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 *IntTy, 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(IntTy, TD->getTypeAllocSize(AllocTy));
2600 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2601 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2602 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2604 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2605 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2606 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2609 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2612 // If we have DataLayout, we can bypass creating a target-independent
2613 // constant expression and then folding it back into a ConstantInt.
2614 // This is just a compile-time optimization.
2616 return getConstant(IntTy,
2617 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2620 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2621 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2622 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2625 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2626 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2629 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2630 // Don't attempt to do anything other than create a SCEVUnknown object
2631 // here. createSCEV only calls getUnknown after checking for all other
2632 // interesting possibilities, and any other code that calls getUnknown
2633 // is doing so in order to hide a value from SCEV canonicalization.
2635 FoldingSetNodeID ID;
2636 ID.AddInteger(scUnknown);
2639 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2640 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2641 "Stale SCEVUnknown in uniquing map!");
2644 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2646 FirstUnknown = cast<SCEVUnknown>(S);
2647 UniqueSCEVs.InsertNode(S, IP);
2651 //===----------------------------------------------------------------------===//
2652 // Basic SCEV Analysis and PHI Idiom Recognition Code
2655 /// isSCEVable - Test if values of the given type are analyzable within
2656 /// the SCEV framework. This primarily includes integer types, and it
2657 /// can optionally include pointer types if the ScalarEvolution class
2658 /// has access to target-specific information.
2659 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2660 // Integers and pointers are always SCEVable.
2661 return Ty->isIntegerTy() || Ty->isPointerTy();
2664 /// getTypeSizeInBits - Return the size in bits of the specified type,
2665 /// for which isSCEVable must return true.
2666 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2667 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2669 // If we have a DataLayout, use it!
2671 return TD->getTypeSizeInBits(Ty);
2673 // Integer types have fixed sizes.
2674 if (Ty->isIntegerTy())
2675 return Ty->getPrimitiveSizeInBits();
2677 // The only other support type is pointer. Without DataLayout, conservatively
2678 // assume pointers are 64-bit.
2679 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2683 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2684 /// the given type and which represents how SCEV will treat the given
2685 /// type, for which isSCEVable must return true. For pointer types,
2686 /// this is the pointer-sized integer type.
2687 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2688 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2690 if (Ty->isIntegerTy()) {
2694 // The only other support type is pointer.
2695 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2698 return TD->getIntPtrType(Ty);
2700 // Without DataLayout, conservatively assume pointers are 64-bit.
2701 return Type::getInt64Ty(getContext());
2704 const SCEV *ScalarEvolution::getCouldNotCompute() {
2705 return &CouldNotCompute;
2709 // Helper class working with SCEVTraversal to figure out if a SCEV contains
2710 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
2711 // is set iff if find such SCEVUnknown.
2713 struct FindInvalidSCEVUnknown {
2715 FindInvalidSCEVUnknown() { FindOne = false; }
2716 bool follow(const SCEV *S) {
2717 switch (S->getSCEVType()) {
2721 if (!cast<SCEVUnknown>(S)->getValue())
2728 bool isDone() const { return FindOne; }
2732 bool ScalarEvolution::checkValidity(const SCEV *S) const {
2733 FindInvalidSCEVUnknown F;
2734 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
2740 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2741 /// expression and create a new one.
2742 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2743 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2745 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
2746 if (I != ValueExprMap.end()) {
2747 const SCEV *S = I->second;
2748 if (checkValidity(S))
2751 ValueExprMap.erase(I);
2753 const SCEV *S = createSCEV(V);
2755 // The process of creating a SCEV for V may have caused other SCEVs
2756 // to have been created, so it's necessary to insert the new entry
2757 // from scratch, rather than trying to remember the insert position
2759 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2763 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2765 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2766 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2768 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2770 Type *Ty = V->getType();
2771 Ty = getEffectiveSCEVType(Ty);
2772 return getMulExpr(V,
2773 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2776 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2777 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2778 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2780 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2782 Type *Ty = V->getType();
2783 Ty = getEffectiveSCEVType(Ty);
2784 const SCEV *AllOnes =
2785 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2786 return getMinusSCEV(AllOnes, V);
2789 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2790 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2791 SCEV::NoWrapFlags Flags) {
2792 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2794 // Fast path: X - X --> 0.
2796 return getConstant(LHS->getType(), 0);
2799 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2802 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2803 /// input value to the specified type. If the type must be extended, it is zero
2806 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2807 Type *SrcTy = V->getType();
2808 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2809 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2810 "Cannot truncate or zero extend with non-integer arguments!");
2811 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2812 return V; // No conversion
2813 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2814 return getTruncateExpr(V, Ty);
2815 return getZeroExtendExpr(V, Ty);
2818 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2819 /// input value to the specified type. If the type must be extended, it is sign
2822 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2824 Type *SrcTy = V->getType();
2825 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2826 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2827 "Cannot truncate or zero extend with non-integer arguments!");
2828 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2829 return V; // No conversion
2830 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2831 return getTruncateExpr(V, Ty);
2832 return getSignExtendExpr(V, Ty);
2835 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2836 /// input value to the specified type. If the type must be extended, it is zero
2837 /// extended. The conversion must not be narrowing.
2839 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2840 Type *SrcTy = V->getType();
2841 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2842 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2843 "Cannot noop or zero extend with non-integer arguments!");
2844 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2845 "getNoopOrZeroExtend cannot truncate!");
2846 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2847 return V; // No conversion
2848 return getZeroExtendExpr(V, Ty);
2851 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2852 /// input value to the specified type. If the type must be extended, it is sign
2853 /// extended. The conversion must not be narrowing.
2855 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2856 Type *SrcTy = V->getType();
2857 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2858 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2859 "Cannot noop or sign extend with non-integer arguments!");
2860 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2861 "getNoopOrSignExtend cannot truncate!");
2862 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2863 return V; // No conversion
2864 return getSignExtendExpr(V, Ty);
2867 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2868 /// the input value to the specified type. If the type must be extended,
2869 /// it is extended with unspecified bits. The conversion must not be
2872 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2873 Type *SrcTy = V->getType();
2874 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2875 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2876 "Cannot noop or any extend with non-integer arguments!");
2877 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2878 "getNoopOrAnyExtend cannot truncate!");
2879 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2880 return V; // No conversion
2881 return getAnyExtendExpr(V, Ty);
2884 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2885 /// input value to the specified type. The conversion must not be widening.
2887 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2888 Type *SrcTy = V->getType();
2889 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2890 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2891 "Cannot truncate or noop with non-integer arguments!");
2892 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2893 "getTruncateOrNoop cannot extend!");
2894 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2895 return V; // No conversion
2896 return getTruncateExpr(V, Ty);
2899 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2900 /// the types using zero-extension, and then perform a umax operation
2902 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2904 const SCEV *PromotedLHS = LHS;
2905 const SCEV *PromotedRHS = RHS;
2907 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2908 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2910 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2912 return getUMaxExpr(PromotedLHS, PromotedRHS);
2915 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2916 /// the types using zero-extension, and then perform a umin operation
2918 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2920 const SCEV *PromotedLHS = LHS;
2921 const SCEV *PromotedRHS = RHS;
2923 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2924 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2926 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2928 return getUMinExpr(PromotedLHS, PromotedRHS);
2931 /// getPointerBase - Transitively follow the chain of pointer-type operands
2932 /// until reaching a SCEV that does not have a single pointer operand. This
2933 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2934 /// but corner cases do exist.
2935 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2936 // A pointer operand may evaluate to a nonpointer expression, such as null.
2937 if (!V->getType()->isPointerTy())
2940 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2941 return getPointerBase(Cast->getOperand());
2943 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2944 const SCEV *PtrOp = 0;
2945 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2947 if ((*I)->getType()->isPointerTy()) {
2948 // Cannot find the base of an expression with multiple pointer operands.
2956 return getPointerBase(PtrOp);
2961 /// PushDefUseChildren - Push users of the given Instruction
2962 /// onto the given Worklist.
2964 PushDefUseChildren(Instruction *I,
2965 SmallVectorImpl<Instruction *> &Worklist) {
2966 // Push the def-use children onto the Worklist stack.
2967 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2969 Worklist.push_back(cast<Instruction>(*UI));
2972 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2973 /// instructions that depend on the given instruction and removes them from
2974 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2977 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2978 SmallVector<Instruction *, 16> Worklist;
2979 PushDefUseChildren(PN, Worklist);
2981 SmallPtrSet<Instruction *, 8> Visited;
2983 while (!Worklist.empty()) {
2984 Instruction *I = Worklist.pop_back_val();
2985 if (!Visited.insert(I)) continue;
2987 ValueExprMapType::iterator It =
2988 ValueExprMap.find_as(static_cast<Value *>(I));
2989 if (It != ValueExprMap.end()) {
2990 const SCEV *Old = It->second;
2992 // Short-circuit the def-use traversal if the symbolic name
2993 // ceases to appear in expressions.
2994 if (Old != SymName && !hasOperand(Old, SymName))
2997 // SCEVUnknown for a PHI either means that it has an unrecognized
2998 // structure, it's a PHI that's in the progress of being computed
2999 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3000 // additional loop trip count information isn't going to change anything.
3001 // In the second case, createNodeForPHI will perform the necessary
3002 // updates on its own when it gets to that point. In the third, we do
3003 // want to forget the SCEVUnknown.
3004 if (!isa<PHINode>(I) ||
3005 !isa<SCEVUnknown>(Old) ||
3006 (I != PN && Old == SymName)) {
3007 forgetMemoizedResults(Old);
3008 ValueExprMap.erase(It);
3012 PushDefUseChildren(I, Worklist);
3016 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3017 /// a loop header, making it a potential recurrence, or it doesn't.
3019 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3020 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3021 if (L->getHeader() == PN->getParent()) {
3022 // The loop may have multiple entrances or multiple exits; we can analyze
3023 // this phi as an addrec if it has a unique entry value and a unique
3025 Value *BEValueV = 0, *StartValueV = 0;
3026 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3027 Value *V = PN->getIncomingValue(i);
3028 if (L->contains(PN->getIncomingBlock(i))) {
3031 } else if (BEValueV != V) {
3035 } else if (!StartValueV) {
3037 } else if (StartValueV != V) {
3042 if (BEValueV && StartValueV) {
3043 // While we are analyzing this PHI node, handle its value symbolically.
3044 const SCEV *SymbolicName = getUnknown(PN);
3045 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3046 "PHI node already processed?");
3047 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3049 // Using this symbolic name for the PHI, analyze the value coming around
3051 const SCEV *BEValue = getSCEV(BEValueV);
3053 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3054 // has a special value for the first iteration of the loop.
3056 // If the value coming around the backedge is an add with the symbolic
3057 // value we just inserted, then we found a simple induction variable!
3058 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3059 // If there is a single occurrence of the symbolic value, replace it
3060 // with a recurrence.
3061 unsigned FoundIndex = Add->getNumOperands();
3062 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3063 if (Add->getOperand(i) == SymbolicName)
3064 if (FoundIndex == e) {
3069 if (FoundIndex != Add->getNumOperands()) {
3070 // Create an add with everything but the specified operand.
3071 SmallVector<const SCEV *, 8> Ops;
3072 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3073 if (i != FoundIndex)
3074 Ops.push_back(Add->getOperand(i));
3075 const SCEV *Accum = getAddExpr(Ops);
3077 // This is not a valid addrec if the step amount is varying each
3078 // loop iteration, but is not itself an addrec in this loop.
3079 if (isLoopInvariant(Accum, L) ||
3080 (isa<SCEVAddRecExpr>(Accum) &&
3081 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3082 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3084 // If the increment doesn't overflow, then neither the addrec nor
3085 // the post-increment will overflow.
3086 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3087 if (OBO->hasNoUnsignedWrap())
3088 Flags = setFlags(Flags, SCEV::FlagNUW);
3089 if (OBO->hasNoSignedWrap())
3090 Flags = setFlags(Flags, SCEV::FlagNSW);
3091 } else if (const GEPOperator *GEP =
3092 dyn_cast<GEPOperator>(BEValueV)) {
3093 // If the increment is an inbounds GEP, then we know the address
3094 // space cannot be wrapped around. We cannot make any guarantee
3095 // about signed or unsigned overflow because pointers are
3096 // unsigned but we may have a negative index from the base
3098 if (GEP->isInBounds())
3099 Flags = setFlags(Flags, SCEV::FlagNW);
3102 const SCEV *StartVal = getSCEV(StartValueV);
3103 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3105 // Since the no-wrap flags are on the increment, they apply to the
3106 // post-incremented value as well.
3107 if (isLoopInvariant(Accum, L))
3108 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3111 // Okay, for the entire analysis of this edge we assumed the PHI
3112 // to be symbolic. We now need to go back and purge all of the
3113 // entries for the scalars that use the symbolic expression.
3114 ForgetSymbolicName(PN, SymbolicName);
3115 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3119 } else if (const SCEVAddRecExpr *AddRec =
3120 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3121 // Otherwise, this could be a loop like this:
3122 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3123 // In this case, j = {1,+,1} and BEValue is j.
3124 // Because the other in-value of i (0) fits the evolution of BEValue
3125 // i really is an addrec evolution.
3126 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3127 const SCEV *StartVal = getSCEV(StartValueV);
3129 // If StartVal = j.start - j.stride, we can use StartVal as the
3130 // initial step of the addrec evolution.
3131 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3132 AddRec->getOperand(1))) {
3133 // FIXME: For constant StartVal, we should be able to infer
3135 const SCEV *PHISCEV =
3136 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3139 // Okay, for the entire analysis of this edge we assumed the PHI
3140 // to be symbolic. We now need to go back and purge all of the
3141 // entries for the scalars that use the symbolic expression.
3142 ForgetSymbolicName(PN, SymbolicName);
3143 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3151 // If the PHI has a single incoming value, follow that value, unless the
3152 // PHI's incoming blocks are in a different loop, in which case doing so
3153 // risks breaking LCSSA form. Instcombine would normally zap these, but
3154 // it doesn't have DominatorTree information, so it may miss cases.
3155 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
3156 if (LI->replacementPreservesLCSSAForm(PN, V))
3159 // If it's not a loop phi, we can't handle it yet.
3160 return getUnknown(PN);
3163 /// createNodeForGEP - Expand GEP instructions into add and multiply
3164 /// operations. This allows them to be analyzed by regular SCEV code.
3166 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3167 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3168 Value *Base = GEP->getOperand(0);
3169 // Don't attempt to analyze GEPs over unsized objects.
3170 if (!Base->getType()->getPointerElementType()->isSized())
3171 return getUnknown(GEP);
3173 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3174 // Add expression, because the Instruction may be guarded by control flow
3175 // and the no-overflow bits may not be valid for the expression in any
3177 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3179 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3180 gep_type_iterator GTI = gep_type_begin(GEP);
3181 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3185 // Compute the (potentially symbolic) offset in bytes for this index.
3186 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3187 // For a struct, add the member offset.
3188 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3189 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3191 // Add the field offset to the running total offset.
3192 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3194 // For an array, add the element offset, explicitly scaled.
3195 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3196 const SCEV *IndexS = getSCEV(Index);
3197 // Getelementptr indices are signed.
3198 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3200 // Multiply the index by the element size to compute the element offset.
3201 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3203 // Add the element offset to the running total offset.
3204 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3208 // Get the SCEV for the GEP base.
3209 const SCEV *BaseS = getSCEV(Base);
3211 // Add the total offset from all the GEP indices to the base.
3212 return getAddExpr(BaseS, TotalOffset, Wrap);
3215 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3216 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3217 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3218 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3220 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3221 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3222 return C->getValue()->getValue().countTrailingZeros();
3224 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3225 return std::min(GetMinTrailingZeros(T->getOperand()),
3226 (uint32_t)getTypeSizeInBits(T->getType()));
3228 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3229 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3230 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3231 getTypeSizeInBits(E->getType()) : OpRes;
3234 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3235 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3236 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3237 getTypeSizeInBits(E->getType()) : OpRes;
3240 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3241 // The result is the min of all operands results.
3242 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3243 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3244 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3248 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3249 // The result is the sum of all operands results.
3250 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3251 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3252 for (unsigned i = 1, e = M->getNumOperands();
3253 SumOpRes != BitWidth && i != e; ++i)
3254 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3259 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3260 // The result is the min of all operands results.
3261 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3262 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3263 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3267 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3268 // The result is the min of all operands results.
3269 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3270 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3271 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3275 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3276 // The result is the min of all operands results.
3277 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3278 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3279 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3283 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3284 // For a SCEVUnknown, ask ValueTracking.
3285 unsigned BitWidth = getTypeSizeInBits(U->getType());
3286 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3287 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3288 return Zeros.countTrailingOnes();
3295 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3298 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3299 // See if we've computed this range already.
3300 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3301 if (I != UnsignedRanges.end())
3304 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3305 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3307 unsigned BitWidth = getTypeSizeInBits(S->getType());
3308 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3310 // If the value has known zeros, the maximum unsigned value will have those
3311 // known zeros as well.
3312 uint32_t TZ = GetMinTrailingZeros(S);
3314 ConservativeResult =
3315 ConstantRange(APInt::getMinValue(BitWidth),
3316 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3318 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3319 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3320 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3321 X = X.add(getUnsignedRange(Add->getOperand(i)));
3322 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3325 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3326 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3327 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3328 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3329 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3332 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3333 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3334 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3335 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3336 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3339 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3340 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3341 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3342 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3343 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3346 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3347 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3348 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3349 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3352 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3353 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3354 return setUnsignedRange(ZExt,
3355 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3358 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3359 ConstantRange X = getUnsignedRange(SExt->getOperand());
3360 return setUnsignedRange(SExt,
3361 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3364 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3365 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3366 return setUnsignedRange(Trunc,
3367 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3370 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3371 // If there's no unsigned wrap, the value will never be less than its
3373 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3374 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3375 if (!C->getValue()->isZero())
3376 ConservativeResult =
3377 ConservativeResult.intersectWith(
3378 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3380 // TODO: non-affine addrec
3381 if (AddRec->isAffine()) {
3382 Type *Ty = AddRec->getType();
3383 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3384 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3385 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3386 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3388 const SCEV *Start = AddRec->getStart();
3389 const SCEV *Step = AddRec->getStepRecurrence(*this);
3391 ConstantRange StartRange = getUnsignedRange(Start);
3392 ConstantRange StepRange = getSignedRange(Step);
3393 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3394 ConstantRange EndRange =
3395 StartRange.add(MaxBECountRange.multiply(StepRange));
3397 // Check for overflow. This must be done with ConstantRange arithmetic
3398 // because we could be called from within the ScalarEvolution overflow
3400 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3401 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3402 ConstantRange ExtMaxBECountRange =
3403 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3404 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3405 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3407 return setUnsignedRange(AddRec, ConservativeResult);
3409 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3410 EndRange.getUnsignedMin());
3411 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3412 EndRange.getUnsignedMax());
3413 if (Min.isMinValue() && Max.isMaxValue())
3414 return setUnsignedRange(AddRec, ConservativeResult);
3415 return setUnsignedRange(AddRec,
3416 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3420 return setUnsignedRange(AddRec, ConservativeResult);
3423 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3424 // For a SCEVUnknown, ask ValueTracking.
3425 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3426 ComputeMaskedBits(U->getValue(), Zeros, Ones, TD);
3427 if (Ones == ~Zeros + 1)
3428 return setUnsignedRange(U, ConservativeResult);
3429 return setUnsignedRange(U,
3430 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3433 return setUnsignedRange(S, ConservativeResult);
3436 /// getSignedRange - Determine the signed range for a particular SCEV.
3439 ScalarEvolution::getSignedRange(const SCEV *S) {
3440 // See if we've computed this range already.
3441 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3442 if (I != SignedRanges.end())
3445 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3446 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3448 unsigned BitWidth = getTypeSizeInBits(S->getType());
3449 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3451 // If the value has known zeros, the maximum signed value will have those
3452 // known zeros as well.
3453 uint32_t TZ = GetMinTrailingZeros(S);
3455 ConservativeResult =
3456 ConstantRange(APInt::getSignedMinValue(BitWidth),
3457 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3459 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3460 ConstantRange X = getSignedRange(Add->getOperand(0));
3461 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3462 X = X.add(getSignedRange(Add->getOperand(i)));
3463 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3466 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3467 ConstantRange X = getSignedRange(Mul->getOperand(0));
3468 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3469 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3470 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3473 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3474 ConstantRange X = getSignedRange(SMax->getOperand(0));
3475 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3476 X = X.smax(getSignedRange(SMax->getOperand(i)));
3477 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3480 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3481 ConstantRange X = getSignedRange(UMax->getOperand(0));
3482 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3483 X = X.umax(getSignedRange(UMax->getOperand(i)));
3484 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3487 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3488 ConstantRange X = getSignedRange(UDiv->getLHS());
3489 ConstantRange Y = getSignedRange(UDiv->getRHS());
3490 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3493 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3494 ConstantRange X = getSignedRange(ZExt->getOperand());
3495 return setSignedRange(ZExt,
3496 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3499 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3500 ConstantRange X = getSignedRange(SExt->getOperand());
3501 return setSignedRange(SExt,
3502 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3505 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3506 ConstantRange X = getSignedRange(Trunc->getOperand());
3507 return setSignedRange(Trunc,
3508 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3511 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3512 // If there's no signed wrap, and all the operands have the same sign or
3513 // zero, the value won't ever change sign.
3514 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3515 bool AllNonNeg = true;
3516 bool AllNonPos = true;
3517 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3518 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3519 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3522 ConservativeResult = ConservativeResult.intersectWith(
3523 ConstantRange(APInt(BitWidth, 0),
3524 APInt::getSignedMinValue(BitWidth)));
3526 ConservativeResult = ConservativeResult.intersectWith(
3527 ConstantRange(APInt::getSignedMinValue(BitWidth),
3528 APInt(BitWidth, 1)));
3531 // TODO: non-affine addrec
3532 if (AddRec->isAffine()) {
3533 Type *Ty = AddRec->getType();
3534 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3535 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3536 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3537 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3539 const SCEV *Start = AddRec->getStart();
3540 const SCEV *Step = AddRec->getStepRecurrence(*this);
3542 ConstantRange StartRange = getSignedRange(Start);
3543 ConstantRange StepRange = getSignedRange(Step);
3544 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3545 ConstantRange EndRange =
3546 StartRange.add(MaxBECountRange.multiply(StepRange));
3548 // Check for overflow. This must be done with ConstantRange arithmetic
3549 // because we could be called from within the ScalarEvolution overflow
3551 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3552 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3553 ConstantRange ExtMaxBECountRange =
3554 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3555 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3556 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3558 return setSignedRange(AddRec, ConservativeResult);
3560 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3561 EndRange.getSignedMin());
3562 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3563 EndRange.getSignedMax());
3564 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3565 return setSignedRange(AddRec, ConservativeResult);
3566 return setSignedRange(AddRec,
3567 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3571 return setSignedRange(AddRec, ConservativeResult);
3574 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3575 // For a SCEVUnknown, ask ValueTracking.
3576 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3577 return setSignedRange(U, ConservativeResult);
3578 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3580 return setSignedRange(U, ConservativeResult);
3581 return setSignedRange(U, ConservativeResult.intersectWith(
3582 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3583 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3586 return setSignedRange(S, ConservativeResult);
3589 /// createSCEV - We know that there is no SCEV for the specified value.
3590 /// Analyze the expression.
3592 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3593 if (!isSCEVable(V->getType()))
3594 return getUnknown(V);
3596 unsigned Opcode = Instruction::UserOp1;
3597 if (Instruction *I = dyn_cast<Instruction>(V)) {
3598 Opcode = I->getOpcode();
3600 // Don't attempt to analyze instructions in blocks that aren't
3601 // reachable. Such instructions don't matter, and they aren't required
3602 // to obey basic rules for definitions dominating uses which this
3603 // analysis depends on.
3604 if (!DT->isReachableFromEntry(I->getParent()))
3605 return getUnknown(V);
3606 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3607 Opcode = CE->getOpcode();
3608 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3609 return getConstant(CI);
3610 else if (isa<ConstantPointerNull>(V))
3611 return getConstant(V->getType(), 0);
3612 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3613 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3615 return getUnknown(V);
3617 Operator *U = cast<Operator>(V);
3619 case Instruction::Add: {
3620 // The simple thing to do would be to just call getSCEV on both operands
3621 // and call getAddExpr with the result. However if we're looking at a
3622 // bunch of things all added together, this can be quite inefficient,
3623 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3624 // Instead, gather up all the operands and make a single getAddExpr call.
3625 // LLVM IR canonical form means we need only traverse the left operands.
3627 // Don't apply this instruction's NSW or NUW flags to the new
3628 // expression. The instruction may be guarded by control flow that the
3629 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3630 // mapped to the same SCEV expression, and it would be incorrect to transfer
3631 // NSW/NUW semantics to those operations.
3632 SmallVector<const SCEV *, 4> AddOps;
3633 AddOps.push_back(getSCEV(U->getOperand(1)));
3634 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3635 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3636 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3638 U = cast<Operator>(Op);
3639 const SCEV *Op1 = getSCEV(U->getOperand(1));
3640 if (Opcode == Instruction::Sub)
3641 AddOps.push_back(getNegativeSCEV(Op1));
3643 AddOps.push_back(Op1);
3645 AddOps.push_back(getSCEV(U->getOperand(0)));
3646 return getAddExpr(AddOps);
3648 case Instruction::Mul: {
3649 // Don't transfer NSW/NUW for the same reason as AddExpr.
3650 SmallVector<const SCEV *, 4> MulOps;
3651 MulOps.push_back(getSCEV(U->getOperand(1)));
3652 for (Value *Op = U->getOperand(0);
3653 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3654 Op = U->getOperand(0)) {
3655 U = cast<Operator>(Op);
3656 MulOps.push_back(getSCEV(U->getOperand(1)));
3658 MulOps.push_back(getSCEV(U->getOperand(0)));
3659 return getMulExpr(MulOps);
3661 case Instruction::UDiv:
3662 return getUDivExpr(getSCEV(U->getOperand(0)),
3663 getSCEV(U->getOperand(1)));
3664 case Instruction::Sub:
3665 return getMinusSCEV(getSCEV(U->getOperand(0)),
3666 getSCEV(U->getOperand(1)));
3667 case Instruction::And:
3668 // For an expression like x&255 that merely masks off the high bits,
3669 // use zext(trunc(x)) as the SCEV expression.
3670 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3671 if (CI->isNullValue())
3672 return getSCEV(U->getOperand(1));
3673 if (CI->isAllOnesValue())
3674 return getSCEV(U->getOperand(0));
3675 const APInt &A = CI->getValue();
3677 // Instcombine's ShrinkDemandedConstant may strip bits out of
3678 // constants, obscuring what would otherwise be a low-bits mask.
3679 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3680 // knew about to reconstruct a low-bits mask value.
3681 unsigned LZ = A.countLeadingZeros();
3682 unsigned BitWidth = A.getBitWidth();
3683 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3684 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD);
3686 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3688 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3690 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3691 IntegerType::get(getContext(), BitWidth - LZ)),
3696 case Instruction::Or:
3697 // If the RHS of the Or is a constant, we may have something like:
3698 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3699 // optimizations will transparently handle this case.
3701 // In order for this transformation to be safe, the LHS must be of the
3702 // form X*(2^n) and the Or constant must be less than 2^n.
3703 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3704 const SCEV *LHS = getSCEV(U->getOperand(0));
3705 const APInt &CIVal = CI->getValue();
3706 if (GetMinTrailingZeros(LHS) >=
3707 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3708 // Build a plain add SCEV.
3709 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3710 // If the LHS of the add was an addrec and it has no-wrap flags,
3711 // transfer the no-wrap flags, since an or won't introduce a wrap.
3712 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3713 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3714 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3715 OldAR->getNoWrapFlags());
3721 case Instruction::Xor:
3722 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3723 // If the RHS of the xor is a signbit, then this is just an add.
3724 // Instcombine turns add of signbit into xor as a strength reduction step.
3725 if (CI->getValue().isSignBit())
3726 return getAddExpr(getSCEV(U->getOperand(0)),
3727 getSCEV(U->getOperand(1)));
3729 // If the RHS of xor is -1, then this is a not operation.
3730 if (CI->isAllOnesValue())
3731 return getNotSCEV(getSCEV(U->getOperand(0)));
3733 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3734 // This is a variant of the check for xor with -1, and it handles
3735 // the case where instcombine has trimmed non-demanded bits out
3736 // of an xor with -1.
3737 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3738 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3739 if (BO->getOpcode() == Instruction::And &&
3740 LCI->getValue() == CI->getValue())
3741 if (const SCEVZeroExtendExpr *Z =
3742 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3743 Type *UTy = U->getType();
3744 const SCEV *Z0 = Z->getOperand();
3745 Type *Z0Ty = Z0->getType();
3746 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3748 // If C is a low-bits mask, the zero extend is serving to
3749 // mask off the high bits. Complement the operand and
3750 // re-apply the zext.
3751 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3752 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3754 // If C is a single bit, it may be in the sign-bit position
3755 // before the zero-extend. In this case, represent the xor
3756 // using an add, which is equivalent, and re-apply the zext.
3757 APInt Trunc = CI->getValue().trunc(Z0TySize);
3758 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3760 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3766 case Instruction::Shl:
3767 // Turn shift left of a constant amount into a multiply.
3768 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3769 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3771 // If the shift count is not less than the bitwidth, the result of
3772 // the shift is undefined. Don't try to analyze it, because the
3773 // resolution chosen here may differ from the resolution chosen in
3774 // other parts of the compiler.
3775 if (SA->getValue().uge(BitWidth))
3778 Constant *X = ConstantInt::get(getContext(),
3779 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3780 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3784 case Instruction::LShr:
3785 // Turn logical shift right of a constant into a unsigned divide.
3786 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3787 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3789 // If the shift count is not less than the bitwidth, the result of
3790 // the shift is undefined. Don't try to analyze it, because the
3791 // resolution chosen here may differ from the resolution chosen in
3792 // other parts of the compiler.
3793 if (SA->getValue().uge(BitWidth))
3796 Constant *X = ConstantInt::get(getContext(),
3797 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3798 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3802 case Instruction::AShr:
3803 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3804 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3805 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3806 if (L->getOpcode() == Instruction::Shl &&
3807 L->getOperand(1) == U->getOperand(1)) {
3808 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3810 // If the shift count is not less than the bitwidth, the result of
3811 // the shift is undefined. Don't try to analyze it, because the
3812 // resolution chosen here may differ from the resolution chosen in
3813 // other parts of the compiler.
3814 if (CI->getValue().uge(BitWidth))
3817 uint64_t Amt = BitWidth - CI->getZExtValue();
3818 if (Amt == BitWidth)
3819 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3821 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3822 IntegerType::get(getContext(),
3828 case Instruction::Trunc:
3829 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3831 case Instruction::ZExt:
3832 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3834 case Instruction::SExt:
3835 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3837 case Instruction::BitCast:
3838 // BitCasts are no-op casts so we just eliminate the cast.
3839 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3840 return getSCEV(U->getOperand(0));
3843 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3844 // lead to pointer expressions which cannot safely be expanded to GEPs,
3845 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3846 // simplifying integer expressions.
3848 case Instruction::GetElementPtr:
3849 return createNodeForGEP(cast<GEPOperator>(U));
3851 case Instruction::PHI:
3852 return createNodeForPHI(cast<PHINode>(U));
3854 case Instruction::Select:
3855 // This could be a smax or umax that was lowered earlier.
3856 // Try to recover it.
3857 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3858 Value *LHS = ICI->getOperand(0);
3859 Value *RHS = ICI->getOperand(1);
3860 switch (ICI->getPredicate()) {
3861 case ICmpInst::ICMP_SLT:
3862 case ICmpInst::ICMP_SLE:
3863 std::swap(LHS, RHS);
3865 case ICmpInst::ICMP_SGT:
3866 case ICmpInst::ICMP_SGE:
3867 // a >s b ? a+x : b+x -> smax(a, b)+x
3868 // a >s b ? b+x : a+x -> smin(a, b)+x
3869 if (LHS->getType() == U->getType()) {
3870 const SCEV *LS = getSCEV(LHS);
3871 const SCEV *RS = getSCEV(RHS);
3872 const SCEV *LA = getSCEV(U->getOperand(1));
3873 const SCEV *RA = getSCEV(U->getOperand(2));
3874 const SCEV *LDiff = getMinusSCEV(LA, LS);
3875 const SCEV *RDiff = getMinusSCEV(RA, RS);
3877 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3878 LDiff = getMinusSCEV(LA, RS);
3879 RDiff = getMinusSCEV(RA, LS);
3881 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3884 case ICmpInst::ICMP_ULT:
3885 case ICmpInst::ICMP_ULE:
3886 std::swap(LHS, RHS);
3888 case ICmpInst::ICMP_UGT:
3889 case ICmpInst::ICMP_UGE:
3890 // a >u b ? a+x : b+x -> umax(a, b)+x
3891 // a >u b ? b+x : a+x -> umin(a, b)+x
3892 if (LHS->getType() == U->getType()) {
3893 const SCEV *LS = getSCEV(LHS);
3894 const SCEV *RS = getSCEV(RHS);
3895 const SCEV *LA = getSCEV(U->getOperand(1));
3896 const SCEV *RA = getSCEV(U->getOperand(2));
3897 const SCEV *LDiff = getMinusSCEV(LA, LS);
3898 const SCEV *RDiff = getMinusSCEV(RA, RS);
3900 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3901 LDiff = getMinusSCEV(LA, RS);
3902 RDiff = getMinusSCEV(RA, LS);
3904 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3907 case ICmpInst::ICMP_NE:
3908 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3909 if (LHS->getType() == U->getType() &&
3910 isa<ConstantInt>(RHS) &&
3911 cast<ConstantInt>(RHS)->isZero()) {
3912 const SCEV *One = getConstant(LHS->getType(), 1);
3913 const SCEV *LS = getSCEV(LHS);
3914 const SCEV *LA = getSCEV(U->getOperand(1));
3915 const SCEV *RA = getSCEV(U->getOperand(2));
3916 const SCEV *LDiff = getMinusSCEV(LA, LS);
3917 const SCEV *RDiff = getMinusSCEV(RA, One);
3919 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3922 case ICmpInst::ICMP_EQ:
3923 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3924 if (LHS->getType() == U->getType() &&
3925 isa<ConstantInt>(RHS) &&
3926 cast<ConstantInt>(RHS)->isZero()) {
3927 const SCEV *One = getConstant(LHS->getType(), 1);
3928 const SCEV *LS = getSCEV(LHS);
3929 const SCEV *LA = getSCEV(U->getOperand(1));
3930 const SCEV *RA = getSCEV(U->getOperand(2));
3931 const SCEV *LDiff = getMinusSCEV(LA, One);
3932 const SCEV *RDiff = getMinusSCEV(RA, LS);
3934 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3942 default: // We cannot analyze this expression.
3946 return getUnknown(V);
3951 //===----------------------------------------------------------------------===//
3952 // Iteration Count Computation Code
3955 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3956 /// normal unsigned value. Returns 0 if the trip count is unknown or not
3957 /// constant. Will also return 0 if the maximum trip count is very large (>=
3960 /// This "trip count" assumes that control exits via ExitingBlock. More
3961 /// precisely, it is the number of times that control may reach ExitingBlock
3962 /// before taking the branch. For loops with multiple exits, it may not be the
3963 /// number times that the loop header executes because the loop may exit
3964 /// prematurely via another branch.
3966 /// FIXME: We conservatively call getBackedgeTakenCount(L) instead of
3967 /// getExitCount(L, ExitingBlock) to compute a safe trip count considering all
3968 /// loop exits. getExitCount() may return an exact count for this branch
3969 /// assuming no-signed-wrap. The number of well-defined iterations may actually
3970 /// be higher than this trip count if this exit test is skipped and the loop
3971 /// exits via a different branch. Ideally, getExitCount() would know whether it
3972 /// depends on a NSW assumption, and we would only fall back to a conservative
3973 /// trip count in that case.
3974 unsigned ScalarEvolution::
3975 getSmallConstantTripCount(Loop *L, BasicBlock * /*ExitingBlock*/) {
3976 const SCEVConstant *ExitCount =
3977 dyn_cast<SCEVConstant>(getBackedgeTakenCount(L));
3981 ConstantInt *ExitConst = ExitCount->getValue();
3983 // Guard against huge trip counts.
3984 if (ExitConst->getValue().getActiveBits() > 32)
3987 // In case of integer overflow, this returns 0, which is correct.
3988 return ((unsigned)ExitConst->getZExtValue()) + 1;
3991 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3992 /// trip count of this loop as a normal unsigned value, if possible. This
3993 /// means that the actual trip count is always a multiple of the returned
3994 /// value (don't forget the trip count could very well be zero as well!).
3996 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3997 /// multiple of a constant (which is also the case if the trip count is simply
3998 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3999 /// if the trip count is very large (>= 2^32).
4001 /// As explained in the comments for getSmallConstantTripCount, this assumes
4002 /// that control exits the loop via ExitingBlock.
4003 unsigned ScalarEvolution::
4004 getSmallConstantTripMultiple(Loop *L, BasicBlock * /*ExitingBlock*/) {
4005 const SCEV *ExitCount = getBackedgeTakenCount(L);
4006 if (ExitCount == getCouldNotCompute())
4009 // Get the trip count from the BE count by adding 1.
4010 const SCEV *TCMul = getAddExpr(ExitCount,
4011 getConstant(ExitCount->getType(), 1));
4012 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4013 // to factor simple cases.
4014 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4015 TCMul = Mul->getOperand(0);
4017 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4021 ConstantInt *Result = MulC->getValue();
4023 // Guard against huge trip counts (this requires checking
4024 // for zero to handle the case where the trip count == -1 and the
4026 if (!Result || Result->getValue().getActiveBits() > 32 ||
4027 Result->getValue().getActiveBits() == 0)
4030 return (unsigned)Result->getZExtValue();
4033 // getExitCount - Get the expression for the number of loop iterations for which
4034 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4035 // SCEVCouldNotCompute.
4036 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4037 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4040 /// getBackedgeTakenCount - If the specified loop has a predictable
4041 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4042 /// object. The backedge-taken count is the number of times the loop header
4043 /// will be branched to from within the loop. This is one less than the
4044 /// trip count of the loop, since it doesn't count the first iteration,
4045 /// when the header is branched to from outside the loop.
4047 /// Note that it is not valid to call this method on a loop without a
4048 /// loop-invariant backedge-taken count (see
4049 /// hasLoopInvariantBackedgeTakenCount).
4051 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4052 return getBackedgeTakenInfo(L).getExact(this);
4055 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4056 /// return the least SCEV value that is known never to be less than the
4057 /// actual backedge taken count.
4058 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4059 return getBackedgeTakenInfo(L).getMax(this);
4062 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4063 /// onto the given Worklist.
4065 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4066 BasicBlock *Header = L->getHeader();
4068 // Push all Loop-header PHIs onto the Worklist stack.
4069 for (BasicBlock::iterator I = Header->begin();
4070 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4071 Worklist.push_back(PN);
4074 const ScalarEvolution::BackedgeTakenInfo &
4075 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4076 // Initially insert an invalid entry for this loop. If the insertion
4077 // succeeds, proceed to actually compute a backedge-taken count and
4078 // update the value. The temporary CouldNotCompute value tells SCEV
4079 // code elsewhere that it shouldn't attempt to request a new
4080 // backedge-taken count, which could result in infinite recursion.
4081 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4082 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4084 return Pair.first->second;
4086 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4087 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4088 // must be cleared in this scope.
4089 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4091 if (Result.getExact(this) != getCouldNotCompute()) {
4092 assert(isLoopInvariant(Result.getExact(this), L) &&
4093 isLoopInvariant(Result.getMax(this), L) &&
4094 "Computed backedge-taken count isn't loop invariant for loop!");
4095 ++NumTripCountsComputed;
4097 else if (Result.getMax(this) == getCouldNotCompute() &&
4098 isa<PHINode>(L->getHeader()->begin())) {
4099 // Only count loops that have phi nodes as not being computable.
4100 ++NumTripCountsNotComputed;
4103 // Now that we know more about the trip count for this loop, forget any
4104 // existing SCEV values for PHI nodes in this loop since they are only
4105 // conservative estimates made without the benefit of trip count
4106 // information. This is similar to the code in forgetLoop, except that
4107 // it handles SCEVUnknown PHI nodes specially.
4108 if (Result.hasAnyInfo()) {
4109 SmallVector<Instruction *, 16> Worklist;
4110 PushLoopPHIs(L, Worklist);
4112 SmallPtrSet<Instruction *, 8> Visited;
4113 while (!Worklist.empty()) {
4114 Instruction *I = Worklist.pop_back_val();
4115 if (!Visited.insert(I)) continue;
4117 ValueExprMapType::iterator It =
4118 ValueExprMap.find_as(static_cast<Value *>(I));
4119 if (It != ValueExprMap.end()) {
4120 const SCEV *Old = It->second;
4122 // SCEVUnknown for a PHI either means that it has an unrecognized
4123 // structure, or it's a PHI that's in the progress of being computed
4124 // by createNodeForPHI. In the former case, additional loop trip
4125 // count information isn't going to change anything. In the later
4126 // case, createNodeForPHI will perform the necessary updates on its
4127 // own when it gets to that point.
4128 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4129 forgetMemoizedResults(Old);
4130 ValueExprMap.erase(It);
4132 if (PHINode *PN = dyn_cast<PHINode>(I))
4133 ConstantEvolutionLoopExitValue.erase(PN);
4136 PushDefUseChildren(I, Worklist);
4140 // Re-lookup the insert position, since the call to
4141 // ComputeBackedgeTakenCount above could result in a
4142 // recusive call to getBackedgeTakenInfo (on a different
4143 // loop), which would invalidate the iterator computed
4145 return BackedgeTakenCounts.find(L)->second = Result;
4148 /// forgetLoop - This method should be called by the client when it has
4149 /// changed a loop in a way that may effect ScalarEvolution's ability to
4150 /// compute a trip count, or if the loop is deleted.
4151 void ScalarEvolution::forgetLoop(const Loop *L) {
4152 // Drop any stored trip count value.
4153 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4154 BackedgeTakenCounts.find(L);
4155 if (BTCPos != BackedgeTakenCounts.end()) {
4156 BTCPos->second.clear();
4157 BackedgeTakenCounts.erase(BTCPos);
4160 // Drop information about expressions based on loop-header PHIs.
4161 SmallVector<Instruction *, 16> Worklist;
4162 PushLoopPHIs(L, Worklist);
4164 SmallPtrSet<Instruction *, 8> Visited;
4165 while (!Worklist.empty()) {
4166 Instruction *I = Worklist.pop_back_val();
4167 if (!Visited.insert(I)) continue;
4169 ValueExprMapType::iterator It =
4170 ValueExprMap.find_as(static_cast<Value *>(I));
4171 if (It != ValueExprMap.end()) {
4172 forgetMemoizedResults(It->second);
4173 ValueExprMap.erase(It);
4174 if (PHINode *PN = dyn_cast<PHINode>(I))
4175 ConstantEvolutionLoopExitValue.erase(PN);
4178 PushDefUseChildren(I, Worklist);
4181 // Forget all contained loops too, to avoid dangling entries in the
4182 // ValuesAtScopes map.
4183 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4187 /// forgetValue - This method should be called by the client when it has
4188 /// changed a value in a way that may effect its value, or which may
4189 /// disconnect it from a def-use chain linking it to a loop.
4190 void ScalarEvolution::forgetValue(Value *V) {
4191 Instruction *I = dyn_cast<Instruction>(V);
4194 // Drop information about expressions based on loop-header PHIs.
4195 SmallVector<Instruction *, 16> Worklist;
4196 Worklist.push_back(I);
4198 SmallPtrSet<Instruction *, 8> Visited;
4199 while (!Worklist.empty()) {
4200 I = Worklist.pop_back_val();
4201 if (!Visited.insert(I)) continue;
4203 ValueExprMapType::iterator It =
4204 ValueExprMap.find_as(static_cast<Value *>(I));
4205 if (It != ValueExprMap.end()) {
4206 forgetMemoizedResults(It->second);
4207 ValueExprMap.erase(It);
4208 if (PHINode *PN = dyn_cast<PHINode>(I))
4209 ConstantEvolutionLoopExitValue.erase(PN);
4212 PushDefUseChildren(I, Worklist);
4216 /// getExact - Get the exact loop backedge taken count considering all loop
4217 /// exits. A computable result can only be return for loops with a single exit.
4218 /// Returning the minimum taken count among all exits is incorrect because one
4219 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4220 /// the limit of each loop test is never skipped. This is a valid assumption as
4221 /// long as the loop exits via that test. For precise results, it is the
4222 /// caller's responsibility to specify the relevant loop exit using
4223 /// getExact(ExitingBlock, SE).
4225 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4226 // If any exits were not computable, the loop is not computable.
4227 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4229 // We need exactly one computable exit.
4230 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4231 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4233 const SCEV *BECount = 0;
4234 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4235 ENT != 0; ENT = ENT->getNextExit()) {
4237 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4240 BECount = ENT->ExactNotTaken;
4241 else if (BECount != ENT->ExactNotTaken)
4242 return SE->getCouldNotCompute();
4244 assert(BECount && "Invalid not taken count for loop exit");
4248 /// getExact - Get the exact not taken count for this loop exit.
4250 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4251 ScalarEvolution *SE) const {
4252 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4253 ENT != 0; ENT = ENT->getNextExit()) {
4255 if (ENT->ExitingBlock == ExitingBlock)
4256 return ENT->ExactNotTaken;
4258 return SE->getCouldNotCompute();
4261 /// getMax - Get the max backedge taken count for the loop.
4263 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4264 return Max ? Max : SE->getCouldNotCompute();
4267 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4268 ScalarEvolution *SE) const {
4269 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4272 if (!ExitNotTaken.ExitingBlock)
4275 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4276 ENT != 0; ENT = ENT->getNextExit()) {
4278 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4279 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4286 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4287 /// computable exit into a persistent ExitNotTakenInfo array.
4288 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4289 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4290 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4293 ExitNotTaken.setIncomplete();
4295 unsigned NumExits = ExitCounts.size();
4296 if (NumExits == 0) return;
4298 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4299 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4300 if (NumExits == 1) return;
4302 // Handle the rare case of multiple computable exits.
4303 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4305 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4306 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4307 PrevENT->setNextExit(ENT);
4308 ENT->ExitingBlock = ExitCounts[i].first;
4309 ENT->ExactNotTaken = ExitCounts[i].second;
4313 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4314 void ScalarEvolution::BackedgeTakenInfo::clear() {
4315 ExitNotTaken.ExitingBlock = 0;
4316 ExitNotTaken.ExactNotTaken = 0;
4317 delete[] ExitNotTaken.getNextExit();
4320 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4321 /// of the specified loop will execute.
4322 ScalarEvolution::BackedgeTakenInfo
4323 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4324 SmallVector<BasicBlock *, 8> ExitingBlocks;
4325 L->getExitingBlocks(ExitingBlocks);
4327 // Examine all exits and pick the most conservative values.
4328 const SCEV *MaxBECount = getCouldNotCompute();
4329 bool CouldComputeBECount = true;
4330 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4331 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4332 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4333 if (EL.Exact == getCouldNotCompute())
4334 // We couldn't compute an exact value for this exit, so
4335 // we won't be able to compute an exact value for the loop.
4336 CouldComputeBECount = false;
4338 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4340 if (MaxBECount == getCouldNotCompute())
4341 MaxBECount = EL.Max;
4342 else if (EL.Max != getCouldNotCompute()) {
4343 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4344 // skip some loop tests. Taking the max over the exits is sufficiently
4345 // conservative. TODO: We could do better taking into consideration
4346 // that (1) the loop has unit stride (2) the last loop test is
4347 // less-than/greater-than (3) any loop test is less-than/greater-than AND
4348 // falls-through some constant times less then the other tests.
4349 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4353 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4356 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4357 /// loop will execute if it exits via the specified block.
4358 ScalarEvolution::ExitLimit
4359 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4361 // Okay, we've chosen an exiting block. See what condition causes us to
4362 // exit at this block.
4364 // FIXME: we should be able to handle switch instructions (with a single exit)
4365 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4366 if (ExitBr == 0) return getCouldNotCompute();
4367 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4369 // At this point, we know we have a conditional branch that determines whether
4370 // the loop is exited. However, we don't know if the branch is executed each
4371 // time through the loop. If not, then the execution count of the branch will
4372 // not be equal to the trip count of the loop.
4374 // Currently we check for this by checking to see if the Exit branch goes to
4375 // the loop header. If so, we know it will always execute the same number of
4376 // times as the loop. We also handle the case where the exit block *is* the
4377 // loop header. This is common for un-rotated loops.
4379 // If both of those tests fail, walk up the unique predecessor chain to the
4380 // header, stopping if there is an edge that doesn't exit the loop. If the
4381 // header is reached, the execution count of the branch will be equal to the
4382 // trip count of the loop.
4384 // More extensive analysis could be done to handle more cases here.
4386 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4387 ExitBr->getSuccessor(1) != L->getHeader() &&
4388 ExitBr->getParent() != L->getHeader()) {
4389 // The simple checks failed, try climbing the unique predecessor chain
4390 // up to the header.
4392 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4393 BasicBlock *Pred = BB->getUniquePredecessor();
4395 return getCouldNotCompute();
4396 TerminatorInst *PredTerm = Pred->getTerminator();
4397 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4398 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4401 // If the predecessor has a successor that isn't BB and isn't
4402 // outside the loop, assume the worst.
4403 if (L->contains(PredSucc))
4404 return getCouldNotCompute();
4406 if (Pred == L->getHeader()) {
4413 return getCouldNotCompute();
4416 // Proceed to the next level to examine the exit condition expression.
4417 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4418 ExitBr->getSuccessor(0),
4419 ExitBr->getSuccessor(1),
4420 /*IsSubExpr=*/false);
4423 /// ComputeExitLimitFromCond - Compute the number of times the
4424 /// backedge of the specified loop will execute if its exit condition
4425 /// were a conditional branch of ExitCond, TBB, and FBB.
4427 /// @param IsSubExpr is true if ExitCond does not directly control the exit
4428 /// branch. In this case, we cannot assume that the loop only exits when the
4429 /// condition is true and cannot infer that failing to meet the condition prior
4430 /// to integer wraparound results in undefined behavior.
4431 ScalarEvolution::ExitLimit
4432 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4437 // Check if the controlling expression for this loop is an And or Or.
4438 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4439 if (BO->getOpcode() == Instruction::And) {
4440 // Recurse on the operands of the and.
4441 bool EitherMayExit = L->contains(TBB);
4442 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4443 IsSubExpr || EitherMayExit);
4444 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4445 IsSubExpr || EitherMayExit);
4446 const SCEV *BECount = getCouldNotCompute();
4447 const SCEV *MaxBECount = getCouldNotCompute();
4448 if (EitherMayExit) {
4449 // Both conditions must be true for the loop to continue executing.
4450 // Choose the less conservative count.
4451 if (EL0.Exact == getCouldNotCompute() ||
4452 EL1.Exact == getCouldNotCompute())
4453 BECount = getCouldNotCompute();
4455 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4456 if (EL0.Max == getCouldNotCompute())
4457 MaxBECount = EL1.Max;
4458 else if (EL1.Max == getCouldNotCompute())
4459 MaxBECount = EL0.Max;
4461 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4463 // Both conditions must be true at the same time for the loop to exit.
4464 // For now, be conservative.
4465 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4466 if (EL0.Max == EL1.Max)
4467 MaxBECount = EL0.Max;
4468 if (EL0.Exact == EL1.Exact)
4469 BECount = EL0.Exact;
4472 return ExitLimit(BECount, MaxBECount);
4474 if (BO->getOpcode() == Instruction::Or) {
4475 // Recurse on the operands of the or.
4476 bool EitherMayExit = L->contains(FBB);
4477 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4478 IsSubExpr || EitherMayExit);
4479 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4480 IsSubExpr || EitherMayExit);
4481 const SCEV *BECount = getCouldNotCompute();
4482 const SCEV *MaxBECount = getCouldNotCompute();
4483 if (EitherMayExit) {
4484 // Both conditions must be false for the loop to continue executing.
4485 // Choose the less conservative count.
4486 if (EL0.Exact == getCouldNotCompute() ||
4487 EL1.Exact == getCouldNotCompute())
4488 BECount = getCouldNotCompute();
4490 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4491 if (EL0.Max == getCouldNotCompute())
4492 MaxBECount = EL1.Max;
4493 else if (EL1.Max == getCouldNotCompute())
4494 MaxBECount = EL0.Max;
4496 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4498 // Both conditions must be false at the same time for the loop to exit.
4499 // For now, be conservative.
4500 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4501 if (EL0.Max == EL1.Max)
4502 MaxBECount = EL0.Max;
4503 if (EL0.Exact == EL1.Exact)
4504 BECount = EL0.Exact;
4507 return ExitLimit(BECount, MaxBECount);
4511 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4512 // Proceed to the next level to examine the icmp.
4513 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4514 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, IsSubExpr);
4516 // Check for a constant condition. These are normally stripped out by
4517 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4518 // preserve the CFG and is temporarily leaving constant conditions
4520 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4521 if (L->contains(FBB) == !CI->getZExtValue())
4522 // The backedge is always taken.
4523 return getCouldNotCompute();
4525 // The backedge is never taken.
4526 return getConstant(CI->getType(), 0);
4529 // If it's not an integer or pointer comparison then compute it the hard way.
4530 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4533 /// ComputeExitLimitFromICmp - Compute the number of times the
4534 /// backedge of the specified loop will execute if its exit condition
4535 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4536 ScalarEvolution::ExitLimit
4537 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4543 // If the condition was exit on true, convert the condition to exit on false
4544 ICmpInst::Predicate Cond;
4545 if (!L->contains(FBB))
4546 Cond = ExitCond->getPredicate();
4548 Cond = ExitCond->getInversePredicate();
4550 // Handle common loops like: for (X = "string"; *X; ++X)
4551 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4552 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4554 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4555 if (ItCnt.hasAnyInfo())
4559 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4560 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4562 // Try to evaluate any dependencies out of the loop.
4563 LHS = getSCEVAtScope(LHS, L);
4564 RHS = getSCEVAtScope(RHS, L);
4566 // At this point, we would like to compute how many iterations of the
4567 // loop the predicate will return true for these inputs.
4568 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4569 // If there is a loop-invariant, force it into the RHS.
4570 std::swap(LHS, RHS);
4571 Cond = ICmpInst::getSwappedPredicate(Cond);
4574 // Simplify the operands before analyzing them.
4575 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4577 // If we have a comparison of a chrec against a constant, try to use value
4578 // ranges to answer this query.
4579 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4580 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4581 if (AddRec->getLoop() == L) {
4582 // Form the constant range.
4583 ConstantRange CompRange(
4584 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4586 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4587 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4591 case ICmpInst::ICMP_NE: { // while (X != Y)
4592 // Convert to: while (X-Y != 0)
4593 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4594 if (EL.hasAnyInfo()) return EL;
4597 case ICmpInst::ICMP_EQ: { // while (X == Y)
4598 // Convert to: while (X-Y == 0)
4599 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4600 if (EL.hasAnyInfo()) return EL;
4603 case ICmpInst::ICMP_SLT: {
4604 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true, IsSubExpr);
4605 if (EL.hasAnyInfo()) return EL;
4608 case ICmpInst::ICMP_SGT: {
4609 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4610 getNotSCEV(RHS), L, true, IsSubExpr);
4611 if (EL.hasAnyInfo()) return EL;
4614 case ICmpInst::ICMP_ULT: {
4615 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false, IsSubExpr);
4616 if (EL.hasAnyInfo()) return EL;
4619 case ICmpInst::ICMP_UGT: {
4620 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4621 getNotSCEV(RHS), L, false, IsSubExpr);
4622 if (EL.hasAnyInfo()) return EL;
4627 dbgs() << "ComputeBackedgeTakenCount ";
4628 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4629 dbgs() << "[unsigned] ";
4630 dbgs() << *LHS << " "
4631 << Instruction::getOpcodeName(Instruction::ICmp)
4632 << " " << *RHS << "\n";
4636 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4639 static ConstantInt *
4640 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4641 ScalarEvolution &SE) {
4642 const SCEV *InVal = SE.getConstant(C);
4643 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4644 assert(isa<SCEVConstant>(Val) &&
4645 "Evaluation of SCEV at constant didn't fold correctly?");
4646 return cast<SCEVConstant>(Val)->getValue();
4649 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4650 /// 'icmp op load X, cst', try to see if we can compute the backedge
4651 /// execution count.
4652 ScalarEvolution::ExitLimit
4653 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4657 ICmpInst::Predicate predicate) {
4659 if (LI->isVolatile()) return getCouldNotCompute();
4661 // Check to see if the loaded pointer is a getelementptr of a global.
4662 // TODO: Use SCEV instead of manually grubbing with GEPs.
4663 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4664 if (!GEP) return getCouldNotCompute();
4666 // Make sure that it is really a constant global we are gepping, with an
4667 // initializer, and make sure the first IDX is really 0.
4668 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4669 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4670 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4671 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4672 return getCouldNotCompute();
4674 // Okay, we allow one non-constant index into the GEP instruction.
4676 std::vector<Constant*> Indexes;
4677 unsigned VarIdxNum = 0;
4678 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4679 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4680 Indexes.push_back(CI);
4681 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4682 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4683 VarIdx = GEP->getOperand(i);
4685 Indexes.push_back(0);
4688 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4690 return getCouldNotCompute();
4692 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4693 // Check to see if X is a loop variant variable value now.
4694 const SCEV *Idx = getSCEV(VarIdx);
4695 Idx = getSCEVAtScope(Idx, L);
4697 // We can only recognize very limited forms of loop index expressions, in
4698 // particular, only affine AddRec's like {C1,+,C2}.
4699 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4700 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4701 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4702 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4703 return getCouldNotCompute();
4705 unsigned MaxSteps = MaxBruteForceIterations;
4706 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4707 ConstantInt *ItCst = ConstantInt::get(
4708 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4709 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4711 // Form the GEP offset.
4712 Indexes[VarIdxNum] = Val;
4714 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4716 if (Result == 0) break; // Cannot compute!
4718 // Evaluate the condition for this iteration.
4719 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4720 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4721 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4723 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4724 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4727 ++NumArrayLenItCounts;
4728 return getConstant(ItCst); // Found terminating iteration!
4731 return getCouldNotCompute();
4735 /// CanConstantFold - Return true if we can constant fold an instruction of the
4736 /// specified type, assuming that all operands were constants.
4737 static bool CanConstantFold(const Instruction *I) {
4738 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4739 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4743 if (const CallInst *CI = dyn_cast<CallInst>(I))
4744 if (const Function *F = CI->getCalledFunction())
4745 return canConstantFoldCallTo(F);
4749 /// Determine whether this instruction can constant evolve within this loop
4750 /// assuming its operands can all constant evolve.
4751 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4752 // An instruction outside of the loop can't be derived from a loop PHI.
4753 if (!L->contains(I)) return false;
4755 if (isa<PHINode>(I)) {
4756 if (L->getHeader() == I->getParent())
4759 // We don't currently keep track of the control flow needed to evaluate
4760 // PHIs, so we cannot handle PHIs inside of loops.
4764 // If we won't be able to constant fold this expression even if the operands
4765 // are constants, bail early.
4766 return CanConstantFold(I);
4769 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4770 /// recursing through each instruction operand until reaching a loop header phi.
4772 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4773 DenseMap<Instruction *, PHINode *> &PHIMap) {
4775 // Otherwise, we can evaluate this instruction if all of its operands are
4776 // constant or derived from a PHI node themselves.
4778 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4779 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4781 if (isa<Constant>(*OpI)) continue;
4783 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4784 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4786 PHINode *P = dyn_cast<PHINode>(OpInst);
4788 // If this operand is already visited, reuse the prior result.
4789 // We may have P != PHI if this is the deepest point at which the
4790 // inconsistent paths meet.
4791 P = PHIMap.lookup(OpInst);
4793 // Recurse and memoize the results, whether a phi is found or not.
4794 // This recursive call invalidates pointers into PHIMap.
4795 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4798 if (P == 0) return 0; // Not evolving from PHI
4799 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4802 // This is a expression evolving from a constant PHI!
4806 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4807 /// in the loop that V is derived from. We allow arbitrary operations along the
4808 /// way, but the operands of an operation must either be constants or a value
4809 /// derived from a constant PHI. If this expression does not fit with these
4810 /// constraints, return null.
4811 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4812 Instruction *I = dyn_cast<Instruction>(V);
4813 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4815 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4819 // Record non-constant instructions contained by the loop.
4820 DenseMap<Instruction *, PHINode *> PHIMap;
4821 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4824 /// EvaluateExpression - Given an expression that passes the
4825 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4826 /// in the loop has the value PHIVal. If we can't fold this expression for some
4827 /// reason, return null.
4828 static Constant *EvaluateExpression(Value *V, const Loop *L,
4829 DenseMap<Instruction *, Constant *> &Vals,
4830 const DataLayout *TD,
4831 const TargetLibraryInfo *TLI) {
4832 // Convenient constant check, but redundant for recursive calls.
4833 if (Constant *C = dyn_cast<Constant>(V)) return C;
4834 Instruction *I = dyn_cast<Instruction>(V);
4837 if (Constant *C = Vals.lookup(I)) return C;
4839 // An instruction inside the loop depends on a value outside the loop that we
4840 // weren't given a mapping for, or a value such as a call inside the loop.
4841 if (!canConstantEvolve(I, L)) return 0;
4843 // An unmapped PHI can be due to a branch or another loop inside this loop,
4844 // or due to this not being the initial iteration through a loop where we
4845 // couldn't compute the evolution of this particular PHI last time.
4846 if (isa<PHINode>(I)) return 0;
4848 std::vector<Constant*> Operands(I->getNumOperands());
4850 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4851 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4853 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4854 if (!Operands[i]) return 0;
4857 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
4863 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4864 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4865 Operands[1], TD, TLI);
4866 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4867 if (!LI->isVolatile())
4868 return ConstantFoldLoadFromConstPtr(Operands[0], TD);
4870 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
4874 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4875 /// in the header of its containing loop, we know the loop executes a
4876 /// constant number of times, and the PHI node is just a recurrence
4877 /// involving constants, fold it.
4879 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4882 DenseMap<PHINode*, Constant*>::const_iterator I =
4883 ConstantEvolutionLoopExitValue.find(PN);
4884 if (I != ConstantEvolutionLoopExitValue.end())
4887 if (BEs.ugt(MaxBruteForceIterations))
4888 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4890 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4892 DenseMap<Instruction *, Constant *> CurrentIterVals;
4893 BasicBlock *Header = L->getHeader();
4894 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4896 // Since the loop is canonicalized, the PHI node must have two entries. One
4897 // entry must be a constant (coming in from outside of the loop), and the
4898 // second must be derived from the same PHI.
4899 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4901 for (BasicBlock::iterator I = Header->begin();
4902 (PHI = dyn_cast<PHINode>(I)); ++I) {
4903 Constant *StartCST =
4904 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4905 if (StartCST == 0) continue;
4906 CurrentIterVals[PHI] = StartCST;
4908 if (!CurrentIterVals.count(PN))
4911 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4913 // Execute the loop symbolically to determine the exit value.
4914 if (BEs.getActiveBits() >= 32)
4915 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4917 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4918 unsigned IterationNum = 0;
4919 for (; ; ++IterationNum) {
4920 if (IterationNum == NumIterations)
4921 return RetVal = CurrentIterVals[PN]; // Got exit value!
4923 // Compute the value of the PHIs for the next iteration.
4924 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
4925 DenseMap<Instruction *, Constant *> NextIterVals;
4926 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
4929 return 0; // Couldn't evaluate!
4930 NextIterVals[PN] = NextPHI;
4932 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
4934 // Also evaluate the other PHI nodes. However, we don't get to stop if we
4935 // cease to be able to evaluate one of them or if they stop evolving,
4936 // because that doesn't necessarily prevent us from computing PN.
4937 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
4938 for (DenseMap<Instruction *, Constant *>::const_iterator
4939 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4940 PHINode *PHI = dyn_cast<PHINode>(I->first);
4941 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
4942 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
4944 // We use two distinct loops because EvaluateExpression may invalidate any
4945 // iterators into CurrentIterVals.
4946 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
4947 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
4948 PHINode *PHI = I->first;
4949 Constant *&NextPHI = NextIterVals[PHI];
4950 if (!NextPHI) { // Not already computed.
4951 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4952 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4954 if (NextPHI != I->second)
4955 StoppedEvolving = false;
4958 // If all entries in CurrentIterVals == NextIterVals then we can stop
4959 // iterating, the loop can't continue to change.
4960 if (StoppedEvolving)
4961 return RetVal = CurrentIterVals[PN];
4963 CurrentIterVals.swap(NextIterVals);
4967 /// ComputeExitCountExhaustively - If the loop is known to execute a
4968 /// constant number of times (the condition evolves only from constants),
4969 /// try to evaluate a few iterations of the loop until we get the exit
4970 /// condition gets a value of ExitWhen (true or false). If we cannot
4971 /// evaluate the trip count of the loop, return getCouldNotCompute().
4972 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4975 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4976 if (PN == 0) return getCouldNotCompute();
4978 // If the loop is canonicalized, the PHI will have exactly two entries.
4979 // That's the only form we support here.
4980 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4982 DenseMap<Instruction *, Constant *> CurrentIterVals;
4983 BasicBlock *Header = L->getHeader();
4984 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4986 // One entry must be a constant (coming in from outside of the loop), and the
4987 // second must be derived from the same PHI.
4988 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4990 for (BasicBlock::iterator I = Header->begin();
4991 (PHI = dyn_cast<PHINode>(I)); ++I) {
4992 Constant *StartCST =
4993 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4994 if (StartCST == 0) continue;
4995 CurrentIterVals[PHI] = StartCST;
4997 if (!CurrentIterVals.count(PN))
4998 return getCouldNotCompute();
5000 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5001 // the loop symbolically to determine when the condition gets a value of
5004 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5005 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5006 ConstantInt *CondVal =
5007 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5010 // Couldn't symbolically evaluate.
5011 if (!CondVal) return getCouldNotCompute();
5013 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5014 ++NumBruteForceTripCountsComputed;
5015 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5018 // Update all the PHI nodes for the next iteration.
5019 DenseMap<Instruction *, Constant *> NextIterVals;
5021 // Create a list of which PHIs we need to compute. We want to do this before
5022 // calling EvaluateExpression on them because that may invalidate iterators
5023 // into CurrentIterVals.
5024 SmallVector<PHINode *, 8> PHIsToCompute;
5025 for (DenseMap<Instruction *, Constant *>::const_iterator
5026 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5027 PHINode *PHI = dyn_cast<PHINode>(I->first);
5028 if (!PHI || PHI->getParent() != Header) continue;
5029 PHIsToCompute.push_back(PHI);
5031 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5032 E = PHIsToCompute.end(); I != E; ++I) {
5034 Constant *&NextPHI = NextIterVals[PHI];
5035 if (NextPHI) continue; // Already computed!
5037 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5038 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
5040 CurrentIterVals.swap(NextIterVals);
5043 // Too many iterations were needed to evaluate.
5044 return getCouldNotCompute();
5047 /// getSCEVAtScope - Return a SCEV expression for the specified value
5048 /// at the specified scope in the program. The L value specifies a loop
5049 /// nest to evaluate the expression at, where null is the top-level or a
5050 /// specified loop is immediately inside of the loop.
5052 /// This method can be used to compute the exit value for a variable defined
5053 /// in a loop by querying what the value will hold in the parent loop.
5055 /// In the case that a relevant loop exit value cannot be computed, the
5056 /// original value V is returned.
5057 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5058 // Check to see if we've folded this expression at this loop before.
5059 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
5060 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
5061 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
5063 return Pair.first->second ? Pair.first->second : V;
5065 // Otherwise compute it.
5066 const SCEV *C = computeSCEVAtScope(V, L);
5067 ValuesAtScopes[V][L] = C;
5071 /// This builds up a Constant using the ConstantExpr interface. That way, we
5072 /// will return Constants for objects which aren't represented by a
5073 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5074 /// Returns NULL if the SCEV isn't representable as a Constant.
5075 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5076 switch (V->getSCEVType()) {
5077 default: // TODO: smax, umax.
5078 case scCouldNotCompute:
5082 return cast<SCEVConstant>(V)->getValue();
5084 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5085 case scSignExtend: {
5086 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5087 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5088 return ConstantExpr::getSExt(CastOp, SS->getType());
5091 case scZeroExtend: {
5092 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5093 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5094 return ConstantExpr::getZExt(CastOp, SZ->getType());
5098 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5099 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5100 return ConstantExpr::getTrunc(CastOp, ST->getType());
5104 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5105 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5106 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5107 unsigned AS = PTy->getAddressSpace();
5108 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5109 C = ConstantExpr::getBitCast(C, DestPtrTy);
5111 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5112 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5116 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5117 unsigned AS = C2->getType()->getPointerAddressSpace();
5119 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5120 // The offsets have been converted to bytes. We can add bytes to an
5121 // i8* by GEP with the byte count in the first index.
5122 C = ConstantExpr::getBitCast(C, DestPtrTy);
5125 // Don't bother trying to sum two pointers. We probably can't
5126 // statically compute a load that results from it anyway.
5127 if (C2->getType()->isPointerTy())
5130 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5131 if (PTy->getElementType()->isStructTy())
5132 C2 = ConstantExpr::getIntegerCast(
5133 C2, Type::getInt32Ty(C->getContext()), true);
5134 C = ConstantExpr::getGetElementPtr(C, C2);
5136 C = ConstantExpr::getAdd(C, C2);
5143 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5144 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5145 // Don't bother with pointers at all.
5146 if (C->getType()->isPointerTy()) return 0;
5147 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5148 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5149 if (!C2 || C2->getType()->isPointerTy()) return 0;
5150 C = ConstantExpr::getMul(C, C2);
5157 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5158 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5159 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5160 if (LHS->getType() == RHS->getType())
5161 return ConstantExpr::getUDiv(LHS, RHS);
5168 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5169 if (isa<SCEVConstant>(V)) return V;
5171 // If this instruction is evolved from a constant-evolving PHI, compute the
5172 // exit value from the loop without using SCEVs.
5173 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5174 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5175 const Loop *LI = (*this->LI)[I->getParent()];
5176 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5177 if (PHINode *PN = dyn_cast<PHINode>(I))
5178 if (PN->getParent() == LI->getHeader()) {
5179 // Okay, there is no closed form solution for the PHI node. Check
5180 // to see if the loop that contains it has a known backedge-taken
5181 // count. If so, we may be able to force computation of the exit
5183 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5184 if (const SCEVConstant *BTCC =
5185 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5186 // Okay, we know how many times the containing loop executes. If
5187 // this is a constant evolving PHI node, get the final value at
5188 // the specified iteration number.
5189 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5190 BTCC->getValue()->getValue(),
5192 if (RV) return getSCEV(RV);
5196 // Okay, this is an expression that we cannot symbolically evaluate
5197 // into a SCEV. Check to see if it's possible to symbolically evaluate
5198 // the arguments into constants, and if so, try to constant propagate the
5199 // result. This is particularly useful for computing loop exit values.
5200 if (CanConstantFold(I)) {
5201 SmallVector<Constant *, 4> Operands;
5202 bool MadeImprovement = false;
5203 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5204 Value *Op = I->getOperand(i);
5205 if (Constant *C = dyn_cast<Constant>(Op)) {
5206 Operands.push_back(C);
5210 // If any of the operands is non-constant and if they are
5211 // non-integer and non-pointer, don't even try to analyze them
5212 // with scev techniques.
5213 if (!isSCEVable(Op->getType()))
5216 const SCEV *OrigV = getSCEV(Op);
5217 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5218 MadeImprovement |= OrigV != OpV;
5220 Constant *C = BuildConstantFromSCEV(OpV);
5222 if (C->getType() != Op->getType())
5223 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5227 Operands.push_back(C);
5230 // Check to see if getSCEVAtScope actually made an improvement.
5231 if (MadeImprovement) {
5233 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5234 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5235 Operands[0], Operands[1], TD,
5237 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5238 if (!LI->isVolatile())
5239 C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
5241 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5249 // This is some other type of SCEVUnknown, just return it.
5253 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5254 // Avoid performing the look-up in the common case where the specified
5255 // expression has no loop-variant portions.
5256 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5257 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5258 if (OpAtScope != Comm->getOperand(i)) {
5259 // Okay, at least one of these operands is loop variant but might be
5260 // foldable. Build a new instance of the folded commutative expression.
5261 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5262 Comm->op_begin()+i);
5263 NewOps.push_back(OpAtScope);
5265 for (++i; i != e; ++i) {
5266 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5267 NewOps.push_back(OpAtScope);
5269 if (isa<SCEVAddExpr>(Comm))
5270 return getAddExpr(NewOps);
5271 if (isa<SCEVMulExpr>(Comm))
5272 return getMulExpr(NewOps);
5273 if (isa<SCEVSMaxExpr>(Comm))
5274 return getSMaxExpr(NewOps);
5275 if (isa<SCEVUMaxExpr>(Comm))
5276 return getUMaxExpr(NewOps);
5277 llvm_unreachable("Unknown commutative SCEV type!");
5280 // If we got here, all operands are loop invariant.
5284 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5285 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5286 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5287 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5288 return Div; // must be loop invariant
5289 return getUDivExpr(LHS, RHS);
5292 // If this is a loop recurrence for a loop that does not contain L, then we
5293 // are dealing with the final value computed by the loop.
5294 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5295 // First, attempt to evaluate each operand.
5296 // Avoid performing the look-up in the common case where the specified
5297 // expression has no loop-variant portions.
5298 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5299 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5300 if (OpAtScope == AddRec->getOperand(i))
5303 // Okay, at least one of these operands is loop variant but might be
5304 // foldable. Build a new instance of the folded commutative expression.
5305 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5306 AddRec->op_begin()+i);
5307 NewOps.push_back(OpAtScope);
5308 for (++i; i != e; ++i)
5309 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5311 const SCEV *FoldedRec =
5312 getAddRecExpr(NewOps, AddRec->getLoop(),
5313 AddRec->getNoWrapFlags(SCEV::FlagNW));
5314 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5315 // The addrec may be folded to a nonrecurrence, for example, if the
5316 // induction variable is multiplied by zero after constant folding. Go
5317 // ahead and return the folded value.
5323 // If the scope is outside the addrec's loop, evaluate it by using the
5324 // loop exit value of the addrec.
5325 if (!AddRec->getLoop()->contains(L)) {
5326 // To evaluate this recurrence, we need to know how many times the AddRec
5327 // loop iterates. Compute this now.
5328 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5329 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5331 // Then, evaluate the AddRec.
5332 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5338 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5339 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5340 if (Op == Cast->getOperand())
5341 return Cast; // must be loop invariant
5342 return getZeroExtendExpr(Op, Cast->getType());
5345 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5346 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5347 if (Op == Cast->getOperand())
5348 return Cast; // must be loop invariant
5349 return getSignExtendExpr(Op, Cast->getType());
5352 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5353 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5354 if (Op == Cast->getOperand())
5355 return Cast; // must be loop invariant
5356 return getTruncateExpr(Op, Cast->getType());
5359 llvm_unreachable("Unknown SCEV type!");
5362 /// getSCEVAtScope - This is a convenience function which does
5363 /// getSCEVAtScope(getSCEV(V), L).
5364 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5365 return getSCEVAtScope(getSCEV(V), L);
5368 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5369 /// following equation:
5371 /// A * X = B (mod N)
5373 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5374 /// A and B isn't important.
5376 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5377 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5378 ScalarEvolution &SE) {
5379 uint32_t BW = A.getBitWidth();
5380 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5381 assert(A != 0 && "A must be non-zero.");
5385 // The gcd of A and N may have only one prime factor: 2. The number of
5386 // trailing zeros in A is its multiplicity
5387 uint32_t Mult2 = A.countTrailingZeros();
5390 // 2. Check if B is divisible by D.
5392 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5393 // is not less than multiplicity of this prime factor for D.
5394 if (B.countTrailingZeros() < Mult2)
5395 return SE.getCouldNotCompute();
5397 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5400 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5401 // bit width during computations.
5402 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5403 APInt Mod(BW + 1, 0);
5404 Mod.setBit(BW - Mult2); // Mod = N / D
5405 APInt I = AD.multiplicativeInverse(Mod);
5407 // 4. Compute the minimum unsigned root of the equation:
5408 // I * (B / D) mod (N / D)
5409 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5411 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5413 return SE.getConstant(Result.trunc(BW));
5416 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5417 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5418 /// might be the same) or two SCEVCouldNotCompute objects.
5420 static std::pair<const SCEV *,const SCEV *>
5421 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5422 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5423 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5424 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5425 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5427 // We currently can only solve this if the coefficients are constants.
5428 if (!LC || !MC || !NC) {
5429 const SCEV *CNC = SE.getCouldNotCompute();
5430 return std::make_pair(CNC, CNC);
5433 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5434 const APInt &L = LC->getValue()->getValue();
5435 const APInt &M = MC->getValue()->getValue();
5436 const APInt &N = NC->getValue()->getValue();
5437 APInt Two(BitWidth, 2);
5438 APInt Four(BitWidth, 4);
5441 using namespace APIntOps;
5443 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5444 // The B coefficient is M-N/2
5448 // The A coefficient is N/2
5449 APInt A(N.sdiv(Two));
5451 // Compute the B^2-4ac term.
5454 SqrtTerm -= Four * (A * C);
5456 if (SqrtTerm.isNegative()) {
5457 // The loop is provably infinite.
5458 const SCEV *CNC = SE.getCouldNotCompute();
5459 return std::make_pair(CNC, CNC);
5462 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5463 // integer value or else APInt::sqrt() will assert.
5464 APInt SqrtVal(SqrtTerm.sqrt());
5466 // Compute the two solutions for the quadratic formula.
5467 // The divisions must be performed as signed divisions.
5470 if (TwoA.isMinValue()) {
5471 const SCEV *CNC = SE.getCouldNotCompute();
5472 return std::make_pair(CNC, CNC);
5475 LLVMContext &Context = SE.getContext();
5477 ConstantInt *Solution1 =
5478 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5479 ConstantInt *Solution2 =
5480 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5482 return std::make_pair(SE.getConstant(Solution1),
5483 SE.getConstant(Solution2));
5484 } // end APIntOps namespace
5487 /// HowFarToZero - Return the number of times a backedge comparing the specified
5488 /// value to zero will execute. If not computable, return CouldNotCompute.
5490 /// This is only used for loops with a "x != y" exit test. The exit condition is
5491 /// now expressed as a single expression, V = x-y. So the exit test is
5492 /// effectively V != 0. We know and take advantage of the fact that this
5493 /// expression only being used in a comparison by zero context.
5494 ScalarEvolution::ExitLimit
5495 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
5496 // If the value is a constant
5497 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5498 // If the value is already zero, the branch will execute zero times.
5499 if (C->getValue()->isZero()) return C;
5500 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5503 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5504 if (!AddRec || AddRec->getLoop() != L)
5505 return getCouldNotCompute();
5507 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5508 // the quadratic equation to solve it.
5509 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5510 std::pair<const SCEV *,const SCEV *> Roots =
5511 SolveQuadraticEquation(AddRec, *this);
5512 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5513 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5516 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5517 << " sol#2: " << *R2 << "\n";
5519 // Pick the smallest positive root value.
5520 if (ConstantInt *CB =
5521 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5524 if (CB->getZExtValue() == false)
5525 std::swap(R1, R2); // R1 is the minimum root now.
5527 // We can only use this value if the chrec ends up with an exact zero
5528 // value at this index. When solving for "X*X != 5", for example, we
5529 // should not accept a root of 2.
5530 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5532 return R1; // We found a quadratic root!
5535 return getCouldNotCompute();
5538 // Otherwise we can only handle this if it is affine.
5539 if (!AddRec->isAffine())
5540 return getCouldNotCompute();
5542 // If this is an affine expression, the execution count of this branch is
5543 // the minimum unsigned root of the following equation:
5545 // Start + Step*N = 0 (mod 2^BW)
5549 // Step*N = -Start (mod 2^BW)
5551 // where BW is the common bit width of Start and Step.
5553 // Get the initial value for the loop.
5554 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5555 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5557 // For now we handle only constant steps.
5559 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5560 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5561 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5562 // We have not yet seen any such cases.
5563 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5564 if (StepC == 0 || StepC->getValue()->equalsInt(0))
5565 return getCouldNotCompute();
5567 // For positive steps (counting up until unsigned overflow):
5568 // N = -Start/Step (as unsigned)
5569 // For negative steps (counting down to zero):
5571 // First compute the unsigned distance from zero in the direction of Step.
5572 bool CountDown = StepC->getValue()->getValue().isNegative();
5573 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5575 // Handle unitary steps, which cannot wraparound.
5576 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5577 // N = Distance (as unsigned)
5578 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5579 ConstantRange CR = getUnsignedRange(Start);
5580 const SCEV *MaxBECount;
5581 if (!CountDown && CR.getUnsignedMin().isMinValue())
5582 // When counting up, the worst starting value is 1, not 0.
5583 MaxBECount = CR.getUnsignedMax().isMinValue()
5584 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5585 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5587 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5588 : -CR.getUnsignedMin());
5589 return ExitLimit(Distance, MaxBECount);
5592 // If the recurrence is known not to wraparound, unsigned divide computes the
5593 // back edge count. (Ideally we would have an "isexact" bit for udiv). We know
5594 // that the value will either become zero (and thus the loop terminates), that
5595 // the loop will terminate through some other exit condition first, or that
5596 // the loop has undefined behavior. This means we can't "miss" the exit
5597 // value, even with nonunit stride.
5599 // This is only valid for expressions that directly compute the loop exit. It
5600 // is invalid for subexpressions in which the loop may exit through this
5601 // branch even if this subexpression is false. In that case, the trip count
5602 // computed by this udiv could be smaller than the number of well-defined
5604 if (!IsSubExpr && AddRec->getNoWrapFlags(SCEV::FlagNW))
5605 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5607 // Then, try to solve the above equation provided that Start is constant.
5608 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5609 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5610 -StartC->getValue()->getValue(),
5612 return getCouldNotCompute();
5615 /// HowFarToNonZero - Return the number of times a backedge checking the
5616 /// specified value for nonzero will execute. If not computable, return
5618 ScalarEvolution::ExitLimit
5619 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5620 // Loops that look like: while (X == 0) are very strange indeed. We don't
5621 // handle them yet except for the trivial case. This could be expanded in the
5622 // future as needed.
5624 // If the value is a constant, check to see if it is known to be non-zero
5625 // already. If so, the backedge will execute zero times.
5626 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5627 if (!C->getValue()->isNullValue())
5628 return getConstant(C->getType(), 0);
5629 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5632 // We could implement others, but I really doubt anyone writes loops like
5633 // this, and if they did, they would already be constant folded.
5634 return getCouldNotCompute();
5637 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5638 /// (which may not be an immediate predecessor) which has exactly one
5639 /// successor from which BB is reachable, or null if no such block is
5642 std::pair<BasicBlock *, BasicBlock *>
5643 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5644 // If the block has a unique predecessor, then there is no path from the
5645 // predecessor to the block that does not go through the direct edge
5646 // from the predecessor to the block.
5647 if (BasicBlock *Pred = BB->getSinglePredecessor())
5648 return std::make_pair(Pred, BB);
5650 // A loop's header is defined to be a block that dominates the loop.
5651 // If the header has a unique predecessor outside the loop, it must be
5652 // a block that has exactly one successor that can reach the loop.
5653 if (Loop *L = LI->getLoopFor(BB))
5654 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5656 return std::pair<BasicBlock *, BasicBlock *>();
5659 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5660 /// testing whether two expressions are equal, however for the purposes of
5661 /// looking for a condition guarding a loop, it can be useful to be a little
5662 /// more general, since a front-end may have replicated the controlling
5665 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5666 // Quick check to see if they are the same SCEV.
5667 if (A == B) return true;
5669 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5670 // two different instructions with the same value. Check for this case.
5671 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5672 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5673 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5674 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5675 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5678 // Otherwise assume they may have a different value.
5682 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5683 /// predicate Pred. Return true iff any changes were made.
5685 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5686 const SCEV *&LHS, const SCEV *&RHS,
5688 bool Changed = false;
5690 // If we hit the max recursion limit bail out.
5694 // Canonicalize a constant to the right side.
5695 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5696 // Check for both operands constant.
5697 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5698 if (ConstantExpr::getICmp(Pred,
5700 RHSC->getValue())->isNullValue())
5701 goto trivially_false;
5703 goto trivially_true;
5705 // Otherwise swap the operands to put the constant on the right.
5706 std::swap(LHS, RHS);
5707 Pred = ICmpInst::getSwappedPredicate(Pred);
5711 // If we're comparing an addrec with a value which is loop-invariant in the
5712 // addrec's loop, put the addrec on the left. Also make a dominance check,
5713 // as both operands could be addrecs loop-invariant in each other's loop.
5714 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5715 const Loop *L = AR->getLoop();
5716 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5717 std::swap(LHS, RHS);
5718 Pred = ICmpInst::getSwappedPredicate(Pred);
5723 // If there's a constant operand, canonicalize comparisons with boundary
5724 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5725 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5726 const APInt &RA = RC->getValue()->getValue();
5728 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5729 case ICmpInst::ICMP_EQ:
5730 case ICmpInst::ICMP_NE:
5731 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5733 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5734 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5735 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5736 ME->getOperand(0)->isAllOnesValue()) {
5737 RHS = AE->getOperand(1);
5738 LHS = ME->getOperand(1);
5742 case ICmpInst::ICMP_UGE:
5743 if ((RA - 1).isMinValue()) {
5744 Pred = ICmpInst::ICMP_NE;
5745 RHS = getConstant(RA - 1);
5749 if (RA.isMaxValue()) {
5750 Pred = ICmpInst::ICMP_EQ;
5754 if (RA.isMinValue()) goto trivially_true;
5756 Pred = ICmpInst::ICMP_UGT;
5757 RHS = getConstant(RA - 1);
5760 case ICmpInst::ICMP_ULE:
5761 if ((RA + 1).isMaxValue()) {
5762 Pred = ICmpInst::ICMP_NE;
5763 RHS = getConstant(RA + 1);
5767 if (RA.isMinValue()) {
5768 Pred = ICmpInst::ICMP_EQ;
5772 if (RA.isMaxValue()) goto trivially_true;
5774 Pred = ICmpInst::ICMP_ULT;
5775 RHS = getConstant(RA + 1);
5778 case ICmpInst::ICMP_SGE:
5779 if ((RA - 1).isMinSignedValue()) {
5780 Pred = ICmpInst::ICMP_NE;
5781 RHS = getConstant(RA - 1);
5785 if (RA.isMaxSignedValue()) {
5786 Pred = ICmpInst::ICMP_EQ;
5790 if (RA.isMinSignedValue()) goto trivially_true;
5792 Pred = ICmpInst::ICMP_SGT;
5793 RHS = getConstant(RA - 1);
5796 case ICmpInst::ICMP_SLE:
5797 if ((RA + 1).isMaxSignedValue()) {
5798 Pred = ICmpInst::ICMP_NE;
5799 RHS = getConstant(RA + 1);
5803 if (RA.isMinSignedValue()) {
5804 Pred = ICmpInst::ICMP_EQ;
5808 if (RA.isMaxSignedValue()) goto trivially_true;
5810 Pred = ICmpInst::ICMP_SLT;
5811 RHS = getConstant(RA + 1);
5814 case ICmpInst::ICMP_UGT:
5815 if (RA.isMinValue()) {
5816 Pred = ICmpInst::ICMP_NE;
5820 if ((RA + 1).isMaxValue()) {
5821 Pred = ICmpInst::ICMP_EQ;
5822 RHS = getConstant(RA + 1);
5826 if (RA.isMaxValue()) goto trivially_false;
5828 case ICmpInst::ICMP_ULT:
5829 if (RA.isMaxValue()) {
5830 Pred = ICmpInst::ICMP_NE;
5834 if ((RA - 1).isMinValue()) {
5835 Pred = ICmpInst::ICMP_EQ;
5836 RHS = getConstant(RA - 1);
5840 if (RA.isMinValue()) goto trivially_false;
5842 case ICmpInst::ICMP_SGT:
5843 if (RA.isMinSignedValue()) {
5844 Pred = ICmpInst::ICMP_NE;
5848 if ((RA + 1).isMaxSignedValue()) {
5849 Pred = ICmpInst::ICMP_EQ;
5850 RHS = getConstant(RA + 1);
5854 if (RA.isMaxSignedValue()) goto trivially_false;
5856 case ICmpInst::ICMP_SLT:
5857 if (RA.isMaxSignedValue()) {
5858 Pred = ICmpInst::ICMP_NE;
5862 if ((RA - 1).isMinSignedValue()) {
5863 Pred = ICmpInst::ICMP_EQ;
5864 RHS = getConstant(RA - 1);
5868 if (RA.isMinSignedValue()) goto trivially_false;
5873 // Check for obvious equality.
5874 if (HasSameValue(LHS, RHS)) {
5875 if (ICmpInst::isTrueWhenEqual(Pred))
5876 goto trivially_true;
5877 if (ICmpInst::isFalseWhenEqual(Pred))
5878 goto trivially_false;
5881 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5882 // adding or subtracting 1 from one of the operands.
5884 case ICmpInst::ICMP_SLE:
5885 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5886 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5888 Pred = ICmpInst::ICMP_SLT;
5890 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5891 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5893 Pred = ICmpInst::ICMP_SLT;
5897 case ICmpInst::ICMP_SGE:
5898 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5899 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5901 Pred = ICmpInst::ICMP_SGT;
5903 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5904 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5906 Pred = ICmpInst::ICMP_SGT;
5910 case ICmpInst::ICMP_ULE:
5911 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5912 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5914 Pred = ICmpInst::ICMP_ULT;
5916 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5917 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5919 Pred = ICmpInst::ICMP_ULT;
5923 case ICmpInst::ICMP_UGE:
5924 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5925 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5927 Pred = ICmpInst::ICMP_UGT;
5929 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5930 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5932 Pred = ICmpInst::ICMP_UGT;
5940 // TODO: More simplifications are possible here.
5942 // Recursively simplify until we either hit a recursion limit or nothing
5945 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
5951 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5952 Pred = ICmpInst::ICMP_EQ;
5957 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5958 Pred = ICmpInst::ICMP_NE;
5962 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5963 return getSignedRange(S).getSignedMax().isNegative();
5966 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5967 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5970 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5971 return !getSignedRange(S).getSignedMin().isNegative();
5974 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5975 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5978 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5979 return isKnownNegative(S) || isKnownPositive(S);
5982 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5983 const SCEV *LHS, const SCEV *RHS) {
5984 // Canonicalize the inputs first.
5985 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5987 // If LHS or RHS is an addrec, check to see if the condition is true in
5988 // every iteration of the loop.
5989 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5990 if (isLoopEntryGuardedByCond(
5991 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5992 isLoopBackedgeGuardedByCond(
5993 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5995 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5996 if (isLoopEntryGuardedByCond(
5997 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5998 isLoopBackedgeGuardedByCond(
5999 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
6002 // Otherwise see what can be done with known constant ranges.
6003 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6007 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6008 const SCEV *LHS, const SCEV *RHS) {
6009 if (HasSameValue(LHS, RHS))
6010 return ICmpInst::isTrueWhenEqual(Pred);
6012 // This code is split out from isKnownPredicate because it is called from
6013 // within isLoopEntryGuardedByCond.
6016 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6017 case ICmpInst::ICMP_SGT:
6018 Pred = ICmpInst::ICMP_SLT;
6019 std::swap(LHS, RHS);
6020 case ICmpInst::ICMP_SLT: {
6021 ConstantRange LHSRange = getSignedRange(LHS);
6022 ConstantRange RHSRange = getSignedRange(RHS);
6023 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6025 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6029 case ICmpInst::ICMP_SGE:
6030 Pred = ICmpInst::ICMP_SLE;
6031 std::swap(LHS, RHS);
6032 case ICmpInst::ICMP_SLE: {
6033 ConstantRange LHSRange = getSignedRange(LHS);
6034 ConstantRange RHSRange = getSignedRange(RHS);
6035 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6037 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6041 case ICmpInst::ICMP_UGT:
6042 Pred = ICmpInst::ICMP_ULT;
6043 std::swap(LHS, RHS);
6044 case ICmpInst::ICMP_ULT: {
6045 ConstantRange LHSRange = getUnsignedRange(LHS);
6046 ConstantRange RHSRange = getUnsignedRange(RHS);
6047 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6049 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6053 case ICmpInst::ICMP_UGE:
6054 Pred = ICmpInst::ICMP_ULE;
6055 std::swap(LHS, RHS);
6056 case ICmpInst::ICMP_ULE: {
6057 ConstantRange LHSRange = getUnsignedRange(LHS);
6058 ConstantRange RHSRange = getUnsignedRange(RHS);
6059 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6061 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6065 case ICmpInst::ICMP_NE: {
6066 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6068 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6071 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6072 if (isKnownNonZero(Diff))
6076 case ICmpInst::ICMP_EQ:
6077 // The check at the top of the function catches the case where
6078 // the values are known to be equal.
6084 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6085 /// protected by a conditional between LHS and RHS. This is used to
6086 /// to eliminate casts.
6088 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6089 ICmpInst::Predicate Pred,
6090 const SCEV *LHS, const SCEV *RHS) {
6091 // Interpret a null as meaning no loop, where there is obviously no guard
6092 // (interprocedural conditions notwithstanding).
6093 if (!L) return true;
6095 BasicBlock *Latch = L->getLoopLatch();
6099 BranchInst *LoopContinuePredicate =
6100 dyn_cast<BranchInst>(Latch->getTerminator());
6101 if (!LoopContinuePredicate ||
6102 LoopContinuePredicate->isUnconditional())
6105 return isImpliedCond(Pred, LHS, RHS,
6106 LoopContinuePredicate->getCondition(),
6107 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6110 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6111 /// by a conditional between LHS and RHS. This is used to help avoid max
6112 /// expressions in loop trip counts, and to eliminate casts.
6114 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6115 ICmpInst::Predicate Pred,
6116 const SCEV *LHS, const SCEV *RHS) {
6117 // Interpret a null as meaning no loop, where there is obviously no guard
6118 // (interprocedural conditions notwithstanding).
6119 if (!L) return false;
6121 // Starting at the loop predecessor, climb up the predecessor chain, as long
6122 // as there are predecessors that can be found that have unique successors
6123 // leading to the original header.
6124 for (std::pair<BasicBlock *, BasicBlock *>
6125 Pair(L->getLoopPredecessor(), L->getHeader());
6127 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6129 BranchInst *LoopEntryPredicate =
6130 dyn_cast<BranchInst>(Pair.first->getTerminator());
6131 if (!LoopEntryPredicate ||
6132 LoopEntryPredicate->isUnconditional())
6135 if (isImpliedCond(Pred, LHS, RHS,
6136 LoopEntryPredicate->getCondition(),
6137 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6144 /// RAII wrapper to prevent recursive application of isImpliedCond.
6145 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6146 /// currently evaluating isImpliedCond.
6147 struct MarkPendingLoopPredicate {
6149 DenseSet<Value*> &LoopPreds;
6152 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6153 : Cond(C), LoopPreds(LP) {
6154 Pending = !LoopPreds.insert(Cond).second;
6156 ~MarkPendingLoopPredicate() {
6158 LoopPreds.erase(Cond);
6162 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6163 /// and RHS is true whenever the given Cond value evaluates to true.
6164 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6165 const SCEV *LHS, const SCEV *RHS,
6166 Value *FoundCondValue,
6168 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6172 // Recursively handle And and Or conditions.
6173 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6174 if (BO->getOpcode() == Instruction::And) {
6176 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6177 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6178 } else if (BO->getOpcode() == Instruction::Or) {
6180 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6181 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6185 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6186 if (!ICI) return false;
6188 // Bail if the ICmp's operands' types are wider than the needed type
6189 // before attempting to call getSCEV on them. This avoids infinite
6190 // recursion, since the analysis of widening casts can require loop
6191 // exit condition information for overflow checking, which would
6193 if (getTypeSizeInBits(LHS->getType()) <
6194 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6197 // Now that we found a conditional branch that dominates the loop or controls
6198 // the loop latch. Check to see if it is the comparison we are looking for.
6199 ICmpInst::Predicate FoundPred;
6201 FoundPred = ICI->getInversePredicate();
6203 FoundPred = ICI->getPredicate();
6205 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6206 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6208 // Balance the types. The case where FoundLHS' type is wider than
6209 // LHS' type is checked for above.
6210 if (getTypeSizeInBits(LHS->getType()) >
6211 getTypeSizeInBits(FoundLHS->getType())) {
6212 if (CmpInst::isSigned(Pred)) {
6213 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6214 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6216 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6217 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6221 // Canonicalize the query to match the way instcombine will have
6222 // canonicalized the comparison.
6223 if (SimplifyICmpOperands(Pred, LHS, RHS))
6225 return CmpInst::isTrueWhenEqual(Pred);
6226 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6227 if (FoundLHS == FoundRHS)
6228 return CmpInst::isFalseWhenEqual(FoundPred);
6230 // Check to see if we can make the LHS or RHS match.
6231 if (LHS == FoundRHS || RHS == FoundLHS) {
6232 if (isa<SCEVConstant>(RHS)) {
6233 std::swap(FoundLHS, FoundRHS);
6234 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6236 std::swap(LHS, RHS);
6237 Pred = ICmpInst::getSwappedPredicate(Pred);
6241 // Check whether the found predicate is the same as the desired predicate.
6242 if (FoundPred == Pred)
6243 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6245 // Check whether swapping the found predicate makes it the same as the
6246 // desired predicate.
6247 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6248 if (isa<SCEVConstant>(RHS))
6249 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6251 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6252 RHS, LHS, FoundLHS, FoundRHS);
6255 // Check whether the actual condition is beyond sufficient.
6256 if (FoundPred == ICmpInst::ICMP_EQ)
6257 if (ICmpInst::isTrueWhenEqual(Pred))
6258 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6260 if (Pred == ICmpInst::ICMP_NE)
6261 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6262 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6265 // Otherwise assume the worst.
6269 /// isImpliedCondOperands - Test whether the condition described by Pred,
6270 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6271 /// and FoundRHS is true.
6272 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6273 const SCEV *LHS, const SCEV *RHS,
6274 const SCEV *FoundLHS,
6275 const SCEV *FoundRHS) {
6276 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6277 FoundLHS, FoundRHS) ||
6278 // ~x < ~y --> x > y
6279 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6280 getNotSCEV(FoundRHS),
6281 getNotSCEV(FoundLHS));
6284 /// isImpliedCondOperandsHelper - Test whether the condition described by
6285 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6286 /// FoundLHS, and FoundRHS is true.
6288 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6289 const SCEV *LHS, const SCEV *RHS,
6290 const SCEV *FoundLHS,
6291 const SCEV *FoundRHS) {
6293 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6294 case ICmpInst::ICMP_EQ:
6295 case ICmpInst::ICMP_NE:
6296 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6299 case ICmpInst::ICMP_SLT:
6300 case ICmpInst::ICMP_SLE:
6301 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6302 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6305 case ICmpInst::ICMP_SGT:
6306 case ICmpInst::ICMP_SGE:
6307 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6308 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6311 case ICmpInst::ICMP_ULT:
6312 case ICmpInst::ICMP_ULE:
6313 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6314 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6317 case ICmpInst::ICMP_UGT:
6318 case ICmpInst::ICMP_UGE:
6319 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6320 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6328 /// getBECount - Subtract the end and start values and divide by the step,
6329 /// rounding up, to get the number of times the backedge is executed. Return
6330 /// CouldNotCompute if an intermediate computation overflows.
6331 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
6335 assert(!isKnownNegative(Step) &&
6336 "This code doesn't handle negative strides yet!");
6338 Type *Ty = Start->getType();
6340 // When Start == End, we have an exact BECount == 0. Short-circuit this case
6341 // here because SCEV may not be able to determine that the unsigned division
6342 // after rounding is zero.
6344 return getConstant(Ty, 0);
6346 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
6347 const SCEV *Diff = getMinusSCEV(End, Start);
6348 const SCEV *RoundUp = getAddExpr(Step, NegOne);
6350 // Add an adjustment to the difference between End and Start so that
6351 // the division will effectively round up.
6352 const SCEV *Add = getAddExpr(Diff, RoundUp);
6355 // Check Add for unsigned overflow.
6356 // TODO: More sophisticated things could be done here.
6357 Type *WideTy = IntegerType::get(getContext(),
6358 getTypeSizeInBits(Ty) + 1);
6359 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
6360 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
6361 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
6362 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
6363 return getCouldNotCompute();
6366 return getUDivExpr(Add, Step);
6369 /// HowManyLessThans - Return the number of times a backedge containing the
6370 /// specified less-than comparison will execute. If not computable, return
6371 /// CouldNotCompute.
6373 /// @param IsSubExpr is true when the LHS < RHS condition does not directly
6374 /// control the branch. In this case, we can only compute an iteration count for
6375 /// a subexpression that cannot overflow before evaluating true.
6376 ScalarEvolution::ExitLimit
6377 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6378 const Loop *L, bool isSigned,
6380 // Only handle: "ADDREC < LoopInvariant".
6381 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
6383 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
6384 if (!AddRec || AddRec->getLoop() != L)
6385 return getCouldNotCompute();
6387 if (AddRec->isAffine()) {
6388 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
6389 const SCEV *Step = AddRec->getStepRecurrence(*this);
6392 return getCouldNotCompute();
6393 if (Step->isOne()) {
6394 // With unit stride, the iteration never steps past the limit value.
6395 } else if (isKnownPositive(Step)) {
6396 // Test whether a positive iteration can step past the limit value and
6397 // past the maximum value for its type in a single step. Constant negative
6398 // stride should be rare because LHS > RHS comparisons are canonicalized
6401 // NSW/NUW flags imply that stepping past RHS would immediately result in
6402 // undefined behavior. No self-wrap is not useful here because the loop
6403 // counter may signed or unsigned wrap but continue iterating and
6404 // terminate with defined behavior without ever self-wrapping.
6405 const SCEV *One = getConstant(Step->getType(), 1);
6407 if (!AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
6408 APInt Max = APInt::getSignedMaxValue(BitWidth);
6409 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
6410 .slt(getSignedRange(RHS).getSignedMax()))
6411 return getCouldNotCompute();
6413 } else if (!AddRec->getNoWrapFlags(SCEV::FlagNUW)){
6414 APInt Max = APInt::getMaxValue(BitWidth);
6415 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
6416 .ult(getUnsignedRange(RHS).getUnsignedMax()))
6417 return getCouldNotCompute();
6420 // Cannot handle variable stride.
6421 return getCouldNotCompute();
6423 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6424 // m. So, we count the number of iterations in which {n,+,s} < m is true.
6425 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6426 // treat m-n as signed nor unsigned due to overflow possibility.
6428 // First, we get the value of the LHS in the first iteration: n
6429 const SCEV *Start = AddRec->getOperand(0);
6431 // Determine the minimum constant start value.
6432 const SCEV *MinStart = getConstant(isSigned ?
6433 getSignedRange(Start).getSignedMin() :
6434 getUnsignedRange(Start).getUnsignedMin());
6436 // If we know that the condition is true in order to enter the loop,
6437 // then we know that it will run exactly (m-n)/s times. Otherwise, we
6438 // only know that it will execute (max(m,n)-n)/s times. In both cases,
6439 // the division must round up.
6440 const SCEV *End = RHS;
6441 if (!isLoopEntryGuardedByCond(L,
6442 isSigned ? ICmpInst::ICMP_SLT :
6444 getMinusSCEV(Start, Step), RHS))
6445 End = isSigned ? getSMaxExpr(RHS, Start)
6446 : getUMaxExpr(RHS, Start);
6448 // Determine the maximum constant end value.
6449 const SCEV *MaxEnd = getConstant(isSigned ?
6450 getSignedRange(End).getSignedMax() :
6451 getUnsignedRange(End).getUnsignedMax());
6453 // If MaxEnd is within a step of the maximum integer value in its type,
6454 // adjust it down to the minimum value which would produce the same effect.
6455 // This allows the subsequent ceiling division of (N+(step-1))/step to
6456 // compute the correct value.
6457 const SCEV *StepMinusOne = getMinusSCEV(Step,
6458 getConstant(Step->getType(), 1));
6461 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6464 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6467 // If the loop counter does not self-wrap, then the trip count may be
6468 // computed by dividing the distance by the step. This is independent of
6469 // signed or unsigned wrap.
6470 bool NoWrap = false;
6472 NoWrap = AddRec->getNoWrapFlags(
6473 (SCEV::NoWrapFlags)(((isSigned ? SCEV::FlagNSW : SCEV::FlagNUW))
6476 // Finally, we subtract these two values and divide, rounding up, to get
6477 // the number of times the backedge is executed.
6478 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6480 // The maximum backedge count is similar, except using the minimum start
6481 // value and the maximum end value.
6482 // If we already have an exact constant BECount, use it instead.
6483 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6484 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6486 // If the stride is nonconstant, and NoWrap == true, then
6487 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6488 // exact BECount and invalid MaxBECount, which should be avoided to catch
6489 // more optimization opportunities.
6490 if (isa<SCEVCouldNotCompute>(MaxBECount))
6491 MaxBECount = BECount;
6493 return ExitLimit(BECount, MaxBECount);
6496 return getCouldNotCompute();
6499 /// getNumIterationsInRange - Return the number of iterations of this loop that
6500 /// produce values in the specified constant range. Another way of looking at
6501 /// this is that it returns the first iteration number where the value is not in
6502 /// the condition, thus computing the exit count. If the iteration count can't
6503 /// be computed, an instance of SCEVCouldNotCompute is returned.
6504 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6505 ScalarEvolution &SE) const {
6506 if (Range.isFullSet()) // Infinite loop.
6507 return SE.getCouldNotCompute();
6509 // If the start is a non-zero constant, shift the range to simplify things.
6510 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6511 if (!SC->getValue()->isZero()) {
6512 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6513 Operands[0] = SE.getConstant(SC->getType(), 0);
6514 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6515 getNoWrapFlags(FlagNW));
6516 if (const SCEVAddRecExpr *ShiftedAddRec =
6517 dyn_cast<SCEVAddRecExpr>(Shifted))
6518 return ShiftedAddRec->getNumIterationsInRange(
6519 Range.subtract(SC->getValue()->getValue()), SE);
6520 // This is strange and shouldn't happen.
6521 return SE.getCouldNotCompute();
6524 // The only time we can solve this is when we have all constant indices.
6525 // Otherwise, we cannot determine the overflow conditions.
6526 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6527 if (!isa<SCEVConstant>(getOperand(i)))
6528 return SE.getCouldNotCompute();
6531 // Okay at this point we know that all elements of the chrec are constants and
6532 // that the start element is zero.
6534 // First check to see if the range contains zero. If not, the first
6536 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6537 if (!Range.contains(APInt(BitWidth, 0)))
6538 return SE.getConstant(getType(), 0);
6541 // If this is an affine expression then we have this situation:
6542 // Solve {0,+,A} in Range === Ax in Range
6544 // We know that zero is in the range. If A is positive then we know that
6545 // the upper value of the range must be the first possible exit value.
6546 // If A is negative then the lower of the range is the last possible loop
6547 // value. Also note that we already checked for a full range.
6548 APInt One(BitWidth,1);
6549 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6550 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6552 // The exit value should be (End+A)/A.
6553 APInt ExitVal = (End + A).udiv(A);
6554 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6556 // Evaluate at the exit value. If we really did fall out of the valid
6557 // range, then we computed our trip count, otherwise wrap around or other
6558 // things must have happened.
6559 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6560 if (Range.contains(Val->getValue()))
6561 return SE.getCouldNotCompute(); // Something strange happened
6563 // Ensure that the previous value is in the range. This is a sanity check.
6564 assert(Range.contains(
6565 EvaluateConstantChrecAtConstant(this,
6566 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6567 "Linear scev computation is off in a bad way!");
6568 return SE.getConstant(ExitValue);
6569 } else if (isQuadratic()) {
6570 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6571 // quadratic equation to solve it. To do this, we must frame our problem in
6572 // terms of figuring out when zero is crossed, instead of when
6573 // Range.getUpper() is crossed.
6574 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6575 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6576 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6577 // getNoWrapFlags(FlagNW)
6580 // Next, solve the constructed addrec
6581 std::pair<const SCEV *,const SCEV *> Roots =
6582 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6583 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6584 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6586 // Pick the smallest positive root value.
6587 if (ConstantInt *CB =
6588 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6589 R1->getValue(), R2->getValue()))) {
6590 if (CB->getZExtValue() == false)
6591 std::swap(R1, R2); // R1 is the minimum root now.
6593 // Make sure the root is not off by one. The returned iteration should
6594 // not be in the range, but the previous one should be. When solving
6595 // for "X*X < 5", for example, we should not return a root of 2.
6596 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6599 if (Range.contains(R1Val->getValue())) {
6600 // The next iteration must be out of the range...
6601 ConstantInt *NextVal =
6602 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6604 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6605 if (!Range.contains(R1Val->getValue()))
6606 return SE.getConstant(NextVal);
6607 return SE.getCouldNotCompute(); // Something strange happened
6610 // If R1 was not in the range, then it is a good return value. Make
6611 // sure that R1-1 WAS in the range though, just in case.
6612 ConstantInt *NextVal =
6613 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6614 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6615 if (Range.contains(R1Val->getValue()))
6617 return SE.getCouldNotCompute(); // Something strange happened
6622 return SE.getCouldNotCompute();
6627 //===----------------------------------------------------------------------===//
6628 // SCEVCallbackVH Class Implementation
6629 //===----------------------------------------------------------------------===//
6631 void ScalarEvolution::SCEVCallbackVH::deleted() {
6632 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6633 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6634 SE->ConstantEvolutionLoopExitValue.erase(PN);
6635 SE->ValueExprMap.erase(getValPtr());
6636 // this now dangles!
6639 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6640 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6642 // Forget all the expressions associated with users of the old value,
6643 // so that future queries will recompute the expressions using the new
6645 Value *Old = getValPtr();
6646 SmallVector<User *, 16> Worklist;
6647 SmallPtrSet<User *, 8> Visited;
6648 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6650 Worklist.push_back(*UI);
6651 while (!Worklist.empty()) {
6652 User *U = Worklist.pop_back_val();
6653 // Deleting the Old value will cause this to dangle. Postpone
6654 // that until everything else is done.
6657 if (!Visited.insert(U))
6659 if (PHINode *PN = dyn_cast<PHINode>(U))
6660 SE->ConstantEvolutionLoopExitValue.erase(PN);
6661 SE->ValueExprMap.erase(U);
6662 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6664 Worklist.push_back(*UI);
6666 // Delete the Old value.
6667 if (PHINode *PN = dyn_cast<PHINode>(Old))
6668 SE->ConstantEvolutionLoopExitValue.erase(PN);
6669 SE->ValueExprMap.erase(Old);
6670 // this now dangles!
6673 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6674 : CallbackVH(V), SE(se) {}
6676 //===----------------------------------------------------------------------===//
6677 // ScalarEvolution Class Implementation
6678 //===----------------------------------------------------------------------===//
6680 ScalarEvolution::ScalarEvolution()
6681 : FunctionPass(ID), FirstUnknown(0) {
6682 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6685 bool ScalarEvolution::runOnFunction(Function &F) {
6687 LI = &getAnalysis<LoopInfo>();
6688 TD = getAnalysisIfAvailable<DataLayout>();
6689 TLI = &getAnalysis<TargetLibraryInfo>();
6690 DT = &getAnalysis<DominatorTree>();
6694 void ScalarEvolution::releaseMemory() {
6695 // Iterate through all the SCEVUnknown instances and call their
6696 // destructors, so that they release their references to their values.
6697 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6701 ValueExprMap.clear();
6703 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6704 // that a loop had multiple computable exits.
6705 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6706 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6711 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
6713 BackedgeTakenCounts.clear();
6714 ConstantEvolutionLoopExitValue.clear();
6715 ValuesAtScopes.clear();
6716 LoopDispositions.clear();
6717 BlockDispositions.clear();
6718 UnsignedRanges.clear();
6719 SignedRanges.clear();
6720 UniqueSCEVs.clear();
6721 SCEVAllocator.Reset();
6724 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6725 AU.setPreservesAll();
6726 AU.addRequiredTransitive<LoopInfo>();
6727 AU.addRequiredTransitive<DominatorTree>();
6728 AU.addRequired<TargetLibraryInfo>();
6731 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6732 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6735 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6737 // Print all inner loops first
6738 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6739 PrintLoopInfo(OS, SE, *I);
6742 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6745 SmallVector<BasicBlock *, 8> ExitBlocks;
6746 L->getExitBlocks(ExitBlocks);
6747 if (ExitBlocks.size() != 1)
6748 OS << "<multiple exits> ";
6750 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6751 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6753 OS << "Unpredictable backedge-taken count. ";
6758 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6761 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6762 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6764 OS << "Unpredictable max backedge-taken count. ";
6770 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6771 // ScalarEvolution's implementation of the print method is to print
6772 // out SCEV values of all instructions that are interesting. Doing
6773 // this potentially causes it to create new SCEV objects though,
6774 // which technically conflicts with the const qualifier. This isn't
6775 // observable from outside the class though, so casting away the
6776 // const isn't dangerous.
6777 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6779 OS << "Classifying expressions for: ";
6780 WriteAsOperand(OS, F, /*PrintType=*/false);
6782 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6783 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6786 const SCEV *SV = SE.getSCEV(&*I);
6789 const Loop *L = LI->getLoopFor((*I).getParent());
6791 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6798 OS << "\t\t" "Exits: ";
6799 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6800 if (!SE.isLoopInvariant(ExitValue, L)) {
6801 OS << "<<Unknown>>";
6810 OS << "Determining loop execution counts for: ";
6811 WriteAsOperand(OS, F, /*PrintType=*/false);
6813 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6814 PrintLoopInfo(OS, &SE, *I);
6817 ScalarEvolution::LoopDisposition
6818 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6819 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6820 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6821 Values.insert(std::make_pair(L, LoopVariant));
6823 return Pair.first->second;
6825 LoopDisposition D = computeLoopDisposition(S, L);
6826 return LoopDispositions[S][L] = D;
6829 ScalarEvolution::LoopDisposition
6830 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6831 switch (S->getSCEVType()) {
6833 return LoopInvariant;
6837 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6838 case scAddRecExpr: {
6839 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6841 // If L is the addrec's loop, it's computable.
6842 if (AR->getLoop() == L)
6843 return LoopComputable;
6845 // Add recurrences are never invariant in the function-body (null loop).
6849 // This recurrence is variant w.r.t. L if L contains AR's loop.
6850 if (L->contains(AR->getLoop()))
6853 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6854 if (AR->getLoop()->contains(L))
6855 return LoopInvariant;
6857 // This recurrence is variant w.r.t. L if any of its operands
6859 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6861 if (!isLoopInvariant(*I, L))
6864 // Otherwise it's loop-invariant.
6865 return LoopInvariant;
6871 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6872 bool HasVarying = false;
6873 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6875 LoopDisposition D = getLoopDisposition(*I, L);
6876 if (D == LoopVariant)
6878 if (D == LoopComputable)
6881 return HasVarying ? LoopComputable : LoopInvariant;
6884 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6885 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6886 if (LD == LoopVariant)
6888 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6889 if (RD == LoopVariant)
6891 return (LD == LoopInvariant && RD == LoopInvariant) ?
6892 LoopInvariant : LoopComputable;
6895 // All non-instruction values are loop invariant. All instructions are loop
6896 // invariant if they are not contained in the specified loop.
6897 // Instructions are never considered invariant in the function body
6898 // (null loop) because they are defined within the "loop".
6899 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6900 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6901 return LoopInvariant;
6902 case scCouldNotCompute:
6903 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6904 default: llvm_unreachable("Unknown SCEV kind!");
6908 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6909 return getLoopDisposition(S, L) == LoopInvariant;
6912 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6913 return getLoopDisposition(S, L) == LoopComputable;
6916 ScalarEvolution::BlockDisposition
6917 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6918 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6919 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6920 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6922 return Pair.first->second;
6924 BlockDisposition D = computeBlockDisposition(S, BB);
6925 return BlockDispositions[S][BB] = D;
6928 ScalarEvolution::BlockDisposition
6929 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6930 switch (S->getSCEVType()) {
6932 return ProperlyDominatesBlock;
6936 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6937 case scAddRecExpr: {
6938 // This uses a "dominates" query instead of "properly dominates" query
6939 // to test for proper dominance too, because the instruction which
6940 // produces the addrec's value is a PHI, and a PHI effectively properly
6941 // dominates its entire containing block.
6942 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6943 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6944 return DoesNotDominateBlock;
6946 // FALL THROUGH into SCEVNAryExpr handling.
6951 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6953 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6955 BlockDisposition D = getBlockDisposition(*I, BB);
6956 if (D == DoesNotDominateBlock)
6957 return DoesNotDominateBlock;
6958 if (D == DominatesBlock)
6961 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6964 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6965 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6966 BlockDisposition LD = getBlockDisposition(LHS, BB);
6967 if (LD == DoesNotDominateBlock)
6968 return DoesNotDominateBlock;
6969 BlockDisposition RD = getBlockDisposition(RHS, BB);
6970 if (RD == DoesNotDominateBlock)
6971 return DoesNotDominateBlock;
6972 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6973 ProperlyDominatesBlock : DominatesBlock;
6976 if (Instruction *I =
6977 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6978 if (I->getParent() == BB)
6979 return DominatesBlock;
6980 if (DT->properlyDominates(I->getParent(), BB))
6981 return ProperlyDominatesBlock;
6982 return DoesNotDominateBlock;
6984 return ProperlyDominatesBlock;
6985 case scCouldNotCompute:
6986 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6988 llvm_unreachable("Unknown SCEV kind!");
6992 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6993 return getBlockDisposition(S, BB) >= DominatesBlock;
6996 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6997 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
7001 // Search for a SCEV expression node within an expression tree.
7002 // Implements SCEVTraversal::Visitor.
7007 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
7009 bool follow(const SCEV *S) {
7010 IsFound |= (S == Node);
7013 bool isDone() const { return IsFound; }
7017 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
7018 SCEVSearch Search(Op);
7019 visitAll(S, Search);
7020 return Search.IsFound;
7023 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
7024 ValuesAtScopes.erase(S);
7025 LoopDispositions.erase(S);
7026 BlockDispositions.erase(S);
7027 UnsignedRanges.erase(S);
7028 SignedRanges.erase(S);
7030 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7031 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
7032 BackedgeTakenInfo &BEInfo = I->second;
7033 if (BEInfo.hasOperand(S, this)) {
7035 BackedgeTakenCounts.erase(I++);
7042 typedef DenseMap<const Loop *, std::string> VerifyMap;
7044 /// replaceSubString - Replaces all occurences of From in Str with To.
7045 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
7047 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
7048 Str.replace(Pos, From.size(), To.data(), To.size());
7053 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
7055 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
7056 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
7057 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
7059 std::string &S = Map[L];
7061 raw_string_ostream OS(S);
7062 SE.getBackedgeTakenCount(L)->print(OS);
7064 // false and 0 are semantically equivalent. This can happen in dead loops.
7065 replaceSubString(OS.str(), "false", "0");
7066 // Remove wrap flags, their use in SCEV is highly fragile.
7067 // FIXME: Remove this when SCEV gets smarter about them.
7068 replaceSubString(OS.str(), "<nw>", "");
7069 replaceSubString(OS.str(), "<nsw>", "");
7070 replaceSubString(OS.str(), "<nuw>", "");
7075 void ScalarEvolution::verifyAnalysis() const {
7079 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7081 // Gather stringified backedge taken counts for all loops using SCEV's caches.
7082 // FIXME: It would be much better to store actual values instead of strings,
7083 // but SCEV pointers will change if we drop the caches.
7084 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
7085 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7086 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
7088 // Gather stringified backedge taken counts for all loops without using
7091 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7092 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
7094 // Now compare whether they're the same with and without caches. This allows
7095 // verifying that no pass changed the cache.
7096 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
7097 "New loops suddenly appeared!");
7099 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
7100 OldE = BackedgeDumpsOld.end(),
7101 NewI = BackedgeDumpsNew.begin();
7102 OldI != OldE; ++OldI, ++NewI) {
7103 assert(OldI->first == NewI->first && "Loop order changed!");
7105 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
7107 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
7108 // means that a pass is buggy or SCEV has to learn a new pattern but is
7109 // usually not harmful.
7110 if (OldI->second != NewI->second &&
7111 OldI->second.find("undef") == std::string::npos &&
7112 NewI->second.find("undef") == std::string::npos &&
7113 OldI->second != "***COULDNOTCOMPUTE***" &&
7114 NewI->second != "***COULDNOTCOMPUTE***") {
7115 dbgs() << "SCEVValidator: SCEV for loop '"
7116 << OldI->first->getHeader()->getName()
7117 << "' changed from '" << OldI->second
7118 << "' to '" << NewI->second << "'!\n";
7123 // TODO: Verify more things.