // If the input value is a chrec scev, and we can prove that the value
1207 // did not overflow the old, smaller, value, we can sign extend all of the
1208 // operands (often constants). This allows analysis of something like
1209 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1210 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1211 if (AR->isAffine()) {
1212 const SCEV *Start = AR->getStart();
1213 const SCEV *Step = AR->getStepRecurrence(*this);
1214 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1215 const Loop *L = AR->getLoop();
1217 // If we have special knowledge that this addrec won't overflow,
1218 // we don't need to do any further analysis.
1219 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1220 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1221 getSignExtendExpr(Step, Ty),
1224 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1225 // Note that this serves two purposes: It filters out loops that are
1226 // simply not analyzable, and it covers the case where this code is
1227 // being called from within backedge-taken count analysis, such that
1228 // attempting to ask for the backedge-taken count would likely result
1229 // in infinite recursion. In the later case, the analysis code will
1230 // cope with a conservative value, and it will take care to purge
1231 // that value once it has finished.
1232 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1233 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1234 // Manually compute the final value for AR, checking for
1237 // Check whether the backedge-taken count can be losslessly casted to
1238 // the addrec's type. The count is always unsigned.
1239 const SCEV *CastedMaxBECount =
1240 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1241 const SCEV *RecastedMaxBECount =
1242 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1243 if (MaxBECount == RecastedMaxBECount) {
1244 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1245 // Check whether Start+Step*MaxBECount has no signed overflow.
1246 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1247 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1248 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1249 const SCEV *WideMaxBECount =
1250 getZeroExtendExpr(CastedMaxBECount, WideTy);
1251 const SCEV *OperandExtendedAdd =
1252 getAddExpr(WideStart,
1253 getMulExpr(WideMaxBECount,
1254 getSignExtendExpr(Step, WideTy)));
1255 if (SAdd == OperandExtendedAdd) {
1256 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1257 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1258 // Return the expression with the addrec on the outside.
1259 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1260 getSignExtendExpr(Step, Ty),
1261 L, AR->getNoWrapFlags());
1263 // Similar to above, only this time treat the step value as unsigned.
1264 // This covers loops that count up with an unsigned step.
1265 OperandExtendedAdd =
1266 getAddExpr(WideStart,
1267 getMulExpr(WideMaxBECount,
1268 getZeroExtendExpr(Step, WideTy)));
1269 if (SAdd == OperandExtendedAdd) {
1270 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1271 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1272 // Return the expression with the addrec on the outside.
1273 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1274 getZeroExtendExpr(Step, Ty),
1275 L, AR->getNoWrapFlags());
1279 // If the backedge is guarded by a comparison with the pre-inc value
1280 // the addrec is safe. Also, if the entry is guarded by a comparison
1281 // with the start value and the backedge is guarded by a comparison
1282 // with the post-inc value, the addrec is safe.
1283 ICmpInst::Predicate Pred;
1284 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1285 if (OverflowLimit &&
1286 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1287 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1288 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1290 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1291 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1292 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1293 getSignExtendExpr(Step, Ty),
1294 L, AR->getNoWrapFlags());
1299 // The cast wasn't folded; create an explicit cast node.
1300 // Recompute the insert position, as it may have been invalidated.
1301 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1302 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1304 UniqueSCEVs.InsertNode(S, IP);
1308 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1309 /// unspecified bits out to the given type.
1311 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1313 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1314 "This is not an extending conversion!");
1315 assert(isSCEVable(Ty) &&
1316 "This is not a conversion to a SCEVable type!");
1317 Ty = getEffectiveSCEVType(Ty);
1319 // Sign-extend negative constants.
1320 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1321 if (SC->getValue()->getValue().isNegative())
1322 return getSignExtendExpr(Op, Ty);
1324 // Peel off a truncate cast.
1325 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1326 const SCEV *NewOp = T->getOperand();
1327 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1328 return getAnyExtendExpr(NewOp, Ty);
1329 return getTruncateOrNoop(NewOp, Ty);
1332 // Next try a zext cast. If the cast is folded, use it.
1333 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1334 if (!isa<SCEVZeroExtendExpr>(ZExt))
1337 // Next try a sext cast. If the cast is folded, use it.
1338 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1339 if (!isa<SCEVSignExtendExpr>(SExt))
1342 // Force the cast to be folded into the operands of an addrec.
1343 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1344 SmallVector<const SCEV *, 4> Ops;
1345 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1347 Ops.push_back(getAnyExtendExpr(*I, Ty));
1348 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1351 // If the expression is obviously signed, use the sext cast value.
1352 if (isa<SCEVSMaxExpr>(Op))
1355 // Absent any other information, use the zext cast value.
1359 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1360 /// a list of operands to be added under the given scale, update the given
1361 /// map. This is a helper function for getAddRecExpr. As an example of
1362 /// what it does, given a sequence of operands that would form an add
1363 /// expression like this:
1365 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1367 /// where A and B are constants, update the map with these values:
1369 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1371 /// and add 13 + A*B*29 to AccumulatedConstant.
1372 /// This will allow getAddRecExpr to produce this:
1374 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1376 /// This form often exposes folding opportunities that are hidden in
1377 /// the original operand list.
1379 /// Return true iff it appears that any interesting folding opportunities
1380 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1381 /// the common case where no interesting opportunities are present, and
1382 /// is also used as a check to avoid infinite recursion.
1385 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1386 SmallVectorImpl<const SCEV *> &NewOps,
1387 APInt &AccumulatedConstant,
1388 const SCEV *const *Ops, size_t NumOperands,
1390 ScalarEvolution &SE) {
1391 bool Interesting = false;
1393 // Iterate over the add operands. They are sorted, with constants first.
1395 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1397 // Pull a buried constant out to the outside.
1398 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1400 AccumulatedConstant += Scale * C->getValue()->getValue();
1403 // Next comes everything else. We're especially interested in multiplies
1404 // here, but they're in the middle, so just visit the rest with one loop.
1405 for (; i != NumOperands; ++i) {
1406 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1407 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1409 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1410 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1411 // A multiplication of a constant with another add; recurse.
1412 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1414 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1415 Add->op_begin(), Add->getNumOperands(),
1418 // A multiplication of a constant with some other value. Update
1420 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1421 const SCEV *Key = SE.getMulExpr(MulOps);
1422 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1423 M.insert(std::make_pair(Key, NewScale));
1425 NewOps.push_back(Pair.first->first);
1427 Pair.first->second += NewScale;
1428 // The map already had an entry for this value, which may indicate
1429 // a folding opportunity.
1434 // An ordinary operand. Update the map.
1435 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1436 M.insert(std::make_pair(Ops[i], Scale));
1438 NewOps.push_back(Pair.first->first);
1440 Pair.first->second += Scale;
1441 // The map already had an entry for this value, which may indicate
1442 // a folding opportunity.
1452 struct APIntCompare {
1453 bool operator()(const APInt &LHS, const APInt &RHS) const {
1454 return LHS.ult(RHS);
1459 /// getAddExpr - Get a canonical add expression, or something simpler if
1461 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1462 SCEV::NoWrapFlags Flags) {
1463 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1464 "only nuw or nsw allowed");
1465 assert(!Ops.empty() && "Cannot get empty add!");
1466 if (Ops.size() == 1) return Ops[0];
1468 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1469 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1470 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1471 "SCEVAddExpr operand types don't match!");
1474 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1476 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1477 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1478 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1480 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1481 E = Ops.end(); I != E; ++I)
1482 if (!isKnownNonNegative(*I)) {
1486 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1489 // Sort by complexity, this groups all similar expression types together.
1490 GroupByComplexity(Ops, LI);
1492 // If there are any constants, fold them together.
1494 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1496 assert(Idx < Ops.size());
1497 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1498 // We found two constants, fold them together!
1499 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1500 RHSC->getValue()->getValue());
1501 if (Ops.size() == 2) return Ops[0];
1502 Ops.erase(Ops.begin()+1); // Erase the folded element
1503 LHSC = cast<SCEVConstant>(Ops[0]);
1506 // If we are left with a constant zero being added, strip it off.
1507 if (LHSC->getValue()->isZero()) {
1508 Ops.erase(Ops.begin());
1512 if (Ops.size() == 1) return Ops[0];
1515 // Okay, check to see if the same value occurs in the operand list more than
1516 // once. If so, merge them together into an multiply expression. Since we
1517 // sorted the list, these values are required to be adjacent.
1518 Type *Ty = Ops[0]->getType();
1519 bool FoundMatch = false;
1520 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1521 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1522 // Scan ahead to count how many equal operands there are.
1524 while (i+Count != e && Ops[i+Count] == Ops[i])
1526 // Merge the values into a multiply.
1527 const SCEV *Scale = getConstant(Ty, Count);
1528 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1529 if (Ops.size() == Count)
1532 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1533 --i; e -= Count - 1;
1537 return getAddExpr(Ops, Flags);
1539 // Check for truncates. If all the operands are truncated from the same
1540 // type, see if factoring out the truncate would permit the result to be
1541 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1542 // if the contents of the resulting outer trunc fold to something simple.
1543 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1544 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1545 Type *DstType = Trunc->getType();
1546 Type *SrcType = Trunc->getOperand()->getType();
1547 SmallVector<const SCEV *, 8> LargeOps;
1549 // Check all the operands to see if they can be represented in the
1550 // source type of the truncate.
1551 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1552 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1553 if (T->getOperand()->getType() != SrcType) {
1557 LargeOps.push_back(T->getOperand());
1558 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1559 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1560 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1561 SmallVector<const SCEV *, 8> LargeMulOps;
1562 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1563 if (const SCEVTruncateExpr *T =
1564 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1565 if (T->getOperand()->getType() != SrcType) {
1569 LargeMulOps.push_back(T->getOperand());
1570 } else if (const SCEVConstant *C =
1571 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1572 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1579 LargeOps.push_back(getMulExpr(LargeMulOps));
1586 // Evaluate the expression in the larger type.
1587 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1588 // If it folds to something simple, use it. Otherwise, don't.
1589 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1590 return getTruncateExpr(Fold, DstType);
1594 // Skip past any other cast SCEVs.
1595 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1598 // If there are add operands they would be next.
1599 if (Idx < Ops.size()) {
1600 bool DeletedAdd = false;
1601 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1602 // If we have an add, expand the add operands onto the end of the operands
1604 Ops.erase(Ops.begin()+Idx);
1605 Ops.append(Add->op_begin(), Add->op_end());
1609 // If we deleted at least one add, we added operands to the end of the list,
1610 // and they are not necessarily sorted. Recurse to resort and resimplify
1611 // any operands we just acquired.
1613 return getAddExpr(Ops);
1616 // Skip over the add expression until we get to a multiply.
1617 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1620 // Check to see if there are any folding opportunities present with
1621 // operands multiplied by constant values.
1622 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1623 uint64_t BitWidth = getTypeSizeInBits(Ty);
1624 DenseMap<const SCEV *, APInt> M;
1625 SmallVector<const SCEV *, 8> NewOps;
1626 APInt AccumulatedConstant(BitWidth, 0);
1627 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1628 Ops.data(), Ops.size(),
1629 APInt(BitWidth, 1), *this)) {
1630 // Some interesting folding opportunity is present, so its worthwhile to
1631 // re-generate the operands list. Group the operands by constant scale,
1632 // to avoid multiplying by the same constant scale multiple times.
1633 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1634 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1635 E = NewOps.end(); I != E; ++I)
1636 MulOpLists[M.find(*I)->second].push_back(*I);
1637 // Re-generate the operands list.
1639 if (AccumulatedConstant != 0)
1640 Ops.push_back(getConstant(AccumulatedConstant));
1641 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1642 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1644 Ops.push_back(getMulExpr(getConstant(I->first),
1645 getAddExpr(I->second)));
1647 return getConstant(Ty, 0);
1648 if (Ops.size() == 1)
1650 return getAddExpr(Ops);
1654 // If we are adding something to a multiply expression, make sure the
1655 // something is not already an operand of the multiply. If so, merge it into
1657 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1658 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1659 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1660 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1661 if (isa<SCEVConstant>(MulOpSCEV))
1663 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1664 if (MulOpSCEV == Ops[AddOp]) {
1665 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1666 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1667 if (Mul->getNumOperands() != 2) {
1668 // If the multiply has more than two operands, we must get the
1670 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1671 Mul->op_begin()+MulOp);
1672 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1673 InnerMul = getMulExpr(MulOps);
1675 const SCEV *One = getConstant(Ty, 1);
1676 const SCEV *AddOne = getAddExpr(One, InnerMul);
1677 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1678 if (Ops.size() == 2) return OuterMul;
1680 Ops.erase(Ops.begin()+AddOp);
1681 Ops.erase(Ops.begin()+Idx-1);
1683 Ops.erase(Ops.begin()+Idx);
1684 Ops.erase(Ops.begin()+AddOp-1);
1686 Ops.push_back(OuterMul);
1687 return getAddExpr(Ops);
1690 // Check this multiply against other multiplies being added together.
1691 for (unsigned OtherMulIdx = Idx+1;
1692 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1694 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1695 // If MulOp occurs in OtherMul, we can fold the two multiplies
1697 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1698 OMulOp != e; ++OMulOp)
1699 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1700 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1701 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1702 if (Mul->getNumOperands() != 2) {
1703 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1704 Mul->op_begin()+MulOp);
1705 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1706 InnerMul1 = getMulExpr(MulOps);
1708 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1709 if (OtherMul->getNumOperands() != 2) {
1710 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1711 OtherMul->op_begin()+OMulOp);
1712 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1713 InnerMul2 = getMulExpr(MulOps);
1715 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1716 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1717 if (Ops.size() == 2) return OuterMul;
1718 Ops.erase(Ops.begin()+Idx);
1719 Ops.erase(Ops.begin()+OtherMulIdx-1);
1720 Ops.push_back(OuterMul);
1721 return getAddExpr(Ops);
1727 // If there are any add recurrences in the operands list, see if any other
1728 // added values are loop invariant. If so, we can fold them into the
1730 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1733 // Scan over all recurrences, trying to fold loop invariants into them.
1734 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1735 // Scan all of the other operands to this add and add them to the vector if
1736 // they are loop invariant w.r.t. the recurrence.
1737 SmallVector<const SCEV *, 8> LIOps;
1738 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1739 const Loop *AddRecLoop = AddRec->getLoop();
1740 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1741 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1742 LIOps.push_back(Ops[i]);
1743 Ops.erase(Ops.begin()+i);
1747 // If we found some loop invariants, fold them into the recurrence.
1748 if (!LIOps.empty()) {
1749 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1750 LIOps.push_back(AddRec->getStart());
1752 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1754 AddRecOps[0] = getAddExpr(LIOps);
1756 // Build the new addrec. Propagate the NUW and NSW flags if both the
1757 // outer add and the inner addrec are guaranteed to have no overflow.
1758 // Always propagate NW.
1759 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1760 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1762 // If all of the other operands were loop invariant, we are done.
1763 if (Ops.size() == 1) return NewRec;
1765 // Otherwise, add the folded AddRec by the non-invariant parts.
1766 for (unsigned i = 0;; ++i)
1767 if (Ops[i] == AddRec) {
1771 return getAddExpr(Ops);
1774 // Okay, if there weren't any loop invariants to be folded, check to see if
1775 // there are multiple AddRec's with the same loop induction variable being
1776 // added together. If so, we can fold them.
1777 for (unsigned OtherIdx = Idx+1;
1778 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1780 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1781 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1782 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1784 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1786 if (const SCEVAddRecExpr *OtherAddRec =
1787 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1788 if (OtherAddRec->getLoop() == AddRecLoop) {
1789 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1791 if (i >= AddRecOps.size()) {
1792 AddRecOps.append(OtherAddRec->op_begin()+i,
1793 OtherAddRec->op_end());
1796 AddRecOps[i] = getAddExpr(AddRecOps[i],
1797 OtherAddRec->getOperand(i));
1799 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1801 // Step size has changed, so we cannot guarantee no self-wraparound.
1802 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1803 return getAddExpr(Ops);
1806 // Otherwise couldn't fold anything into this recurrence. Move onto the
1810 // Okay, it looks like we really DO need an add expr. Check to see if we
1811 // already have one, otherwise create a new one.
1812 FoldingSetNodeID ID;
1813 ID.AddInteger(scAddExpr);
1814 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1815 ID.AddPointer(Ops[i]);
1818 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1820 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1821 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1822 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1824 UniqueSCEVs.InsertNode(S, IP);
1826 S->setNoWrapFlags(Flags);
1830 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1832 if (j > 1 && k / j != i) Overflow = true;
1836 /// Compute the result of "n choose k", the binomial coefficient. If an
1837 /// intermediate computation overflows, Overflow will be set and the return will
1838 /// be garbage. Overflow is not cleared on absence of overflow.
1839 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1840 // We use the multiplicative formula:
1841 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1842 // At each iteration, we take the n-th term of the numeral and divide by the
1843 // (k-n)th term of the denominator. This division will always produce an
1844 // integral result, and helps reduce the chance of overflow in the
1845 // intermediate computations. However, we can still overflow even when the
1846 // final result would fit.
1848 if (n == 0 || n == k) return 1;
1849 if (k > n) return 0;
1855 for (uint64_t i = 1; i <= k; ++i) {
1856 r = umul_ov(r, n-(i-1), Overflow);
1862 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1864 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1865 SCEV::NoWrapFlags Flags) {
1866 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1867 "only nuw or nsw allowed");
1868 assert(!Ops.empty() && "Cannot get empty mul!");
1869 if (Ops.size() == 1) return Ops[0];
1871 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1872 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1873 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1874 "SCEVMulExpr operand types don't match!");
1877 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1879 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1880 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1881 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1883 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1884 E = Ops.end(); I != E; ++I)
1885 if (!isKnownNonNegative(*I)) {
1889 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1892 // Sort by complexity, this groups all similar expression types together.
1893 GroupByComplexity(Ops, LI);
1895 // If there are any constants, fold them together.
1897 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1899 // C1*(C2+V) -> C1*C2 + C1*V
1900 if (Ops.size() == 2)
1901 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1902 if (Add->getNumOperands() == 2 &&
1903 isa<SCEVConstant>(Add->getOperand(0)))
1904 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1905 getMulExpr(LHSC, Add->getOperand(1)));
1908 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1909 // We found two constants, fold them together!
1910 ConstantInt *Fold = ConstantInt::get(getContext(),
1911 LHSC->getValue()->getValue() *
1912 RHSC->getValue()->getValue());
1913 Ops[0] = getConstant(Fold);
1914 Ops.erase(Ops.begin()+1); // Erase the folded element
1915 if (Ops.size() == 1) return Ops[0];
1916 LHSC = cast<SCEVConstant>(Ops[0]);
1919 // If we are left with a constant one being multiplied, strip it off.
1920 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1921 Ops.erase(Ops.begin());
1923 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1924 // If we have a multiply of zero, it will always be zero.
1926 } else if (Ops[0]->isAllOnesValue()) {
1927 // If we have a mul by -1 of an add, try distributing the -1 among the
1929 if (Ops.size() == 2) {
1930 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1931 SmallVector<const SCEV *, 4> NewOps;
1932 bool AnyFolded = false;
1933 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1934 E = Add->op_end(); I != E; ++I) {
1935 const SCEV *Mul = getMulExpr(Ops[0], *I);
1936 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1937 NewOps.push_back(Mul);
1940 return getAddExpr(NewOps);
1942 else if (const SCEVAddRecExpr *
1943 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1944 // Negation preserves a recurrence's no self-wrap property.
1945 SmallVector<const SCEV *, 4> Operands;
1946 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1947 E = AddRec->op_end(); I != E; ++I) {
1948 Operands.push_back(getMulExpr(Ops[0], *I));
1950 return getAddRecExpr(Operands, AddRec->getLoop(),
1951 AddRec->getNoWrapFlags(SCEV::FlagNW));
1956 if (Ops.size() == 1)
1960 // Skip over the add expression until we get to a multiply.
1961 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1964 // If there are mul operands inline them all into this expression.
1965 if (Idx < Ops.size()) {
1966 bool DeletedMul = false;
1967 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1968 // If we have an mul, expand the mul operands onto the end of the operands
1970 Ops.erase(Ops.begin()+Idx);
1971 Ops.append(Mul->op_begin(), Mul->op_end());
1975 // If we deleted at least one mul, we added operands to the end of the list,
1976 // and they are not necessarily sorted. Recurse to resort and resimplify
1977 // any operands we just acquired.
1979 return getMulExpr(Ops);
1982 // If there are any add recurrences in the operands list, see if any other
1983 // added values are loop invariant. If so, we can fold them into the
1985 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1988 // Scan over all recurrences, trying to fold loop invariants into them.
1989 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1990 // Scan all of the other operands to this mul and add them to the vector if
1991 // they are loop invariant w.r.t. the recurrence.
1992 SmallVector<const SCEV *, 8> LIOps;
1993 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1994 const Loop *AddRecLoop = AddRec->getLoop();
1995 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1996 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1997 LIOps.push_back(Ops[i]);
1998 Ops.erase(Ops.begin()+i);
2002 // If we found some loop invariants, fold them into the recurrence.
2003 if (!LIOps.empty()) {
2004 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2005 SmallVector<const SCEV *, 4> NewOps;
2006 NewOps.reserve(AddRec->getNumOperands());
2007 const SCEV *Scale = getMulExpr(LIOps);
2008 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2009 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2011 // Build the new addrec. Propagate the NUW and NSW flags if both the
2012 // outer mul and the inner addrec are guaranteed to have no overflow.
2014 // No self-wrap cannot be guaranteed after changing the step size, but
2015 // will be inferred if either NUW or NSW is true.
2016 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2017 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2019 // If all of the other operands were loop invariant, we are done.
2020 if (Ops.size() == 1) return NewRec;
2022 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2023 for (unsigned i = 0;; ++i)
2024 if (Ops[i] == AddRec) {
2028 return getMulExpr(Ops);
2031 // Okay, if there weren't any loop invariants to be folded, check to see if
2032 // there are multiple AddRec's with the same loop induction variable being
2033 // multiplied together. If so, we can fold them.
2034 for (unsigned OtherIdx = Idx+1;
2035 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2037 if (AddRecLoop != cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop())
2040 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2041 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2042 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2043 // ]]],+,...up to x=2n}.
2044 // Note that the arguments to choose() are always integers with values
2045 // known at compile time, never SCEV objects.
2047 // The implementation avoids pointless extra computations when the two
2048 // addrec's are of different length (mathematically, it's equivalent to
2049 // an infinite stream of zeros on the right).
2050 bool OpsModified = false;
2051 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2053 const SCEVAddRecExpr *OtherAddRec =
2054 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2055 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2058 bool Overflow = false;
2059 Type *Ty = AddRec->getType();
2060 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2061 SmallVector<const SCEV*, 7> AddRecOps;
2062 for (int x = 0, xe = AddRec->getNumOperands() +
2063 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2064 const SCEV *Term = getConstant(Ty, 0);
2065 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2066 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2067 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2068 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2069 z < ze && !Overflow; ++z) {
2070 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2072 if (LargerThan64Bits)
2073 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2075 Coeff = Coeff1*Coeff2;
2076 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2077 const SCEV *Term1 = AddRec->getOperand(y-z);
2078 const SCEV *Term2 = OtherAddRec->getOperand(z);
2079 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2082 AddRecOps.push_back(Term);
2085 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2087 if (Ops.size() == 2) return NewAddRec;
2088 Ops[Idx] = NewAddRec;
2089 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2091 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2097 return getMulExpr(Ops);
2100 // Otherwise couldn't fold anything into this recurrence. Move onto the
2104 // Okay, it looks like we really DO need an mul expr. Check to see if we
2105 // already have one, otherwise create a new one.
2106 FoldingSetNodeID ID;
2107 ID.AddInteger(scMulExpr);
2108 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2109 ID.AddPointer(Ops[i]);
2112 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2114 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2115 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2116 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2118 UniqueSCEVs.InsertNode(S, IP);
2120 S->setNoWrapFlags(Flags);
2124 /// getUDivExpr - Get a canonical unsigned division expression, or something
2125 /// simpler if possible.
2126 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2128 assert(getEffectiveSCEVType(LHS->getType()) ==
2129 getEffectiveSCEVType(RHS->getType()) &&
2130 "SCEVUDivExpr operand types don't match!");
2132 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2133 if (RHSC->getValue()->equalsInt(1))
2134 return LHS; // X udiv 1 --> x
2135 // If the denominator is zero, the result of the udiv is undefined. Don't
2136 // try to analyze it, because the resolution chosen here may differ from
2137 // the resolution chosen in other parts of the compiler.
2138 if (!RHSC->getValue()->isZero()) {
2139 // Determine if the division can be folded into the operands of
2141 // TODO: Generalize this to non-constants by using known-bits information.
2142 Type *Ty = LHS->getType();
2143 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2144 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2145 // For non-power-of-two values, effectively round the value up to the
2146 // nearest power of two.
2147 if (!RHSC->getValue()->getValue().isPowerOf2())
2149 IntegerType *ExtTy =
2150 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2151 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2152 if (const SCEVConstant *Step =
2153 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2154 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2155 const APInt &StepInt = Step->getValue()->getValue();
2156 const APInt &DivInt = RHSC->getValue()->getValue();
2157 if (!StepInt.urem(DivInt) &&
2158 getZeroExtendExpr(AR, ExtTy) ==
2159 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2160 getZeroExtendExpr(Step, ExtTy),
2161 AR->getLoop(), SCEV::FlagAnyWrap)) {
2162 SmallVector<const SCEV *, 4> Operands;
2163 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2164 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2165 return getAddRecExpr(Operands, AR->getLoop(),
2168 /// Get a canonical UDivExpr for a recurrence.
2169 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2170 // We can currently only fold X%N if X is constant.
2171 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2172 if (StartC && !DivInt.urem(StepInt) &&
2173 getZeroExtendExpr(AR, ExtTy) ==
2174 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2175 getZeroExtendExpr(Step, ExtTy),
2176 AR->getLoop(), SCEV::FlagAnyWrap)) {
2177 const APInt &StartInt = StartC->getValue()->getValue();
2178 const APInt &StartRem = StartInt.urem(StepInt);
2180 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2181 AR->getLoop(), SCEV::FlagNW);
2184 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2185 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2186 SmallVector<const SCEV *, 4> Operands;
2187 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2188 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2189 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2190 // Find an operand that's safely divisible.
2191 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2192 const SCEV *Op = M->getOperand(i);
2193 const SCEV *Div = getUDivExpr(Op, RHSC);
2194 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2195 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2198 return getMulExpr(Operands);
2202 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2203 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2204 SmallVector<const SCEV *, 4> Operands;
2205 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2206 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2207 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2209 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2210 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2211 if (isa<SCEVUDivExpr>(Op) ||
2212 getMulExpr(Op, RHS) != A->getOperand(i))
2214 Operands.push_back(Op);
2216 if (Operands.size() == A->getNumOperands())
2217 return getAddExpr(Operands);
2221 // Fold if both operands are constant.
2222 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2223 Constant *LHSCV = LHSC->getValue();
2224 Constant *RHSCV = RHSC->getValue();
2225 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2231 FoldingSetNodeID ID;
2232 ID.AddInteger(scUDivExpr);
2236 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2237 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2239 UniqueSCEVs.InsertNode(S, IP);
2244 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2245 /// Simplify the expression as much as possible.
2246 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2248 SCEV::NoWrapFlags Flags) {
2249 SmallVector<const SCEV *, 4> Operands;
2250 Operands.push_back(Start);
2251 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2252 if (StepChrec->getLoop() == L) {
2253 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2254 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2257 Operands.push_back(Step);
2258 return getAddRecExpr(Operands, L, Flags);
2261 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2262 /// Simplify the expression as much as possible.
2264 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2265 const Loop *L, SCEV::NoWrapFlags Flags) {
2266 if (Operands.size() == 1) return Operands[0];
2268 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2269 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2270 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2271 "SCEVAddRecExpr operand types don't match!");
2272 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2273 assert(isLoopInvariant(Operands[i], L) &&
2274 "SCEVAddRecExpr operand is not loop-invariant!");
2277 if (Operands.back()->isZero()) {
2278 Operands.pop_back();
2279 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2282 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2283 // use that information to infer NUW and NSW flags. However, computing a
2284 // BE count requires calling getAddRecExpr, so we may not yet have a
2285 // meaningful BE count at this point (and if we don't, we'd be stuck
2286 // with a SCEVCouldNotCompute as the cached BE count).
2288 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2290 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2291 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2292 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2294 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2295 E = Operands.end(); I != E; ++I)
2296 if (!isKnownNonNegative(*I)) {
2300 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2303 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2304 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2305 const Loop *NestedLoop = NestedAR->getLoop();
2306 if (L->contains(NestedLoop) ?
2307 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2308 (!NestedLoop->contains(L) &&
2309 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2310 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2311 NestedAR->op_end());
2312 Operands[0] = NestedAR->getStart();
2313 // AddRecs require their operands be loop-invariant with respect to their
2314 // loops. Don't perform this transformation if it would break this
2316 bool AllInvariant = true;
2317 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2318 if (!isLoopInvariant(Operands[i], L)) {
2319 AllInvariant = false;
2323 // Create a recurrence for the outer loop with the same step size.
2325 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2326 // inner recurrence has the same property.
2327 SCEV::NoWrapFlags OuterFlags =
2328 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2330 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2331 AllInvariant = true;
2332 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2333 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2334 AllInvariant = false;
2338 // Ok, both add recurrences are valid after the transformation.
2340 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2341 // the outer recurrence has the same property.
2342 SCEV::NoWrapFlags InnerFlags =
2343 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2344 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2347 // Reset Operands to its original state.
2348 Operands[0] = NestedAR;
2352 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2353 // already have one, otherwise create a new one.
2354 FoldingSetNodeID ID;
2355 ID.AddInteger(scAddRecExpr);
2356 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2357 ID.AddPointer(Operands[i]);
2361 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2363 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2364 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2365 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2366 O, Operands.size(), L);
2367 UniqueSCEVs.InsertNode(S, IP);
2369 S->setNoWrapFlags(Flags);
2373 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2375 SmallVector<const SCEV *, 2> Ops;
2378 return getSMaxExpr(Ops);
2382 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2383 assert(!Ops.empty() && "Cannot get empty smax!");
2384 if (Ops.size() == 1) return Ops[0];
2386 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2387 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2388 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2389 "SCEVSMaxExpr operand types don't match!");
2392 // Sort by complexity, this groups all similar expression types together.
2393 GroupByComplexity(Ops, LI);
2395 // If there are any constants, fold them together.
2397 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2399 assert(Idx < Ops.size());
2400 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2401 // We found two constants, fold them together!
2402 ConstantInt *Fold = ConstantInt::get(getContext(),
2403 APIntOps::smax(LHSC->getValue()->getValue(),
2404 RHSC->getValue()->getValue()));
2405 Ops[0] = getConstant(Fold);
2406 Ops.erase(Ops.begin()+1); // Erase the folded element
2407 if (Ops.size() == 1) return Ops[0];
2408 LHSC = cast<SCEVConstant>(Ops[0]);
2411 // If we are left with a constant minimum-int, strip it off.
2412 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2413 Ops.erase(Ops.begin());
2415 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2416 // If we have an smax with a constant maximum-int, it will always be
2421 if (Ops.size() == 1) return Ops[0];
2424 // Find the first SMax
2425 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2428 // Check to see if one of the operands is an SMax. If so, expand its operands
2429 // onto our operand list, and recurse to simplify.
2430 if (Idx < Ops.size()) {
2431 bool DeletedSMax = false;
2432 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2433 Ops.erase(Ops.begin()+Idx);
2434 Ops.append(SMax->op_begin(), SMax->op_end());
2439 return getSMaxExpr(Ops);
2442 // Okay, check to see if the same value occurs in the operand list twice. If
2443 // so, delete one. Since we sorted the list, these values are required to
2445 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2446 // X smax Y smax Y --> X smax Y
2447 // X smax Y --> X, if X is always greater than Y
2448 if (Ops[i] == Ops[i+1] ||
2449 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2450 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2452 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2453 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2457 if (Ops.size() == 1) return Ops[0];
2459 assert(!Ops.empty() && "Reduced smax down to nothing!");
2461 // Okay, it looks like we really DO need an smax expr. Check to see if we
2462 // already have one, otherwise create a new one.
2463 FoldingSetNodeID ID;
2464 ID.AddInteger(scSMaxExpr);
2465 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2466 ID.AddPointer(Ops[i]);
2468 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2469 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2470 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2471 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2473 UniqueSCEVs.InsertNode(S, IP);
2477 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2479 SmallVector<const SCEV *, 2> Ops;
2482 return getUMaxExpr(Ops);
2486 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2487 assert(!Ops.empty() && "Cannot get empty umax!");
2488 if (Ops.size() == 1) return Ops[0];
2490 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2491 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2492 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2493 "SCEVUMaxExpr operand types don't match!");
2496 // Sort by complexity, this groups all similar expression types together.
2497 GroupByComplexity(Ops, LI);
2499 // If there are any constants, fold them together.
2501 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2503 assert(Idx < Ops.size());
2504 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2505 // We found two constants, fold them together!
2506 ConstantInt *Fold = ConstantInt::get(getContext(),
2507 APIntOps::umax(LHSC->getValue()->getValue(),
2508 RHSC->getValue()->getValue()));
2509 Ops[0] = getConstant(Fold);
2510 Ops.erase(Ops.begin()+1); // Erase the folded element
2511 if (Ops.size() == 1) return Ops[0];
2512 LHSC = cast<SCEVConstant>(Ops[0]);
2515 // If we are left with a constant minimum-int, strip it off.
2516 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2517 Ops.erase(Ops.begin());
2519 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2520 // If we have an umax with a constant maximum-int, it will always be
2525 if (Ops.size() == 1) return Ops[0];
2528 // Find the first UMax
2529 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2532 // Check to see if one of the operands is a UMax. If so, expand its operands
2533 // onto our operand list, and recurse to simplify.
2534 if (Idx < Ops.size()) {
2535 bool DeletedUMax = false;
2536 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2537 Ops.erase(Ops.begin()+Idx);
2538 Ops.append(UMax->op_begin(), UMax->op_end());
2543 return getUMaxExpr(Ops);
2546 // Okay, check to see if the same value occurs in the operand list twice. If
2547 // so, delete one. Since we sorted the list, these values are required to
2549 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2550 // X umax Y umax Y --> X umax Y
2551 // X umax Y --> X, if X is always greater than Y
2552 if (Ops[i] == Ops[i+1] ||
2553 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2554 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2556 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2557 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2561 if (Ops.size() == 1) return Ops[0];
2563 assert(!Ops.empty() && "Reduced umax down to nothing!");
2565 // Okay, it looks like we really DO need a umax expr. Check to see if we
2566 // already have one, otherwise create a new one.
2567 FoldingSetNodeID ID;
2568 ID.AddInteger(scUMaxExpr);
2569 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2570 ID.AddPointer(Ops[i]);
2572 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2573 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2574 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2575 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2577 UniqueSCEVs.InsertNode(S, IP);
2581 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2583 // ~smax(~x, ~y) == smin(x, y).
2584 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2587 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2589 // ~umax(~x, ~y) == umin(x, y)
2590 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2593 const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) {
2594 // If we have DataLayout, we can bypass creating a target-independent
2595 // constant expression and then folding it back into a ConstantInt.
2596 // This is just a compile-time optimization.
2598 return getConstant(TD->getIntPtrType(getContext()),
2599 TD->getTypeAllocSize(AllocTy));
2601 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2602 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2603 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2605 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2606 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2609 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2610 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2611 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2612 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2614 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2615 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2618 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy,
2620 // If we have DataLayout, we can bypass creating a target-independent
2621 // constant expression and then folding it back into a ConstantInt.
2622 // This is just a compile-time optimization.
2624 return getConstant(TD->getIntPtrType(getContext()),
2625 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2627 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2628 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2629 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2631 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2632 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2635 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2636 Constant *FieldNo) {
2637 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2638 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2639 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2641 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2642 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2645 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2646 // Don't attempt to do anything other than create a SCEVUnknown object
2647 // here. createSCEV only calls getUnknown after checking for all other
2648 // interesting possibilities, and any other code that calls getUnknown
2649 // is doing so in order to hide a value from SCEV canonicalization.
2651 FoldingSetNodeID ID;
2652 ID.AddInteger(scUnknown);
2655 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2656 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2657 "Stale SCEVUnknown in uniquing map!");
2660 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2662 FirstUnknown = cast<SCEVUnknown>(S);
2663 UniqueSCEVs.InsertNode(S, IP);
2667 //===----------------------------------------------------------------------===//
2668 // Basic SCEV Analysis and PHI Idiom Recognition Code
2671 /// isSCEVable - Test if values of the given type are analyzable within
2672 /// the SCEV framework. This primarily includes integer types, and it
2673 /// can optionally include pointer types if the ScalarEvolution class
2674 /// has access to target-specific information.
2675 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2676 // Integers and pointers are always SCEVable.
2677 return Ty->isIntegerTy() || Ty->isPointerTy();
2680 /// getTypeSizeInBits - Return the size in bits of the specified type,
2681 /// for which isSCEVable must return true.
2682 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2683 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2685 // If we have a DataLayout, use it!
2687 return TD->getTypeSizeInBits(Ty);
2689 // Integer types have fixed sizes.
2690 if (Ty->isIntegerTy())
2691 return Ty->getPrimitiveSizeInBits();
2693 // The only other support type is pointer. Without DataLayout, conservatively
2694 // assume pointers are 64-bit.
2695 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2699 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2700 /// the given type and which represents how SCEV will treat the given
2701 /// type, for which isSCEVable must return true. For pointer types,
2702 /// this is the pointer-sized integer type.
2703 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2704 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2706 if (Ty->isIntegerTy())
2709 // The only other support type is pointer.
2710 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2711 if (TD) return TD->getIntPtrType(getContext());
2713 // Without DataLayout, conservatively assume pointers are 64-bit.
2714 return Type::getInt64Ty(getContext());
2717 const SCEV *ScalarEvolution::getCouldNotCompute() {
2718 return &CouldNotCompute;
2722 // Helper class working with SCEVTraversal to figure out if a SCEV contains
2723 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
2724 // is set iff if find such SCEVUnknown.
2726 struct FindInvalidSCEVUnknown {
2728 FindInvalidSCEVUnknown() { FindOne = false; }
2729 bool follow(const SCEV *S) {
2730 switch (S->getSCEVType()) {
2734 if (!cast<SCEVUnknown>(S)->getValue())
2741 bool isDone() const { return FindOne; }
2745 bool ScalarEvolution::checkValidity(const SCEV *S) const {
2746 FindInvalidSCEVUnknown F;
2747 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
2753 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2754 /// expression and create a new one.
2755 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2756 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2758 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
2759 if (I != ValueExprMap.end()) {
2760 const SCEV *S = I->second;
2761 if (checkValidity(S))
2764 ValueExprMap.erase(I);
2766 const SCEV *S = createSCEV(V);
2768 // The process of creating a SCEV for V may have caused other SCEVs
2769 // to have been created, so it's necessary to insert the new entry
2770 // from scratch, rather than trying to remember the insert position
2772 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2776 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2778 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2779 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2781 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2783 Type *Ty = V->getType();
2784 Ty = getEffectiveSCEVType(Ty);
2785 return getMulExpr(V,
2786 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2789 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2790 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2791 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2793 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2795 Type *Ty = V->getType();
2796 Ty = getEffectiveSCEVType(Ty);
2797 const SCEV *AllOnes =
2798 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2799 return getMinusSCEV(AllOnes, V);
2802 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2803 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2804 SCEV::NoWrapFlags Flags) {
2805 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2807 // Fast path: X - X --> 0.
2809 return getConstant(LHS->getType(), 0);
2812 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2815 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2816 /// input value to the specified type. If the type must be extended, it is zero
2819 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2820 Type *SrcTy = V->getType();
2821 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2822 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2823 "Cannot truncate or zero extend with non-integer arguments!");
2824 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2825 return V; // No conversion
2826 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2827 return getTruncateExpr(V, Ty);
2828 return getZeroExtendExpr(V, Ty);
2831 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2832 /// input value to the specified type. If the type must be extended, it is sign
2835 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2837 Type *SrcTy = V->getType();
2838 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2839 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2840 "Cannot truncate or zero extend with non-integer arguments!");
2841 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2842 return V; // No conversion
2843 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2844 return getTruncateExpr(V, Ty);
2845 return getSignExtendExpr(V, Ty);
2848 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2849 /// input value to the specified type. If the type must be extended, it is zero
2850 /// extended. The conversion must not be narrowing.
2852 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2853 Type *SrcTy = V->getType();
2854 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2855 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2856 "Cannot noop or zero extend with non-integer arguments!");
2857 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2858 "getNoopOrZeroExtend cannot truncate!");
2859 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2860 return V; // No conversion
2861 return getZeroExtendExpr(V, Ty);
2864 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2865 /// input value to the specified type. If the type must be extended, it is sign
2866 /// extended. The conversion must not be narrowing.
2868 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2869 Type *SrcTy = V->getType();
2870 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2871 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2872 "Cannot noop or sign extend with non-integer arguments!");
2873 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2874 "getNoopOrSignExtend cannot truncate!");
2875 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2876 return V; // No conversion
2877 return getSignExtendExpr(V, Ty);
2880 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2881 /// the input value to the specified type. If the type must be extended,
2882 /// it is extended with unspecified bits. The conversion must not be
2885 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2886 Type *SrcTy = V->getType();
2887 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2888 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2889 "Cannot noop or any extend with non-integer arguments!");
2890 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2891 "getNoopOrAnyExtend cannot truncate!");
2892 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2893 return V; // No conversion
2894 return getAnyExtendExpr(V, Ty);
2897 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2898 /// input value to the specified type. The conversion must not be widening.
2900 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2901 Type *SrcTy = V->getType();
2902 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2903 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2904 "Cannot truncate or noop with non-integer arguments!");
2905 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2906 "getTruncateOrNoop cannot extend!");
2907 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2908 return V; // No conversion
2909 return getTruncateExpr(V, Ty);
2912 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2913 /// the types using zero-extension, and then perform a umax operation
2915 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2917 const SCEV *PromotedLHS = LHS;
2918 const SCEV *PromotedRHS = RHS;
2920 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2921 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2923 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2925 return getUMaxExpr(PromotedLHS, PromotedRHS);
2928 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2929 /// the types using zero-extension, and then perform a umin operation
2931 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2933 const SCEV *PromotedLHS = LHS;
2934 const SCEV *PromotedRHS = RHS;
2936 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2937 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2939 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2941 return getUMinExpr(PromotedLHS, PromotedRHS);
2944 /// getPointerBase - Transitively follow the chain of pointer-type operands
2945 /// until reaching a SCEV that does not have a single pointer operand. This
2946 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2947 /// but corner cases do exist.
2948 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2949 // A pointer operand may evaluate to a nonpointer expression, such as null.
2950 if (!V->getType()->isPointerTy())
2953 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2954 return getPointerBase(Cast->getOperand());
2956 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2957 const SCEV *PtrOp = 0;
2958 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2960 if ((*I)->getType()->isPointerTy()) {
2961 // Cannot find the base of an expression with multiple pointer operands.
2969 return getPointerBase(PtrOp);
2974 /// PushDefUseChildren - Push users of the given Instruction
2975 /// onto the given Worklist.
2977 PushDefUseChildren(Instruction *I,
2978 SmallVectorImpl<Instruction *> &Worklist) {
2979 // Push the def-use children onto the Worklist stack.
2980 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2982 Worklist.push_back(cast<Instruction>(*UI));
2985 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2986 /// instructions that depend on the given instruction and removes them from
2987 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2990 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2991 SmallVector<Instruction *, 16> Worklist;
2992 PushDefUseChildren(PN, Worklist);
2994 SmallPtrSet<Instruction *, 8> Visited;
2996 while (!Worklist.empty()) {
2997 Instruction *I = Worklist.pop_back_val();
2998 if (!Visited.insert(I)) continue;
3000 ValueExprMapType::iterator It =
3001 ValueExprMap.find_as(static_cast<Value *>(I));
3002 if (It != ValueExprMap.end()) {
3003 const SCEV *Old = It->second;
3005 // Short-circuit the def-use traversal if the symbolic name
3006 // ceases to appear in expressions.
3007 if (Old != SymName && !hasOperand(Old, SymName))
3010 // SCEVUnknown for a PHI either means that it has an unrecognized
3011 // structure, it's a PHI that's in the progress of being computed
3012 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3013 // additional loop trip count information isn't going to change anything.
3014 // In the second case, createNodeForPHI will perform the necessary
3015 // updates on its own when it gets to that point. In the third, we do
3016 // want to forget the SCEVUnknown.
3017 if (!isa<PHINode>(I) ||
3018 !isa<SCEVUnknown>(Old) ||
3019 (I != PN && Old == SymName)) {
3020 forgetMemoizedResults(Old);
3021 ValueExprMap.erase(It);
3025 PushDefUseChildren(I, Worklist);
3029 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3030 /// a loop header, making it a potential recurrence, or it doesn't.
3032 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3033 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3034 if (L->getHeader() == PN->getParent()) {
3035 // The loop may have multiple entrances or multiple exits; we can analyze
3036 // this phi as an addrec if it has a unique entry value and a unique
3038 Value *BEValueV = 0, *StartValueV = 0;
3039 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3040 Value *V = PN->getIncomingValue(i);
3041 if (L->contains(PN->getIncomingBlock(i))) {
3044 } else if (BEValueV != V) {
3048 } else if (!StartValueV) {
3050 } else if (StartValueV != V) {
3055 if (BEValueV && StartValueV) {
3056 // While we are analyzing this PHI node, handle its value symbolically.
3057 const SCEV *SymbolicName = getUnknown(PN);
3058 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3059 "PHI node already processed?");
3060 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3062 // Using this symbolic name for the PHI, analyze the value coming around
3064 const SCEV *BEValue = getSCEV(BEValueV);
3066 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3067 // has a special value for the first iteration of the loop.
3069 // If the value coming around the backedge is an add with the symbolic
3070 // value we just inserted, then we found a simple induction variable!
3071 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3072 // If there is a single occurrence of the symbolic value, replace it
3073 // with a recurrence.
3074 unsigned FoundIndex = Add->getNumOperands();
3075 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3076 if (Add->getOperand(i) == SymbolicName)
3077 if (FoundIndex == e) {
3082 if (FoundIndex != Add->getNumOperands()) {
3083 // Create an add with everything but the specified operand.
3084 SmallVector<const SCEV *, 8> Ops;
3085 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3086 if (i != FoundIndex)
3087 Ops.push_back(Add->getOperand(i));
3088 const SCEV *Accum = getAddExpr(Ops);
3090 // This is not a valid addrec if the step amount is varying each
3091 // loop iteration, but is not itself an addrec in this loop.
3092 if (isLoopInvariant(Accum, L) ||
3093 (isa<SCEVAddRecExpr>(Accum) &&
3094 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3095 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3097 // If the increment doesn't overflow, then neither the addrec nor
3098 // the post-increment will overflow.
3099 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3100 if (OBO->hasNoUnsignedWrap())
3101 Flags = setFlags(Flags, SCEV::FlagNUW);
3102 if (OBO->hasNoSignedWrap())
3103 Flags = setFlags(Flags, SCEV::FlagNSW);
3104 } else if (const GEPOperator *GEP =
3105 dyn_cast<GEPOperator>(BEValueV)) {
3106 // If the increment is an inbounds GEP, then we know the address
3107 // space cannot be wrapped around. We cannot make any guarantee
3108 // about signed or unsigned overflow because pointers are
3109 // unsigned but we may have a negative index from the base
3111 if (GEP->isInBounds())
3112 Flags = setFlags(Flags, SCEV::FlagNW);
3115 const SCEV *StartVal = getSCEV(StartValueV);
3116 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3118 // Since the no-wrap flags are on the increment, they apply to the
3119 // post-incremented value as well.
3120 if (isLoopInvariant(Accum, L))
3121 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3124 // Okay, for the entire analysis of this edge we assumed the PHI
3125 // to be symbolic. We now need to go back and purge all of the
3126 // entries for the scalars that use the symbolic expression.
3127 ForgetSymbolicName(PN, SymbolicName);
3128 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3132 } else if (const SCEVAddRecExpr *AddRec =
3133 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3134 // Otherwise, this could be a loop like this:
3135 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3136 // In this case, j = {1,+,1} and BEValue is j.
3137 // Because the other in-value of i (0) fits the evolution of BEValue
3138 // i really is an addrec evolution.
3139 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3140 const SCEV *StartVal = getSCEV(StartValueV);
3142 // If StartVal = j.start - j.stride, we can use StartVal as the
3143 // initial step of the addrec evolution.
3144 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3145 AddRec->getOperand(1))) {
3146 // FIXME: For constant StartVal, we should be able to infer
3148 const SCEV *PHISCEV =
3149 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3152 // Okay, for the entire analysis of this edge we assumed the PHI
3153 // to be symbolic. We now need to go back and purge all of the
3154 // entries for the scalars that use the symbolic expression.
3155 ForgetSymbolicName(PN, SymbolicName);
3156 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3164 // If the PHI has a single incoming value, follow that value, unless the
3165 // PHI's incoming blocks are in a different loop, in which case doing so
3166 // risks breaking LCSSA form. Instcombine would normally zap these, but
3167 // it doesn't have DominatorTree information, so it may miss cases.
3168 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
3169 if (LI->replacementPreservesLCSSAForm(PN, V))
3172 // If it's not a loop phi, we can't handle it yet.
3173 return getUnknown(PN);
3176 /// createNodeForGEP - Expand GEP instructions into add and multiply
3177 /// operations. This allows them to be analyzed by regular SCEV code.
3179 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3181 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3182 // Add expression, because the Instruction may be guarded by control flow
3183 // and the no-overflow bits may not be valid for the expression in any
3185 bool isInBounds = GEP->isInBounds();
3187 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3188 Value *Base = GEP->getOperand(0);
3189 // Don't attempt to analyze GEPs over unsized objects.
3190 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3191 return getUnknown(GEP);
3192 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3193 gep_type_iterator GTI = gep_type_begin(GEP);
3194 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3198 // Compute the (potentially symbolic) offset in bytes for this index.
3199 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3200 // For a struct, add the member offset.
3201 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3202 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
3204 // Add the field offset to the running total offset.
3205 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3207 // For an array, add the element offset, explicitly scaled.
3208 const SCEV *ElementSize = getSizeOfExpr(*GTI);
3209 const SCEV *IndexS = getSCEV(Index);
3210 // Getelementptr indices are signed.
3211 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3213 // Multiply the index by the element size to compute the element offset.
3214 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3215 isInBounds ? SCEV::FlagNSW :
3218 // Add the element offset to the running total offset.
3219 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3223 // Get the SCEV for the GEP base.
3224 const SCEV *BaseS = getSCEV(Base);
3226 // Add the total offset from all the GEP indices to the base.
3227 return getAddExpr(BaseS, TotalOffset,
3228 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3231 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3232 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3233 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3234 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3236 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3237 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3238 return C->getValue()->getValue().countTrailingZeros();
3240 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3241 return std::min(GetMinTrailingZeros(T->getOperand()),
3242 (uint32_t)getTypeSizeInBits(T->getType()));
3244 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3245 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3246 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3247 getTypeSizeInBits(E->getType()) : OpRes;
3250 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3251 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3252 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3253 getTypeSizeInBits(E->getType()) : OpRes;
3256 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3257 // The result is the min of all operands results.
3258 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3259 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3260 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3264 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3265 // The result is the sum of all operands results.
3266 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3267 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3268 for (unsigned i = 1, e = M->getNumOperands();
3269 SumOpRes != BitWidth && i != e; ++i)
3270 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3275 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3276 // The result is the min of all operands results.
3277 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3278 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3279 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3283 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3284 // The result is the min of all operands results.
3285 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3286 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3287 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3291 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3292 // The result is the min of all operands results.
3293 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3294 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3295 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3299 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3300 // For a SCEVUnknown, ask ValueTracking.
3301 unsigned BitWidth = getTypeSizeInBits(U->getType());
3302 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3303 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3304 return Zeros.countTrailingOnes();
3311 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3314 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3315 // See if we've computed this range already.
3316 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3317 if (I != UnsignedRanges.end())
3320 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3321 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3323 unsigned BitWidth = getTypeSizeInBits(S->getType());
3324 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3326 // If the value has known zeros, the maximum unsigned value will have those
3327 // known zeros as well.
3328 uint32_t TZ = GetMinTrailingZeros(S);
3330 ConservativeResult =
3331 ConstantRange(APInt::getMinValue(BitWidth),
3332 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3334 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3335 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3336 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3337 X = X.add(getUnsignedRange(Add->getOperand(i)));
3338 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3341 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3342 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3343 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3344 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3345 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3348 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3349 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3350 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3351 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3352 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3355 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3356 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3357 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3358 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3359 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3362 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3363 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3364 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3365 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3368 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3369 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3370 return setUnsignedRange(ZExt,
3371 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3374 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3375 ConstantRange X = getUnsignedRange(SExt->getOperand());
3376 return setUnsignedRange(SExt,
3377 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3380 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3381 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3382 return setUnsignedRange(Trunc,
3383 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3386 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3387 // If there's no unsigned wrap, the value will never be less than its
3389 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3390 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3391 if (!C->getValue()->isZero())
3392 ConservativeResult =
3393 ConservativeResult.intersectWith(
3394 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3396 // TODO: non-affine addrec
3397 if (AddRec->isAffine()) {
3398 Type *Ty = AddRec->getType();
3399 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3400 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3401 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3402 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3404 const SCEV *Start = AddRec->getStart();
3405 const SCEV *Step = AddRec->getStepRecurrence(*this);
3407 ConstantRange StartRange = getUnsignedRange(Start);
3408 ConstantRange StepRange = getSignedRange(Step);
3409 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3410 ConstantRange EndRange =
3411 StartRange.add(MaxBECountRange.multiply(StepRange));
3413 // Check for overflow. This must be done with ConstantRange arithmetic
3414 // because we could be called from within the ScalarEvolution overflow
3416 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3417 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3418 ConstantRange ExtMaxBECountRange =
3419 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3420 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3421 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3423 return setUnsignedRange(AddRec, ConservativeResult);
3425 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3426 EndRange.getUnsignedMin());
3427 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3428 EndRange.getUnsignedMax());
3429 if (Min.isMinValue() && Max.isMaxValue())
3430 return setUnsignedRange(AddRec, ConservativeResult);
3431 return setUnsignedRange(AddRec,
3432 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3436 return setUnsignedRange(AddRec, ConservativeResult);
3439 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3440 // For a SCEVUnknown, ask ValueTracking.
3441 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3442 ComputeMaskedBits(U->getValue(), Zeros, Ones, TD);
3443 if (Ones == ~Zeros + 1)
3444 return setUnsignedRange(U, ConservativeResult);
3445 return setUnsignedRange(U,
3446 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3449 return setUnsignedRange(S, ConservativeResult);
3452 /// getSignedRange - Determine the signed range for a particular SCEV.
3455 ScalarEvolution::getSignedRange(const SCEV *S) {
3456 // See if we've computed this range already.
3457 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3458 if (I != SignedRanges.end())
3461 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3462 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3464 unsigned BitWidth = getTypeSizeInBits(S->getType());
3465 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3467 // If the value has known zeros, the maximum signed value will have those
3468 // known zeros as well.
3469 uint32_t TZ = GetMinTrailingZeros(S);
3471 ConservativeResult =
3472 ConstantRange(APInt::getSignedMinValue(BitWidth),
3473 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3475 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3476 ConstantRange X = getSignedRange(Add->getOperand(0));
3477 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3478 X = X.add(getSignedRange(Add->getOperand(i)));
3479 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3482 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3483 ConstantRange X = getSignedRange(Mul->getOperand(0));
3484 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3485 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3486 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3489 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3490 ConstantRange X = getSignedRange(SMax->getOperand(0));
3491 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3492 X = X.smax(getSignedRange(SMax->getOperand(i)));
3493 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3496 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3497 ConstantRange X = getSignedRange(UMax->getOperand(0));
3498 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3499 X = X.umax(getSignedRange(UMax->getOperand(i)));
3500 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3503 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3504 ConstantRange X = getSignedRange(UDiv->getLHS());
3505 ConstantRange Y = getSignedRange(UDiv->getRHS());
3506 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3509 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3510 ConstantRange X = getSignedRange(ZExt->getOperand());
3511 return setSignedRange(ZExt,
3512 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3515 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3516 ConstantRange X = getSignedRange(SExt->getOperand());
3517 return setSignedRange(SExt,
3518 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3521 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3522 ConstantRange X = getSignedRange(Trunc->getOperand());
3523 return setSignedRange(Trunc,
3524 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3527 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3528 // If there's no signed wrap, and all the operands have the same sign or
3529 // zero, the value won't ever change sign.
3530 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3531 bool AllNonNeg = true;
3532 bool AllNonPos = true;
3533 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3534 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3535 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3538 ConservativeResult = ConservativeResult.intersectWith(
3539 ConstantRange(APInt(BitWidth, 0),
3540 APInt::getSignedMinValue(BitWidth)));
3542 ConservativeResult = ConservativeResult.intersectWith(
3543 ConstantRange(APInt::getSignedMinValue(BitWidth),
3544 APInt(BitWidth, 1)));
3547 // TODO: non-affine addrec
3548 if (AddRec->isAffine()) {
3549 Type *Ty = AddRec->getType();
3550 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3551 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3552 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3553 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3555 const SCEV *Start = AddRec->getStart();
3556 const SCEV *Step = AddRec->getStepRecurrence(*this);
3558 ConstantRange StartRange = getSignedRange(Start);
3559 ConstantRange StepRange = getSignedRange(Step);
3560 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3561 ConstantRange EndRange =
3562 StartRange.add(MaxBECountRange.multiply(StepRange));
3564 // Check for overflow. This must be done with ConstantRange arithmetic
3565 // because we could be called from within the ScalarEvolution overflow
3567 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3568 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3569 ConstantRange ExtMaxBECountRange =
3570 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3571 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3572 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3574 return setSignedRange(AddRec, ConservativeResult);
3576 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3577 EndRange.getSignedMin());
3578 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3579 EndRange.getSignedMax());
3580 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3581 return setSignedRange(AddRec, ConservativeResult);
3582 return setSignedRange(AddRec,
3583 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3587 return setSignedRange(AddRec, ConservativeResult);
3590 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3591 // For a SCEVUnknown, ask ValueTracking.
3592 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3593 return setSignedRange(U, ConservativeResult);
3594 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3596 return setSignedRange(U, ConservativeResult);
3597 return setSignedRange(U, ConservativeResult.intersectWith(
3598 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3599 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3602 return setSignedRange(S, ConservativeResult);
3605 /// createSCEV - We know that there is no SCEV for the specified value.
3606 /// Analyze the expression.
3608 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3609 if (!isSCEVable(V->getType()))
3610 return getUnknown(V);
3612 unsigned Opcode = Instruction::UserOp1;
3613 if (Instruction *I = dyn_cast<Instruction>(V)) {
3614 Opcode = I->getOpcode();
3616 // Don't attempt to analyze instructions in blocks that aren't
3617 // reachable. Such instructions don't matter, and they aren't required
3618 // to obey basic rules for definitions dominating uses which this
3619 // analysis depends on.
3620 if (!DT->isReachableFromEntry(I->getParent()))
3621 return getUnknown(V);
3622 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3623 Opcode = CE->getOpcode();
3624 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3625 return getConstant(CI);
3626 else if (isa<ConstantPointerNull>(V))
3627 return getConstant(V->getType(), 0);
3628 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3629 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3631 return getUnknown(V);
3633 Operator *U = cast<Operator>(V);
3635 case Instruction::Add: {
3636 // The simple thing to do would be to just call getSCEV on both operands
3637 // and call getAddExpr with the result. However if we're looking at a
3638 // bunch of things all added together, this can be quite inefficient,
3639 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3640 // Instead, gather up all the operands and make a single getAddExpr call.
3641 // LLVM IR canonical form means we need only traverse the left operands.
3643 // Don't apply this instruction's NSW or NUW flags to the new
3644 // expression. The instruction may be guarded by control flow that the
3645 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3646 // mapped to the same SCEV expression, and it would be incorrect to transfer
3647 // NSW/NUW semantics to those operations.
3648 SmallVector<const SCEV *, 4> AddOps;
3649 AddOps.push_back(getSCEV(U->getOperand(1)));
3650 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3651 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3652 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3654 U = cast<Operator>(Op);
3655 const SCEV *Op1 = getSCEV(U->getOperand(1));
3656 if (Opcode == Instruction::Sub)
3657 AddOps.push_back(getNegativeSCEV(Op1));
3659 AddOps.push_back(Op1);
3661 AddOps.push_back(getSCEV(U->getOperand(0)));
3662 return getAddExpr(AddOps);
3664 case Instruction::Mul: {
3665 // Don't transfer NSW/NUW for the same reason as AddExpr.
3666 SmallVector<const SCEV *, 4> MulOps;
3667 MulOps.push_back(getSCEV(U->getOperand(1)));
3668 for (Value *Op = U->getOperand(0);
3669 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3670 Op = U->getOperand(0)) {
3671 U = cast<Operator>(Op);
3672 MulOps.push_back(getSCEV(U->getOperand(1)));
3674 MulOps.push_back(getSCEV(U->getOperand(0)));
3675 return getMulExpr(MulOps);
3677 case Instruction::UDiv:
3678 return getUDivExpr(getSCEV(U->getOperand(0)),
3679 getSCEV(U->getOperand(1)));
3680 case Instruction::Sub:
3681 return getMinusSCEV(getSCEV(U->getOperand(0)),
3682 getSCEV(U->getOperand(1)));
3683 case Instruction::And:
3684 // For an expression like x&255 that merely masks off the high bits,
3685 // use zext(trunc(x)) as the SCEV expression.
3686 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3687 if (CI->isNullValue())
3688 return getSCEV(U->getOperand(1));
3689 if (CI->isAllOnesValue())
3690 return getSCEV(U->getOperand(0));
3691 const APInt &A = CI->getValue();
3693 // Instcombine's ShrinkDemandedConstant may strip bits out of
3694 // constants, obscuring what would otherwise be a low-bits mask.
3695 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3696 // knew about to reconstruct a low-bits mask value.
3697 unsigned LZ = A.countLeadingZeros();
3698 unsigned BitWidth = A.getBitWidth();
3699 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3700 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD);
3702 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3704 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3706 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3707 IntegerType::get(getContext(), BitWidth - LZ)),
3712 case Instruction::Or:
3713 // If the RHS of the Or is a constant, we may have something like:
3714 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3715 // optimizations will transparently handle this case.
3717 // In order for this transformation to be safe, the LHS must be of the
3718 // form X*(2^n) and the Or constant must be less than 2^n.
3719 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3720 const SCEV *LHS = getSCEV(U->getOperand(0));
3721 const APInt &CIVal = CI->getValue();
3722 if (GetMinTrailingZeros(LHS) >=
3723 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3724 // Build a plain add SCEV.
3725 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3726 // If the LHS of the add was an addrec and it has no-wrap flags,
3727 // transfer the no-wrap flags, since an or won't introduce a wrap.
3728 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3729 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3730 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3731 OldAR->getNoWrapFlags());
3737 case Instruction::Xor:
3738 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3739 // If the RHS of the xor is a signbit, then this is just an add.
3740 // Instcombine turns add of signbit into xor as a strength reduction step.
3741 if (CI->getValue().isSignBit())
3742 return getAddExpr(getSCEV(U->getOperand(0)),
3743 getSCEV(U->getOperand(1)));
3745 // If the RHS of xor is -1, then this is a not operation.
3746 if (CI->isAllOnesValue())
3747 return getNotSCEV(getSCEV(U->getOperand(0)));
3749 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3750 // This is a variant of the check for xor with -1, and it handles
3751 // the case where instcombine has trimmed non-demanded bits out
3752 // of an xor with -1.
3753 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3754 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3755 if (BO->getOpcode() == Instruction::And &&
3756 LCI->getValue() == CI->getValue())
3757 if (const SCEVZeroExtendExpr *Z =
3758 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3759 Type *UTy = U->getType();
3760 const SCEV *Z0 = Z->getOperand();
3761 Type *Z0Ty = Z0->getType();
3762 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3764 // If C is a low-bits mask, the zero extend is serving to
3765 // mask off the high bits. Complement the operand and
3766 // re-apply the zext.
3767 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3768 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3770 // If C is a single bit, it may be in the sign-bit position
3771 // before the zero-extend. In this case, represent the xor
3772 // using an add, which is equivalent, and re-apply the zext.
3773 APInt Trunc = CI->getValue().trunc(Z0TySize);
3774 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3776 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3782 case Instruction::Shl:
3783 // Turn shift left of a constant amount into a multiply.
3784 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3785 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3787 // If the shift count is not less than the bitwidth, the result of
3788 // the shift is undefined. Don't try to analyze it, because the
3789 // resolution chosen here may differ from the resolution chosen in
3790 // other parts of the compiler.
3791 if (SA->getValue().uge(BitWidth))
3794 Constant *X = ConstantInt::get(getContext(),
3795 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3796 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3800 case Instruction::LShr:
3801 // Turn logical shift right of a constant into a unsigned divide.
3802 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3803 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3805 // If the shift count is not less than the bitwidth, the result of
3806 // the shift is undefined. Don't try to analyze it, because the
3807 // resolution chosen here may differ from the resolution chosen in
3808 // other parts of the compiler.
3809 if (SA->getValue().uge(BitWidth))
3812 Constant *X = ConstantInt::get(getContext(),
3813 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3814 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3818 case Instruction::AShr:
3819 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3820 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3821 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3822 if (L->getOpcode() == Instruction::Shl &&
3823 L->getOperand(1) == U->getOperand(1)) {
3824 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3826 // If the shift count is not less than the bitwidth, the result of
3827 // the shift is undefined. Don't try to analyze it, because the
3828 // resolution chosen here may differ from the resolution chosen in
3829 // other parts of the compiler.
3830 if (CI->getValue().uge(BitWidth))
3833 uint64_t Amt = BitWidth - CI->getZExtValue();
3834 if (Amt == BitWidth)
3835 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3837 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3838 IntegerType::get(getContext(),
3844 case Instruction::Trunc:
3845 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3847 case Instruction::ZExt:
3848 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3850 case Instruction::SExt:
3851 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3853 case Instruction::BitCast:
3854 // BitCasts are no-op casts so we just eliminate the cast.
3855 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3856 return getSCEV(U->getOperand(0));
3859 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3860 // lead to pointer expressions which cannot safely be expanded to GEPs,
3861 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3862 // simplifying integer expressions.
3864 case Instruction::GetElementPtr:
3865 return createNodeForGEP(cast<GEPOperator>(U));
3867 case Instruction::PHI:
3868 return createNodeForPHI(cast<PHINode>(U));
3870 case Instruction::Select:
3871 // This could be a smax or umax that was lowered earlier.
3872 // Try to recover it.
3873 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3874 Value *LHS = ICI->getOperand(0);
3875 Value *RHS = ICI->getOperand(1);
3876 switch (ICI->getPredicate()) {
3877 case ICmpInst::ICMP_SLT:
3878 case ICmpInst::ICMP_SLE:
3879 std::swap(LHS, RHS);
3881 case ICmpInst::ICMP_SGT:
3882 case ICmpInst::ICMP_SGE:
3883 // a >s b ? a+x : b+x -> smax(a, b)+x
3884 // a >s b ? b+x : a+x -> smin(a, b)+x
3885 if (LHS->getType() == U->getType()) {
3886 const SCEV *LS = getSCEV(LHS);
3887 const SCEV *RS = getSCEV(RHS);
3888 const SCEV *LA = getSCEV(U->getOperand(1));
3889 const SCEV *RA = getSCEV(U->getOperand(2));
3890 const SCEV *LDiff = getMinusSCEV(LA, LS);
3891 const SCEV *RDiff = getMinusSCEV(RA, RS);
3893 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3894 LDiff = getMinusSCEV(LA, RS);
3895 RDiff = getMinusSCEV(RA, LS);
3897 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3900 case ICmpInst::ICMP_ULT:
3901 case ICmpInst::ICMP_ULE:
3902 std::swap(LHS, RHS);
3904 case ICmpInst::ICMP_UGT:
3905 case ICmpInst::ICMP_UGE:
3906 // a >u b ? a+x : b+x -> umax(a, b)+x
3907 // a >u b ? b+x : a+x -> umin(a, b)+x
3908 if (LHS->getType() == U->getType()) {
3909 const SCEV *LS = getSCEV(LHS);
3910 const SCEV *RS = getSCEV(RHS);
3911 const SCEV *LA = getSCEV(U->getOperand(1));
3912 const SCEV *RA = getSCEV(U->getOperand(2));
3913 const SCEV *LDiff = getMinusSCEV(LA, LS);
3914 const SCEV *RDiff = getMinusSCEV(RA, RS);
3916 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3917 LDiff = getMinusSCEV(LA, RS);
3918 RDiff = getMinusSCEV(RA, LS);
3920 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3923 case ICmpInst::ICMP_NE:
3924 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3925 if (LHS->getType() == U->getType() &&
3926 isa<ConstantInt>(RHS) &&
3927 cast<ConstantInt>(RHS)->isZero()) {
3928 const SCEV *One = getConstant(LHS->getType(), 1);
3929 const SCEV *LS = getSCEV(LHS);
3930 const SCEV *LA = getSCEV(U->getOperand(1));
3931 const SCEV *RA = getSCEV(U->getOperand(2));
3932 const SCEV *LDiff = getMinusSCEV(LA, LS);
3933 const SCEV *RDiff = getMinusSCEV(RA, One);
3935 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3938 case ICmpInst::ICMP_EQ:
3939 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3940 if (LHS->getType() == U->getType() &&
3941 isa<ConstantInt>(RHS) &&
3942 cast<ConstantInt>(RHS)->isZero()) {
3943 const SCEV *One = getConstant(LHS->getType(), 1);
3944 const SCEV *LS = getSCEV(LHS);
3945 const SCEV *LA = getSCEV(U->getOperand(1));
3946 const SCEV *RA = getSCEV(U->getOperand(2));
3947 const SCEV *LDiff = getMinusSCEV(LA, One);
3948 const SCEV *RDiff = getMinusSCEV(RA, LS);
3950 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3958 default: // We cannot analyze this expression.
3962 return getUnknown(V);
3967 //===----------------------------------------------------------------------===//
3968 // Iteration Count Computation Code
3971 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3972 /// normal unsigned value. Returns 0 if the trip count is unknown or not
3973 /// constant. Will also return 0 if the maximum trip count is very large (>=
3976 /// This "trip count" assumes that control exits via ExitingBlock. More
3977 /// precisely, it is the number of times that control may reach ExitingBlock
3978 /// before taking the branch. For loops with multiple exits, it may not be the
3979 /// number times that the loop header executes because the loop may exit
3980 /// prematurely via another branch.
3982 /// FIXME: We conservatively call getBackedgeTakenCount(L) instead of
3983 /// getExitCount(L, ExitingBlock) to compute a safe trip count considering all
3984 /// loop exits. getExitCount() may return an exact count for this branch
3985 /// assuming no-signed-wrap. The number of well-defined iterations may actually
3986 /// be higher than this trip count if this exit test is skipped and the loop
3987 /// exits via a different branch. Ideally, getExitCount() would know whether it
3988 /// depends on a NSW assumption, and we would only fall back to a conservative
3989 /// trip count in that case.
3990 unsigned ScalarEvolution::
3991 getSmallConstantTripCount(Loop *L, BasicBlock * /*ExitingBlock*/) {
3992 const SCEVConstant *ExitCount =
3993 dyn_cast<SCEVConstant>(getBackedgeTakenCount(L));
3997 ConstantInt *ExitConst = ExitCount->getValue();
3999 // Guard against huge trip counts.
4000 if (ExitConst->getValue().getActiveBits() > 32)
4003 // In case of integer overflow, this returns 0, which is correct.
4004 return ((unsigned)ExitConst->getZExtValue()) + 1;
4007 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4008 /// trip count of this loop as a normal unsigned value, if possible. This
4009 /// means that the actual trip count is always a multiple of the returned
4010 /// value (don't forget the trip count could very well be zero as well!).
4012 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4013 /// multiple of a constant (which is also the case if the trip count is simply
4014 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4015 /// if the trip count is very large (>= 2^32).
4017 /// As explained in the comments for getSmallConstantTripCount, this assumes
4018 /// that control exits the loop via ExitingBlock.
4019 unsigned ScalarEvolution::
4020 getSmallConstantTripMultiple(Loop *L, BasicBlock * /*ExitingBlock*/) {
4021 const SCEV *ExitCount = getBackedgeTakenCount(L);
4022 if (ExitCount == getCouldNotCompute())
4025 // Get the trip count from the BE count by adding 1.
4026 const SCEV *TCMul = getAddExpr(ExitCount,
4027 getConstant(ExitCount->getType(), 1));
4028 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4029 // to factor simple cases.
4030 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4031 TCMul = Mul->getOperand(0);
4033 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4037 ConstantInt *Result = MulC->getValue();
4039 // Guard against huge trip counts (this requires checking
4040 // for zero to handle the case where the trip count == -1 and the
4042 if (!Result || Result->getValue().getActiveBits() > 32 ||
4043 Result->getValue().getActiveBits() == 0)
4046 return (unsigned)Result->getZExtValue();
4049 // getExitCount - Get the expression for the number of loop iterations for which
4050 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4051 // SCEVCouldNotCompute.
4052 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4053 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4056 /// getBackedgeTakenCount - If the specified loop has a predictable
4057 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4058 /// object. The backedge-taken count is the number of times the loop header
4059 /// will be branched to from within the loop. This is one less than the
4060 /// trip count of the loop, since it doesn't count the first iteration,
4061 /// when the header is branched to from outside the loop.
4063 /// Note that it is not valid to call this method on a loop without a
4064 /// loop-invariant backedge-taken count (see
4065 /// hasLoopInvariantBackedgeTakenCount).
4067 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4068 return getBackedgeTakenInfo(L).getExact(this);
4071 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4072 /// return the least SCEV value that is known never to be less than the
4073 /// actual backedge taken count.
4074 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4075 return getBackedgeTakenInfo(L).getMax(this);
4078 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4079 /// onto the given Worklist.
4081 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4082 BasicBlock *Header = L->getHeader();
4084 // Push all Loop-header PHIs onto the Worklist stack.
4085 for (BasicBlock::iterator I = Header->begin();
4086 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4087 Worklist.push_back(PN);
4090 const ScalarEvolution::BackedgeTakenInfo &
4091 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4092 // Initially insert an invalid entry for this loop. If the insertion
4093 // succeeds, proceed to actually compute a backedge-taken count and
4094 // update the value. The temporary CouldNotCompute value tells SCEV
4095 // code elsewhere that it shouldn't attempt to request a new
4096 // backedge-taken count, which could result in infinite recursion.
4097 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4098 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4100 return Pair.first->second;
4102 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4103 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4104 // must be cleared in this scope.
4105 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4107 if (Result.getExact(this) != getCouldNotCompute()) {
4108 assert(isLoopInvariant(Result.getExact(this), L) &&
4109 isLoopInvariant(Result.getMax(this), L) &&
4110 "Computed backedge-taken count isn't loop invariant for loop!");
4111 ++NumTripCountsComputed;
4113 else if (Result.getMax(this) == getCouldNotCompute() &&
4114 isa<PHINode>(L->getHeader()->begin())) {
4115 // Only count loops that have phi nodes as not being computable.
4116 ++NumTripCountsNotComputed;
4119 // Now that we know more about the trip count for this loop, forget any
4120 // existing SCEV values for PHI nodes in this loop since they are only
4121 // conservative estimates made without the benefit of trip count
4122 // information. This is similar to the code in forgetLoop, except that
4123 // it handles SCEVUnknown PHI nodes specially.
4124 if (Result.hasAnyInfo()) {
4125 SmallVector<Instruction *, 16> Worklist;
4126 PushLoopPHIs(L, Worklist);
4128 SmallPtrSet<Instruction *, 8> Visited;
4129 while (!Worklist.empty()) {
4130 Instruction *I = Worklist.pop_back_val();
4131 if (!Visited.insert(I)) continue;
4133 ValueExprMapType::iterator It =
4134 ValueExprMap.find_as(static_cast<Value *>(I));
4135 if (It != ValueExprMap.end()) {
4136 const SCEV *Old = It->second;
4138 // SCEVUnknown for a PHI either means that it has an unrecognized
4139 // structure, or it's a PHI that's in the progress of being computed
4140 // by createNodeForPHI. In the former case, additional loop trip
4141 // count information isn't going to change anything. In the later
4142 // case, createNodeForPHI will perform the necessary updates on its
4143 // own when it gets to that point.
4144 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4145 forgetMemoizedResults(Old);
4146 ValueExprMap.erase(It);
4148 if (PHINode *PN = dyn_cast<PHINode>(I))
4149 ConstantEvolutionLoopExitValue.erase(PN);
4152 PushDefUseChildren(I, Worklist);
4156 // Re-lookup the insert position, since the call to
4157 // ComputeBackedgeTakenCount above could result in a
4158 // recusive call to getBackedgeTakenInfo (on a different
4159 // loop), which would invalidate the iterator computed
4161 return BackedgeTakenCounts.find(L)->second = Result;
4164 /// forgetLoop - This method should be called by the client when it has
4165 /// changed a loop in a way that may effect ScalarEvolution's ability to
4166 /// compute a trip count, or if the loop is deleted.
4167 void ScalarEvolution::forgetLoop(const Loop *L) {
4168 // Drop any stored trip count value.
4169 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4170 BackedgeTakenCounts.find(L);
4171 if (BTCPos != BackedgeTakenCounts.end()) {
4172 BTCPos->second.clear();
4173 BackedgeTakenCounts.erase(BTCPos);
4176 // Drop information about expressions based on loop-header PHIs.
4177 SmallVector<Instruction *, 16> Worklist;
4178 PushLoopPHIs(L, Worklist);
4180 SmallPtrSet<Instruction *, 8> Visited;
4181 while (!Worklist.empty()) {
4182 Instruction *I = Worklist.pop_back_val();
4183 if (!Visited.insert(I)) continue;
4185 ValueExprMapType::iterator It =
4186 ValueExprMap.find_as(static_cast<Value *>(I));
4187 if (It != ValueExprMap.end()) {
4188 forgetMemoizedResults(It->second);
4189 ValueExprMap.erase(It);
4190 if (PHINode *PN = dyn_cast<PHINode>(I))
4191 ConstantEvolutionLoopExitValue.erase(PN);
4194 PushDefUseChildren(I, Worklist);
4197 // Forget all contained loops too, to avoid dangling entries in the
4198 // ValuesAtScopes map.
4199 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4203 /// forgetValue - This method should be called by the client when it has
4204 /// changed a value in a way that may effect its value, or which may
4205 /// disconnect it from a def-use chain linking it to a loop.
4206 void ScalarEvolution::forgetValue(Value *V) {
4207 Instruction *I = dyn_cast<Instruction>(V);
4210 // Drop information about expressions based on loop-header PHIs.
4211 SmallVector<Instruction *, 16> Worklist;
4212 Worklist.push_back(I);
4214 SmallPtrSet<Instruction *, 8> Visited;
4215 while (!Worklist.empty()) {
4216 I = Worklist.pop_back_val();
4217 if (!Visited.insert(I)) continue;
4219 ValueExprMapType::iterator It =
4220 ValueExprMap.find_as(static_cast<Value *>(I));
4221 if (It != ValueExprMap.end()) {
4222 forgetMemoizedResults(It->second);
4223 ValueExprMap.erase(It);
4224 if (PHINode *PN = dyn_cast<PHINode>(I))
4225 ConstantEvolutionLoopExitValue.erase(PN);
4228 PushDefUseChildren(I, Worklist);
4232 /// getExact - Get the exact loop backedge taken count considering all loop
4233 /// exits. A computable result can only be return for loops with a single exit.
4234 /// Returning the minimum taken count among all exits is incorrect because one
4235 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4236 /// the limit of each loop test is never skipped. This is a valid assumption as
4237 /// long as the loop exits via that test. For precise results, it is the
4238 /// caller's responsibility to specify the relevant loop exit using
4239 /// getExact(ExitingBlock, SE).
4241 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4242 // If any exits were not computable, the loop is not computable.
4243 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4245 // We need exactly one computable exit.
4246 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4247 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4249 const SCEV *BECount = 0;
4250 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4251 ENT != 0; ENT = ENT->getNextExit()) {
4253 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4256 BECount = ENT->ExactNotTaken;
4257 else if (BECount != ENT->ExactNotTaken)
4258 return SE->getCouldNotCompute();
4260 assert(BECount && "Invalid not taken count for loop exit");
4264 /// getExact - Get the exact not taken count for this loop exit.
4266 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4267 ScalarEvolution *SE) const {
4268 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4269 ENT != 0; ENT = ENT->getNextExit()) {
4271 if (ENT->ExitingBlock == ExitingBlock)
4272 return ENT->ExactNotTaken;
4274 return SE->getCouldNotCompute();
4277 /// getMax - Get the max backedge taken count for the loop.
4279 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4280 return Max ? Max : SE->getCouldNotCompute();
4283 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4284 ScalarEvolution *SE) const {
4285 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4288 if (!ExitNotTaken.ExitingBlock)
4291 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4292 ENT != 0; ENT = ENT->getNextExit()) {
4294 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4295 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4302 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4303 /// computable exit into a persistent ExitNotTakenInfo array.
4304 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4305 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4306 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4309 ExitNotTaken.setIncomplete();
4311 unsigned NumExits = ExitCounts.size();
4312 if (NumExits == 0) return;
4314 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4315 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4316 if (NumExits == 1) return;
4318 // Handle the rare case of multiple computable exits.
4319 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4321 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4322 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4323 PrevENT->setNextExit(ENT);
4324 ENT->ExitingBlock = ExitCounts[i].first;
4325 ENT->ExactNotTaken = ExitCounts[i].second;
4329 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4330 void ScalarEvolution::BackedgeTakenInfo::clear() {
4331 ExitNotTaken.ExitingBlock = 0;
4332 ExitNotTaken.ExactNotTaken = 0;
4333 delete[] ExitNotTaken.getNextExit();
4336 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4337 /// of the specified loop will execute.
4338 ScalarEvolution::BackedgeTakenInfo
4339 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4340 SmallVector<BasicBlock *, 8> ExitingBlocks;
4341 L->getExitingBlocks(ExitingBlocks);
4343 // Examine all exits and pick the most conservative values.
4344 const SCEV *MaxBECount = getCouldNotCompute();
4345 bool CouldComputeBECount = true;
4346 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4347 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4348 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4349 if (EL.Exact == getCouldNotCompute())
4350 // We couldn't compute an exact value for this exit, so
4351 // we won't be able to compute an exact value for the loop.
4352 CouldComputeBECount = false;
4354 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4356 if (MaxBECount == getCouldNotCompute())
4357 MaxBECount = EL.Max;
4358 else if (EL.Max != getCouldNotCompute()) {
4359 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4360 // skip some loop tests. Taking the max over the exits is sufficiently
4361 // conservative. TODO: We could do better taking into consideration
4362 // that (1) the loop has unit stride (2) the last loop test is
4363 // less-than/greater-than (3) any loop test is less-than/greater-than AND
4364 // falls-through some constant times less then the other tests.
4365 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4369 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4372 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4373 /// loop will execute if it exits via the specified block.
4374 ScalarEvolution::ExitLimit
4375 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4377 // Okay, we've chosen an exiting block. See what condition causes us to
4378 // exit at this block.
4380 // FIXME: we should be able to handle switch instructions (with a single exit)
4381 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4382 if (ExitBr == 0) return getCouldNotCompute();
4383 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4385 // At this point, we know we have a conditional branch that determines whether
4386 // the loop is exited. However, we don't know if the branch is executed each
4387 // time through the loop. If not, then the execution count of the branch will
4388 // not be equal to the trip count of the loop.
4390 // Currently we check for this by checking to see if the Exit branch goes to
4391 // the loop header. If so, we know it will always execute the same number of
4392 // times as the loop. We also handle the case where the exit block *is* the
4393 // loop header. This is common for un-rotated loops.
4395 // If both of those tests fail, walk up the unique predecessor chain to the
4396 // header, stopping if there is an edge that doesn't exit the loop. If the
4397 // header is reached, the execution count of the branch will be equal to the
4398 // trip count of the loop.
4400 // More extensive analysis could be done to handle more cases here.
4402 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4403 ExitBr->getSuccessor(1) != L->getHeader() &&
4404 ExitBr->getParent() != L->getHeader()) {
4405 // The simple checks failed, try climbing the unique predecessor chain
4406 // up to the header.
4408 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4409 BasicBlock *Pred = BB->getUniquePredecessor();
4411 return getCouldNotCompute();
4412 TerminatorInst *PredTerm = Pred->getTerminator();
4413 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4414 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4417 // If the predecessor has a successor that isn't BB and isn't
4418 // outside the loop, assume the worst.
4419 if (L->contains(PredSucc))
4420 return getCouldNotCompute();
4422 if (Pred == L->getHeader()) {
4429 return getCouldNotCompute();
4432 // Proceed to the next level to examine the exit condition expression.
4433 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4434 ExitBr->getSuccessor(0),
4435 ExitBr->getSuccessor(1),
4436 /*IsSubExpr=*/false);
4439 /// ComputeExitLimitFromCond - Compute the number of times the
4440 /// backedge of the specified loop will execute if its exit condition
4441 /// were a conditional branch of ExitCond, TBB, and FBB.
4443 /// @param IsSubExpr is true if ExitCond does not directly control the exit
4444 /// branch. In this case, we cannot assume that the loop only exits when the
4445 /// condition is true and cannot infer that failing to meet the condition prior
4446 /// to integer wraparound results in undefined behavior.
4447 ScalarEvolution::ExitLimit
4448 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4453 // Check if the controlling expression for this loop is an And or Or.
4454 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4455 if (BO->getOpcode() == Instruction::And) {
4456 // Recurse on the operands of the and.
4457 bool EitherMayExit = L->contains(TBB);
4458 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4459 IsSubExpr || EitherMayExit);
4460 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4461 IsSubExpr || EitherMayExit);
4462 const SCEV *BECount = getCouldNotCompute();
4463 const SCEV *MaxBECount = getCouldNotCompute();
4464 if (EitherMayExit) {
4465 // Both conditions must be true for the loop to continue executing.
4466 // Choose the less conservative count.
4467 if (EL0.Exact == getCouldNotCompute() ||
4468 EL1.Exact == getCouldNotCompute())
4469 BECount = getCouldNotCompute();
4471 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4472 if (EL0.Max == getCouldNotCompute())
4473 MaxBECount = EL1.Max;
4474 else if (EL1.Max == getCouldNotCompute())
4475 MaxBECount = EL0.Max;
4477 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4479 // Both conditions must be true at the same time for the loop to exit.
4480 // For now, be conservative.
4481 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4482 if (EL0.Max == EL1.Max)
4483 MaxBECount = EL0.Max;
4484 if (EL0.Exact == EL1.Exact)
4485 BECount = EL0.Exact;
4488 return ExitLimit(BECount, MaxBECount);
4490 if (BO->getOpcode() == Instruction::Or) {
4491 // Recurse on the operands of the or.
4492 bool EitherMayExit = L->contains(FBB);
4493 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4494 IsSubExpr || EitherMayExit);
4495 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4496 IsSubExpr || EitherMayExit);
4497 const SCEV *BECount = getCouldNotCompute();
4498 const SCEV *MaxBECount = getCouldNotCompute();
4499 if (EitherMayExit) {
4500 // Both conditions must be false for the loop to continue executing.
4501 // Choose the less conservative count.
4502 if (EL0.Exact == getCouldNotCompute() ||
4503 EL1.Exact == getCouldNotCompute())
4504 BECount = getCouldNotCompute();
4506 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4507 if (EL0.Max == getCouldNotCompute())
4508 MaxBECount = EL1.Max;
4509 else if (EL1.Max == getCouldNotCompute())
4510 MaxBECount = EL0.Max;
4512 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4514 // Both conditions must be false at the same time for the loop to exit.
4515 // For now, be conservative.
4516 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4517 if (EL0.Max == EL1.Max)
4518 MaxBECount = EL0.Max;
4519 if (EL0.Exact == EL1.Exact)
4520 BECount = EL0.Exact;
4523 return ExitLimit(BECount, MaxBECount);
4527 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4528 // Proceed to the next level to examine the icmp.
4529 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4530 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, IsSubExpr);
4532 // Check for a constant condition. These are normally stripped out by
4533 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4534 // preserve the CFG and is temporarily leaving constant conditions
4536 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4537 if (L->contains(FBB) == !CI->getZExtValue())
4538 // The backedge is always taken.
4539 return getCouldNotCompute();
4541 // The backedge is never taken.
4542 return getConstant(CI->getType(), 0);
4545 // If it's not an integer or pointer comparison then compute it the hard way.
4546 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4549 /// ComputeExitLimitFromICmp - Compute the number of times the
4550 /// backedge of the specified loop will execute if its exit condition
4551 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4552 ScalarEvolution::ExitLimit
4553 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4559 // If the condition was exit on true, convert the condition to exit on false
4560 ICmpInst::Predicate Cond;
4561 if (!L->contains(FBB))
4562 Cond = ExitCond->getPredicate();
4564 Cond = ExitCond->getInversePredicate();
4566 // Handle common loops like: for (X = "string"; *X; ++X)
4567 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4568 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4570 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4571 if (ItCnt.hasAnyInfo())
4575 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4576 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4578 // Try to evaluate any dependencies out of the loop.
4579 LHS = getSCEVAtScope(LHS, L);
4580 RHS = getSCEVAtScope(RHS, L);
4582 // At this point, we would like to compute how many iterations of the
4583 // loop the predicate will return true for these inputs.
4584 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4585 // If there is a loop-invariant, force it into the RHS.
4586 std::swap(LHS, RHS);
4587 Cond = ICmpInst::getSwappedPredicate(Cond);
4590 // Simplify the operands before analyzing them.
4591 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4593 // If we have a comparison of a chrec against a constant, try to use value
4594 // ranges to answer this query.
4595 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4596 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4597 if (AddRec->getLoop() == L) {
4598 // Form the constant range.
4599 ConstantRange CompRange(
4600 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4602 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4603 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4607 case ICmpInst::ICMP_NE: { // while (X != Y)
4608 // Convert to: while (X-Y != 0)
4609 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4610 if (EL.hasAnyInfo()) return EL;
4613 case ICmpInst::ICMP_EQ: { // while (X == Y)
4614 // Convert to: while (X-Y == 0)
4615 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4616 if (EL.hasAnyInfo()) return EL;
4619 case ICmpInst::ICMP_SLT: {
4620 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true, IsSubExpr);
4621 if (EL.hasAnyInfo()) return EL;
4624 case ICmpInst::ICMP_SGT: {
4625 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4626 getNotSCEV(RHS), L, true, IsSubExpr);
4627 if (EL.hasAnyInfo()) return EL;
4630 case ICmpInst::ICMP_ULT: {
4631 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false, IsSubExpr);
4632 if (EL.hasAnyInfo()) return EL;
4635 case ICmpInst::ICMP_UGT: {
4636 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4637 getNotSCEV(RHS), L, false, IsSubExpr);
4638 if (EL.hasAnyInfo()) return EL;
4643 dbgs() << "ComputeBackedgeTakenCount ";
4644 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4645 dbgs() << "[unsigned] ";
4646 dbgs() << *LHS << " "
4647 << Instruction::getOpcodeName(Instruction::ICmp)
4648 << " " << *RHS << "\n";
4652 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4655 static ConstantInt *
4656 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4657 ScalarEvolution &SE) {
4658 const SCEV *InVal = SE.getConstant(C);
4659 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4660 assert(isa<SCEVConstant>(Val) &&
4661 "Evaluation of SCEV at constant didn't fold correctly?");
4662 return cast<SCEVConstant>(Val)->getValue();
4665 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4666 /// 'icmp op load X, cst', try to see if we can compute the backedge
4667 /// execution count.
4668 ScalarEvolution::ExitLimit
4669 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4673 ICmpInst::Predicate predicate) {
4675 if (LI->isVolatile()) return getCouldNotCompute();
4677 // Check to see if the loaded pointer is a getelementptr of a global.
4678 // TODO: Use SCEV instead of manually grubbing with GEPs.
4679 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4680 if (!GEP) return getCouldNotCompute();
4682 // Make sure that it is really a constant global we are gepping, with an
4683 // initializer, and make sure the first IDX is really 0.
4684 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4685 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4686 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4687 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4688 return getCouldNotCompute();
4690 // Okay, we allow one non-constant index into the GEP instruction.
4692 std::vector<Constant*> Indexes;
4693 unsigned VarIdxNum = 0;
4694 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4695 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4696 Indexes.push_back(CI);
4697 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4698 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4699 VarIdx = GEP->getOperand(i);
4701 Indexes.push_back(0);
4704 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4706 return getCouldNotCompute();
4708 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4709 // Check to see if X is a loop variant variable value now.
4710 const SCEV *Idx = getSCEV(VarIdx);
4711 Idx = getSCEVAtScope(Idx, L);
4713 // We can only recognize very limited forms of loop index expressions, in
4714 // particular, only affine AddRec's like {C1,+,C2}.
4715 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4716 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4717 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4718 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4719 return getCouldNotCompute();
4721 unsigned MaxSteps = MaxBruteForceIterations;
4722 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4723 ConstantInt *ItCst = ConstantInt::get(
4724 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4725 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4727 // Form the GEP offset.
4728 Indexes[VarIdxNum] = Val;
4730 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4732 if (Result == 0) break; // Cannot compute!
4734 // Evaluate the condition for this iteration.
4735 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4736 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4737 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4739 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4740 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4743 ++NumArrayLenItCounts;
4744 return getConstant(ItCst); // Found terminating iteration!
4747 return getCouldNotCompute();
4751 /// CanConstantFold - Return true if we can constant fold an instruction of the
4752 /// specified type, assuming that all operands were constants.
4753 static bool CanConstantFold(const Instruction *I) {
4754 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4755 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4759 if (const CallInst *CI = dyn_cast<CallInst>(I))
4760 if (const Function *F = CI->getCalledFunction())
4761 return canConstantFoldCallTo(F);
4765 /// Determine whether this instruction can constant evolve within this loop
4766 /// assuming its operands can all constant evolve.
4767 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4768 // An instruction outside of the loop can't be derived from a loop PHI.
4769 if (!L->contains(I)) return false;
4771 if (isa<PHINode>(I)) {
4772 if (L->getHeader() == I->getParent())
4775 // We don't currently keep track of the control flow needed to evaluate
4776 // PHIs, so we cannot handle PHIs inside of loops.
4780 // If we won't be able to constant fold this expression even if the operands
4781 // are constants, bail early.
4782 return CanConstantFold(I);
4785 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4786 /// recursing through each instruction operand until reaching a loop header phi.
4788 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4789 DenseMap<Instruction *, PHINode *> &PHIMap) {
4791 // Otherwise, we can evaluate this instruction if all of its operands are
4792 // constant or derived from a PHI node themselves.
4794 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4795 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4797 if (isa<Constant>(*OpI)) continue;
4799 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4800 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4802 PHINode *P = dyn_cast<PHINode>(OpInst);
4804 // If this operand is already visited, reuse the prior result.
4805 // We may have P != PHI if this is the deepest point at which the
4806 // inconsistent paths meet.
4807 P = PHIMap.lookup(OpInst);
4809 // Recurse and memoize the results, whether a phi is found or not.
4810 // This recursive call invalidates pointers into PHIMap.
4811 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4814 if (P == 0) return 0; // Not evolving from PHI
4815 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4818 // This is a expression evolving from a constant PHI!
4822 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4823 /// in the loop that V is derived from. We allow arbitrary operations along the
4824 /// way, but the operands of an operation must either be constants or a value
4825 /// derived from a constant PHI. If this expression does not fit with these
4826 /// constraints, return null.
4827 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4828 Instruction *I = dyn_cast<Instruction>(V);
4829 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4831 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4835 // Record non-constant instructions contained by the loop.
4836 DenseMap<Instruction *, PHINode *> PHIMap;
4837 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4840 /// EvaluateExpression - Given an expression that passes the
4841 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4842 /// in the loop has the value PHIVal. If we can't fold this expression for some
4843 /// reason, return null.
4844 static Constant *EvaluateExpression(Value *V, const Loop *L,
4845 DenseMap<Instruction *, Constant *> &Vals,
4846 const DataLayout *TD,
4847 const TargetLibraryInfo *TLI) {
4848 // Convenient constant check, but redundant for recursive calls.
4849 if (Constant *C = dyn_cast<Constant>(V)) return C;
4850 Instruction *I = dyn_cast<Instruction>(V);
4853 if (Constant *C = Vals.lookup(I)) return C;
4855 // An instruction inside the loop depends on a value outside the loop that we
4856 // weren't given a mapping for, or a value such as a call inside the loop.
4857 if (!canConstantEvolve(I, L)) return 0;
4859 // An unmapped PHI can be due to a branch or another loop inside this loop,
4860 // or due to this not being the initial iteration through a loop where we
4861 // couldn't compute the evolution of this particular PHI last time.
4862 if (isa<PHINode>(I)) return 0;
4864 std::vector<Constant*> Operands(I->getNumOperands());
4866 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4867 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4869 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4870 if (!Operands[i]) return 0;
4873 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
4879 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4880 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4881 Operands[1], TD, TLI);
4882 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4883 if (!LI->isVolatile())
4884 return ConstantFoldLoadFromConstPtr(Operands[0], TD);
4886 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
4890 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4891 /// in the header of its containing loop, we know the loop executes a
4892 /// constant number of times, and the PHI node is just a recurrence
4893 /// involving constants, fold it.
4895 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4898 DenseMap<PHINode*, Constant*>::const_iterator I =
4899 ConstantEvolutionLoopExitValue.find(PN);
4900 if (I != ConstantEvolutionLoopExitValue.end())
4903 if (BEs.ugt(MaxBruteForceIterations))
4904 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4906 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4908 DenseMap<Instruction *, Constant *> CurrentIterVals;
4909 BasicBlock *Header = L->getHeader();
4910 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4912 // Since the loop is canonicalized, the PHI node must have two entries. One
4913 // entry must be a constant (coming in from outside of the loop), and the
4914 // second must be derived from the same PHI.
4915 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4917 for (BasicBlock::iterator I = Header->begin();
4918 (PHI = dyn_cast<PHINode>(I)); ++I) {
4919 Constant *StartCST =
4920 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4921 if (StartCST == 0) continue;
4922 CurrentIterVals[PHI] = StartCST;
4924 if (!CurrentIterVals.count(PN))
4927 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4929 // Execute the loop symbolically to determine the exit value.
4930 if (BEs.getActiveBits() >= 32)
4931 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4933 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4934 unsigned IterationNum = 0;
4935 for (; ; ++IterationNum) {
4936 if (IterationNum == NumIterations)
4937 return RetVal = CurrentIterVals[PN]; // Got exit value!
4939 // Compute the value of the PHIs for the next iteration.
4940 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
4941 DenseMap<Instruction *, Constant *> NextIterVals;
4942 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
4945 return 0; // Couldn't evaluate!
4946 NextIterVals[PN] = NextPHI;
4948 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
4950 // Also evaluate the other PHI nodes. However, we don't get to stop if we
4951 // cease to be able to evaluate one of them or if they stop evolving,
4952 // because that doesn't necessarily prevent us from computing PN.
4953 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
4954 for (DenseMap<Instruction *, Constant *>::const_iterator
4955 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4956 PHINode *PHI = dyn_cast<PHINode>(I->first);
4957 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
4958 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
4960 // We use two distinct loops because EvaluateExpression may invalidate any
4961 // iterators into CurrentIterVals.
4962 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
4963 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
4964 PHINode *PHI = I->first;
4965 Constant *&NextPHI = NextIterVals[PHI];
4966 if (!NextPHI) { // Not already computed.
4967 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4968 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4970 if (NextPHI != I->second)
4971 StoppedEvolving = false;
4974 // If all entries in CurrentIterVals == NextIterVals then we can stop
4975 // iterating, the loop can't continue to change.
4976 if (StoppedEvolving)
4977 return RetVal = CurrentIterVals[PN];
4979 CurrentIterVals.swap(NextIterVals);
4983 /// ComputeExitCountExhaustively - If the loop is known to execute a
4984 /// constant number of times (the condition evolves only from constants),
4985 /// try to evaluate a few iterations of the loop until we get the exit
4986 /// condition gets a value of ExitWhen (true or false). If we cannot
4987 /// evaluate the trip count of the loop, return getCouldNotCompute().
4988 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4991 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4992 if (PN == 0) return getCouldNotCompute();
4994 // If the loop is canonicalized, the PHI will have exactly two entries.
4995 // That's the only form we support here.
4996 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4998 DenseMap<Instruction *, Constant *> CurrentIterVals;
4999 BasicBlock *Header = L->getHeader();
5000 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5002 // One entry must be a constant (coming in from outside of the loop), and the
5003 // second must be derived from the same PHI.
5004 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5006 for (BasicBlock::iterator I = Header->begin();
5007 (PHI = dyn_cast<PHINode>(I)); ++I) {
5008 Constant *StartCST =
5009 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5010 if (StartCST == 0) continue;
5011 CurrentIterVals[PHI] = StartCST;
5013 if (!CurrentIterVals.count(PN))
5014 return getCouldNotCompute();
5016 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5017 // the loop symbolically to determine when the condition gets a value of
5020 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5021 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5022 ConstantInt *CondVal =
5023 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5026 // Couldn't symbolically evaluate.
5027 if (!CondVal) return getCouldNotCompute();
5029 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5030 ++NumBruteForceTripCountsComputed;
5031 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5034 // Update all the PHI nodes for the next iteration.
5035 DenseMap<Instruction *, Constant *> NextIterVals;
5037 // Create a list of which PHIs we need to compute. We want to do this before
5038 // calling EvaluateExpression on them because that may invalidate iterators
5039 // into CurrentIterVals.
5040 SmallVector<PHINode *, 8> PHIsToCompute;
5041 for (DenseMap<Instruction *, Constant *>::const_iterator
5042 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5043 PHINode *PHI = dyn_cast<PHINode>(I->first);
5044 if (!PHI || PHI->getParent() != Header) continue;
5045 PHIsToCompute.push_back(PHI);
5047 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5048 E = PHIsToCompute.end(); I != E; ++I) {
5050 Constant *&NextPHI = NextIterVals[PHI];
5051 if (NextPHI) continue; // Already computed!
5053 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5054 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
5056 CurrentIterVals.swap(NextIterVals);
5059 // Too many iterations were needed to evaluate.
5060 return getCouldNotCompute();
5063 /// getSCEVAtScope - Return a SCEV expression for the specified value
5064 /// at the specified scope in the program. The L value specifies a loop
5065 /// nest to evaluate the expression at, where null is the top-level or a
5066 /// specified loop is immediately inside of the loop.
5068 /// This method can be used to compute the exit value for a variable defined
5069 /// in a loop by querying what the value will hold in the parent loop.
5071 /// In the case that a relevant loop exit value cannot be computed, the
5072 /// original value V is returned.
5073 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5074 // Check to see if we've folded this expression at this loop before.
5075 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
5076 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
5077 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
5079 return Pair.first->second ? Pair.first->second : V;
5081 // Otherwise compute it.
5082 const SCEV *C = computeSCEVAtScope(V, L);
5083 ValuesAtScopes[V][L] = C;
5087 /// This builds up a Constant using the ConstantExpr interface. That way, we
5088 /// will return Constants for objects which aren't represented by a
5089 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5090 /// Returns NULL if the SCEV isn't representable as a Constant.
5091 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5092 switch (V->getSCEVType()) {
5093 default: // TODO: smax, umax.
5094 case scCouldNotCompute:
5098 return cast<SCEVConstant>(V)->getValue();
5100 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5101 case scSignExtend: {
5102 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5103 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5104 return ConstantExpr::getSExt(CastOp, SS->getType());
5107 case scZeroExtend: {
5108 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5109 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5110 return ConstantExpr::getZExt(CastOp, SZ->getType());
5114 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5115 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5116 return ConstantExpr::getTrunc(CastOp, ST->getType());
5120 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5121 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5122 if (C->getType()->isPointerTy())
5123 C = ConstantExpr::getBitCast(C, Type::getInt8PtrTy(C->getContext()));
5124 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5125 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5129 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5131 // The offsets have been converted to bytes. We can add bytes to an
5132 // i8* by GEP with the byte count in the first index.
5133 C = ConstantExpr::getBitCast(C,Type::getInt8PtrTy(C->getContext()));
5136 // Don't bother trying to sum two pointers. We probably can't
5137 // statically compute a load that results from it anyway.
5138 if (C2->getType()->isPointerTy())
5141 if (C->getType()->isPointerTy()) {
5142 if (cast<PointerType>(C->getType())->getElementType()->isStructTy())
5143 C2 = ConstantExpr::getIntegerCast(
5144 C2, Type::getInt32Ty(C->getContext()), true);
5145 C = ConstantExpr::getGetElementPtr(C, C2);
5147 C = ConstantExpr::getAdd(C, C2);
5154 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5155 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5156 // Don't bother with pointers at all.
5157 if (C->getType()->isPointerTy()) return 0;
5158 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5159 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5160 if (!C2 || C2->getType()->isPointerTy()) return 0;
5161 C = ConstantExpr::getMul(C, C2);
5168 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5169 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5170 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5171 if (LHS->getType() == RHS->getType())
5172 return ConstantExpr::getUDiv(LHS, RHS);
5179 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5180 if (isa<SCEVConstant>(V)) return V;
5182 // If this instruction is evolved from a constant-evolving PHI, compute the
5183 // exit value from the loop without using SCEVs.
5184 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5185 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5186 const Loop *LI = (*this->LI)[I->getParent()];
5187 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5188 if (PHINode *PN = dyn_cast<PHINode>(I))
5189 if (PN->getParent() == LI->getHeader()) {
5190 // Okay, there is no closed form solution for the PHI node. Check
5191 // to see if the loop that contains it has a known backedge-taken
5192 // count. If so, we may be able to force computation of the exit
5194 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5195 if (const SCEVConstant *BTCC =
5196 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5197 // Okay, we know how many times the containing loop executes. If
5198 // this is a constant evolving PHI node, get the final value at
5199 // the specified iteration number.
5200 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5201 BTCC->getValue()->getValue(),
5203 if (RV) return getSCEV(RV);
5207 // Okay, this is an expression that we cannot symbolically evaluate
5208 // into a SCEV. Check to see if it's possible to symbolically evaluate
5209 // the arguments into constants, and if so, try to constant propagate the
5210 // result. This is particularly useful for computing loop exit values.
5211 if (CanConstantFold(I)) {
5212 SmallVector<Constant *, 4> Operands;
5213 bool MadeImprovement = false;
5214 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5215 Value *Op = I->getOperand(i);
5216 if (Constant *C = dyn_cast<Constant>(Op)) {
5217 Operands.push_back(C);
5221 // If any of the operands is non-constant and if they are
5222 // non-integer and non-pointer, don't even try to analyze them
5223 // with scev techniques.
5224 if (!isSCEVable(Op->getType()))
5227 const SCEV *OrigV = getSCEV(Op);
5228 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5229 MadeImprovement |= OrigV != OpV;
5231 Constant *C = BuildConstantFromSCEV(OpV);
5233 if (C->getType() != Op->getType())
5234 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5238 Operands.push_back(C);
5241 // Check to see if getSCEVAtScope actually made an improvement.
5242 if (MadeImprovement) {
5244 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5245 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5246 Operands[0], Operands[1], TD,
5248 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5249 if (!LI->isVolatile())
5250 C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
5252 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5260 // This is some other type of SCEVUnknown, just return it.
5264 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5265 // Avoid performing the look-up in the common case where the specified
5266 // expression has no loop-variant portions.
5267 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5268 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5269 if (OpAtScope != Comm->getOperand(i)) {
5270 // Okay, at least one of these operands is loop variant but might be
5271 // foldable. Build a new instance of the folded commutative expression.
5272 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5273 Comm->op_begin()+i);
5274 NewOps.push_back(OpAtScope);
5276 for (++i; i != e; ++i) {
5277 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5278 NewOps.push_back(OpAtScope);
5280 if (isa<SCEVAddExpr>(Comm))
5281 return getAddExpr(NewOps);
5282 if (isa<SCEVMulExpr>(Comm))
5283 return getMulExpr(NewOps);
5284 if (isa<SCEVSMaxExpr>(Comm))
5285 return getSMaxExpr(NewOps);
5286 if (isa<SCEVUMaxExpr>(Comm))
5287 return getUMaxExpr(NewOps);
5288 llvm_unreachable("Unknown commutative SCEV type!");
5291 // If we got here, all operands are loop invariant.
5295 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5296 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5297 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5298 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5299 return Div; // must be loop invariant
5300 return getUDivExpr(LHS, RHS);
5303 // If this is a loop recurrence for a loop that does not contain L, then we
5304 // are dealing with the final value computed by the loop.
5305 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5306 // First, attempt to evaluate each operand.
5307 // Avoid performing the look-up in the common case where the specified
5308 // expression has no loop-variant portions.
5309 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5310 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5311 if (OpAtScope == AddRec->getOperand(i))
5314 // Okay, at least one of these operands is loop variant but might be
5315 // foldable. Build a new instance of the folded commutative expression.
5316 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5317 AddRec->op_begin()+i);
5318 NewOps.push_back(OpAtScope);
5319 for (++i; i != e; ++i)
5320 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5322 const SCEV *FoldedRec =
5323 getAddRecExpr(NewOps, AddRec->getLoop(),
5324 AddRec->getNoWrapFlags(SCEV::FlagNW));
5325 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5326 // The addrec may be folded to a nonrecurrence, for example, if the
5327 // induction variable is multiplied by zero after constant folding. Go
5328 // ahead and return the folded value.
5334 // If the scope is outside the addrec's loop, evaluate it by using the
5335 // loop exit value of the addrec.
5336 if (!AddRec->getLoop()->contains(L)) {
5337 // To evaluate this recurrence, we need to know how many times the AddRec
5338 // loop iterates. Compute this now.
5339 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5340 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5342 // Then, evaluate the AddRec.
5343 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5349 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5350 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5351 if (Op == Cast->getOperand())
5352 return Cast; // must be loop invariant
5353 return getZeroExtendExpr(Op, Cast->getType());
5356 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5357 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5358 if (Op == Cast->getOperand())
5359 return Cast; // must be loop invariant
5360 return getSignExtendExpr(Op, Cast->getType());
5363 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5364 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5365 if (Op == Cast->getOperand())
5366 return Cast; // must be loop invariant
5367 return getTruncateExpr(Op, Cast->getType());
5370 llvm_unreachable("Unknown SCEV type!");
5373 /// getSCEVAtScope - This is a convenience function which does
5374 /// getSCEVAtScope(getSCEV(V), L).
5375 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5376 return getSCEVAtScope(getSCEV(V), L);
5379 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5380 /// following equation:
5382 /// A * X = B (mod N)
5384 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5385 /// A and B isn't important.
5387 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5388 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5389 ScalarEvolution &SE) {
5390 uint32_t BW = A.getBitWidth();
5391 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5392 assert(A != 0 && "A must be non-zero.");
5396 // The gcd of A and N may have only one prime factor: 2. The number of
5397 // trailing zeros in A is its multiplicity
5398 uint32_t Mult2 = A.countTrailingZeros();
5401 // 2. Check if B is divisible by D.
5403 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5404 // is not less than multiplicity of this prime factor for D.
5405 if (B.countTrailingZeros() < Mult2)
5406 return SE.getCouldNotCompute();
5408 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5411 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5412 // bit width during computations.
5413 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5414 APInt Mod(BW + 1, 0);
5415 Mod.setBit(BW - Mult2); // Mod = N / D
5416 APInt I = AD.multiplicativeInverse(Mod);
5418 // 4. Compute the minimum unsigned root of the equation:
5419 // I * (B / D) mod (N / D)
5420 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5422 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5424 return SE.getConstant(Result.trunc(BW));
5427 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5428 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5429 /// might be the same) or two SCEVCouldNotCompute objects.
5431 static std::pair<const SCEV *,const SCEV *>
5432 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5433 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5434 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5435 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5436 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5438 // We currently can only solve this if the coefficients are constants.
5439 if (!LC || !MC || !NC) {
5440 const SCEV *CNC = SE.getCouldNotCompute();
5441 return std::make_pair(CNC, CNC);
5444 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5445 const APInt &L = LC->getValue()->getValue();
5446 const APInt &M = MC->getValue()->getValue();
5447 const APInt &N = NC->getValue()->getValue();
5448 APInt Two(BitWidth, 2);
5449 APInt Four(BitWidth, 4);
5452 using namespace APIntOps;
5454 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5455 // The B coefficient is M-N/2
5459 // The A coefficient is N/2
5460 APInt A(N.sdiv(Two));
5462 // Compute the B^2-4ac term.
5465 SqrtTerm -= Four * (A * C);
5467 if (SqrtTerm.isNegative()) {
5468 // The loop is provably infinite.
5469 const SCEV *CNC = SE.getCouldNotCompute();
5470 return std::make_pair(CNC, CNC);
5473 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5474 // integer value or else APInt::sqrt() will assert.
5475 APInt SqrtVal(SqrtTerm.sqrt());
5477 // Compute the two solutions for the quadratic formula.
5478 // The divisions must be performed as signed divisions.
5481 if (TwoA.isMinValue()) {
5482 const SCEV *CNC = SE.getCouldNotCompute();
5483 return std::make_pair(CNC, CNC);
5486 LLVMContext &Context = SE.getContext();
5488 ConstantInt *Solution1 =
5489 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5490 ConstantInt *Solution2 =
5491 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5493 return std::make_pair(SE.getConstant(Solution1),
5494 SE.getConstant(Solution2));
5495 } // end APIntOps namespace
5498 /// HowFarToZero - Return the number of times a backedge comparing the specified
5499 /// value to zero will execute. If not computable, return CouldNotCompute.
5501 /// This is only used for loops with a "x != y" exit test. The exit condition is
5502 /// now expressed as a single expression, V = x-y. So the exit test is
5503 /// effectively V != 0. We know and take advantage of the fact that this
5504 /// expression only being used in a comparison by zero context.
5505 ScalarEvolution::ExitLimit
5506 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
5507 // If the value is a constant
5508 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5509 // If the value is already zero, the branch will execute zero times.
5510 if (C->getValue()->isZero()) return C;
5511 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5514 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5515 if (!AddRec || AddRec->getLoop() != L)
5516 return getCouldNotCompute();
5518 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5519 // the quadratic equation to solve it.
5520 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5521 std::pair<const SCEV *,const SCEV *> Roots =
5522 SolveQuadraticEquation(AddRec, *this);
5523 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5524 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5527 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5528 << " sol#2: " << *R2 << "\n";
5530 // Pick the smallest positive root value.
5531 if (ConstantInt *CB =
5532 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5535 if (CB->getZExtValue() == false)
5536 std::swap(R1, R2); // R1 is the minimum root now.
5538 // We can only use this value if the chrec ends up with an exact zero
5539 // value at this index. When solving for "X*X != 5", for example, we
5540 // should not accept a root of 2.
5541 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5543 return R1; // We found a quadratic root!
5546 return getCouldNotCompute();
5549 // Otherwise we can only handle this if it is affine.
5550 if (!AddRec->isAffine())
5551 return getCouldNotCompute();
5553 // If this is an affine expression, the execution count of this branch is
5554 // the minimum unsigned root of the following equation:
5556 // Start + Step*N = 0 (mod 2^BW)
5560 // Step*N = -Start (mod 2^BW)
5562 // where BW is the common bit width of Start and Step.
5564 // Get the initial value for the loop.
5565 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5566 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5568 // For now we handle only constant steps.
5570 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5571 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5572 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5573 // We have not yet seen any such cases.
5574 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5575 if (StepC == 0 || StepC->getValue()->equalsInt(0))
5576 return getCouldNotCompute();
5578 // For positive steps (counting up until unsigned overflow):
5579 // N = -Start/Step (as unsigned)
5580 // For negative steps (counting down to zero):
5582 // First compute the unsigned distance from zero in the direction of Step.
5583 bool CountDown = StepC->getValue()->getValue().isNegative();
5584 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5586 // Handle unitary steps, which cannot wraparound.
5587 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5588 // N = Distance (as unsigned)
5589 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5590 ConstantRange CR = getUnsignedRange(Start);
5591 const SCEV *MaxBECount;
5592 if (!CountDown && CR.getUnsignedMin().isMinValue())
5593 // When counting up, the worst starting value is 1, not 0.
5594 MaxBECount = CR.getUnsignedMax().isMinValue()
5595 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5596 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5598 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5599 : -CR.getUnsignedMin());
5600 return ExitLimit(Distance, MaxBECount);
5603 // If the recurrence is known not to wraparound, unsigned divide computes the
5604 // back edge count. (Ideally we would have an "isexact" bit for udiv). We know
5605 // that the value will either become zero (and thus the loop terminates), that
5606 // the loop will terminate through some other exit condition first, or that
5607 // the loop has undefined behavior. This means we can't "miss" the exit
5608 // value, even with nonunit stride.
5610 // This is only valid for expressions that directly compute the loop exit. It
5611 // is invalid for subexpressions in which the loop may exit through this
5612 // branch even if this subexpression is false. In that case, the trip count
5613 // computed by this udiv could be smaller than the number of well-defined
5615 if (!IsSubExpr && AddRec->getNoWrapFlags(SCEV::FlagNW))
5616 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5618 // Then, try to solve the above equation provided that Start is constant.
5619 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5620 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5621 -StartC->getValue()->getValue(),
5623 return getCouldNotCompute();
5626 /// HowFarToNonZero - Return the number of times a backedge checking the
5627 /// specified value for nonzero will execute. If not computable, return
5629 ScalarEvolution::ExitLimit
5630 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5631 // Loops that look like: while (X == 0) are very strange indeed. We don't
5632 // handle them yet except for the trivial case. This could be expanded in the
5633 // future as needed.
5635 // If the value is a constant, check to see if it is known to be non-zero
5636 // already. If so, the backedge will execute zero times.
5637 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5638 if (!C->getValue()->isNullValue())
5639 return getConstant(C->getType(), 0);
5640 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5643 // We could implement others, but I really doubt anyone writes loops like
5644 // this, and if they did, they would already be constant folded.
5645 return getCouldNotCompute();
5648 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5649 /// (which may not be an immediate predecessor) which has exactly one
5650 /// successor from which BB is reachable, or null if no such block is
5653 std::pair<BasicBlock *, BasicBlock *>
5654 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5655 // If the block has a unique predecessor, then there is no path from the
5656 // predecessor to the block that does not go through the direct edge
5657 // from the predecessor to the block.
5658 if (BasicBlock *Pred = BB->getSinglePredecessor())
5659 return std::make_pair(Pred, BB);
5661 // A loop's header is defined to be a block that dominates the loop.
5662 // If the header has a unique predecessor outside the loop, it must be
5663 // a block that has exactly one successor that can reach the loop.
5664 if (Loop *L = LI->getLoopFor(BB))
5665 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5667 return std::pair<BasicBlock *, BasicBlock *>();
5670 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5671 /// testing whether two expressions are equal, however for the purposes of
5672 /// looking for a condition guarding a loop, it can be useful to be a little
5673 /// more general, since a front-end may have replicated the controlling
5676 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5677 // Quick check to see if they are the same SCEV.
5678 if (A == B) return true;
5680 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5681 // two different instructions with the same value. Check for this case.
5682 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5683 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5684 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5685 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5686 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5689 // Otherwise assume they may have a different value.
5693 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5694 /// predicate Pred. Return true iff any changes were made.
5696 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5697 const SCEV *&LHS, const SCEV *&RHS,
5699 bool Changed = false;
5701 // If we hit the max recursion limit bail out.
5705 // Canonicalize a constant to the right side.
5706 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5707 // Check for both operands constant.
5708 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5709 if (ConstantExpr::getICmp(Pred,
5711 RHSC->getValue())->isNullValue())
5712 goto trivially_false;
5714 goto trivially_true;
5716 // Otherwise swap the operands to put the constant on the right.
5717 std::swap(LHS, RHS);
5718 Pred = ICmpInst::getSwappedPredicate(Pred);
5722 // If we're comparing an addrec with a value which is loop-invariant in the
5723 // addrec's loop, put the addrec on the left. Also make a dominance check,
5724 // as both operands could be addrecs loop-invariant in each other's loop.
5725 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5726 const Loop *L = AR->getLoop();
5727 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5728 std::swap(LHS, RHS);
5729 Pred = ICmpInst::getSwappedPredicate(Pred);
5734 // If there's a constant operand, canonicalize comparisons with boundary
5735 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5736 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5737 const APInt &RA = RC->getValue()->getValue();
5739 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5740 case ICmpInst::ICMP_EQ:
5741 case ICmpInst::ICMP_NE:
5742 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5744 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5745 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5746 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5747 ME->getOperand(0)->isAllOnesValue()) {
5748 RHS = AE->getOperand(1);
5749 LHS = ME->getOperand(1);
5753 case ICmpInst::ICMP_UGE:
5754 if ((RA - 1).isMinValue()) {
5755 Pred = ICmpInst::ICMP_NE;
5756 RHS = getConstant(RA - 1);
5760 if (RA.isMaxValue()) {
5761 Pred = ICmpInst::ICMP_EQ;
5765 if (RA.isMinValue()) goto trivially_true;
5767 Pred = ICmpInst::ICMP_UGT;
5768 RHS = getConstant(RA - 1);
5771 case ICmpInst::ICMP_ULE:
5772 if ((RA + 1).isMaxValue()) {
5773 Pred = ICmpInst::ICMP_NE;
5774 RHS = getConstant(RA + 1);
5778 if (RA.isMinValue()) {
5779 Pred = ICmpInst::ICMP_EQ;
5783 if (RA.isMaxValue()) goto trivially_true;
5785 Pred = ICmpInst::ICMP_ULT;
5786 RHS = getConstant(RA + 1);
5789 case ICmpInst::ICMP_SGE:
5790 if ((RA - 1).isMinSignedValue()) {
5791 Pred = ICmpInst::ICMP_NE;
5792 RHS = getConstant(RA - 1);
5796 if (RA.isMaxSignedValue()) {
5797 Pred = ICmpInst::ICMP_EQ;
5801 if (RA.isMinSignedValue()) goto trivially_true;
5803 Pred = ICmpInst::ICMP_SGT;
5804 RHS = getConstant(RA - 1);
5807 case ICmpInst::ICMP_SLE:
5808 if ((RA + 1).isMaxSignedValue()) {
5809 Pred = ICmpInst::ICMP_NE;
5810 RHS = getConstant(RA + 1);
5814 if (RA.isMinSignedValue()) {
5815 Pred = ICmpInst::ICMP_EQ;
5819 if (RA.isMaxSignedValue()) goto trivially_true;
5821 Pred = ICmpInst::ICMP_SLT;
5822 RHS = getConstant(RA + 1);
5825 case ICmpInst::ICMP_UGT:
5826 if (RA.isMinValue()) {
5827 Pred = ICmpInst::ICMP_NE;
5831 if ((RA + 1).isMaxValue()) {
5832 Pred = ICmpInst::ICMP_EQ;
5833 RHS = getConstant(RA + 1);
5837 if (RA.isMaxValue()) goto trivially_false;
5839 case ICmpInst::ICMP_ULT:
5840 if (RA.isMaxValue()) {
5841 Pred = ICmpInst::ICMP_NE;
5845 if ((RA - 1).isMinValue()) {
5846 Pred = ICmpInst::ICMP_EQ;
5847 RHS = getConstant(RA - 1);
5851 if (RA.isMinValue()) goto trivially_false;
5853 case ICmpInst::ICMP_SGT:
5854 if (RA.isMinSignedValue()) {
5855 Pred = ICmpInst::ICMP_NE;
5859 if ((RA + 1).isMaxSignedValue()) {
5860 Pred = ICmpInst::ICMP_EQ;
5861 RHS = getConstant(RA + 1);
5865 if (RA.isMaxSignedValue()) goto trivially_false;
5867 case ICmpInst::ICMP_SLT:
5868 if (RA.isMaxSignedValue()) {
5869 Pred = ICmpInst::ICMP_NE;
5873 if ((RA - 1).isMinSignedValue()) {
5874 Pred = ICmpInst::ICMP_EQ;
5875 RHS = getConstant(RA - 1);
5879 if (RA.isMinSignedValue()) goto trivially_false;
5884 // Check for obvious equality.
5885 if (HasSameValue(LHS, RHS)) {
5886 if (ICmpInst::isTrueWhenEqual(Pred))
5887 goto trivially_true;
5888 if (ICmpInst::isFalseWhenEqual(Pred))
5889 goto trivially_false;
5892 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5893 // adding or subtracting 1 from one of the operands.
5895 case ICmpInst::ICMP_SLE:
5896 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5897 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5899 Pred = ICmpInst::ICMP_SLT;
5901 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5902 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5904 Pred = ICmpInst::ICMP_SLT;
5908 case ICmpInst::ICMP_SGE:
5909 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5910 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5912 Pred = ICmpInst::ICMP_SGT;
5914 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5915 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5917 Pred = ICmpInst::ICMP_SGT;
5921 case ICmpInst::ICMP_ULE:
5922 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5923 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5925 Pred = ICmpInst::ICMP_ULT;
5927 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5928 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5930 Pred = ICmpInst::ICMP_ULT;
5934 case ICmpInst::ICMP_UGE:
5935 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5936 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5938 Pred = ICmpInst::ICMP_UGT;
5940 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5941 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5943 Pred = ICmpInst::ICMP_UGT;
5951 // TODO: More simplifications are possible here.
5953 // Recursively simplify until we either hit a recursion limit or nothing
5956 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
5962 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5963 Pred = ICmpInst::ICMP_EQ;
5968 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5969 Pred = ICmpInst::ICMP_NE;
5973 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5974 return getSignedRange(S).getSignedMax().isNegative();
5977 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5978 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5981 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5982 return !getSignedRange(S).getSignedMin().isNegative();
5985 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5986 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5989 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5990 return isKnownNegative(S) || isKnownPositive(S);
5993 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5994 const SCEV *LHS, const SCEV *RHS) {
5995 // Canonicalize the inputs first.
5996 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5998 // If LHS or RHS is an addrec, check to see if the condition is true in
5999 // every iteration of the loop.
6000 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
6001 if (isLoopEntryGuardedByCond(
6002 AR->getLoop(), Pred, AR->getStart(), RHS) &&
6003 isLoopBackedgeGuardedByCond(
6004 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
6006 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
6007 if (isLoopEntryGuardedByCond(
6008 AR->getLoop(), Pred, LHS, AR->getStart()) &&
6009 isLoopBackedgeGuardedByCond(
6010 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
6013 // Otherwise see what can be done with known constant ranges.
6014 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6018 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6019 const SCEV *LHS, const SCEV *RHS) {
6020 if (HasSameValue(LHS, RHS))
6021 return ICmpInst::isTrueWhenEqual(Pred);
6023 // This code is split out from isKnownPredicate because it is called from
6024 // within isLoopEntryGuardedByCond.
6027 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6028 case ICmpInst::ICMP_SGT:
6029 Pred = ICmpInst::ICMP_SLT;
6030 std::swap(LHS, RHS);
6031 case ICmpInst::ICMP_SLT: {
6032 ConstantRange LHSRange = getSignedRange(LHS);
6033 ConstantRange RHSRange = getSignedRange(RHS);
6034 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6036 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6040 case ICmpInst::ICMP_SGE:
6041 Pred = ICmpInst::ICMP_SLE;
6042 std::swap(LHS, RHS);
6043 case ICmpInst::ICMP_SLE: {
6044 ConstantRange LHSRange = getSignedRange(LHS);
6045 ConstantRange RHSRange = getSignedRange(RHS);
6046 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6048 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6052 case ICmpInst::ICMP_UGT:
6053 Pred = ICmpInst::ICMP_ULT;
6054 std::swap(LHS, RHS);
6055 case ICmpInst::ICMP_ULT: {
6056 ConstantRange LHSRange = getUnsignedRange(LHS);
6057 ConstantRange RHSRange = getUnsignedRange(RHS);
6058 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6060 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6064 case ICmpInst::ICMP_UGE:
6065 Pred = ICmpInst::ICMP_ULE;
6066 std::swap(LHS, RHS);
6067 case ICmpInst::ICMP_ULE: {
6068 ConstantRange LHSRange = getUnsignedRange(LHS);
6069 ConstantRange RHSRange = getUnsignedRange(RHS);
6070 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6072 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6076 case ICmpInst::ICMP_NE: {
6077 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6079 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6082 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6083 if (isKnownNonZero(Diff))
6087 case ICmpInst::ICMP_EQ:
6088 // The check at the top of the function catches the case where
6089 // the values are known to be equal.
6095 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6096 /// protected by a conditional between LHS and RHS. This is used to
6097 /// to eliminate casts.
6099 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6100 ICmpInst::Predicate Pred,
6101 const SCEV *LHS, const SCEV *RHS) {
6102 // Interpret a null as meaning no loop, where there is obviously no guard
6103 // (interprocedural conditions notwithstanding).
6104 if (!L) return true;
6106 BasicBlock *Latch = L->getLoopLatch();
6110 BranchInst *LoopContinuePredicate =
6111 dyn_cast<BranchInst>(Latch->getTerminator());
6112 if (!LoopContinuePredicate ||
6113 LoopContinuePredicate->isUnconditional())
6116 return isImpliedCond(Pred, LHS, RHS,
6117 LoopContinuePredicate->getCondition(),
6118 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6121 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6122 /// by a conditional between LHS and RHS. This is used to help avoid max
6123 /// expressions in loop trip counts, and to eliminate casts.
6125 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6126 ICmpInst::Predicate Pred,
6127 const SCEV *LHS, const SCEV *RHS) {
6128 // Interpret a null as meaning no loop, where there is obviously no guard
6129 // (interprocedural conditions notwithstanding).
6130 if (!L) return false;
6132 // Starting at the loop predecessor, climb up the predecessor chain, as long
6133 // as there are predecessors that can be found that have unique successors
6134 // leading to the original header.
6135 for (std::pair<BasicBlock *, BasicBlock *>
6136 Pair(L->getLoopPredecessor(), L->getHeader());
6138 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6140 BranchInst *LoopEntryPredicate =
6141 dyn_cast<BranchInst>(Pair.first->getTerminator());
6142 if (!LoopEntryPredicate ||
6143 LoopEntryPredicate->isUnconditional())
6146 if (isImpliedCond(Pred, LHS, RHS,
6147 LoopEntryPredicate->getCondition(),
6148 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6155 /// RAII wrapper to prevent recursive application of isImpliedCond.
6156 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6157 /// currently evaluating isImpliedCond.
6158 struct MarkPendingLoopPredicate {
6160 DenseSet<Value*> &LoopPreds;
6163 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6164 : Cond(C), LoopPreds(LP) {
6165 Pending = !LoopPreds.insert(Cond).second;
6167 ~MarkPendingLoopPredicate() {
6169 LoopPreds.erase(Cond);
6173 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6174 /// and RHS is true whenever the given Cond value evaluates to true.
6175 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6176 const SCEV *LHS, const SCEV *RHS,
6177 Value *FoundCondValue,
6179 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6183 // Recursively handle And and Or conditions.
6184 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6185 if (BO->getOpcode() == Instruction::And) {
6187 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6188 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6189 } else if (BO->getOpcode() == Instruction::Or) {
6191 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6192 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6196 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6197 if (!ICI) return false;
6199 // Bail if the ICmp's operands' types are wider than the needed type
6200 // before attempting to call getSCEV on them. This avoids infinite
6201 // recursion, since the analysis of widening casts can require loop
6202 // exit condition information for overflow checking, which would
6204 if (getTypeSizeInBits(LHS->getType()) <
6205 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6208 // Now that we found a conditional branch that dominates the loop or controls
6209 // the loop latch. Check to see if it is the comparison we are looking for.
6210 ICmpInst::Predicate FoundPred;
6212 FoundPred = ICI->getInversePredicate();
6214 FoundPred = ICI->getPredicate();
6216 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6217 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6219 // Balance the types. The case where FoundLHS' type is wider than
6220 // LHS' type is checked for above.
6221 if (getTypeSizeInBits(LHS->getType()) >
6222 getTypeSizeInBits(FoundLHS->getType())) {
6223 if (CmpInst::isSigned(Pred)) {
6224 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6225 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6227 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6228 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6232 // Canonicalize the query to match the way instcombine will have
6233 // canonicalized the comparison.
6234 if (SimplifyICmpOperands(Pred, LHS, RHS))
6236 return CmpInst::isTrueWhenEqual(Pred);
6237 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6238 if (FoundLHS == FoundRHS)
6239 return CmpInst::isFalseWhenEqual(FoundPred);
6241 // Check to see if we can make the LHS or RHS match.
6242 if (LHS == FoundRHS || RHS == FoundLHS) {
6243 if (isa<SCEVConstant>(RHS)) {
6244 std::swap(FoundLHS, FoundRHS);
6245 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6247 std::swap(LHS, RHS);
6248 Pred = ICmpInst::getSwappedPredicate(Pred);
6252 // Check whether the found predicate is the same as the desired predicate.
6253 if (FoundPred == Pred)
6254 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6256 // Check whether swapping the found predicate makes it the same as the
6257 // desired predicate.
6258 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6259 if (isa<SCEVConstant>(RHS))
6260 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6262 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6263 RHS, LHS, FoundLHS, FoundRHS);
6266 // Check whether the actual condition is beyond sufficient.
6267 if (FoundPred == ICmpInst::ICMP_EQ)
6268 if (ICmpInst::isTrueWhenEqual(Pred))
6269 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6271 if (Pred == ICmpInst::ICMP_NE)
6272 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6273 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6276 // Otherwise assume the worst.
6280 /// isImpliedCondOperands - Test whether the condition described by Pred,
6281 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6282 /// and FoundRHS is true.
6283 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6284 const SCEV *LHS, const SCEV *RHS,
6285 const SCEV *FoundLHS,
6286 const SCEV *FoundRHS) {
6287 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6288 FoundLHS, FoundRHS) ||
6289 // ~x < ~y --> x > y
6290 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6291 getNotSCEV(FoundRHS),
6292 getNotSCEV(FoundLHS));
6295 /// isImpliedCondOperandsHelper - Test whether the condition described by
6296 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6297 /// FoundLHS, and FoundRHS is true.
6299 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6300 const SCEV *LHS, const SCEV *RHS,
6301 const SCEV *FoundLHS,
6302 const SCEV *FoundRHS) {
6304 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6305 case ICmpInst::ICMP_EQ:
6306 case ICmpInst::ICMP_NE:
6307 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6310 case ICmpInst::ICMP_SLT:
6311 case ICmpInst::ICMP_SLE:
6312 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6313 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6316 case ICmpInst::ICMP_SGT:
6317 case ICmpInst::ICMP_SGE:
6318 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6319 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6322 case ICmpInst::ICMP_ULT:
6323 case ICmpInst::ICMP_ULE:
6324 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6325 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6328 case ICmpInst::ICMP_UGT:
6329 case ICmpInst::ICMP_UGE:
6330 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6331 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6339 /// getBECount - Subtract the end and start values and divide by the step,
6340 /// rounding up, to get the number of times the backedge is executed. Return
6341 /// CouldNotCompute if an intermediate computation overflows.
6342 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
6346 assert(!isKnownNegative(Step) &&
6347 "This code doesn't handle negative strides yet!");
6349 Type *Ty = Start->getType();
6351 // When Start == End, we have an exact BECount == 0. Short-circuit this case
6352 // here because SCEV may not be able to determine that the unsigned division
6353 // after rounding is zero.
6355 return getConstant(Ty, 0);
6357 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
6358 const SCEV *Diff = getMinusSCEV(End, Start);
6359 const SCEV *RoundUp = getAddExpr(Step, NegOne);
6361 // Add an adjustment to the difference between End and Start so that
6362 // the division will effectively round up.
6363 const SCEV *Add = getAddExpr(Diff, RoundUp);
6366 // Check Add for unsigned overflow.
6367 // TODO: More sophisticated things could be done here.
6368 Type *WideTy = IntegerType::get(getContext(),
6369 getTypeSizeInBits(Ty) + 1);
6370 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
6371 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
6372 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
6373 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
6374 return getCouldNotCompute();
6377 return getUDivExpr(Add, Step);
6380 /// HowManyLessThans - Return the number of times a backedge containing the
6381 /// specified less-than comparison will execute. If not computable, return
6382 /// CouldNotCompute.
6384 /// @param IsSubExpr is true when the LHS < RHS condition does not directly
6385 /// control the branch. In this case, we can only compute an iteration count for
6386 /// a subexpression that cannot overflow before evaluating true.
6387 ScalarEvolution::ExitLimit
6388 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6389 const Loop *L, bool isSigned,
6391 // Only handle: "ADDREC < LoopInvariant".
6392 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
6394 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
6395 if (!AddRec || AddRec->getLoop() != L)
6396 return getCouldNotCompute();
6398 // Check to see if we have a flag which makes analysis easy.
6399 bool NoWrap = false;
6401 NoWrap = AddRec->getNoWrapFlags(
6402 (SCEV::NoWrapFlags)(((isSigned ? SCEV::FlagNSW : SCEV::FlagNUW))
6405 if (AddRec->isAffine()) {
6406 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
6407 const SCEV *Step = AddRec->getStepRecurrence(*this);
6410 return getCouldNotCompute();
6411 if (Step->isOne()) {
6412 // With unit stride, the iteration never steps past the limit value.
6413 } else if (isKnownPositive(Step)) {
6414 // Test whether a positive iteration can step past the limit
6415 // value and past the maximum value for its type in a single step.
6416 // Note that it's not sufficient to check NoWrap here, because even
6417 // though the value after a wrap is undefined, it's not undefined
6418 // behavior, so if wrap does occur, the loop could either terminate or
6419 // loop infinitely, but in either case, the loop is guaranteed to
6420 // iterate at least until the iteration where the wrapping occurs.
6421 const SCEV *One = getConstant(Step->getType(), 1);
6423 APInt Max = APInt::getSignedMaxValue(BitWidth);
6424 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
6425 .slt(getSignedRange(RHS).getSignedMax()))
6426 return getCouldNotCompute();
6428 APInt Max = APInt::getMaxValue(BitWidth);
6429 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
6430 .ult(getUnsignedRange(RHS).getUnsignedMax()))
6431 return getCouldNotCompute();
6434 // TODO: Handle negative strides here and below.
6435 return getCouldNotCompute();
6437 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6438 // m. So, we count the number of iterations in which {n,+,s} < m is true.
6439 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6440 // treat m-n as signed nor unsigned due to overflow possibility.
6442 // First, we get the value of the LHS in the first iteration: n
6443 const SCEV *Start = AddRec->getOperand(0);
6445 // Determine the minimum constant start value.
6446 const SCEV *MinStart = getConstant(isSigned ?
6447 getSignedRange(Start).getSignedMin() :
6448 getUnsignedRange(Start).getUnsignedMin());
6450 // If we know that the condition is true in order to enter the loop,
6451 // then we know that it will run exactly (m-n)/s times. Otherwise, we
6452 // only know that it will execute (max(m,n)-n)/s times. In both cases,
6453 // the division must round up.
6454 const SCEV *End = RHS;
6455 if (!isLoopEntryGuardedByCond(L,
6456 isSigned ? ICmpInst::ICMP_SLT :
6458 getMinusSCEV(Start, Step), RHS))
6459 End = isSigned ? getSMaxExpr(RHS, Start)
6460 : getUMaxExpr(RHS, Start);
6462 // Determine the maximum constant end value.
6463 const SCEV *MaxEnd = getConstant(isSigned ?
6464 getSignedRange(End).getSignedMax() :
6465 getUnsignedRange(End).getUnsignedMax());
6467 // If MaxEnd is within a step of the maximum integer value in its type,
6468 // adjust it down to the minimum value which would produce the same effect.
6469 // This allows the subsequent ceiling division of (N+(step-1))/step to
6470 // compute the correct value.
6471 const SCEV *StepMinusOne = getMinusSCEV(Step,
6472 getConstant(Step->getType(), 1));
6475 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6478 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6481 // Finally, we subtract these two values and divide, rounding up, to get
6482 // the number of times the backedge is executed.
6483 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6485 // The maximum backedge count is similar, except using the minimum start
6486 // value and the maximum end value.
6487 // If we already have an exact constant BECount, use it instead.
6488 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6489 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6491 // If the stride is nonconstant, and NoWrap == true, then
6492 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6493 // exact BECount and invalid MaxBECount, which should be avoided to catch
6494 // more optimization opportunities.
6495 if (isa<SCEVCouldNotCompute>(MaxBECount))
6496 MaxBECount = BECount;
6498 return ExitLimit(BECount, MaxBECount);
6501 return getCouldNotCompute();
6504 /// getNumIterationsInRange - Return the number of iterations of this loop that
6505 /// produce values in the specified constant range. Another way of looking at
6506 /// this is that it returns the first iteration number where the value is not in
6507 /// the condition, thus computing the exit count. If the iteration count can't
6508 /// be computed, an instance of SCEVCouldNotCompute is returned.
6509 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6510 ScalarEvolution &SE) const {
6511 if (Range.isFullSet()) // Infinite loop.
6512 return SE.getCouldNotCompute();
6514 // If the start is a non-zero constant, shift the range to simplify things.
6515 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6516 if (!SC->getValue()->isZero()) {
6517 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6518 Operands[0] = SE.getConstant(SC->getType(), 0);
6519 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6520 getNoWrapFlags(FlagNW));
6521 if (const SCEVAddRecExpr *ShiftedAddRec =
6522 dyn_cast<SCEVAddRecExpr>(Shifted))
6523 return ShiftedAddRec->getNumIterationsInRange(
6524 Range.subtract(SC->getValue()->getValue()), SE);
6525 // This is strange and shouldn't happen.
6526 return SE.getCouldNotCompute();
6529 // The only time we can solve this is when we have all constant indices.
6530 // Otherwise, we cannot determine the overflow conditions.
6531 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6532 if (!isa<SCEVConstant>(getOperand(i)))
6533 return SE.getCouldNotCompute();
6536 // Okay at this point we know that all elements of the chrec are constants and
6537 // that the start element is zero.
6539 // First check to see if the range contains zero. If not, the first
6541 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6542 if (!Range.contains(APInt(BitWidth, 0)))
6543 return SE.getConstant(getType(), 0);
6546 // If this is an affine expression then we have this situation:
6547 // Solve {0,+,A} in Range === Ax in Range
6549 // We know that zero is in the range. If A is positive then we know that
6550 // the upper value of the range must be the first possible exit value.
6551 // If A is negative then the lower of the range is the last possible loop
6552 // value. Also note that we already checked for a full range.
6553 APInt One(BitWidth,1);
6554 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6555 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6557 // The exit value should be (End+A)/A.
6558 APInt ExitVal = (End + A).udiv(A);
6559 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6561 // Evaluate at the exit value. If we really did fall out of the valid
6562 // range, then we computed our trip count, otherwise wrap around or other
6563 // things must have happened.
6564 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6565 if (Range.contains(Val->getValue()))
6566 return SE.getCouldNotCompute(); // Something strange happened
6568 // Ensure that the previous value is in the range. This is a sanity check.
6569 assert(Range.contains(
6570 EvaluateConstantChrecAtConstant(this,
6571 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6572 "Linear scev computation is off in a bad way!");
6573 return SE.getConstant(ExitValue);
6574 } else if (isQuadratic()) {
6575 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6576 // quadratic equation to solve it. To do this, we must frame our problem in
6577 // terms of figuring out when zero is crossed, instead of when
6578 // Range.getUpper() is crossed.
6579 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6580 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6581 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6582 // getNoWrapFlags(FlagNW)
6585 // Next, solve the constructed addrec
6586 std::pair<const SCEV *,const SCEV *> Roots =
6587 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6588 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6589 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6591 // Pick the smallest positive root value.
6592 if (ConstantInt *CB =
6593 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6594 R1->getValue(), R2->getValue()))) {
6595 if (CB->getZExtValue() == false)
6596 std::swap(R1, R2); // R1 is the minimum root now.
6598 // Make sure the root is not off by one. The returned iteration should
6599 // not be in the range, but the previous one should be. When solving
6600 // for "X*X < 5", for example, we should not return a root of 2.
6601 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6604 if (Range.contains(R1Val->getValue())) {
6605 // The next iteration must be out of the range...
6606 ConstantInt *NextVal =
6607 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6609 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6610 if (!Range.contains(R1Val->getValue()))
6611 return SE.getConstant(NextVal);
6612 return SE.getCouldNotCompute(); // Something strange happened
6615 // If R1 was not in the range, then it is a good return value. Make
6616 // sure that R1-1 WAS in the range though, just in case.
6617 ConstantInt *NextVal =
6618 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6619 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6620 if (Range.contains(R1Val->getValue()))
6622 return SE.getCouldNotCompute(); // Something strange happened
6627 return SE.getCouldNotCompute();
6632 //===----------------------------------------------------------------------===//
6633 // SCEVCallbackVH Class Implementation
6634 //===----------------------------------------------------------------------===//
6636 void ScalarEvolution::SCEVCallbackVH::deleted() {
6637 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6638 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6639 SE->ConstantEvolutionLoopExitValue.erase(PN);
6640 SE->ValueExprMap.erase(getValPtr());
6641 // this now dangles!
6644 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6645 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6647 // Forget all the expressions associated with users of the old value,
6648 // so that future queries will recompute the expressions using the new
6650 Value *Old = getValPtr();
6651 SmallVector<User *, 16> Worklist;
6652 SmallPtrSet<User *, 8> Visited;
6653 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6655 Worklist.push_back(*UI);
6656 while (!Worklist.empty()) {
6657 User *U = Worklist.pop_back_val();
6658 // Deleting the Old value will cause this to dangle. Postpone
6659 // that until everything else is done.
6662 if (!Visited.insert(U))
6664 if (PHINode *PN = dyn_cast<PHINode>(U))
6665 SE->ConstantEvolutionLoopExitValue.erase(PN);
6666 SE->ValueExprMap.erase(U);
6667 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6669 Worklist.push_back(*UI);
6671 // Delete the Old value.
6672 if (PHINode *PN = dyn_cast<PHINode>(Old))
6673 SE->ConstantEvolutionLoopExitValue.erase(PN);
6674 SE->ValueExprMap.erase(Old);
6675 // this now dangles!
6678 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6679 : CallbackVH(V), SE(se) {}
6681 //===----------------------------------------------------------------------===//
6682 // ScalarEvolution Class Implementation
6683 //===----------------------------------------------------------------------===//
6685 ScalarEvolution::ScalarEvolution()
6686 : FunctionPass(ID), FirstUnknown(0) {
6687 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6690 bool ScalarEvolution::runOnFunction(Function &F) {
6692 LI = &getAnalysis<LoopInfo>();
6693 TD = getAnalysisIfAvailable<DataLayout>();
6694 TLI = &getAnalysis<TargetLibraryInfo>();
6695 DT = &getAnalysis<DominatorTree>();
6699 void ScalarEvolution::releaseMemory() {
6700 // Iterate through all the SCEVUnknown instances and call their
6701 // destructors, so that they release their references to their values.
6702 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6706 ValueExprMap.clear();
6708 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6709 // that a loop had multiple computable exits.
6710 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6711 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6716 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
6718 BackedgeTakenCounts.clear();
6719 ConstantEvolutionLoopExitValue.clear();
6720 ValuesAtScopes.clear();
6721 LoopDispositions.clear();
6722 BlockDispositions.clear();
6723 UnsignedRanges.clear();
6724 SignedRanges.clear();
6725 UniqueSCEVs.clear();
6726 SCEVAllocator.Reset();
6729 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6730 AU.setPreservesAll();
6731 AU.addRequiredTransitive<LoopInfo>();
6732 AU.addRequiredTransitive<DominatorTree>();
6733 AU.addRequired<TargetLibraryInfo>();
6736 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6737 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6740 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6742 // Print all inner loops first
6743 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6744 PrintLoopInfo(OS, SE, *I);
6747 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6750 SmallVector<BasicBlock *, 8> ExitBlocks;
6751 L->getExitBlocks(ExitBlocks);
6752 if (ExitBlocks.size() != 1)
6753 OS << "<multiple exits> ";
6755 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6756 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6758 OS << "Unpredictable backedge-taken count. ";
6763 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6766 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6767 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6769 OS << "Unpredictable max backedge-taken count. ";
6775 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6776 // ScalarEvolution's implementation of the print method is to print
6777 // out SCEV values of all instructions that are interesting. Doing
6778 // this potentially causes it to create new SCEV objects though,
6779 // which technically conflicts with the const qualifier. This isn't
6780 // observable from outside the class though, so casting away the
6781 // const isn't dangerous.
6782 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6784 OS << "Classifying expressions for: ";
6785 WriteAsOperand(OS, F, /*PrintType=*/false);
6787 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6788 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6791 const SCEV *SV = SE.getSCEV(&*I);
6794 const Loop *L = LI->getLoopFor((*I).getParent());
6796 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6803 OS << "\t\t" "Exits: ";
6804 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6805 if (!SE.isLoopInvariant(ExitValue, L)) {
6806 OS << "<<Unknown>>";
6815 OS << "Determining loop execution counts for: ";
6816 WriteAsOperand(OS, F, /*PrintType=*/false);
6818 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6819 PrintLoopInfo(OS, &SE, *I);
6822 ScalarEvolution::LoopDisposition
6823 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6824 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6825 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6826 Values.insert(std::make_pair(L, LoopVariant));
6828 return Pair.first->second;
6830 LoopDisposition D = computeLoopDisposition(S, L);
6831 return LoopDispositions[S][L] = D;
6834 ScalarEvolution::LoopDisposition
6835 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6836 switch (S->getSCEVType()) {
6838 return LoopInvariant;
6842 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6843 case scAddRecExpr: {
6844 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6846 // If L is the addrec's loop, it's computable.
6847 if (AR->getLoop() == L)
6848 return LoopComputable;
6850 // Add recurrences are never invariant in the function-body (null loop).
6854 // This recurrence is variant w.r.t. L if L contains AR's loop.
6855 if (L->contains(AR->getLoop()))
6858 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6859 if (AR->getLoop()->contains(L))
6860 return LoopInvariant;
6862 // This recurrence is variant w.r.t. L if any of its operands
6864 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6866 if (!isLoopInvariant(*I, L))
6869 // Otherwise it's loop-invariant.
6870 return LoopInvariant;
6876 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6877 bool HasVarying = false;
6878 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6880 LoopDisposition D = getLoopDisposition(*I, L);
6881 if (D == LoopVariant)
6883 if (D == LoopComputable)
6886 return HasVarying ? LoopComputable : LoopInvariant;
6889 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6890 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6891 if (LD == LoopVariant)
6893 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6894 if (RD == LoopVariant)
6896 return (LD == LoopInvariant && RD == LoopInvariant) ?
6897 LoopInvariant : LoopComputable;
6900 // All non-instruction values are loop invariant. All instructions are loop
6901 // invariant if they are not contained in the specified loop.
6902 // Instructions are never considered invariant in the function body
6903 // (null loop) because they are defined within the "loop".
6904 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6905 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6906 return LoopInvariant;
6907 case scCouldNotCompute:
6908 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6909 default: llvm_unreachable("Unknown SCEV kind!");
6913 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6914 return getLoopDisposition(S, L) == LoopInvariant;
6917 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6918 return getLoopDisposition(S, L) == LoopComputable;
6921 ScalarEvolution::BlockDisposition
6922 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6923 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6924 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6925 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6927 return Pair.first->second;
6929 BlockDisposition D = computeBlockDisposition(S, BB);
6930 return BlockDispositions[S][BB] = D;
6933 ScalarEvolution::BlockDisposition
6934 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6935 switch (S->getSCEVType()) {
6937 return ProperlyDominatesBlock;
6941 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6942 case scAddRecExpr: {
6943 // This uses a "dominates" query instead of "properly dominates" query
6944 // to test for proper dominance too, because the instruction which
6945 // produces the addrec's value is a PHI, and a PHI effectively properly
6946 // dominates its entire containing block.
6947 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6948 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6949 return DoesNotDominateBlock;
6951 // FALL THROUGH into SCEVNAryExpr handling.
6956 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6958 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6960 BlockDisposition D = getBlockDisposition(*I, BB);
6961 if (D == DoesNotDominateBlock)
6962 return DoesNotDominateBlock;
6963 if (D == DominatesBlock)
6966 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6969 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6970 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6971 BlockDisposition LD = getBlockDisposition(LHS, BB);
6972 if (LD == DoesNotDominateBlock)
6973 return DoesNotDominateBlock;
6974 BlockDisposition RD = getBlockDisposition(RHS, BB);
6975 if (RD == DoesNotDominateBlock)
6976 return DoesNotDominateBlock;
6977 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6978 ProperlyDominatesBlock : DominatesBlock;
6981 if (Instruction *I =
6982 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6983 if (I->getParent() == BB)
6984 return DominatesBlock;
6985 if (DT->properlyDominates(I->getParent(), BB))
6986 return ProperlyDominatesBlock;
6987 return DoesNotDominateBlock;
6989 return ProperlyDominatesBlock;
6990 case scCouldNotCompute:
6991 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6993 llvm_unreachable("Unknown SCEV kind!");
6997 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6998 return getBlockDisposition(S, BB) >= DominatesBlock;
7001 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
7002 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
7006 // Search for a SCEV expression node within an expression tree.
7007 // Implements SCEVTraversal::Visitor.
7012 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
7014 bool follow(const SCEV *S) {
7015 IsFound |= (S == Node);
7018 bool isDone() const { return IsFound; }
7022 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
7023 SCEVSearch Search(Op);
7024 visitAll(S, Search);
7025 return Search.IsFound;
7028 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
7029 ValuesAtScopes.erase(S);
7030 LoopDispositions.erase(S);
7031 BlockDispositions.erase(S);
7032 UnsignedRanges.erase(S);
7033 SignedRanges.erase(S);
7035 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7036 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
7037 BackedgeTakenInfo &BEInfo = I->second;
7038 if (BEInfo.hasOperand(S, this)) {
7040 BackedgeTakenCounts.erase(I++);
7047 typedef DenseMap<const Loop *, std::string> VerifyMap;
7049 /// replaceSubString - Replaces all occurences of From in Str with To.
7050 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
7052 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
7053 Str.replace(Pos, From.size(), To.data(), To.size());
7058 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
7060 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
7061 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
7062 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
7064 std::string &S = Map[L];
7066 raw_string_ostream OS(S);
7067 SE.getBackedgeTakenCount(L)->print(OS);
7069 // false and 0 are semantically equivalent. This can happen in dead loops.
7070 replaceSubString(OS.str(), "false", "0");
7071 // Remove wrap flags, their use in SCEV is highly fragile.
7072 // FIXME: Remove this when SCEV gets smarter about them.
7073 replaceSubString(OS.str(), "<nw>", "");
7074 replaceSubString(OS.str(), "<nsw>", "");
7075 replaceSubString(OS.str(), "<nuw>", "");
7080 void ScalarEvolution::verifyAnalysis() const {
7084 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7086 // Gather stringified backedge taken counts for all loops using SCEV's caches.
7087 // FIXME: It would be much better to store actual values instead of strings,
7088 // but SCEV pointers will change if we drop the caches.
7089 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
7090 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7091 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
7093 // Gather stringified backedge taken counts for all loops without using
7096 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7097 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
7099 // Now compare whether they're the same with and without caches. This allows
7100 // verifying that no pass changed the cache.
7101 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
7102 "New loops suddenly appeared!");
7104 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
7105 OldE = BackedgeDumpsOld.end(),
7106 NewI = BackedgeDumpsNew.begin();
7107 OldI != OldE; ++OldI, ++NewI) {
7108 assert(OldI->first == NewI->first && "Loop order changed!");
7110 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
7112 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
7113 // means that a pass is buggy or SCEV has to learn a new pattern but is
7114 // usually not harmful.
7115 if (OldI->second != NewI->second &&
7116 OldI->second.find("undef") == std::string::npos &&
7117 NewI->second.find("undef") == std::string::npos &&
7118 OldI->second != "***COULDNOTCOMPUTE***" &&
7119 NewI->second != "***COULDNOTCOMPUTE***") {
7120 dbgs() << "SCEVValidator: SCEV for loop '"
7121 << OldI->first->getHeader()->getName()
7122 << "' changed from '" << OldI->second
7123 << "' to '" << NewI->second << "'!\n";
7128 // TODO: Verify more things.