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/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/GlobalAlias.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/Operator.h"
70 #include "llvm/Analysis/ConstantFolding.h"
71 #include "llvm/Analysis/Dominators.h"
72 #include "llvm/Analysis/InstructionSimplify.h"
73 #include "llvm/Analysis/LoopInfo.h"
74 #include "llvm/Analysis/ValueTracking.h"
75 #include "llvm/Assembly/Writer.h"
76 #include "llvm/Target/TargetData.h"
77 #include "llvm/Target/TargetLibraryInfo.h"
78 #include "llvm/Support/CommandLine.h"
79 #include "llvm/Support/ConstantRange.h"
80 #include "llvm/Support/Debug.h"
81 #include "llvm/Support/ErrorHandling.h"
82 #include "llvm/Support/GetElementPtrTypeIterator.h"
83 #include "llvm/Support/InstIterator.h"
84 #include "llvm/Support/MathExtras.h"
85 #include "llvm/Support/raw_ostream.h"
86 #include "llvm/ADT/Statistic.h"
87 #include "llvm/ADT/STLExtras.h"
88 #include "llvm/ADT/SmallPtrSet.h"
92 STATISTIC(NumArrayLenItCounts,
93 "Number of trip counts computed with array length");
94 STATISTIC(NumTripCountsComputed,
95 "Number of loops with predictable loop counts");
96 STATISTIC(NumTripCountsNotComputed,
97 "Number of loops without predictable loop counts");
98 STATISTIC(NumBruteForceTripCountsComputed,
99 "Number of loops with trip counts computed by force");
101 static cl::opt<unsigned>
102 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
103 cl::desc("Maximum number of iterations SCEV will "
104 "symbolically execute a constant "
108 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
109 "Scalar Evolution Analysis", false, true)
110 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
111 INITIALIZE_PASS_DEPENDENCY(DominatorTree)
112 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
113 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
114 "Scalar Evolution Analysis", false, true)
115 char ScalarEvolution::ID = 0;
117 //===----------------------------------------------------------------------===//
118 // SCEV class definitions
119 //===----------------------------------------------------------------------===//
121 //===----------------------------------------------------------------------===//
122 // Implementation of the SCEV class.
125 void SCEV::dump() const {
130 void SCEV::print(raw_ostream &OS) const {
131 switch (getSCEVType()) {
133 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false);
136 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
137 const SCEV *Op = Trunc->getOperand();
138 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
139 << *Trunc->getType() << ")";
143 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
144 const SCEV *Op = ZExt->getOperand();
145 OS << "(zext " << *Op->getType() << " " << *Op << " to "
146 << *ZExt->getType() << ")";
150 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
151 const SCEV *Op = SExt->getOperand();
152 OS << "(sext " << *Op->getType() << " " << *Op << " to "
153 << *SExt->getType() << ")";
157 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
158 OS << "{" << *AR->getOperand(0);
159 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
160 OS << ",+," << *AR->getOperand(i);
162 if (AR->getNoWrapFlags(FlagNUW))
164 if (AR->getNoWrapFlags(FlagNSW))
166 if (AR->getNoWrapFlags(FlagNW) &&
167 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
169 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false);
177 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
178 const char *OpStr = 0;
179 switch (NAry->getSCEVType()) {
180 case scAddExpr: OpStr = " + "; break;
181 case scMulExpr: OpStr = " * "; break;
182 case scUMaxExpr: OpStr = " umax "; break;
183 case scSMaxExpr: OpStr = " smax "; break;
186 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
189 if (llvm::next(I) != E)
193 switch (NAry->getSCEVType()) {
196 if (NAry->getNoWrapFlags(FlagNUW))
198 if (NAry->getNoWrapFlags(FlagNSW))
204 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
205 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
209 const SCEVUnknown *U = cast<SCEVUnknown>(this);
211 if (U->isSizeOf(AllocTy)) {
212 OS << "sizeof(" << *AllocTy << ")";
215 if (U->isAlignOf(AllocTy)) {
216 OS << "alignof(" << *AllocTy << ")";
222 if (U->isOffsetOf(CTy, FieldNo)) {
223 OS << "offsetof(" << *CTy << ", ";
224 WriteAsOperand(OS, FieldNo, false);
229 // Otherwise just print it normally.
230 WriteAsOperand(OS, U->getValue(), false);
233 case scCouldNotCompute:
234 OS << "***COULDNOTCOMPUTE***";
238 llvm_unreachable("Unknown SCEV kind!");
241 Type *SCEV::getType() const {
242 switch (getSCEVType()) {
244 return cast<SCEVConstant>(this)->getType();
248 return cast<SCEVCastExpr>(this)->getType();
253 return cast<SCEVNAryExpr>(this)->getType();
255 return cast<SCEVAddExpr>(this)->getType();
257 return cast<SCEVUDivExpr>(this)->getType();
259 return cast<SCEVUnknown>(this)->getType();
260 case scCouldNotCompute:
261 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
263 llvm_unreachable("Unknown SCEV kind!");
267 bool SCEV::isZero() const {
268 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
269 return SC->getValue()->isZero();
273 bool SCEV::isOne() const {
274 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
275 return SC->getValue()->isOne();
279 bool SCEV::isAllOnesValue() const {
280 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
281 return SC->getValue()->isAllOnesValue();
285 /// isNonConstantNegative - Return true if the specified scev is negated, but
287 bool SCEV::isNonConstantNegative() const {
288 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
289 if (!Mul) return false;
291 // If there is a constant factor, it will be first.
292 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
293 if (!SC) return false;
295 // Return true if the value is negative, this matches things like (-42 * V).
296 return SC->getValue()->getValue().isNegative();
299 SCEVCouldNotCompute::SCEVCouldNotCompute() :
300 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
302 bool SCEVCouldNotCompute::classof(const SCEV *S) {
303 return S->getSCEVType() == scCouldNotCompute;
306 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
308 ID.AddInteger(scConstant);
311 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
312 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
313 UniqueSCEVs.InsertNode(S, IP);
317 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
318 return getConstant(ConstantInt::get(getContext(), Val));
322 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
323 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
324 return getConstant(ConstantInt::get(ITy, V, isSigned));
327 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
328 unsigned SCEVTy, const SCEV *op, Type *ty)
329 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
331 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
332 const SCEV *op, Type *ty)
333 : SCEVCastExpr(ID, scTruncate, op, ty) {
334 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
335 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
336 "Cannot truncate non-integer value!");
339 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
340 const SCEV *op, Type *ty)
341 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
342 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
343 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
344 "Cannot zero extend non-integer value!");
347 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
348 const SCEV *op, Type *ty)
349 : SCEVCastExpr(ID, scSignExtend, op, ty) {
350 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
351 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
352 "Cannot sign extend non-integer value!");
355 void SCEVUnknown::deleted() {
356 // Clear this SCEVUnknown from various maps.
357 SE->forgetMemoizedResults(this);
359 // Remove this SCEVUnknown from the uniquing map.
360 SE->UniqueSCEVs.RemoveNode(this);
362 // Release the value.
366 void SCEVUnknown::allUsesReplacedWith(Value *New) {
367 // Clear this SCEVUnknown from various maps.
368 SE->forgetMemoizedResults(this);
370 // Remove this SCEVUnknown from the uniquing map.
371 SE->UniqueSCEVs.RemoveNode(this);
373 // Update this SCEVUnknown to point to the new value. This is needed
374 // because there may still be outstanding SCEVs which still point to
379 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
380 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
381 if (VCE->getOpcode() == Instruction::PtrToInt)
382 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
383 if (CE->getOpcode() == Instruction::GetElementPtr &&
384 CE->getOperand(0)->isNullValue() &&
385 CE->getNumOperands() == 2)
386 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
388 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
396 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
397 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
398 if (VCE->getOpcode() == Instruction::PtrToInt)
399 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
400 if (CE->getOpcode() == Instruction::GetElementPtr &&
401 CE->getOperand(0)->isNullValue()) {
403 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
404 if (StructType *STy = dyn_cast<StructType>(Ty))
405 if (!STy->isPacked() &&
406 CE->getNumOperands() == 3 &&
407 CE->getOperand(1)->isNullValue()) {
408 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
410 STy->getNumElements() == 2 &&
411 STy->getElementType(0)->isIntegerTy(1)) {
412 AllocTy = STy->getElementType(1);
421 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
422 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
423 if (VCE->getOpcode() == Instruction::PtrToInt)
424 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
425 if (CE->getOpcode() == Instruction::GetElementPtr &&
426 CE->getNumOperands() == 3 &&
427 CE->getOperand(0)->isNullValue() &&
428 CE->getOperand(1)->isNullValue()) {
430 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
431 // Ignore vector types here so that ScalarEvolutionExpander doesn't
432 // emit getelementptrs that index into vectors.
433 if (Ty->isStructTy() || Ty->isArrayTy()) {
435 FieldNo = CE->getOperand(2);
443 //===----------------------------------------------------------------------===//
445 //===----------------------------------------------------------------------===//
448 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
449 /// than the complexity of the RHS. This comparator is used to canonicalize
451 class SCEVComplexityCompare {
452 const LoopInfo *const LI;
454 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
456 // Return true or false if LHS is less than, or at least RHS, respectively.
457 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
458 return compare(LHS, RHS) < 0;
461 // Return negative, zero, or positive, if LHS is less than, equal to, or
462 // greater than RHS, respectively. A three-way result allows recursive
463 // comparisons to be more efficient.
464 int compare(const SCEV *LHS, const SCEV *RHS) const {
465 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
469 // Primarily, sort the SCEVs by their getSCEVType().
470 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
472 return (int)LType - (int)RType;
474 // Aside from the getSCEVType() ordering, the particular ordering
475 // isn't very important except that it's beneficial to be consistent,
476 // so that (a + b) and (b + a) don't end up as different expressions.
479 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
480 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
482 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
483 // not as complete as it could be.
484 const Value *LV = LU->getValue(), *RV = RU->getValue();
486 // Order pointer values after integer values. This helps SCEVExpander
488 bool LIsPointer = LV->getType()->isPointerTy(),
489 RIsPointer = RV->getType()->isPointerTy();
490 if (LIsPointer != RIsPointer)
491 return (int)LIsPointer - (int)RIsPointer;
493 // Compare getValueID values.
494 unsigned LID = LV->getValueID(),
495 RID = RV->getValueID();
497 return (int)LID - (int)RID;
499 // Sort arguments by their position.
500 if (const Argument *LA = dyn_cast<Argument>(LV)) {
501 const Argument *RA = cast<Argument>(RV);
502 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
503 return (int)LArgNo - (int)RArgNo;
506 // For instructions, compare their loop depth, and their operand
507 // count. This is pretty loose.
508 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
509 const Instruction *RInst = cast<Instruction>(RV);
511 // Compare loop depths.
512 const BasicBlock *LParent = LInst->getParent(),
513 *RParent = RInst->getParent();
514 if (LParent != RParent) {
515 unsigned LDepth = LI->getLoopDepth(LParent),
516 RDepth = LI->getLoopDepth(RParent);
517 if (LDepth != RDepth)
518 return (int)LDepth - (int)RDepth;
521 // Compare the number of operands.
522 unsigned LNumOps = LInst->getNumOperands(),
523 RNumOps = RInst->getNumOperands();
524 return (int)LNumOps - (int)RNumOps;
531 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
532 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
534 // Compare constant values.
535 const APInt &LA = LC->getValue()->getValue();
536 const APInt &RA = RC->getValue()->getValue();
537 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
538 if (LBitWidth != RBitWidth)
539 return (int)LBitWidth - (int)RBitWidth;
540 return LA.ult(RA) ? -1 : 1;
544 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
545 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
547 // Compare addrec loop depths.
548 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
549 if (LLoop != RLoop) {
550 unsigned LDepth = LLoop->getLoopDepth(),
551 RDepth = RLoop->getLoopDepth();
552 if (LDepth != RDepth)
553 return (int)LDepth - (int)RDepth;
556 // Addrec complexity grows with operand count.
557 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
558 if (LNumOps != RNumOps)
559 return (int)LNumOps - (int)RNumOps;
561 // Lexicographically compare.
562 for (unsigned i = 0; i != LNumOps; ++i) {
563 long X = compare(LA->getOperand(i), RA->getOperand(i));
575 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
576 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
578 // Lexicographically compare n-ary expressions.
579 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
580 for (unsigned i = 0; i != LNumOps; ++i) {
583 long X = compare(LC->getOperand(i), RC->getOperand(i));
587 return (int)LNumOps - (int)RNumOps;
591 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
592 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
594 // Lexicographically compare udiv expressions.
595 long X = compare(LC->getLHS(), RC->getLHS());
598 return compare(LC->getRHS(), RC->getRHS());
604 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
605 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
607 // Compare cast expressions by operand.
608 return compare(LC->getOperand(), RC->getOperand());
612 llvm_unreachable("Unknown SCEV kind!");
618 /// GroupByComplexity - Given a list of SCEV objects, order them by their
619 /// complexity, and group objects of the same complexity together by value.
620 /// When this routine is finished, we know that any duplicates in the vector are
621 /// consecutive and that complexity is monotonically increasing.
623 /// Note that we go take special precautions to ensure that we get deterministic
624 /// results from this routine. In other words, we don't want the results of
625 /// this to depend on where the addresses of various SCEV objects happened to
628 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
630 if (Ops.size() < 2) return; // Noop
631 if (Ops.size() == 2) {
632 // This is the common case, which also happens to be trivially simple.
634 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
635 if (SCEVComplexityCompare(LI)(RHS, LHS))
640 // Do the rough sort by complexity.
641 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
643 // Now that we are sorted by complexity, group elements of the same
644 // complexity. Note that this is, at worst, N^2, but the vector is likely to
645 // be extremely short in practice. Note that we take this approach because we
646 // do not want to depend on the addresses of the objects we are grouping.
647 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
648 const SCEV *S = Ops[i];
649 unsigned Complexity = S->getSCEVType();
651 // If there are any objects of the same complexity and same value as this
653 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
654 if (Ops[j] == S) { // Found a duplicate.
655 // Move it to immediately after i'th element.
656 std::swap(Ops[i+1], Ops[j]);
657 ++i; // no need to rescan it.
658 if (i == e-2) return; // Done!
666 //===----------------------------------------------------------------------===//
667 // Simple SCEV method implementations
668 //===----------------------------------------------------------------------===//
670 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
672 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
675 // Handle the simplest case efficiently.
677 return SE.getTruncateOrZeroExtend(It, ResultTy);
679 // We are using the following formula for BC(It, K):
681 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
683 // Suppose, W is the bitwidth of the return value. We must be prepared for
684 // overflow. Hence, we must assure that the result of our computation is
685 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
686 // safe in modular arithmetic.
688 // However, this code doesn't use exactly that formula; the formula it uses
689 // is something like the following, where T is the number of factors of 2 in
690 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
693 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
695 // This formula is trivially equivalent to the previous formula. However,
696 // this formula can be implemented much more efficiently. The trick is that
697 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
698 // arithmetic. To do exact division in modular arithmetic, all we have
699 // to do is multiply by the inverse. Therefore, this step can be done at
702 // The next issue is how to safely do the division by 2^T. The way this
703 // is done is by doing the multiplication step at a width of at least W + T
704 // bits. This way, the bottom W+T bits of the product are accurate. Then,
705 // when we perform the division by 2^T (which is equivalent to a right shift
706 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
707 // truncated out after the division by 2^T.
709 // In comparison to just directly using the first formula, this technique
710 // is much more efficient; using the first formula requires W * K bits,
711 // but this formula less than W + K bits. Also, the first formula requires
712 // a division step, whereas this formula only requires multiplies and shifts.
714 // It doesn't matter whether the subtraction step is done in the calculation
715 // width or the input iteration count's width; if the subtraction overflows,
716 // the result must be zero anyway. We prefer here to do it in the width of
717 // the induction variable because it helps a lot for certain cases; CodeGen
718 // isn't smart enough to ignore the overflow, which leads to much less
719 // efficient code if the width of the subtraction is wider than the native
722 // (It's possible to not widen at all by pulling out factors of 2 before
723 // the multiplication; for example, K=2 can be calculated as
724 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
725 // extra arithmetic, so it's not an obvious win, and it gets
726 // much more complicated for K > 3.)
728 // Protection from insane SCEVs; this bound is conservative,
729 // but it probably doesn't matter.
731 return SE.getCouldNotCompute();
733 unsigned W = SE.getTypeSizeInBits(ResultTy);
735 // Calculate K! / 2^T and T; we divide out the factors of two before
736 // multiplying for calculating K! / 2^T to avoid overflow.
737 // Other overflow doesn't matter because we only care about the bottom
738 // W bits of the result.
739 APInt OddFactorial(W, 1);
741 for (unsigned i = 3; i <= K; ++i) {
743 unsigned TwoFactors = Mult.countTrailingZeros();
745 Mult = Mult.lshr(TwoFactors);
746 OddFactorial *= Mult;
749 // We need at least W + T bits for the multiplication step
750 unsigned CalculationBits = W + T;
752 // Calculate 2^T, at width T+W.
753 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
755 // Calculate the multiplicative inverse of K! / 2^T;
756 // this multiplication factor will perform the exact division by
758 APInt Mod = APInt::getSignedMinValue(W+1);
759 APInt MultiplyFactor = OddFactorial.zext(W+1);
760 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
761 MultiplyFactor = MultiplyFactor.trunc(W);
763 // Calculate the product, at width T+W
764 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
766 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
767 for (unsigned i = 1; i != K; ++i) {
768 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
769 Dividend = SE.getMulExpr(Dividend,
770 SE.getTruncateOrZeroExtend(S, CalculationTy));
774 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
776 // Truncate the result, and divide by K! / 2^T.
778 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
779 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
782 /// evaluateAtIteration - Return the value of this chain of recurrences at
783 /// the specified iteration number. We can evaluate this recurrence by
784 /// multiplying each element in the chain by the binomial coefficient
785 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
787 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
789 /// where BC(It, k) stands for binomial coefficient.
791 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
792 ScalarEvolution &SE) const {
793 const SCEV *Result = getStart();
794 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
795 // The computation is correct in the face of overflow provided that the
796 // multiplication is performed _after_ the evaluation of the binomial
798 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
799 if (isa<SCEVCouldNotCompute>(Coeff))
802 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
807 //===----------------------------------------------------------------------===//
808 // SCEV Expression folder implementations
809 //===----------------------------------------------------------------------===//
811 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
813 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
814 "This is not a truncating conversion!");
815 assert(isSCEVable(Ty) &&
816 "This is not a conversion to a SCEVable type!");
817 Ty = getEffectiveSCEVType(Ty);
820 ID.AddInteger(scTruncate);
824 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
826 // Fold if the operand is constant.
827 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
829 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
831 // trunc(trunc(x)) --> trunc(x)
832 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
833 return getTruncateExpr(ST->getOperand(), Ty);
835 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
836 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
837 return getTruncateOrSignExtend(SS->getOperand(), Ty);
839 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
840 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
841 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
843 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
844 // eliminate all the truncates.
845 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
846 SmallVector<const SCEV *, 4> Operands;
847 bool hasTrunc = false;
848 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
849 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
850 hasTrunc = isa<SCEVTruncateExpr>(S);
851 Operands.push_back(S);
854 return getAddExpr(Operands);
855 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
858 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
859 // eliminate all the truncates.
860 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
861 SmallVector<const SCEV *, 4> Operands;
862 bool hasTrunc = false;
863 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
864 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
865 hasTrunc = isa<SCEVTruncateExpr>(S);
866 Operands.push_back(S);
869 return getMulExpr(Operands);
870 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
873 // If the input value is a chrec scev, truncate the chrec's operands.
874 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
875 SmallVector<const SCEV *, 4> Operands;
876 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
877 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
878 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
881 // As a special case, fold trunc(undef) to undef. We don't want to
882 // know too much about SCEVUnknowns, but this special case is handy
884 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
885 if (isa<UndefValue>(U->getValue()))
886 return getSCEV(UndefValue::get(Ty));
888 // The cast wasn't folded; create an explicit cast node. We can reuse
889 // the existing insert position since if we get here, we won't have
890 // made any changes which would invalidate it.
891 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
893 UniqueSCEVs.InsertNode(S, IP);
897 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
899 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
900 "This is not an extending conversion!");
901 assert(isSCEVable(Ty) &&
902 "This is not a conversion to a SCEVable type!");
903 Ty = getEffectiveSCEVType(Ty);
905 // Fold if the operand is constant.
906 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
908 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
910 // zext(zext(x)) --> zext(x)
911 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
912 return getZeroExtendExpr(SZ->getOperand(), Ty);
914 // Before doing any expensive analysis, check to see if we've already
915 // computed a SCEV for this Op and Ty.
917 ID.AddInteger(scZeroExtend);
921 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
923 // zext(trunc(x)) --> zext(x) or x or trunc(x)
924 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
925 // It's possible the bits taken off by the truncate were all zero bits. If
926 // so, we should be able to simplify this further.
927 const SCEV *X = ST->getOperand();
928 ConstantRange CR = getUnsignedRange(X);
929 unsigned TruncBits = getTypeSizeInBits(ST->getType());
930 unsigned NewBits = getTypeSizeInBits(Ty);
931 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
932 CR.zextOrTrunc(NewBits)))
933 return getTruncateOrZeroExtend(X, Ty);
936 // If the input value is a chrec scev, and we can prove that the value
937 // did not overflow the old, smaller, value, we can zero extend all of the
938 // operands (often constants). This allows analysis of something like
939 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
940 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
941 if (AR->isAffine()) {
942 const SCEV *Start = AR->getStart();
943 const SCEV *Step = AR->getStepRecurrence(*this);
944 unsigned BitWidth = getTypeSizeInBits(AR->getType());
945 const Loop *L = AR->getLoop();
947 // If we have special knowledge that this addrec won't overflow,
948 // we don't need to do any further analysis.
949 if (AR->getNoWrapFlags(SCEV::FlagNUW))
950 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
951 getZeroExtendExpr(Step, Ty),
952 L, AR->getNoWrapFlags());
954 // Check whether the backedge-taken count is SCEVCouldNotCompute.
955 // Note that this serves two purposes: It filters out loops that are
956 // simply not analyzable, and it covers the case where this code is
957 // being called from within backedge-taken count analysis, such that
958 // attempting to ask for the backedge-taken count would likely result
959 // in infinite recursion. In the later case, the analysis code will
960 // cope with a conservative value, and it will take care to purge
961 // that value once it has finished.
962 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
963 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
964 // Manually compute the final value for AR, checking for
967 // Check whether the backedge-taken count can be losslessly casted to
968 // the addrec's type. The count is always unsigned.
969 const SCEV *CastedMaxBECount =
970 getTruncateOrZeroExtend(MaxBECount, Start->getType());
971 const SCEV *RecastedMaxBECount =
972 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
973 if (MaxBECount == RecastedMaxBECount) {
974 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
975 // Check whether Start+Step*MaxBECount has no unsigned overflow.
976 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
977 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
978 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
979 const SCEV *WideMaxBECount =
980 getZeroExtendExpr(CastedMaxBECount, WideTy);
981 const SCEV *OperandExtendedAdd =
982 getAddExpr(WideStart,
983 getMulExpr(WideMaxBECount,
984 getZeroExtendExpr(Step, WideTy)));
985 if (ZAdd == OperandExtendedAdd) {
986 // Cache knowledge of AR NUW, which is propagated to this AddRec.
987 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
988 // Return the expression with the addrec on the outside.
989 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
990 getZeroExtendExpr(Step, Ty),
991 L, AR->getNoWrapFlags());
993 // Similar to above, only this time treat the step value as signed.
994 // This covers loops that count down.
996 getAddExpr(WideStart,
997 getMulExpr(WideMaxBECount,
998 getSignExtendExpr(Step, WideTy)));
999 if (ZAdd == OperandExtendedAdd) {
1000 // Cache knowledge of AR NW, which is propagated to this AddRec.
1001 // Negative step causes unsigned wrap, but it still can't self-wrap.
1002 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1003 // Return the expression with the addrec on the outside.
1004 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1005 getSignExtendExpr(Step, Ty),
1006 L, AR->getNoWrapFlags());
1010 // If the backedge is guarded by a comparison with the pre-inc value
1011 // the addrec is safe. Also, if the entry is guarded by a comparison
1012 // with the start value and the backedge is guarded by a comparison
1013 // with the post-inc value, the addrec is safe.
1014 if (isKnownPositive(Step)) {
1015 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1016 getUnsignedRange(Step).getUnsignedMax());
1017 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1018 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1019 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1020 AR->getPostIncExpr(*this), N))) {
1021 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1022 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1023 // Return the expression with the addrec on the outside.
1024 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1025 getZeroExtendExpr(Step, Ty),
1026 L, AR->getNoWrapFlags());
1028 } else if (isKnownNegative(Step)) {
1029 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1030 getSignedRange(Step).getSignedMin());
1031 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1032 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1033 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1034 AR->getPostIncExpr(*this), N))) {
1035 // Cache knowledge of AR NW, which is propagated to this AddRec.
1036 // Negative step causes unsigned wrap, but it still can't self-wrap.
1037 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1038 // Return the expression with the addrec on the outside.
1039 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1040 getSignExtendExpr(Step, Ty),
1041 L, AR->getNoWrapFlags());
1047 // The cast wasn't folded; create an explicit cast node.
1048 // Recompute the insert position, as it may have been invalidated.
1049 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1050 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1052 UniqueSCEVs.InsertNode(S, IP);
1056 // Get the limit of a recurrence such that incrementing by Step cannot cause
1057 // signed overflow as long as the value of the recurrence within the loop does
1058 // not exceed this limit before incrementing.
1059 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1060 ICmpInst::Predicate *Pred,
1061 ScalarEvolution *SE) {
1062 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1063 if (SE->isKnownPositive(Step)) {
1064 *Pred = ICmpInst::ICMP_SLT;
1065 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1066 SE->getSignedRange(Step).getSignedMax());
1068 if (SE->isKnownNegative(Step)) {
1069 *Pred = ICmpInst::ICMP_SGT;
1070 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1071 SE->getSignedRange(Step).getSignedMin());
1076 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1077 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1078 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1079 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1080 // result, the expression "Step + sext(PreIncAR)" is congruent with
1081 // "sext(PostIncAR)"
1082 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1084 ScalarEvolution *SE) {
1085 const Loop *L = AR->getLoop();
1086 const SCEV *Start = AR->getStart();
1087 const SCEV *Step = AR->getStepRecurrence(*SE);
1089 // Check for a simple looking step prior to loop entry.
1090 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1094 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1095 // subtraction is expensive. For this purpose, perform a quick and dirty
1096 // difference, by checking for Step in the operand list.
1097 SmallVector<const SCEV *, 4> DiffOps;
1098 for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end();
1101 DiffOps.push_back(*I);
1103 if (DiffOps.size() == SA->getNumOperands())
1106 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1107 // same three conditions that getSignExtendedExpr checks.
1109 // 1. NSW flags on the step increment.
1110 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1111 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1112 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1114 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1117 // 2. Direct overflow check on the step operation's expression.
1118 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1119 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1120 const SCEV *OperandExtendedStart =
1121 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1122 SE->getSignExtendExpr(Step, WideTy));
1123 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1124 // Cache knowledge of PreAR NSW.
1126 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1127 // FIXME: this optimization needs a unit test
1128 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1132 // 3. Loop precondition.
1133 ICmpInst::Predicate Pred;
1134 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1136 if (OverflowLimit &&
1137 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1143 // Get the normalized sign-extended expression for this AddRec's Start.
1144 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1146 ScalarEvolution *SE) {
1147 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1149 return SE->getSignExtendExpr(AR->getStart(), Ty);
1151 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1152 SE->getSignExtendExpr(PreStart, Ty));
1155 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1157 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1158 "This is not an extending conversion!");
1159 assert(isSCEVable(Ty) &&
1160 "This is not a conversion to a SCEVable type!");
1161 Ty = getEffectiveSCEVType(Ty);
1163 // Fold if the operand is constant.
1164 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1166 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1168 // sext(sext(x)) --> sext(x)
1169 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1170 return getSignExtendExpr(SS->getOperand(), Ty);
1172 // sext(zext(x)) --> zext(x)
1173 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1174 return getZeroExtendExpr(SZ->getOperand(), Ty);
1176 // Before doing any expensive analysis, check to see if we've already
1177 // computed a SCEV for this Op and Ty.
1178 FoldingSetNodeID ID;
1179 ID.AddInteger(scSignExtend);
1183 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1185 // If the input value is provably positive, build a zext instead.
1186 if (isKnownNonNegative(Op))
1187 return getZeroExtendExpr(Op, Ty);
1189 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1190 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1191 // It's possible the bits taken off by the truncate were all sign bits. If
1192 // so, we should be able to simplify this further.
1193 const SCEV *X = ST->getOperand();
1194 ConstantRange CR = getSignedRange(X);
1195 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1196 unsigned NewBits = getTypeSizeInBits(Ty);
1197 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1198 CR.sextOrTrunc(NewBits)))
1199 return getTruncateOrSignExtend(X, Ty);
1202 // If the input value is a chrec scev, and we can prove that the value
1203 // did not overflow the old, smaller, value, we can sign extend all of the
1204 // operands (often constants). This allows analysis of something like
1205 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1206 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1207 if (AR->isAffine()) {
1208 const SCEV *Start = AR->getStart();
1209 const SCEV *Step = AR->getStepRecurrence(*this);
1210 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1211 const Loop *L = AR->getLoop();
1213 // If we have special knowledge that this addrec won't overflow,
1214 // we don't need to do any further analysis.
1215 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1216 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1217 getSignExtendExpr(Step, Ty),
1220 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1221 // Note that this serves two purposes: It filters out loops that are
1222 // simply not analyzable, and it covers the case where this code is
1223 // being called from within backedge-taken count analysis, such that
1224 // attempting to ask for the backedge-taken count would likely result
1225 // in infinite recursion. In the later case, the analysis code will
1226 // cope with a conservative value, and it will take care to purge
1227 // that value once it has finished.
1228 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1229 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1230 // Manually compute the final value for AR, checking for
1233 // Check whether the backedge-taken count can be losslessly casted to
1234 // the addrec's type. The count is always unsigned.
1235 const SCEV *CastedMaxBECount =
1236 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1237 const SCEV *RecastedMaxBECount =
1238 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1239 if (MaxBECount == RecastedMaxBECount) {
1240 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1241 // Check whether Start+Step*MaxBECount has no signed overflow.
1242 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1243 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1244 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1245 const SCEV *WideMaxBECount =
1246 getZeroExtendExpr(CastedMaxBECount, WideTy);
1247 const SCEV *OperandExtendedAdd =
1248 getAddExpr(WideStart,
1249 getMulExpr(WideMaxBECount,
1250 getSignExtendExpr(Step, WideTy)));
1251 if (SAdd == OperandExtendedAdd) {
1252 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1253 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1254 // Return the expression with the addrec on the outside.
1255 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1256 getSignExtendExpr(Step, Ty),
1257 L, AR->getNoWrapFlags());
1259 // Similar to above, only this time treat the step value as unsigned.
1260 // This covers loops that count up with an unsigned step.
1261 OperandExtendedAdd =
1262 getAddExpr(WideStart,
1263 getMulExpr(WideMaxBECount,
1264 getZeroExtendExpr(Step, WideTy)));
1265 if (SAdd == OperandExtendedAdd) {
1266 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1267 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1268 // Return the expression with the addrec on the outside.
1269 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1270 getZeroExtendExpr(Step, Ty),
1271 L, AR->getNoWrapFlags());
1275 // If the backedge is guarded by a comparison with the pre-inc value
1276 // the addrec is safe. Also, if the entry is guarded by a comparison
1277 // with the start value and the backedge is guarded by a comparison
1278 // with the post-inc value, the addrec is safe.
1279 ICmpInst::Predicate Pred;
1280 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1281 if (OverflowLimit &&
1282 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1283 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1284 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1286 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1287 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1288 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1289 getSignExtendExpr(Step, Ty),
1290 L, AR->getNoWrapFlags());
1295 // The cast wasn't folded; create an explicit cast node.
1296 // Recompute the insert position, as it may have been invalidated.
1297 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1298 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1300 UniqueSCEVs.InsertNode(S, IP);
1304 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1305 /// unspecified bits out to the given type.
1307 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1309 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1310 "This is not an extending conversion!");
1311 assert(isSCEVable(Ty) &&
1312 "This is not a conversion to a SCEVable type!");
1313 Ty = getEffectiveSCEVType(Ty);
1315 // Sign-extend negative constants.
1316 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1317 if (SC->getValue()->getValue().isNegative())
1318 return getSignExtendExpr(Op, Ty);
1320 // Peel off a truncate cast.
1321 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1322 const SCEV *NewOp = T->getOperand();
1323 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1324 return getAnyExtendExpr(NewOp, Ty);
1325 return getTruncateOrNoop(NewOp, Ty);
1328 // Next try a zext cast. If the cast is folded, use it.
1329 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1330 if (!isa<SCEVZeroExtendExpr>(ZExt))
1333 // Next try a sext cast. If the cast is folded, use it.
1334 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1335 if (!isa<SCEVSignExtendExpr>(SExt))
1338 // Force the cast to be folded into the operands of an addrec.
1339 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1340 SmallVector<const SCEV *, 4> Ops;
1341 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1343 Ops.push_back(getAnyExtendExpr(*I, Ty));
1344 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1347 // As a special case, fold anyext(undef) to undef. We don't want to
1348 // know too much about SCEVUnknowns, but this special case is handy
1350 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1351 if (isa<UndefValue>(U->getValue()))
1352 return getSCEV(UndefValue::get(Ty));
1354 // If the expression is obviously signed, use the sext cast value.
1355 if (isa<SCEVSMaxExpr>(Op))
1358 // Absent any other information, use the zext cast value.
1362 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1363 /// a list of operands to be added under the given scale, update the given
1364 /// map. This is a helper function for getAddRecExpr. As an example of
1365 /// what it does, given a sequence of operands that would form an add
1366 /// expression like this:
1368 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1370 /// where A and B are constants, update the map with these values:
1372 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1374 /// and add 13 + A*B*29 to AccumulatedConstant.
1375 /// This will allow getAddRecExpr to produce this:
1377 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1379 /// This form often exposes folding opportunities that are hidden in
1380 /// the original operand list.
1382 /// Return true iff it appears that any interesting folding opportunities
1383 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1384 /// the common case where no interesting opportunities are present, and
1385 /// is also used as a check to avoid infinite recursion.
1388 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1389 SmallVector<const SCEV *, 8> &NewOps,
1390 APInt &AccumulatedConstant,
1391 const SCEV *const *Ops, size_t NumOperands,
1393 ScalarEvolution &SE) {
1394 bool Interesting = false;
1396 // Iterate over the add operands. They are sorted, with constants first.
1398 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1400 // Pull a buried constant out to the outside.
1401 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1403 AccumulatedConstant += Scale * C->getValue()->getValue();
1406 // Next comes everything else. We're especially interested in multiplies
1407 // here, but they're in the middle, so just visit the rest with one loop.
1408 for (; i != NumOperands; ++i) {
1409 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1410 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1412 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1413 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1414 // A multiplication of a constant with another add; recurse.
1415 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1417 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1418 Add->op_begin(), Add->getNumOperands(),
1421 // A multiplication of a constant with some other value. Update
1423 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1424 const SCEV *Key = SE.getMulExpr(MulOps);
1425 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1426 M.insert(std::make_pair(Key, NewScale));
1428 NewOps.push_back(Pair.first->first);
1430 Pair.first->second += NewScale;
1431 // The map already had an entry for this value, which may indicate
1432 // a folding opportunity.
1437 // An ordinary operand. Update the map.
1438 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1439 M.insert(std::make_pair(Ops[i], Scale));
1441 NewOps.push_back(Pair.first->first);
1443 Pair.first->second += Scale;
1444 // The map already had an entry for this value, which may indicate
1445 // a folding opportunity.
1455 struct APIntCompare {
1456 bool operator()(const APInt &LHS, const APInt &RHS) const {
1457 return LHS.ult(RHS);
1462 /// getAddExpr - Get a canonical add expression, or something simpler if
1464 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1465 SCEV::NoWrapFlags Flags) {
1466 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1467 "only nuw or nsw allowed");
1468 assert(!Ops.empty() && "Cannot get empty add!");
1469 if (Ops.size() == 1) return Ops[0];
1471 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1472 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1473 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1474 "SCEVAddExpr operand types don't match!");
1477 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1479 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1480 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1481 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1483 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1484 E = Ops.end(); I != E; ++I)
1485 if (!isKnownNonNegative(*I)) {
1489 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1492 // Sort by complexity, this groups all similar expression types together.
1493 GroupByComplexity(Ops, LI);
1495 // If there are any constants, fold them together.
1497 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1499 assert(Idx < Ops.size());
1500 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1501 // We found two constants, fold them together!
1502 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1503 RHSC->getValue()->getValue());
1504 if (Ops.size() == 2) return Ops[0];
1505 Ops.erase(Ops.begin()+1); // Erase the folded element
1506 LHSC = cast<SCEVConstant>(Ops[0]);
1509 // If we are left with a constant zero being added, strip it off.
1510 if (LHSC->getValue()->isZero()) {
1511 Ops.erase(Ops.begin());
1515 if (Ops.size() == 1) return Ops[0];
1518 // Okay, check to see if the same value occurs in the operand list more than
1519 // once. If so, merge them together into an multiply expression. Since we
1520 // sorted the list, these values are required to be adjacent.
1521 Type *Ty = Ops[0]->getType();
1522 bool FoundMatch = false;
1523 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1524 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1525 // Scan ahead to count how many equal operands there are.
1527 while (i+Count != e && Ops[i+Count] == Ops[i])
1529 // Merge the values into a multiply.
1530 const SCEV *Scale = getConstant(Ty, Count);
1531 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1532 if (Ops.size() == Count)
1535 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1536 --i; e -= Count - 1;
1540 return getAddExpr(Ops, Flags);
1542 // Check for truncates. If all the operands are truncated from the same
1543 // type, see if factoring out the truncate would permit the result to be
1544 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1545 // if the contents of the resulting outer trunc fold to something simple.
1546 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1547 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1548 Type *DstType = Trunc->getType();
1549 Type *SrcType = Trunc->getOperand()->getType();
1550 SmallVector<const SCEV *, 8> LargeOps;
1552 // Check all the operands to see if they can be represented in the
1553 // source type of the truncate.
1554 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1555 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1556 if (T->getOperand()->getType() != SrcType) {
1560 LargeOps.push_back(T->getOperand());
1561 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1562 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1563 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1564 SmallVector<const SCEV *, 8> LargeMulOps;
1565 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1566 if (const SCEVTruncateExpr *T =
1567 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1568 if (T->getOperand()->getType() != SrcType) {
1572 LargeMulOps.push_back(T->getOperand());
1573 } else if (const SCEVConstant *C =
1574 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1575 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1582 LargeOps.push_back(getMulExpr(LargeMulOps));
1589 // Evaluate the expression in the larger type.
1590 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1591 // If it folds to something simple, use it. Otherwise, don't.
1592 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1593 return getTruncateExpr(Fold, DstType);
1597 // Skip past any other cast SCEVs.
1598 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1601 // If there are add operands they would be next.
1602 if (Idx < Ops.size()) {
1603 bool DeletedAdd = false;
1604 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1605 // If we have an add, expand the add operands onto the end of the operands
1607 Ops.erase(Ops.begin()+Idx);
1608 Ops.append(Add->op_begin(), Add->op_end());
1612 // If we deleted at least one add, we added operands to the end of the list,
1613 // and they are not necessarily sorted. Recurse to resort and resimplify
1614 // any operands we just acquired.
1616 return getAddExpr(Ops);
1619 // Skip over the add expression until we get to a multiply.
1620 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1623 // Check to see if there are any folding opportunities present with
1624 // operands multiplied by constant values.
1625 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1626 uint64_t BitWidth = getTypeSizeInBits(Ty);
1627 DenseMap<const SCEV *, APInt> M;
1628 SmallVector<const SCEV *, 8> NewOps;
1629 APInt AccumulatedConstant(BitWidth, 0);
1630 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1631 Ops.data(), Ops.size(),
1632 APInt(BitWidth, 1), *this)) {
1633 // Some interesting folding opportunity is present, so its worthwhile to
1634 // re-generate the operands list. Group the operands by constant scale,
1635 // to avoid multiplying by the same constant scale multiple times.
1636 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1637 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1638 E = NewOps.end(); I != E; ++I)
1639 MulOpLists[M.find(*I)->second].push_back(*I);
1640 // Re-generate the operands list.
1642 if (AccumulatedConstant != 0)
1643 Ops.push_back(getConstant(AccumulatedConstant));
1644 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1645 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1647 Ops.push_back(getMulExpr(getConstant(I->first),
1648 getAddExpr(I->second)));
1650 return getConstant(Ty, 0);
1651 if (Ops.size() == 1)
1653 return getAddExpr(Ops);
1657 // If we are adding something to a multiply expression, make sure the
1658 // something is not already an operand of the multiply. If so, merge it into
1660 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1661 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1662 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1663 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1664 if (isa<SCEVConstant>(MulOpSCEV))
1666 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1667 if (MulOpSCEV == Ops[AddOp]) {
1668 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1669 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1670 if (Mul->getNumOperands() != 2) {
1671 // If the multiply has more than two operands, we must get the
1673 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1674 Mul->op_begin()+MulOp);
1675 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1676 InnerMul = getMulExpr(MulOps);
1678 const SCEV *One = getConstant(Ty, 1);
1679 const SCEV *AddOne = getAddExpr(One, InnerMul);
1680 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1681 if (Ops.size() == 2) return OuterMul;
1683 Ops.erase(Ops.begin()+AddOp);
1684 Ops.erase(Ops.begin()+Idx-1);
1686 Ops.erase(Ops.begin()+Idx);
1687 Ops.erase(Ops.begin()+AddOp-1);
1689 Ops.push_back(OuterMul);
1690 return getAddExpr(Ops);
1693 // Check this multiply against other multiplies being added together.
1694 for (unsigned OtherMulIdx = Idx+1;
1695 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1697 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1698 // If MulOp occurs in OtherMul, we can fold the two multiplies
1700 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1701 OMulOp != e; ++OMulOp)
1702 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1703 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1704 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1705 if (Mul->getNumOperands() != 2) {
1706 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1707 Mul->op_begin()+MulOp);
1708 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1709 InnerMul1 = getMulExpr(MulOps);
1711 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1712 if (OtherMul->getNumOperands() != 2) {
1713 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1714 OtherMul->op_begin()+OMulOp);
1715 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1716 InnerMul2 = getMulExpr(MulOps);
1718 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1719 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1720 if (Ops.size() == 2) return OuterMul;
1721 Ops.erase(Ops.begin()+Idx);
1722 Ops.erase(Ops.begin()+OtherMulIdx-1);
1723 Ops.push_back(OuterMul);
1724 return getAddExpr(Ops);
1730 // If there are any add recurrences in the operands list, see if any other
1731 // added values are loop invariant. If so, we can fold them into the
1733 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1736 // Scan over all recurrences, trying to fold loop invariants into them.
1737 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1738 // Scan all of the other operands to this add and add them to the vector if
1739 // they are loop invariant w.r.t. the recurrence.
1740 SmallVector<const SCEV *, 8> LIOps;
1741 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1742 const Loop *AddRecLoop = AddRec->getLoop();
1743 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1744 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1745 LIOps.push_back(Ops[i]);
1746 Ops.erase(Ops.begin()+i);
1750 // If we found some loop invariants, fold them into the recurrence.
1751 if (!LIOps.empty()) {
1752 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1753 LIOps.push_back(AddRec->getStart());
1755 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1757 AddRecOps[0] = getAddExpr(LIOps);
1759 // Build the new addrec. Propagate the NUW and NSW flags if both the
1760 // outer add and the inner addrec are guaranteed to have no overflow.
1761 // Always propagate NW.
1762 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1763 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1765 // If all of the other operands were loop invariant, we are done.
1766 if (Ops.size() == 1) return NewRec;
1768 // Otherwise, add the folded AddRec by the non-invariant parts.
1769 for (unsigned i = 0;; ++i)
1770 if (Ops[i] == AddRec) {
1774 return getAddExpr(Ops);
1777 // Okay, if there weren't any loop invariants to be folded, check to see if
1778 // there are multiple AddRec's with the same loop induction variable being
1779 // added together. If so, we can fold them.
1780 for (unsigned OtherIdx = Idx+1;
1781 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1783 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1784 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1785 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1787 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1789 if (const SCEVAddRecExpr *OtherAddRec =
1790 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1791 if (OtherAddRec->getLoop() == AddRecLoop) {
1792 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1794 if (i >= AddRecOps.size()) {
1795 AddRecOps.append(OtherAddRec->op_begin()+i,
1796 OtherAddRec->op_end());
1799 AddRecOps[i] = getAddExpr(AddRecOps[i],
1800 OtherAddRec->getOperand(i));
1802 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1804 // Step size has changed, so we cannot guarantee no self-wraparound.
1805 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1806 return getAddExpr(Ops);
1809 // Otherwise couldn't fold anything into this recurrence. Move onto the
1813 // Okay, it looks like we really DO need an add expr. Check to see if we
1814 // already have one, otherwise create a new one.
1815 FoldingSetNodeID ID;
1816 ID.AddInteger(scAddExpr);
1817 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1818 ID.AddPointer(Ops[i]);
1821 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1823 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1824 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1825 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1827 UniqueSCEVs.InsertNode(S, IP);
1829 S->setNoWrapFlags(Flags);
1833 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1835 if (j > 1 && k / j != i) Overflow = true;
1839 /// Compute the result of "n choose k", the binomial coefficient. If an
1840 /// intermediate computation overflows, Overflow will be set and the return will
1841 /// be garbage. Overflow is not cleared on absense of overflow.
1842 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1843 // We use the multiplicative formula:
1844 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1845 // At each iteration, we take the n-th term of the numeral and divide by the
1846 // (k-n)th term of the denominator. This division will always produce an
1847 // integral result, and helps reduce the chance of overflow in the
1848 // intermediate computations. However, we can still overflow even when the
1849 // final result would fit.
1851 if (n == 0 || n == k) return 1;
1852 if (k > n) return 0;
1858 for (uint64_t i = 1; i <= k; ++i) {
1859 r = umul_ov(r, n-(i-1), Overflow);
1865 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1867 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1868 SCEV::NoWrapFlags Flags) {
1869 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1870 "only nuw or nsw allowed");
1871 assert(!Ops.empty() && "Cannot get empty mul!");
1872 if (Ops.size() == 1) return Ops[0];
1874 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1875 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1876 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1877 "SCEVMulExpr operand types don't match!");
1880 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1882 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1883 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1884 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1886 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1887 E = Ops.end(); I != E; ++I)
1888 if (!isKnownNonNegative(*I)) {
1892 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1895 // Sort by complexity, this groups all similar expression types together.
1896 GroupByComplexity(Ops, LI);
1898 // If there are any constants, fold them together.
1900 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1902 // C1*(C2+V) -> C1*C2 + C1*V
1903 if (Ops.size() == 2)
1904 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1905 if (Add->getNumOperands() == 2 &&
1906 isa<SCEVConstant>(Add->getOperand(0)))
1907 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1908 getMulExpr(LHSC, Add->getOperand(1)));
1911 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1912 // We found two constants, fold them together!
1913 ConstantInt *Fold = ConstantInt::get(getContext(),
1914 LHSC->getValue()->getValue() *
1915 RHSC->getValue()->getValue());
1916 Ops[0] = getConstant(Fold);
1917 Ops.erase(Ops.begin()+1); // Erase the folded element
1918 if (Ops.size() == 1) return Ops[0];
1919 LHSC = cast<SCEVConstant>(Ops[0]);
1922 // If we are left with a constant one being multiplied, strip it off.
1923 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1924 Ops.erase(Ops.begin());
1926 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1927 // If we have a multiply of zero, it will always be zero.
1929 } else if (Ops[0]->isAllOnesValue()) {
1930 // If we have a mul by -1 of an add, try distributing the -1 among the
1932 if (Ops.size() == 2) {
1933 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1934 SmallVector<const SCEV *, 4> NewOps;
1935 bool AnyFolded = false;
1936 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1937 E = Add->op_end(); I != E; ++I) {
1938 const SCEV *Mul = getMulExpr(Ops[0], *I);
1939 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1940 NewOps.push_back(Mul);
1943 return getAddExpr(NewOps);
1945 else if (const SCEVAddRecExpr *
1946 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1947 // Negation preserves a recurrence's no self-wrap property.
1948 SmallVector<const SCEV *, 4> Operands;
1949 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1950 E = AddRec->op_end(); I != E; ++I) {
1951 Operands.push_back(getMulExpr(Ops[0], *I));
1953 return getAddRecExpr(Operands, AddRec->getLoop(),
1954 AddRec->getNoWrapFlags(SCEV::FlagNW));
1959 if (Ops.size() == 1)
1963 // Skip over the add expression until we get to a multiply.
1964 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1967 // If there are mul operands inline them all into this expression.
1968 if (Idx < Ops.size()) {
1969 bool DeletedMul = false;
1970 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1971 // If we have an mul, expand the mul operands onto the end of the operands
1973 Ops.erase(Ops.begin()+Idx);
1974 Ops.append(Mul->op_begin(), Mul->op_end());
1978 // If we deleted at least one mul, we added operands to the end of the list,
1979 // and they are not necessarily sorted. Recurse to resort and resimplify
1980 // any operands we just acquired.
1982 return getMulExpr(Ops);
1985 // If there are any add recurrences in the operands list, see if any other
1986 // added values are loop invariant. If so, we can fold them into the
1988 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1991 // Scan over all recurrences, trying to fold loop invariants into them.
1992 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1993 // Scan all of the other operands to this mul and add them to the vector if
1994 // they are loop invariant w.r.t. the recurrence.
1995 SmallVector<const SCEV *, 8> LIOps;
1996 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1997 const Loop *AddRecLoop = AddRec->getLoop();
1998 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1999 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2000 LIOps.push_back(Ops[i]);
2001 Ops.erase(Ops.begin()+i);
2005 // If we found some loop invariants, fold them into the recurrence.
2006 if (!LIOps.empty()) {
2007 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2008 SmallVector<const SCEV *, 4> NewOps;
2009 NewOps.reserve(AddRec->getNumOperands());
2010 const SCEV *Scale = getMulExpr(LIOps);
2011 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2012 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2014 // Build the new addrec. Propagate the NUW and NSW flags if both the
2015 // outer mul and the inner addrec are guaranteed to have no overflow.
2017 // No self-wrap cannot be guaranteed after changing the step size, but
2018 // will be inferred if either NUW or NSW is true.
2019 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2020 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2022 // If all of the other operands were loop invariant, we are done.
2023 if (Ops.size() == 1) return NewRec;
2025 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2026 for (unsigned i = 0;; ++i)
2027 if (Ops[i] == AddRec) {
2031 return getMulExpr(Ops);
2034 // Okay, if there weren't any loop invariants to be folded, check to see if
2035 // there are multiple AddRec's with the same loop induction variable being
2036 // multiplied together. If so, we can fold them.
2037 for (unsigned OtherIdx = Idx+1;
2038 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2040 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2041 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2042 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2043 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2044 // ]]],+,...up to x=2n}.
2045 // Note that the arguments to choose() are always integers with values
2046 // known at compile time, never SCEV objects.
2048 // The implementation avoids pointless extra computations when the two
2049 // addrec's are of different length (mathematically, it's equivalent to
2050 // an infinite stream of zeros on the right).
2051 bool OpsModified = false;
2052 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2054 if (const SCEVAddRecExpr *OtherAddRec =
2055 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2056 if (OtherAddRec->getLoop() == AddRecLoop) {
2057 bool Overflow = false;
2058 Type *Ty = AddRec->getType();
2059 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2060 SmallVector<const SCEV*, 7> AddRecOps;
2061 for (int x = 0, xe = AddRec->getNumOperands() +
2062 OtherAddRec->getNumOperands() - 1;
2063 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,
2088 if (Ops.size() == 2) return NewAddRec;
2089 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
2090 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2095 return getMulExpr(Ops);
2099 // Otherwise couldn't fold anything into this recurrence. Move onto the
2103 // Okay, it looks like we really DO need an mul expr. Check to see if we
2104 // already have one, otherwise create a new one.
2105 FoldingSetNodeID ID;
2106 ID.AddInteger(scMulExpr);
2107 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2108 ID.AddPointer(Ops[i]);
2111 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2113 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2114 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2115 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2117 UniqueSCEVs.InsertNode(S, IP);
2119 S->setNoWrapFlags(Flags);
2123 /// getUDivExpr - Get a canonical unsigned division expression, or something
2124 /// simpler if possible.
2125 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2127 assert(getEffectiveSCEVType(LHS->getType()) ==
2128 getEffectiveSCEVType(RHS->getType()) &&
2129 "SCEVUDivExpr operand types don't match!");
2131 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2132 if (RHSC->getValue()->equalsInt(1))
2133 return LHS; // X udiv 1 --> x
2134 // If the denominator is zero, the result of the udiv is undefined. Don't
2135 // try to analyze it, because the resolution chosen here may differ from
2136 // the resolution chosen in other parts of the compiler.
2137 if (!RHSC->getValue()->isZero()) {
2138 // Determine if the division can be folded into the operands of
2140 // TODO: Generalize this to non-constants by using known-bits information.
2141 Type *Ty = LHS->getType();
2142 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2143 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2144 // For non-power-of-two values, effectively round the value up to the
2145 // nearest power of two.
2146 if (!RHSC->getValue()->getValue().isPowerOf2())
2148 IntegerType *ExtTy =
2149 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2150 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2151 if (const SCEVConstant *Step =
2152 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2153 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2154 const APInt &StepInt = Step->getValue()->getValue();
2155 const APInt &DivInt = RHSC->getValue()->getValue();
2156 if (!StepInt.urem(DivInt) &&
2157 getZeroExtendExpr(AR, ExtTy) ==
2158 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2159 getZeroExtendExpr(Step, ExtTy),
2160 AR->getLoop(), SCEV::FlagAnyWrap)) {
2161 SmallVector<const SCEV *, 4> Operands;
2162 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2163 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2164 return getAddRecExpr(Operands, AR->getLoop(),
2167 /// Get a canonical UDivExpr for a recurrence.
2168 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2169 // We can currently only fold X%N if X is constant.
2170 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2171 if (StartC && !DivInt.urem(StepInt) &&
2172 getZeroExtendExpr(AR, ExtTy) ==
2173 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2174 getZeroExtendExpr(Step, ExtTy),
2175 AR->getLoop(), SCEV::FlagAnyWrap)) {
2176 const APInt &StartInt = StartC->getValue()->getValue();
2177 const APInt &StartRem = StartInt.urem(StepInt);
2179 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2180 AR->getLoop(), SCEV::FlagNW);
2183 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2184 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2185 SmallVector<const SCEV *, 4> Operands;
2186 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2187 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2188 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2189 // Find an operand that's safely divisible.
2190 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2191 const SCEV *Op = M->getOperand(i);
2192 const SCEV *Div = getUDivExpr(Op, RHSC);
2193 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2194 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2197 return getMulExpr(Operands);
2201 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2202 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2203 SmallVector<const SCEV *, 4> Operands;
2204 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2205 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2206 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2208 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2209 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2210 if (isa<SCEVUDivExpr>(Op) ||
2211 getMulExpr(Op, RHS) != A->getOperand(i))
2213 Operands.push_back(Op);
2215 if (Operands.size() == A->getNumOperands())
2216 return getAddExpr(Operands);
2220 // Fold if both operands are constant.
2221 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2222 Constant *LHSCV = LHSC->getValue();
2223 Constant *RHSCV = RHSC->getValue();
2224 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2230 FoldingSetNodeID ID;
2231 ID.AddInteger(scUDivExpr);
2235 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2236 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2238 UniqueSCEVs.InsertNode(S, IP);
2243 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2244 /// Simplify the expression as much as possible.
2245 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2247 SCEV::NoWrapFlags Flags) {
2248 SmallVector<const SCEV *, 4> Operands;
2249 Operands.push_back(Start);
2250 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2251 if (StepChrec->getLoop() == L) {
2252 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2253 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2256 Operands.push_back(Step);
2257 return getAddRecExpr(Operands, L, Flags);
2260 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2261 /// Simplify the expression as much as possible.
2263 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2264 const Loop *L, SCEV::NoWrapFlags Flags) {
2265 if (Operands.size() == 1) return Operands[0];
2267 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2268 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2269 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2270 "SCEVAddRecExpr operand types don't match!");
2271 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2272 assert(isLoopInvariant(Operands[i], L) &&
2273 "SCEVAddRecExpr operand is not loop-invariant!");
2276 if (Operands.back()->isZero()) {
2277 Operands.pop_back();
2278 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2281 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2282 // use that information to infer NUW and NSW flags. However, computing a
2283 // BE count requires calling getAddRecExpr, so we may not yet have a
2284 // meaningful BE count at this point (and if we don't, we'd be stuck
2285 // with a SCEVCouldNotCompute as the cached BE count).
2287 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2289 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2290 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2291 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2293 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2294 E = Operands.end(); I != E; ++I)
2295 if (!isKnownNonNegative(*I)) {
2299 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2302 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2303 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2304 const Loop *NestedLoop = NestedAR->getLoop();
2305 if (L->contains(NestedLoop) ?
2306 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2307 (!NestedLoop->contains(L) &&
2308 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2309 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2310 NestedAR->op_end());
2311 Operands[0] = NestedAR->getStart();
2312 // AddRecs require their operands be loop-invariant with respect to their
2313 // loops. Don't perform this transformation if it would break this
2315 bool AllInvariant = true;
2316 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2317 if (!isLoopInvariant(Operands[i], L)) {
2318 AllInvariant = false;
2322 // Create a recurrence for the outer loop with the same step size.
2324 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2325 // inner recurrence has the same property.
2326 SCEV::NoWrapFlags OuterFlags =
2327 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2329 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2330 AllInvariant = true;
2331 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2332 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2333 AllInvariant = false;
2337 // Ok, both add recurrences are valid after the transformation.
2339 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2340 // the outer recurrence has the same property.
2341 SCEV::NoWrapFlags InnerFlags =
2342 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2343 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2346 // Reset Operands to its original state.
2347 Operands[0] = NestedAR;
2351 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2352 // already have one, otherwise create a new one.
2353 FoldingSetNodeID ID;
2354 ID.AddInteger(scAddRecExpr);
2355 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2356 ID.AddPointer(Operands[i]);
2360 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2362 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2363 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2364 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2365 O, Operands.size(), L);
2366 UniqueSCEVs.InsertNode(S, IP);
2368 S->setNoWrapFlags(Flags);
2372 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2374 SmallVector<const SCEV *, 2> Ops;
2377 return getSMaxExpr(Ops);
2381 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2382 assert(!Ops.empty() && "Cannot get empty smax!");
2383 if (Ops.size() == 1) return Ops[0];
2385 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2386 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2387 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2388 "SCEVSMaxExpr operand types don't match!");
2391 // Sort by complexity, this groups all similar expression types together.
2392 GroupByComplexity(Ops, LI);
2394 // If there are any constants, fold them together.
2396 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2398 assert(Idx < Ops.size());
2399 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2400 // We found two constants, fold them together!
2401 ConstantInt *Fold = ConstantInt::get(getContext(),
2402 APIntOps::smax(LHSC->getValue()->getValue(),
2403 RHSC->getValue()->getValue()));
2404 Ops[0] = getConstant(Fold);
2405 Ops.erase(Ops.begin()+1); // Erase the folded element
2406 if (Ops.size() == 1) return Ops[0];
2407 LHSC = cast<SCEVConstant>(Ops[0]);
2410 // If we are left with a constant minimum-int, strip it off.
2411 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2412 Ops.erase(Ops.begin());
2414 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2415 // If we have an smax with a constant maximum-int, it will always be
2420 if (Ops.size() == 1) return Ops[0];
2423 // Find the first SMax
2424 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2427 // Check to see if one of the operands is an SMax. If so, expand its operands
2428 // onto our operand list, and recurse to simplify.
2429 if (Idx < Ops.size()) {
2430 bool DeletedSMax = false;
2431 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2432 Ops.erase(Ops.begin()+Idx);
2433 Ops.append(SMax->op_begin(), SMax->op_end());
2438 return getSMaxExpr(Ops);
2441 // Okay, check to see if the same value occurs in the operand list twice. If
2442 // so, delete one. Since we sorted the list, these values are required to
2444 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2445 // X smax Y smax Y --> X smax Y
2446 // X smax Y --> X, if X is always greater than Y
2447 if (Ops[i] == Ops[i+1] ||
2448 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2449 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2451 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2452 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2456 if (Ops.size() == 1) return Ops[0];
2458 assert(!Ops.empty() && "Reduced smax down to nothing!");
2460 // Okay, it looks like we really DO need an smax expr. Check to see if we
2461 // already have one, otherwise create a new one.
2462 FoldingSetNodeID ID;
2463 ID.AddInteger(scSMaxExpr);
2464 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2465 ID.AddPointer(Ops[i]);
2467 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2468 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2469 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2470 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2472 UniqueSCEVs.InsertNode(S, IP);
2476 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2478 SmallVector<const SCEV *, 2> Ops;
2481 return getUMaxExpr(Ops);
2485 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2486 assert(!Ops.empty() && "Cannot get empty umax!");
2487 if (Ops.size() == 1) return Ops[0];
2489 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2490 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2491 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2492 "SCEVUMaxExpr operand types don't match!");
2495 // Sort by complexity, this groups all similar expression types together.
2496 GroupByComplexity(Ops, LI);
2498 // If there are any constants, fold them together.
2500 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2502 assert(Idx < Ops.size());
2503 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2504 // We found two constants, fold them together!
2505 ConstantInt *Fold = ConstantInt::get(getContext(),
2506 APIntOps::umax(LHSC->getValue()->getValue(),
2507 RHSC->getValue()->getValue()));
2508 Ops[0] = getConstant(Fold);
2509 Ops.erase(Ops.begin()+1); // Erase the folded element
2510 if (Ops.size() == 1) return Ops[0];
2511 LHSC = cast<SCEVConstant>(Ops[0]);
2514 // If we are left with a constant minimum-int, strip it off.
2515 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2516 Ops.erase(Ops.begin());
2518 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2519 // If we have an umax with a constant maximum-int, it will always be
2524 if (Ops.size() == 1) return Ops[0];
2527 // Find the first UMax
2528 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2531 // Check to see if one of the operands is a UMax. If so, expand its operands
2532 // onto our operand list, and recurse to simplify.
2533 if (Idx < Ops.size()) {
2534 bool DeletedUMax = false;
2535 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2536 Ops.erase(Ops.begin()+Idx);
2537 Ops.append(UMax->op_begin(), UMax->op_end());
2542 return getUMaxExpr(Ops);
2545 // Okay, check to see if the same value occurs in the operand list twice. If
2546 // so, delete one. Since we sorted the list, these values are required to
2548 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2549 // X umax Y umax Y --> X umax Y
2550 // X umax Y --> X, if X is always greater than Y
2551 if (Ops[i] == Ops[i+1] ||
2552 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2553 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2555 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2556 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2560 if (Ops.size() == 1) return Ops[0];
2562 assert(!Ops.empty() && "Reduced umax down to nothing!");
2564 // Okay, it looks like we really DO need a umax expr. Check to see if we
2565 // already have one, otherwise create a new one.
2566 FoldingSetNodeID ID;
2567 ID.AddInteger(scUMaxExpr);
2568 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2569 ID.AddPointer(Ops[i]);
2571 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2572 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2573 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2574 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2576 UniqueSCEVs.InsertNode(S, IP);
2580 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2582 // ~smax(~x, ~y) == smin(x, y).
2583 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2586 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2588 // ~umax(~x, ~y) == umin(x, y)
2589 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2592 const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) {
2593 // If we have TargetData, we can bypass creating a target-independent
2594 // constant expression and then folding it back into a ConstantInt.
2595 // This is just a compile-time optimization.
2597 return getConstant(TD->getIntPtrType(getContext()),
2598 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 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2608 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2609 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2610 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2611 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2613 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2614 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2617 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy,
2619 // If we have TargetData, we can bypass creating a target-independent
2620 // constant expression and then folding it back into a ConstantInt.
2621 // This is just a compile-time optimization.
2623 return getConstant(TD->getIntPtrType(getContext()),
2624 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2626 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2627 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2628 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2630 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2631 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2634 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2635 Constant *FieldNo) {
2636 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2637 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2638 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2640 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2641 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2644 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2645 // Don't attempt to do anything other than create a SCEVUnknown object
2646 // here. createSCEV only calls getUnknown after checking for all other
2647 // interesting possibilities, and any other code that calls getUnknown
2648 // is doing so in order to hide a value from SCEV canonicalization.
2650 FoldingSetNodeID ID;
2651 ID.AddInteger(scUnknown);
2654 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2655 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2656 "Stale SCEVUnknown in uniquing map!");
2659 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2661 FirstUnknown = cast<SCEVUnknown>(S);
2662 UniqueSCEVs.InsertNode(S, IP);
2666 //===----------------------------------------------------------------------===//
2667 // Basic SCEV Analysis and PHI Idiom Recognition Code
2670 /// isSCEVable - Test if values of the given type are analyzable within
2671 /// the SCEV framework. This primarily includes integer types, and it
2672 /// can optionally include pointer types if the ScalarEvolution class
2673 /// has access to target-specific information.
2674 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2675 // Integers and pointers are always SCEVable.
2676 return Ty->isIntegerTy() || Ty->isPointerTy();
2679 /// getTypeSizeInBits - Return the size in bits of the specified type,
2680 /// for which isSCEVable must return true.
2681 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2682 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2684 // If we have a TargetData, use it!
2686 return TD->getTypeSizeInBits(Ty);
2688 // Integer types have fixed sizes.
2689 if (Ty->isIntegerTy())
2690 return Ty->getPrimitiveSizeInBits();
2692 // The only other support type is pointer. Without TargetData, conservatively
2693 // assume pointers are 64-bit.
2694 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2698 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2699 /// the given type and which represents how SCEV will treat the given
2700 /// type, for which isSCEVable must return true. For pointer types,
2701 /// this is the pointer-sized integer type.
2702 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2703 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2705 if (Ty->isIntegerTy())
2708 // The only other support type is pointer.
2709 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2710 if (TD) return TD->getIntPtrType(getContext());
2712 // Without TargetData, conservatively assume pointers are 64-bit.
2713 return Type::getInt64Ty(getContext());
2716 const SCEV *ScalarEvolution::getCouldNotCompute() {
2717 return &CouldNotCompute;
2720 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2721 /// expression and create a new one.
2722 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2723 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2725 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2726 if (I != ValueExprMap.end()) return I->second;
2727 const SCEV *S = createSCEV(V);
2729 // The process of creating a SCEV for V may have caused other SCEVs
2730 // to have been created, so it's necessary to insert the new entry
2731 // from scratch, rather than trying to remember the insert position
2733 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2737 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2739 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2740 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2742 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2744 Type *Ty = V->getType();
2745 Ty = getEffectiveSCEVType(Ty);
2746 return getMulExpr(V,
2747 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2750 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2751 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2752 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2754 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2756 Type *Ty = V->getType();
2757 Ty = getEffectiveSCEVType(Ty);
2758 const SCEV *AllOnes =
2759 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2760 return getMinusSCEV(AllOnes, V);
2763 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2764 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2765 SCEV::NoWrapFlags Flags) {
2766 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2768 // Fast path: X - X --> 0.
2770 return getConstant(LHS->getType(), 0);
2773 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2776 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2777 /// input value to the specified type. If the type must be extended, it is zero
2780 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2781 Type *SrcTy = V->getType();
2782 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2783 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2784 "Cannot truncate or zero extend with non-integer arguments!");
2785 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2786 return V; // No conversion
2787 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2788 return getTruncateExpr(V, Ty);
2789 return getZeroExtendExpr(V, Ty);
2792 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2793 /// input value to the specified type. If the type must be extended, it is sign
2796 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2798 Type *SrcTy = V->getType();
2799 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2800 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2801 "Cannot truncate or zero extend with non-integer arguments!");
2802 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2803 return V; // No conversion
2804 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2805 return getTruncateExpr(V, Ty);
2806 return getSignExtendExpr(V, Ty);
2809 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2810 /// input value to the specified type. If the type must be extended, it is zero
2811 /// extended. The conversion must not be narrowing.
2813 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2814 Type *SrcTy = V->getType();
2815 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2816 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2817 "Cannot noop or zero extend with non-integer arguments!");
2818 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2819 "getNoopOrZeroExtend cannot truncate!");
2820 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2821 return V; // No conversion
2822 return getZeroExtendExpr(V, Ty);
2825 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2826 /// input value to the specified type. If the type must be extended, it is sign
2827 /// extended. The conversion must not be narrowing.
2829 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2830 Type *SrcTy = V->getType();
2831 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2832 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2833 "Cannot noop or sign extend with non-integer arguments!");
2834 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2835 "getNoopOrSignExtend cannot truncate!");
2836 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2837 return V; // No conversion
2838 return getSignExtendExpr(V, Ty);
2841 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2842 /// the input value to the specified type. If the type must be extended,
2843 /// it is extended with unspecified bits. The conversion must not be
2846 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2847 Type *SrcTy = V->getType();
2848 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2849 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2850 "Cannot noop or any extend with non-integer arguments!");
2851 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2852 "getNoopOrAnyExtend cannot truncate!");
2853 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2854 return V; // No conversion
2855 return getAnyExtendExpr(V, Ty);
2858 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2859 /// input value to the specified type. The conversion must not be widening.
2861 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2862 Type *SrcTy = V->getType();
2863 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2864 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2865 "Cannot truncate or noop with non-integer arguments!");
2866 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2867 "getTruncateOrNoop cannot extend!");
2868 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2869 return V; // No conversion
2870 return getTruncateExpr(V, Ty);
2873 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2874 /// the types using zero-extension, and then perform a umax operation
2876 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2878 const SCEV *PromotedLHS = LHS;
2879 const SCEV *PromotedRHS = RHS;
2881 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2882 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2884 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2886 return getUMaxExpr(PromotedLHS, PromotedRHS);
2889 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2890 /// the types using zero-extension, and then perform a umin operation
2892 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2894 const SCEV *PromotedLHS = LHS;
2895 const SCEV *PromotedRHS = RHS;
2897 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2898 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2900 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2902 return getUMinExpr(PromotedLHS, PromotedRHS);
2905 /// getPointerBase - Transitively follow the chain of pointer-type operands
2906 /// until reaching a SCEV that does not have a single pointer operand. This
2907 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2908 /// but corner cases do exist.
2909 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2910 // A pointer operand may evaluate to a nonpointer expression, such as null.
2911 if (!V->getType()->isPointerTy())
2914 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2915 return getPointerBase(Cast->getOperand());
2917 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2918 const SCEV *PtrOp = 0;
2919 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2921 if ((*I)->getType()->isPointerTy()) {
2922 // Cannot find the base of an expression with multiple pointer operands.
2930 return getPointerBase(PtrOp);
2935 /// PushDefUseChildren - Push users of the given Instruction
2936 /// onto the given Worklist.
2938 PushDefUseChildren(Instruction *I,
2939 SmallVectorImpl<Instruction *> &Worklist) {
2940 // Push the def-use children onto the Worklist stack.
2941 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2943 Worklist.push_back(cast<Instruction>(*UI));
2946 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2947 /// instructions that depend on the given instruction and removes them from
2948 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2951 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2952 SmallVector<Instruction *, 16> Worklist;
2953 PushDefUseChildren(PN, Worklist);
2955 SmallPtrSet<Instruction *, 8> Visited;
2957 while (!Worklist.empty()) {
2958 Instruction *I = Worklist.pop_back_val();
2959 if (!Visited.insert(I)) continue;
2961 ValueExprMapType::iterator It =
2962 ValueExprMap.find(static_cast<Value *>(I));
2963 if (It != ValueExprMap.end()) {
2964 const SCEV *Old = It->second;
2966 // Short-circuit the def-use traversal if the symbolic name
2967 // ceases to appear in expressions.
2968 if (Old != SymName && !hasOperand(Old, SymName))
2971 // SCEVUnknown for a PHI either means that it has an unrecognized
2972 // structure, it's a PHI that's in the progress of being computed
2973 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2974 // additional loop trip count information isn't going to change anything.
2975 // In the second case, createNodeForPHI will perform the necessary
2976 // updates on its own when it gets to that point. In the third, we do
2977 // want to forget the SCEVUnknown.
2978 if (!isa<PHINode>(I) ||
2979 !isa<SCEVUnknown>(Old) ||
2980 (I != PN && Old == SymName)) {
2981 forgetMemoizedResults(Old);
2982 ValueExprMap.erase(It);
2986 PushDefUseChildren(I, Worklist);
2990 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2991 /// a loop header, making it a potential recurrence, or it doesn't.
2993 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2994 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2995 if (L->getHeader() == PN->getParent()) {
2996 // The loop may have multiple entrances or multiple exits; we can analyze
2997 // this phi as an addrec if it has a unique entry value and a unique
2999 Value *BEValueV = 0, *StartValueV = 0;
3000 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3001 Value *V = PN->getIncomingValue(i);
3002 if (L->contains(PN->getIncomingBlock(i))) {
3005 } else if (BEValueV != V) {
3009 } else if (!StartValueV) {
3011 } else if (StartValueV != V) {
3016 if (BEValueV && StartValueV) {
3017 // While we are analyzing this PHI node, handle its value symbolically.
3018 const SCEV *SymbolicName = getUnknown(PN);
3019 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
3020 "PHI node already processed?");
3021 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3023 // Using this symbolic name for the PHI, analyze the value coming around
3025 const SCEV *BEValue = getSCEV(BEValueV);
3027 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3028 // has a special value for the first iteration of the loop.
3030 // If the value coming around the backedge is an add with the symbolic
3031 // value we just inserted, then we found a simple induction variable!
3032 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3033 // If there is a single occurrence of the symbolic value, replace it
3034 // with a recurrence.
3035 unsigned FoundIndex = Add->getNumOperands();
3036 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3037 if (Add->getOperand(i) == SymbolicName)
3038 if (FoundIndex == e) {
3043 if (FoundIndex != Add->getNumOperands()) {
3044 // Create an add with everything but the specified operand.
3045 SmallVector<const SCEV *, 8> Ops;
3046 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3047 if (i != FoundIndex)
3048 Ops.push_back(Add->getOperand(i));
3049 const SCEV *Accum = getAddExpr(Ops);
3051 // This is not a valid addrec if the step amount is varying each
3052 // loop iteration, but is not itself an addrec in this loop.
3053 if (isLoopInvariant(Accum, L) ||
3054 (isa<SCEVAddRecExpr>(Accum) &&
3055 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3056 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3058 // If the increment doesn't overflow, then neither the addrec nor
3059 // the post-increment will overflow.
3060 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3061 if (OBO->hasNoUnsignedWrap())
3062 Flags = setFlags(Flags, SCEV::FlagNUW);
3063 if (OBO->hasNoSignedWrap())
3064 Flags = setFlags(Flags, SCEV::FlagNSW);
3065 } else if (const GEPOperator *GEP =
3066 dyn_cast<GEPOperator>(BEValueV)) {
3067 // If the increment is an inbounds GEP, then we know the address
3068 // space cannot be wrapped around. We cannot make any guarantee
3069 // about signed or unsigned overflow because pointers are
3070 // unsigned but we may have a negative index from the base
3072 if (GEP->isInBounds())
3073 Flags = setFlags(Flags, SCEV::FlagNW);
3076 const SCEV *StartVal = getSCEV(StartValueV);
3077 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3079 // Since the no-wrap flags are on the increment, they apply to the
3080 // post-incremented value as well.
3081 if (isLoopInvariant(Accum, L))
3082 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3085 // Okay, for the entire analysis of this edge we assumed the PHI
3086 // to be symbolic. We now need to go back and purge all of the
3087 // entries for the scalars that use the symbolic expression.
3088 ForgetSymbolicName(PN, SymbolicName);
3089 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3093 } else if (const SCEVAddRecExpr *AddRec =
3094 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3095 // Otherwise, this could be a loop like this:
3096 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3097 // In this case, j = {1,+,1} and BEValue is j.
3098 // Because the other in-value of i (0) fits the evolution of BEValue
3099 // i really is an addrec evolution.
3100 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3101 const SCEV *StartVal = getSCEV(StartValueV);
3103 // If StartVal = j.start - j.stride, we can use StartVal as the
3104 // initial step of the addrec evolution.
3105 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3106 AddRec->getOperand(1))) {
3107 // FIXME: For constant StartVal, we should be able to infer
3109 const SCEV *PHISCEV =
3110 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3113 // Okay, for the entire analysis of this edge we assumed the PHI
3114 // to be symbolic. We now need to go back and purge all of the
3115 // entries for the scalars that use the symbolic expression.
3116 ForgetSymbolicName(PN, SymbolicName);
3117 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3125 // If the PHI has a single incoming value, follow that value, unless the
3126 // PHI's incoming blocks are in a different loop, in which case doing so
3127 // risks breaking LCSSA form. Instcombine would normally zap these, but
3128 // it doesn't have DominatorTree information, so it may miss cases.
3129 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
3130 if (LI->replacementPreservesLCSSAForm(PN, V))
3133 // If it's not a loop phi, we can't handle it yet.
3134 return getUnknown(PN);
3137 /// createNodeForGEP - Expand GEP instructions into add and multiply
3138 /// operations. This allows them to be analyzed by regular SCEV code.
3140 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3142 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3143 // Add expression, because the Instruction may be guarded by control flow
3144 // and the no-overflow bits may not be valid for the expression in any
3146 bool isInBounds = GEP->isInBounds();
3148 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3149 Value *Base = GEP->getOperand(0);
3150 // Don't attempt to analyze GEPs over unsized objects.
3151 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3152 return getUnknown(GEP);
3153 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3154 gep_type_iterator GTI = gep_type_begin(GEP);
3155 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3159 // Compute the (potentially symbolic) offset in bytes for this index.
3160 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3161 // For a struct, add the member offset.
3162 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3163 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
3165 // Add the field offset to the running total offset.
3166 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3168 // For an array, add the element offset, explicitly scaled.
3169 const SCEV *ElementSize = getSizeOfExpr(*GTI);
3170 const SCEV *IndexS = getSCEV(Index);
3171 // Getelementptr indices are signed.
3172 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3174 // Multiply the index by the element size to compute the element offset.
3175 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3176 isInBounds ? SCEV::FlagNSW :
3179 // Add the element offset to the running total offset.
3180 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3184 // Get the SCEV for the GEP base.
3185 const SCEV *BaseS = getSCEV(Base);
3187 // Add the total offset from all the GEP indices to the base.
3188 return getAddExpr(BaseS, TotalOffset,
3189 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3192 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3193 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3194 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3195 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3197 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3198 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3199 return C->getValue()->getValue().countTrailingZeros();
3201 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3202 return std::min(GetMinTrailingZeros(T->getOperand()),
3203 (uint32_t)getTypeSizeInBits(T->getType()));
3205 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3206 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3207 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3208 getTypeSizeInBits(E->getType()) : OpRes;
3211 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3212 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3213 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3214 getTypeSizeInBits(E->getType()) : OpRes;
3217 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3218 // The result is the min of all operands results.
3219 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3220 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3221 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3225 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3226 // The result is the sum of all operands results.
3227 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3228 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3229 for (unsigned i = 1, e = M->getNumOperands();
3230 SumOpRes != BitWidth && i != e; ++i)
3231 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3236 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3237 // The result is the min of all operands results.
3238 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3239 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3240 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3244 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3245 // The result is the min of all operands results.
3246 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3247 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3248 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3252 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3253 // The result is the min of all operands results.
3254 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3255 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3256 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3260 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3261 // For a SCEVUnknown, ask ValueTracking.
3262 unsigned BitWidth = getTypeSizeInBits(U->getType());
3263 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3264 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3265 return Zeros.countTrailingOnes();
3272 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3275 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3276 // See if we've computed this range already.
3277 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3278 if (I != UnsignedRanges.end())
3281 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3282 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3284 unsigned BitWidth = getTypeSizeInBits(S->getType());
3285 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3287 // If the value has known zeros, the maximum unsigned value will have those
3288 // known zeros as well.
3289 uint32_t TZ = GetMinTrailingZeros(S);
3291 ConservativeResult =
3292 ConstantRange(APInt::getMinValue(BitWidth),
3293 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3295 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3296 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3297 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3298 X = X.add(getUnsignedRange(Add->getOperand(i)));
3299 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3302 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3303 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3304 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3305 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3306 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3309 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3310 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3311 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3312 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3313 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3316 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3317 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3318 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3319 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3320 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3323 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3324 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3325 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3326 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3329 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3330 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3331 return setUnsignedRange(ZExt,
3332 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3335 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3336 ConstantRange X = getUnsignedRange(SExt->getOperand());
3337 return setUnsignedRange(SExt,
3338 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3341 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3342 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3343 return setUnsignedRange(Trunc,
3344 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3347 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3348 // If there's no unsigned wrap, the value will never be less than its
3350 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3351 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3352 if (!C->getValue()->isZero())
3353 ConservativeResult =
3354 ConservativeResult.intersectWith(
3355 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3357 // TODO: non-affine addrec
3358 if (AddRec->isAffine()) {
3359 Type *Ty = AddRec->getType();
3360 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3361 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3362 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3363 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3365 const SCEV *Start = AddRec->getStart();
3366 const SCEV *Step = AddRec->getStepRecurrence(*this);
3368 ConstantRange StartRange = getUnsignedRange(Start);
3369 ConstantRange StepRange = getSignedRange(Step);
3370 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3371 ConstantRange EndRange =
3372 StartRange.add(MaxBECountRange.multiply(StepRange));
3374 // Check for overflow. This must be done with ConstantRange arithmetic
3375 // because we could be called from within the ScalarEvolution overflow
3377 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3378 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3379 ConstantRange ExtMaxBECountRange =
3380 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3381 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3382 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3384 return setUnsignedRange(AddRec, ConservativeResult);
3386 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3387 EndRange.getUnsignedMin());
3388 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3389 EndRange.getUnsignedMax());
3390 if (Min.isMinValue() && Max.isMaxValue())
3391 return setUnsignedRange(AddRec, ConservativeResult);
3392 return setUnsignedRange(AddRec,
3393 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3397 return setUnsignedRange(AddRec, ConservativeResult);
3400 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3401 // For a SCEVUnknown, ask ValueTracking.
3402 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3403 ComputeMaskedBits(U->getValue(), Zeros, Ones, TD);
3404 if (Ones == ~Zeros + 1)
3405 return setUnsignedRange(U, ConservativeResult);
3406 return setUnsignedRange(U,
3407 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3410 return setUnsignedRange(S, ConservativeResult);
3413 /// getSignedRange - Determine the signed range for a particular SCEV.
3416 ScalarEvolution::getSignedRange(const SCEV *S) {
3417 // See if we've computed this range already.
3418 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3419 if (I != SignedRanges.end())
3422 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3423 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3425 unsigned BitWidth = getTypeSizeInBits(S->getType());
3426 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3428 // If the value has known zeros, the maximum signed value will have those
3429 // known zeros as well.
3430 uint32_t TZ = GetMinTrailingZeros(S);
3432 ConservativeResult =
3433 ConstantRange(APInt::getSignedMinValue(BitWidth),
3434 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3436 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3437 ConstantRange X = getSignedRange(Add->getOperand(0));
3438 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3439 X = X.add(getSignedRange(Add->getOperand(i)));
3440 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3443 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3444 ConstantRange X = getSignedRange(Mul->getOperand(0));
3445 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3446 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3447 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3450 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3451 ConstantRange X = getSignedRange(SMax->getOperand(0));
3452 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3453 X = X.smax(getSignedRange(SMax->getOperand(i)));
3454 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3457 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3458 ConstantRange X = getSignedRange(UMax->getOperand(0));
3459 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3460 X = X.umax(getSignedRange(UMax->getOperand(i)));
3461 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3464 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3465 ConstantRange X = getSignedRange(UDiv->getLHS());
3466 ConstantRange Y = getSignedRange(UDiv->getRHS());
3467 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3470 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3471 ConstantRange X = getSignedRange(ZExt->getOperand());
3472 return setSignedRange(ZExt,
3473 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3476 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3477 ConstantRange X = getSignedRange(SExt->getOperand());
3478 return setSignedRange(SExt,
3479 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3482 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3483 ConstantRange X = getSignedRange(Trunc->getOperand());
3484 return setSignedRange(Trunc,
3485 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3488 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3489 // If there's no signed wrap, and all the operands have the same sign or
3490 // zero, the value won't ever change sign.
3491 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3492 bool AllNonNeg = true;
3493 bool AllNonPos = true;
3494 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3495 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3496 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3499 ConservativeResult = ConservativeResult.intersectWith(
3500 ConstantRange(APInt(BitWidth, 0),
3501 APInt::getSignedMinValue(BitWidth)));
3503 ConservativeResult = ConservativeResult.intersectWith(
3504 ConstantRange(APInt::getSignedMinValue(BitWidth),
3505 APInt(BitWidth, 1)));
3508 // TODO: non-affine addrec
3509 if (AddRec->isAffine()) {
3510 Type *Ty = AddRec->getType();
3511 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3512 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3513 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3514 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3516 const SCEV *Start = AddRec->getStart();
3517 const SCEV *Step = AddRec->getStepRecurrence(*this);
3519 ConstantRange StartRange = getSignedRange(Start);
3520 ConstantRange StepRange = getSignedRange(Step);
3521 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3522 ConstantRange EndRange =
3523 StartRange.add(MaxBECountRange.multiply(StepRange));
3525 // Check for overflow. This must be done with ConstantRange arithmetic
3526 // because we could be called from within the ScalarEvolution overflow
3528 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3529 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3530 ConstantRange ExtMaxBECountRange =
3531 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3532 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3533 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3535 return setSignedRange(AddRec, ConservativeResult);
3537 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3538 EndRange.getSignedMin());
3539 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3540 EndRange.getSignedMax());
3541 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3542 return setSignedRange(AddRec, ConservativeResult);
3543 return setSignedRange(AddRec,
3544 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3548 return setSignedRange(AddRec, ConservativeResult);
3551 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3552 // For a SCEVUnknown, ask ValueTracking.
3553 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3554 return setSignedRange(U, ConservativeResult);
3555 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3557 return setSignedRange(U, ConservativeResult);
3558 return setSignedRange(U, ConservativeResult.intersectWith(
3559 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3560 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3563 return setSignedRange(S, ConservativeResult);
3566 /// createSCEV - We know that there is no SCEV for the specified value.
3567 /// Analyze the expression.
3569 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3570 if (!isSCEVable(V->getType()))
3571 return getUnknown(V);
3573 unsigned Opcode = Instruction::UserOp1;
3574 if (Instruction *I = dyn_cast<Instruction>(V)) {
3575 Opcode = I->getOpcode();
3577 // Don't attempt to analyze instructions in blocks that aren't
3578 // reachable. Such instructions don't matter, and they aren't required
3579 // to obey basic rules for definitions dominating uses which this
3580 // analysis depends on.
3581 if (!DT->isReachableFromEntry(I->getParent()))
3582 return getUnknown(V);
3583 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3584 Opcode = CE->getOpcode();
3585 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3586 return getConstant(CI);
3587 else if (isa<ConstantPointerNull>(V))
3588 return getConstant(V->getType(), 0);
3589 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3590 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3592 return getUnknown(V);
3594 Operator *U = cast<Operator>(V);
3596 case Instruction::Add: {
3597 // The simple thing to do would be to just call getSCEV on both operands
3598 // and call getAddExpr with the result. However if we're looking at a
3599 // bunch of things all added together, this can be quite inefficient,
3600 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3601 // Instead, gather up all the operands and make a single getAddExpr call.
3602 // LLVM IR canonical form means we need only traverse the left operands.
3604 // Don't apply this instruction's NSW or NUW flags to the new
3605 // expression. The instruction may be guarded by control flow that the
3606 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3607 // mapped to the same SCEV expression, and it would be incorrect to transfer
3608 // NSW/NUW semantics to those operations.
3609 SmallVector<const SCEV *, 4> AddOps;
3610 AddOps.push_back(getSCEV(U->getOperand(1)));
3611 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3612 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3613 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3615 U = cast<Operator>(Op);
3616 const SCEV *Op1 = getSCEV(U->getOperand(1));
3617 if (Opcode == Instruction::Sub)
3618 AddOps.push_back(getNegativeSCEV(Op1));
3620 AddOps.push_back(Op1);
3622 AddOps.push_back(getSCEV(U->getOperand(0)));
3623 return getAddExpr(AddOps);
3625 case Instruction::Mul: {
3626 // Don't transfer NSW/NUW for the same reason as AddExpr.
3627 SmallVector<const SCEV *, 4> MulOps;
3628 MulOps.push_back(getSCEV(U->getOperand(1)));
3629 for (Value *Op = U->getOperand(0);
3630 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3631 Op = U->getOperand(0)) {
3632 U = cast<Operator>(Op);
3633 MulOps.push_back(getSCEV(U->getOperand(1)));
3635 MulOps.push_back(getSCEV(U->getOperand(0)));
3636 return getMulExpr(MulOps);
3638 case Instruction::UDiv:
3639 return getUDivExpr(getSCEV(U->getOperand(0)),
3640 getSCEV(U->getOperand(1)));
3641 case Instruction::Sub:
3642 return getMinusSCEV(getSCEV(U->getOperand(0)),
3643 getSCEV(U->getOperand(1)));
3644 case Instruction::And:
3645 // For an expression like x&255 that merely masks off the high bits,
3646 // use zext(trunc(x)) as the SCEV expression.
3647 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3648 if (CI->isNullValue())
3649 return getSCEV(U->getOperand(1));
3650 if (CI->isAllOnesValue())
3651 return getSCEV(U->getOperand(0));
3652 const APInt &A = CI->getValue();
3654 // Instcombine's ShrinkDemandedConstant may strip bits out of
3655 // constants, obscuring what would otherwise be a low-bits mask.
3656 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3657 // knew about to reconstruct a low-bits mask value.
3658 unsigned LZ = A.countLeadingZeros();
3659 unsigned BitWidth = A.getBitWidth();
3660 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3661 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD);
3663 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3665 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3667 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3668 IntegerType::get(getContext(), BitWidth - LZ)),
3673 case Instruction::Or:
3674 // If the RHS of the Or is a constant, we may have something like:
3675 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3676 // optimizations will transparently handle this case.
3678 // In order for this transformation to be safe, the LHS must be of the
3679 // form X*(2^n) and the Or constant must be less than 2^n.
3680 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3681 const SCEV *LHS = getSCEV(U->getOperand(0));
3682 const APInt &CIVal = CI->getValue();
3683 if (GetMinTrailingZeros(LHS) >=
3684 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3685 // Build a plain add SCEV.
3686 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3687 // If the LHS of the add was an addrec and it has no-wrap flags,
3688 // transfer the no-wrap flags, since an or won't introduce a wrap.
3689 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3690 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3691 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3692 OldAR->getNoWrapFlags());
3698 case Instruction::Xor:
3699 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3700 // If the RHS of the xor is a signbit, then this is just an add.
3701 // Instcombine turns add of signbit into xor as a strength reduction step.
3702 if (CI->getValue().isSignBit())
3703 return getAddExpr(getSCEV(U->getOperand(0)),
3704 getSCEV(U->getOperand(1)));
3706 // If the RHS of xor is -1, then this is a not operation.
3707 if (CI->isAllOnesValue())
3708 return getNotSCEV(getSCEV(U->getOperand(0)));
3710 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3711 // This is a variant of the check for xor with -1, and it handles
3712 // the case where instcombine has trimmed non-demanded bits out
3713 // of an xor with -1.
3714 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3715 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3716 if (BO->getOpcode() == Instruction::And &&
3717 LCI->getValue() == CI->getValue())
3718 if (const SCEVZeroExtendExpr *Z =
3719 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3720 Type *UTy = U->getType();
3721 const SCEV *Z0 = Z->getOperand();
3722 Type *Z0Ty = Z0->getType();
3723 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3725 // If C is a low-bits mask, the zero extend is serving to
3726 // mask off the high bits. Complement the operand and
3727 // re-apply the zext.
3728 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3729 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3731 // If C is a single bit, it may be in the sign-bit position
3732 // before the zero-extend. In this case, represent the xor
3733 // using an add, which is equivalent, and re-apply the zext.
3734 APInt Trunc = CI->getValue().trunc(Z0TySize);
3735 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3737 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3743 case Instruction::Shl:
3744 // Turn shift left of a constant amount into a multiply.
3745 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3746 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3748 // If the shift count is not less than the bitwidth, the result of
3749 // the shift is undefined. Don't try to analyze it, because the
3750 // resolution chosen here may differ from the resolution chosen in
3751 // other parts of the compiler.
3752 if (SA->getValue().uge(BitWidth))
3755 Constant *X = ConstantInt::get(getContext(),
3756 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3757 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3761 case Instruction::LShr:
3762 // Turn logical shift right of a constant into a unsigned divide.
3763 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3764 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3766 // If the shift count is not less than the bitwidth, the result of
3767 // the shift is undefined. Don't try to analyze it, because the
3768 // resolution chosen here may differ from the resolution chosen in
3769 // other parts of the compiler.
3770 if (SA->getValue().uge(BitWidth))
3773 Constant *X = ConstantInt::get(getContext(),
3774 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3775 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3779 case Instruction::AShr:
3780 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3781 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3782 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3783 if (L->getOpcode() == Instruction::Shl &&
3784 L->getOperand(1) == U->getOperand(1)) {
3785 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3787 // If the shift count is not less than the bitwidth, the result of
3788 // the shift is undefined. Don't try to analyze it, because the
3789 // resolution chosen here may differ from the resolution chosen in
3790 // other parts of the compiler.
3791 if (CI->getValue().uge(BitWidth))
3794 uint64_t Amt = BitWidth - CI->getZExtValue();
3795 if (Amt == BitWidth)
3796 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3798 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3799 IntegerType::get(getContext(),
3805 case Instruction::Trunc:
3806 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3808 case Instruction::ZExt:
3809 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3811 case Instruction::SExt:
3812 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3814 case Instruction::BitCast:
3815 // BitCasts are no-op casts so we just eliminate the cast.
3816 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3817 return getSCEV(U->getOperand(0));
3820 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3821 // lead to pointer expressions which cannot safely be expanded to GEPs,
3822 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3823 // simplifying integer expressions.
3825 case Instruction::GetElementPtr:
3826 return createNodeForGEP(cast<GEPOperator>(U));
3828 case Instruction::PHI:
3829 return createNodeForPHI(cast<PHINode>(U));
3831 case Instruction::Select:
3832 // This could be a smax or umax that was lowered earlier.
3833 // Try to recover it.
3834 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3835 Value *LHS = ICI->getOperand(0);
3836 Value *RHS = ICI->getOperand(1);
3837 switch (ICI->getPredicate()) {
3838 case ICmpInst::ICMP_SLT:
3839 case ICmpInst::ICMP_SLE:
3840 std::swap(LHS, RHS);
3842 case ICmpInst::ICMP_SGT:
3843 case ICmpInst::ICMP_SGE:
3844 // a >s b ? a+x : b+x -> smax(a, b)+x
3845 // a >s b ? b+x : a+x -> smin(a, b)+x
3846 if (LHS->getType() == U->getType()) {
3847 const SCEV *LS = getSCEV(LHS);
3848 const SCEV *RS = getSCEV(RHS);
3849 const SCEV *LA = getSCEV(U->getOperand(1));
3850 const SCEV *RA = getSCEV(U->getOperand(2));
3851 const SCEV *LDiff = getMinusSCEV(LA, LS);
3852 const SCEV *RDiff = getMinusSCEV(RA, RS);
3854 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3855 LDiff = getMinusSCEV(LA, RS);
3856 RDiff = getMinusSCEV(RA, LS);
3858 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3861 case ICmpInst::ICMP_ULT:
3862 case ICmpInst::ICMP_ULE:
3863 std::swap(LHS, RHS);
3865 case ICmpInst::ICMP_UGT:
3866 case ICmpInst::ICMP_UGE:
3867 // a >u b ? a+x : b+x -> umax(a, b)+x
3868 // a >u b ? b+x : a+x -> umin(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(getUMaxExpr(LS, RS), LDiff);
3878 LDiff = getMinusSCEV(LA, RS);
3879 RDiff = getMinusSCEV(RA, LS);
3881 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3884 case ICmpInst::ICMP_NE:
3885 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3886 if (LHS->getType() == U->getType() &&
3887 isa<ConstantInt>(RHS) &&
3888 cast<ConstantInt>(RHS)->isZero()) {
3889 const SCEV *One = getConstant(LHS->getType(), 1);
3890 const SCEV *LS = getSCEV(LHS);
3891 const SCEV *LA = getSCEV(U->getOperand(1));
3892 const SCEV *RA = getSCEV(U->getOperand(2));
3893 const SCEV *LDiff = getMinusSCEV(LA, LS);
3894 const SCEV *RDiff = getMinusSCEV(RA, One);
3896 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3899 case ICmpInst::ICMP_EQ:
3900 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3901 if (LHS->getType() == U->getType() &&
3902 isa<ConstantInt>(RHS) &&
3903 cast<ConstantInt>(RHS)->isZero()) {
3904 const SCEV *One = getConstant(LHS->getType(), 1);
3905 const SCEV *LS = getSCEV(LHS);
3906 const SCEV *LA = getSCEV(U->getOperand(1));
3907 const SCEV *RA = getSCEV(U->getOperand(2));
3908 const SCEV *LDiff = getMinusSCEV(LA, One);
3909 const SCEV *RDiff = getMinusSCEV(RA, LS);
3911 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3919 default: // We cannot analyze this expression.
3923 return getUnknown(V);
3928 //===----------------------------------------------------------------------===//
3929 // Iteration Count Computation Code
3932 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3933 /// normal unsigned value. Returns 0 if the trip count is unknown or not
3934 /// constant. Will also return 0 if the maximum trip count is very large (>=
3937 /// This "trip count" assumes that control exits via ExitingBlock. More
3938 /// precisely, it is the number of times that control may reach ExitingBlock
3939 /// before taking the branch. For loops with multiple exits, it may not be the
3940 /// number times that the loop header executes because the loop may exit
3941 /// prematurely via another branch.
3942 unsigned ScalarEvolution::
3943 getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock) {
3944 const SCEVConstant *ExitCount =
3945 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
3949 ConstantInt *ExitConst = ExitCount->getValue();
3951 // Guard against huge trip counts.
3952 if (ExitConst->getValue().getActiveBits() > 32)
3955 // In case of integer overflow, this returns 0, which is correct.
3956 return ((unsigned)ExitConst->getZExtValue()) + 1;
3959 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3960 /// trip count of this loop as a normal unsigned value, if possible. This
3961 /// means that the actual trip count is always a multiple of the returned
3962 /// value (don't forget the trip count could very well be zero as well!).
3964 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3965 /// multiple of a constant (which is also the case if the trip count is simply
3966 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3967 /// if the trip count is very large (>= 2^32).
3969 /// As explained in the comments for getSmallConstantTripCount, this assumes
3970 /// that control exits the loop via ExitingBlock.
3971 unsigned ScalarEvolution::
3972 getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock) {
3973 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
3974 if (ExitCount == getCouldNotCompute())
3977 // Get the trip count from the BE count by adding 1.
3978 const SCEV *TCMul = getAddExpr(ExitCount,
3979 getConstant(ExitCount->getType(), 1));
3980 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
3981 // to factor simple cases.
3982 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
3983 TCMul = Mul->getOperand(0);
3985 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
3989 ConstantInt *Result = MulC->getValue();
3991 // Guard against huge trip counts.
3992 if (!Result || Result->getValue().getActiveBits() > 32)
3995 return (unsigned)Result->getZExtValue();
3998 // getExitCount - Get the expression for the number of loop iterations for which
3999 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return
4000 // SCEVCouldNotCompute.
4001 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4002 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4005 /// getBackedgeTakenCount - If the specified loop has a predictable
4006 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4007 /// object. The backedge-taken count is the number of times the loop header
4008 /// will be branched to from within the loop. This is one less than the
4009 /// trip count of the loop, since it doesn't count the first iteration,
4010 /// when the header is branched to from outside the loop.
4012 /// Note that it is not valid to call this method on a loop without a
4013 /// loop-invariant backedge-taken count (see
4014 /// hasLoopInvariantBackedgeTakenCount).
4016 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4017 return getBackedgeTakenInfo(L).getExact(this);
4020 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4021 /// return the least SCEV value that is known never to be less than the
4022 /// actual backedge taken count.
4023 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4024 return getBackedgeTakenInfo(L).getMax(this);
4027 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4028 /// onto the given Worklist.
4030 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4031 BasicBlock *Header = L->getHeader();
4033 // Push all Loop-header PHIs onto the Worklist stack.
4034 for (BasicBlock::iterator I = Header->begin();
4035 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4036 Worklist.push_back(PN);
4039 const ScalarEvolution::BackedgeTakenInfo &
4040 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4041 // Initially insert an invalid entry for this loop. If the insertion
4042 // succeeds, proceed to actually compute a backedge-taken count and
4043 // update the value. The temporary CouldNotCompute value tells SCEV
4044 // code elsewhere that it shouldn't attempt to request a new
4045 // backedge-taken count, which could result in infinite recursion.
4046 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4047 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4049 return Pair.first->second;
4051 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4052 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4053 // must be cleared in this scope.
4054 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4056 if (Result.getExact(this) != getCouldNotCompute()) {
4057 assert(isLoopInvariant(Result.getExact(this), L) &&
4058 isLoopInvariant(Result.getMax(this), L) &&
4059 "Computed backedge-taken count isn't loop invariant for loop!");
4060 ++NumTripCountsComputed;
4062 else if (Result.getMax(this) == getCouldNotCompute() &&
4063 isa<PHINode>(L->getHeader()->begin())) {
4064 // Only count loops that have phi nodes as not being computable.
4065 ++NumTripCountsNotComputed;
4068 // Now that we know more about the trip count for this loop, forget any
4069 // existing SCEV values for PHI nodes in this loop since they are only
4070 // conservative estimates made without the benefit of trip count
4071 // information. This is similar to the code in forgetLoop, except that
4072 // it handles SCEVUnknown PHI nodes specially.
4073 if (Result.hasAnyInfo()) {
4074 SmallVector<Instruction *, 16> Worklist;
4075 PushLoopPHIs(L, Worklist);
4077 SmallPtrSet<Instruction *, 8> Visited;
4078 while (!Worklist.empty()) {
4079 Instruction *I = Worklist.pop_back_val();
4080 if (!Visited.insert(I)) continue;
4082 ValueExprMapType::iterator It =
4083 ValueExprMap.find(static_cast<Value *>(I));
4084 if (It != ValueExprMap.end()) {
4085 const SCEV *Old = It->second;
4087 // SCEVUnknown for a PHI either means that it has an unrecognized
4088 // structure, or it's a PHI that's in the progress of being computed
4089 // by createNodeForPHI. In the former case, additional loop trip
4090 // count information isn't going to change anything. In the later
4091 // case, createNodeForPHI will perform the necessary updates on its
4092 // own when it gets to that point.
4093 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4094 forgetMemoizedResults(Old);
4095 ValueExprMap.erase(It);
4097 if (PHINode *PN = dyn_cast<PHINode>(I))
4098 ConstantEvolutionLoopExitValue.erase(PN);
4101 PushDefUseChildren(I, Worklist);
4105 // Re-lookup the insert position, since the call to
4106 // ComputeBackedgeTakenCount above could result in a
4107 // recusive call to getBackedgeTakenInfo (on a different
4108 // loop), which would invalidate the iterator computed
4110 return BackedgeTakenCounts.find(L)->second = Result;
4113 /// forgetLoop - This method should be called by the client when it has
4114 /// changed a loop in a way that may effect ScalarEvolution's ability to
4115 /// compute a trip count, or if the loop is deleted.
4116 void ScalarEvolution::forgetLoop(const Loop *L) {
4117 // Drop any stored trip count value.
4118 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4119 BackedgeTakenCounts.find(L);
4120 if (BTCPos != BackedgeTakenCounts.end()) {
4121 BTCPos->second.clear();
4122 BackedgeTakenCounts.erase(BTCPos);
4125 // Drop information about expressions based on loop-header PHIs.
4126 SmallVector<Instruction *, 16> Worklist;
4127 PushLoopPHIs(L, Worklist);
4129 SmallPtrSet<Instruction *, 8> Visited;
4130 while (!Worklist.empty()) {
4131 Instruction *I = Worklist.pop_back_val();
4132 if (!Visited.insert(I)) continue;
4134 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4135 if (It != ValueExprMap.end()) {
4136 forgetMemoizedResults(It->second);
4137 ValueExprMap.erase(It);
4138 if (PHINode *PN = dyn_cast<PHINode>(I))
4139 ConstantEvolutionLoopExitValue.erase(PN);
4142 PushDefUseChildren(I, Worklist);
4145 // Forget all contained loops too, to avoid dangling entries in the
4146 // ValuesAtScopes map.
4147 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4151 /// forgetValue - This method should be called by the client when it has
4152 /// changed a value in a way that may effect its value, or which may
4153 /// disconnect it from a def-use chain linking it to a loop.
4154 void ScalarEvolution::forgetValue(Value *V) {
4155 Instruction *I = dyn_cast<Instruction>(V);
4158 // Drop information about expressions based on loop-header PHIs.
4159 SmallVector<Instruction *, 16> Worklist;
4160 Worklist.push_back(I);
4162 SmallPtrSet<Instruction *, 8> Visited;
4163 while (!Worklist.empty()) {
4164 I = Worklist.pop_back_val();
4165 if (!Visited.insert(I)) continue;
4167 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4168 if (It != ValueExprMap.end()) {
4169 forgetMemoizedResults(It->second);
4170 ValueExprMap.erase(It);
4171 if (PHINode *PN = dyn_cast<PHINode>(I))
4172 ConstantEvolutionLoopExitValue.erase(PN);
4175 PushDefUseChildren(I, Worklist);
4179 /// getExact - Get the exact loop backedge taken count considering all loop
4180 /// exits. A computable result can only be return for loops with a single exit.
4181 /// Returning the minimum taken count among all exits is incorrect because one
4182 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4183 /// the limit of each loop test is never skipped. This is a valid assumption as
4184 /// long as the loop exits via that test. For precise results, it is the
4185 /// caller's responsibility to specify the relevant loop exit using
4186 /// getExact(ExitingBlock, SE).
4188 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4189 // If any exits were not computable, the loop is not computable.
4190 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4192 // We need exactly one computable exit.
4193 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4194 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4196 const SCEV *BECount = 0;
4197 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4198 ENT != 0; ENT = ENT->getNextExit()) {
4200 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4203 BECount = ENT->ExactNotTaken;
4204 else if (BECount != ENT->ExactNotTaken)
4205 return SE->getCouldNotCompute();
4207 assert(BECount && "Invalid not taken count for loop exit");
4211 /// getExact - Get the exact not taken count for this loop exit.
4213 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4214 ScalarEvolution *SE) const {
4215 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4216 ENT != 0; ENT = ENT->getNextExit()) {
4218 if (ENT->ExitingBlock == ExitingBlock)
4219 return ENT->ExactNotTaken;
4221 return SE->getCouldNotCompute();
4224 /// getMax - Get the max backedge taken count for the loop.
4226 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4227 return Max ? Max : SE->getCouldNotCompute();
4230 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4231 /// computable exit into a persistent ExitNotTakenInfo array.
4232 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4233 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4234 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4237 ExitNotTaken.setIncomplete();
4239 unsigned NumExits = ExitCounts.size();
4240 if (NumExits == 0) return;
4242 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4243 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4244 if (NumExits == 1) return;
4246 // Handle the rare case of multiple computable exits.
4247 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4249 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4250 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4251 PrevENT->setNextExit(ENT);
4252 ENT->ExitingBlock = ExitCounts[i].first;
4253 ENT->ExactNotTaken = ExitCounts[i].second;
4257 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4258 void ScalarEvolution::BackedgeTakenInfo::clear() {
4259 ExitNotTaken.ExitingBlock = 0;
4260 ExitNotTaken.ExactNotTaken = 0;
4261 delete[] ExitNotTaken.getNextExit();
4264 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4265 /// of the specified loop will execute.
4266 ScalarEvolution::BackedgeTakenInfo
4267 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4268 SmallVector<BasicBlock *, 8> ExitingBlocks;
4269 L->getExitingBlocks(ExitingBlocks);
4271 // Examine all exits and pick the most conservative values.
4272 const SCEV *MaxBECount = getCouldNotCompute();
4273 bool CouldComputeBECount = true;
4274 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4275 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4276 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4277 if (EL.Exact == getCouldNotCompute())
4278 // We couldn't compute an exact value for this exit, so
4279 // we won't be able to compute an exact value for the loop.
4280 CouldComputeBECount = false;
4282 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4284 if (MaxBECount == getCouldNotCompute())
4285 MaxBECount = EL.Max;
4286 else if (EL.Max != getCouldNotCompute()) {
4287 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4288 // skip some loop tests. Taking the max over the exits is sufficiently
4289 // conservative. TODO: We could do better taking into consideration
4290 // that (1) the loop has unit stride (2) the last loop test is
4291 // less-than/greater-than (3) any loop test is less-than/greater-than AND
4292 // falls-through some constant times less then the other tests.
4293 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4297 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4300 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4301 /// loop will execute if it exits via the specified block.
4302 ScalarEvolution::ExitLimit
4303 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4305 // Okay, we've chosen an exiting block. See what condition causes us to
4306 // exit at this block.
4308 // FIXME: we should be able to handle switch instructions (with a single exit)
4309 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4310 if (ExitBr == 0) return getCouldNotCompute();
4311 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4313 // At this point, we know we have a conditional branch that determines whether
4314 // the loop is exited. However, we don't know if the branch is executed each
4315 // time through the loop. If not, then the execution count of the branch will
4316 // not be equal to the trip count of the loop.
4318 // Currently we check for this by checking to see if the Exit branch goes to
4319 // the loop header. If so, we know it will always execute the same number of
4320 // times as the loop. We also handle the case where the exit block *is* the
4321 // loop header. This is common for un-rotated loops.
4323 // If both of those tests fail, walk up the unique predecessor chain to the
4324 // header, stopping if there is an edge that doesn't exit the loop. If the
4325 // header is reached, the execution count of the branch will be equal to the
4326 // trip count of the loop.
4328 // More extensive analysis could be done to handle more cases here.
4330 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4331 ExitBr->getSuccessor(1) != L->getHeader() &&
4332 ExitBr->getParent() != L->getHeader()) {
4333 // The simple checks failed, try climbing the unique predecessor chain
4334 // up to the header.
4336 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4337 BasicBlock *Pred = BB->getUniquePredecessor();
4339 return getCouldNotCompute();
4340 TerminatorInst *PredTerm = Pred->getTerminator();
4341 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4342 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4345 // If the predecessor has a successor that isn't BB and isn't
4346 // outside the loop, assume the worst.
4347 if (L->contains(PredSucc))
4348 return getCouldNotCompute();
4350 if (Pred == L->getHeader()) {
4357 return getCouldNotCompute();
4360 // Proceed to the next level to examine the exit condition expression.
4361 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4362 ExitBr->getSuccessor(0),
4363 ExitBr->getSuccessor(1));
4366 /// ComputeExitLimitFromCond - Compute the number of times the
4367 /// backedge of the specified loop will execute if its exit condition
4368 /// were a conditional branch of ExitCond, TBB, and FBB.
4369 ScalarEvolution::ExitLimit
4370 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4374 // Check if the controlling expression for this loop is an And or Or.
4375 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4376 if (BO->getOpcode() == Instruction::And) {
4377 // Recurse on the operands of the and.
4378 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4379 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4380 const SCEV *BECount = getCouldNotCompute();
4381 const SCEV *MaxBECount = getCouldNotCompute();
4382 if (L->contains(TBB)) {
4383 // Both conditions must be true for the loop to continue executing.
4384 // Choose the less conservative count.
4385 if (EL0.Exact == getCouldNotCompute() ||
4386 EL1.Exact == getCouldNotCompute())
4387 BECount = getCouldNotCompute();
4389 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4390 if (EL0.Max == getCouldNotCompute())
4391 MaxBECount = EL1.Max;
4392 else if (EL1.Max == getCouldNotCompute())
4393 MaxBECount = EL0.Max;
4395 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4397 // Both conditions must be true at the same time for the loop to exit.
4398 // For now, be conservative.
4399 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4400 if (EL0.Max == EL1.Max)
4401 MaxBECount = EL0.Max;
4402 if (EL0.Exact == EL1.Exact)
4403 BECount = EL0.Exact;
4406 return ExitLimit(BECount, MaxBECount);
4408 if (BO->getOpcode() == Instruction::Or) {
4409 // Recurse on the operands of the or.
4410 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4411 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4412 const SCEV *BECount = getCouldNotCompute();
4413 const SCEV *MaxBECount = getCouldNotCompute();
4414 if (L->contains(FBB)) {
4415 // Both conditions must be false for the loop to continue executing.
4416 // Choose the less conservative count.
4417 if (EL0.Exact == getCouldNotCompute() ||
4418 EL1.Exact == getCouldNotCompute())
4419 BECount = getCouldNotCompute();
4421 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4422 if (EL0.Max == getCouldNotCompute())
4423 MaxBECount = EL1.Max;
4424 else if (EL1.Max == getCouldNotCompute())
4425 MaxBECount = EL0.Max;
4427 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4429 // Both conditions must be false at the same time for the loop to exit.
4430 // For now, be conservative.
4431 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4432 if (EL0.Max == EL1.Max)
4433 MaxBECount = EL0.Max;
4434 if (EL0.Exact == EL1.Exact)
4435 BECount = EL0.Exact;
4438 return ExitLimit(BECount, MaxBECount);
4442 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4443 // Proceed to the next level to examine the icmp.
4444 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4445 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB);
4447 // Check for a constant condition. These are normally stripped out by
4448 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4449 // preserve the CFG and is temporarily leaving constant conditions
4451 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4452 if (L->contains(FBB) == !CI->getZExtValue())
4453 // The backedge is always taken.
4454 return getCouldNotCompute();
4456 // The backedge is never taken.
4457 return getConstant(CI->getType(), 0);
4460 // If it's not an integer or pointer comparison then compute it the hard way.
4461 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4464 /// ComputeExitLimitFromICmp - Compute the number of times the
4465 /// backedge of the specified loop will execute if its exit condition
4466 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4467 ScalarEvolution::ExitLimit
4468 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4473 // If the condition was exit on true, convert the condition to exit on false
4474 ICmpInst::Predicate Cond;
4475 if (!L->contains(FBB))
4476 Cond = ExitCond->getPredicate();
4478 Cond = ExitCond->getInversePredicate();
4480 // Handle common loops like: for (X = "string"; *X; ++X)
4481 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4482 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4484 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4485 if (ItCnt.hasAnyInfo())
4489 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4490 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4492 // Try to evaluate any dependencies out of the loop.
4493 LHS = getSCEVAtScope(LHS, L);
4494 RHS = getSCEVAtScope(RHS, L);
4496 // At this point, we would like to compute how many iterations of the
4497 // loop the predicate will return true for these inputs.
4498 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4499 // If there is a loop-invariant, force it into the RHS.
4500 std::swap(LHS, RHS);
4501 Cond = ICmpInst::getSwappedPredicate(Cond);
4504 // Simplify the operands before analyzing them.
4505 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4507 // If we have a comparison of a chrec against a constant, try to use value
4508 // ranges to answer this query.
4509 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4510 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4511 if (AddRec->getLoop() == L) {
4512 // Form the constant range.
4513 ConstantRange CompRange(
4514 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4516 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4517 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4521 case ICmpInst::ICMP_NE: { // while (X != Y)
4522 // Convert to: while (X-Y != 0)
4523 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4524 if (EL.hasAnyInfo()) return EL;
4527 case ICmpInst::ICMP_EQ: { // while (X == Y)
4528 // Convert to: while (X-Y == 0)
4529 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4530 if (EL.hasAnyInfo()) return EL;
4533 case ICmpInst::ICMP_SLT: {
4534 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true);
4535 if (EL.hasAnyInfo()) return EL;
4538 case ICmpInst::ICMP_SGT: {
4539 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4540 getNotSCEV(RHS), L, true);
4541 if (EL.hasAnyInfo()) return EL;
4544 case ICmpInst::ICMP_ULT: {
4545 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false);
4546 if (EL.hasAnyInfo()) return EL;
4549 case ICmpInst::ICMP_UGT: {
4550 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4551 getNotSCEV(RHS), L, false);
4552 if (EL.hasAnyInfo()) return EL;
4557 dbgs() << "ComputeBackedgeTakenCount ";
4558 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4559 dbgs() << "[unsigned] ";
4560 dbgs() << *LHS << " "
4561 << Instruction::getOpcodeName(Instruction::ICmp)
4562 << " " << *RHS << "\n";
4566 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4569 static ConstantInt *
4570 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4571 ScalarEvolution &SE) {
4572 const SCEV *InVal = SE.getConstant(C);
4573 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4574 assert(isa<SCEVConstant>(Val) &&
4575 "Evaluation of SCEV at constant didn't fold correctly?");
4576 return cast<SCEVConstant>(Val)->getValue();
4579 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4580 /// 'icmp op load X, cst', try to see if we can compute the backedge
4581 /// execution count.
4582 ScalarEvolution::ExitLimit
4583 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4587 ICmpInst::Predicate predicate) {
4589 if (LI->isVolatile()) return getCouldNotCompute();
4591 // Check to see if the loaded pointer is a getelementptr of a global.
4592 // TODO: Use SCEV instead of manually grubbing with GEPs.
4593 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4594 if (!GEP) return getCouldNotCompute();
4596 // Make sure that it is really a constant global we are gepping, with an
4597 // initializer, and make sure the first IDX is really 0.
4598 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4599 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4600 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4601 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4602 return getCouldNotCompute();
4604 // Okay, we allow one non-constant index into the GEP instruction.
4606 std::vector<Constant*> Indexes;
4607 unsigned VarIdxNum = 0;
4608 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4609 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4610 Indexes.push_back(CI);
4611 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4612 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4613 VarIdx = GEP->getOperand(i);
4615 Indexes.push_back(0);
4618 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4620 return getCouldNotCompute();
4622 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4623 // Check to see if X is a loop variant variable value now.
4624 const SCEV *Idx = getSCEV(VarIdx);
4625 Idx = getSCEVAtScope(Idx, L);
4627 // We can only recognize very limited forms of loop index expressions, in
4628 // particular, only affine AddRec's like {C1,+,C2}.
4629 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4630 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4631 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4632 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4633 return getCouldNotCompute();
4635 unsigned MaxSteps = MaxBruteForceIterations;
4636 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4637 ConstantInt *ItCst = ConstantInt::get(
4638 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4639 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4641 // Form the GEP offset.
4642 Indexes[VarIdxNum] = Val;
4644 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4646 if (Result == 0) break; // Cannot compute!
4648 // Evaluate the condition for this iteration.
4649 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4650 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4651 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4653 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4654 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4657 ++NumArrayLenItCounts;
4658 return getConstant(ItCst); // Found terminating iteration!
4661 return getCouldNotCompute();
4665 /// CanConstantFold - Return true if we can constant fold an instruction of the
4666 /// specified type, assuming that all operands were constants.
4667 static bool CanConstantFold(const Instruction *I) {
4668 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4669 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4673 if (const CallInst *CI = dyn_cast<CallInst>(I))
4674 if (const Function *F = CI->getCalledFunction())
4675 return canConstantFoldCallTo(F);
4679 /// Determine whether this instruction can constant evolve within this loop
4680 /// assuming its operands can all constant evolve.
4681 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4682 // An instruction outside of the loop can't be derived from a loop PHI.
4683 if (!L->contains(I)) return false;
4685 if (isa<PHINode>(I)) {
4686 if (L->getHeader() == I->getParent())
4689 // We don't currently keep track of the control flow needed to evaluate
4690 // PHIs, so we cannot handle PHIs inside of loops.
4694 // If we won't be able to constant fold this expression even if the operands
4695 // are constants, bail early.
4696 return CanConstantFold(I);
4699 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4700 /// recursing through each instruction operand until reaching a loop header phi.
4702 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4703 DenseMap<Instruction *, PHINode *> &PHIMap) {
4705 // Otherwise, we can evaluate this instruction if all of its operands are
4706 // constant or derived from a PHI node themselves.
4708 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4709 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4711 if (isa<Constant>(*OpI)) continue;
4713 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4714 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4716 PHINode *P = dyn_cast<PHINode>(OpInst);
4718 // If this operand is already visited, reuse the prior result.
4719 // We may have P != PHI if this is the deepest point at which the
4720 // inconsistent paths meet.
4721 P = PHIMap.lookup(OpInst);
4723 // Recurse and memoize the results, whether a phi is found or not.
4724 // This recursive call invalidates pointers into PHIMap.
4725 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4728 if (P == 0) return 0; // Not evolving from PHI
4729 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4732 // This is a expression evolving from a constant PHI!
4736 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4737 /// in the loop that V is derived from. We allow arbitrary operations along the
4738 /// way, but the operands of an operation must either be constants or a value
4739 /// derived from a constant PHI. If this expression does not fit with these
4740 /// constraints, return null.
4741 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4742 Instruction *I = dyn_cast<Instruction>(V);
4743 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4745 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4749 // Record non-constant instructions contained by the loop.
4750 DenseMap<Instruction *, PHINode *> PHIMap;
4751 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4754 /// EvaluateExpression - Given an expression that passes the
4755 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4756 /// in the loop has the value PHIVal. If we can't fold this expression for some
4757 /// reason, return null.
4758 static Constant *EvaluateExpression(Value *V, const Loop *L,
4759 DenseMap<Instruction *, Constant *> &Vals,
4760 const TargetData *TD,
4761 const TargetLibraryInfo *TLI) {
4762 // Convenient constant check, but redundant for recursive calls.
4763 if (Constant *C = dyn_cast<Constant>(V)) return C;
4764 Instruction *I = dyn_cast<Instruction>(V);
4767 if (Constant *C = Vals.lookup(I)) return C;
4769 // An instruction inside the loop depends on a value outside the loop that we
4770 // weren't given a mapping for, or a value such as a call inside the loop.
4771 if (!canConstantEvolve(I, L)) return 0;
4773 // An unmapped PHI can be due to a branch or another loop inside this loop,
4774 // or due to this not being the initial iteration through a loop where we
4775 // couldn't compute the evolution of this particular PHI last time.
4776 if (isa<PHINode>(I)) return 0;
4778 std::vector<Constant*> Operands(I->getNumOperands());
4780 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4781 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4783 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4784 if (!Operands[i]) return 0;
4787 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
4793 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4794 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4795 Operands[1], TD, TLI);
4796 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4797 if (!LI->isVolatile())
4798 return ConstantFoldLoadFromConstPtr(Operands[0], TD);
4800 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
4804 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4805 /// in the header of its containing loop, we know the loop executes a
4806 /// constant number of times, and the PHI node is just a recurrence
4807 /// involving constants, fold it.
4809 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4812 DenseMap<PHINode*, Constant*>::const_iterator I =
4813 ConstantEvolutionLoopExitValue.find(PN);
4814 if (I != ConstantEvolutionLoopExitValue.end())
4817 if (BEs.ugt(MaxBruteForceIterations))
4818 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4820 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4822 DenseMap<Instruction *, Constant *> CurrentIterVals;
4823 BasicBlock *Header = L->getHeader();
4824 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4826 // Since the loop is canonicalized, the PHI node must have two entries. One
4827 // entry must be a constant (coming in from outside of the loop), and the
4828 // second must be derived from the same PHI.
4829 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4831 for (BasicBlock::iterator I = Header->begin();
4832 (PHI = dyn_cast<PHINode>(I)); ++I) {
4833 Constant *StartCST =
4834 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4835 if (StartCST == 0) continue;
4836 CurrentIterVals[PHI] = StartCST;
4838 if (!CurrentIterVals.count(PN))
4841 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4843 // Execute the loop symbolically to determine the exit value.
4844 if (BEs.getActiveBits() >= 32)
4845 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4847 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4848 unsigned IterationNum = 0;
4849 for (; ; ++IterationNum) {
4850 if (IterationNum == NumIterations)
4851 return RetVal = CurrentIterVals[PN]; // Got exit value!
4853 // Compute the value of the PHIs for the next iteration.
4854 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
4855 DenseMap<Instruction *, Constant *> NextIterVals;
4856 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
4859 return 0; // Couldn't evaluate!
4860 NextIterVals[PN] = NextPHI;
4862 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
4864 // Also evaluate the other PHI nodes. However, we don't get to stop if we
4865 // cease to be able to evaluate one of them or if they stop evolving,
4866 // because that doesn't necessarily prevent us from computing PN.
4867 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
4868 for (DenseMap<Instruction *, Constant *>::const_iterator
4869 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4870 PHINode *PHI = dyn_cast<PHINode>(I->first);
4871 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
4872 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
4874 // We use two distinct loops because EvaluateExpression may invalidate any
4875 // iterators into CurrentIterVals.
4876 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
4877 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
4878 PHINode *PHI = I->first;
4879 Constant *&NextPHI = NextIterVals[PHI];
4880 if (!NextPHI) { // Not already computed.
4881 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4882 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4884 if (NextPHI != I->second)
4885 StoppedEvolving = false;
4888 // If all entries in CurrentIterVals == NextIterVals then we can stop
4889 // iterating, the loop can't continue to change.
4890 if (StoppedEvolving)
4891 return RetVal = CurrentIterVals[PN];
4893 CurrentIterVals.swap(NextIterVals);
4897 /// ComputeExitCountExhaustively - If the loop is known to execute a
4898 /// constant number of times (the condition evolves only from constants),
4899 /// try to evaluate a few iterations of the loop until we get the exit
4900 /// condition gets a value of ExitWhen (true or false). If we cannot
4901 /// evaluate the trip count of the loop, return getCouldNotCompute().
4902 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4905 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4906 if (PN == 0) return getCouldNotCompute();
4908 // If the loop is canonicalized, the PHI will have exactly two entries.
4909 // That's the only form we support here.
4910 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4912 DenseMap<Instruction *, Constant *> CurrentIterVals;
4913 BasicBlock *Header = L->getHeader();
4914 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4916 // One entry must be a constant (coming in from outside of the loop), and the
4917 // second must be derived from the same PHI.
4918 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4920 for (BasicBlock::iterator I = Header->begin();
4921 (PHI = dyn_cast<PHINode>(I)); ++I) {
4922 Constant *StartCST =
4923 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4924 if (StartCST == 0) continue;
4925 CurrentIterVals[PHI] = StartCST;
4927 if (!CurrentIterVals.count(PN))
4928 return getCouldNotCompute();
4930 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4931 // the loop symbolically to determine when the condition gets a value of
4934 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4935 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
4936 ConstantInt *CondVal =
4937 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
4940 // Couldn't symbolically evaluate.
4941 if (!CondVal) return getCouldNotCompute();
4943 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4944 ++NumBruteForceTripCountsComputed;
4945 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4948 // Update all the PHI nodes for the next iteration.
4949 DenseMap<Instruction *, Constant *> NextIterVals;
4951 // Create a list of which PHIs we need to compute. We want to do this before
4952 // calling EvaluateExpression on them because that may invalidate iterators
4953 // into CurrentIterVals.
4954 SmallVector<PHINode *, 8> PHIsToCompute;
4955 for (DenseMap<Instruction *, Constant *>::const_iterator
4956 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4957 PHINode *PHI = dyn_cast<PHINode>(I->first);
4958 if (!PHI || PHI->getParent() != Header) continue;
4959 PHIsToCompute.push_back(PHI);
4961 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
4962 E = PHIsToCompute.end(); I != E; ++I) {
4964 Constant *&NextPHI = NextIterVals[PHI];
4965 if (NextPHI) continue; // Already computed!
4967 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4968 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4970 CurrentIterVals.swap(NextIterVals);
4973 // Too many iterations were needed to evaluate.
4974 return getCouldNotCompute();
4977 /// getSCEVAtScope - Return a SCEV expression for the specified value
4978 /// at the specified scope in the program. The L value specifies a loop
4979 /// nest to evaluate the expression at, where null is the top-level or a
4980 /// specified loop is immediately inside of the loop.
4982 /// This method can be used to compute the exit value for a variable defined
4983 /// in a loop by querying what the value will hold in the parent loop.
4985 /// In the case that a relevant loop exit value cannot be computed, the
4986 /// original value V is returned.
4987 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4988 // Check to see if we've folded this expression at this loop before.
4989 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4990 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4991 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4993 return Pair.first->second ? Pair.first->second : V;
4995 // Otherwise compute it.
4996 const SCEV *C = computeSCEVAtScope(V, L);
4997 ValuesAtScopes[V][L] = C;
5001 /// This builds up a Constant using the ConstantExpr interface. That way, we
5002 /// will return Constants for objects which aren't represented by a
5003 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5004 /// Returns NULL if the SCEV isn't representable as a Constant.
5005 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5006 switch (V->getSCEVType()) {
5007 default: // TODO: smax, umax.
5008 case scCouldNotCompute:
5012 return cast<SCEVConstant>(V)->getValue();
5014 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5015 case scSignExtend: {
5016 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5017 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5018 return ConstantExpr::getSExt(CastOp, SS->getType());
5021 case scZeroExtend: {
5022 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5023 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5024 return ConstantExpr::getZExt(CastOp, SZ->getType());
5028 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5029 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5030 return ConstantExpr::getTrunc(CastOp, ST->getType());
5034 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5035 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5036 if (C->getType()->isPointerTy())
5037 C = ConstantExpr::getBitCast(C, Type::getInt8PtrTy(C->getContext()));
5038 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5039 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5043 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5045 // The offsets have been converted to bytes. We can add bytes to an
5046 // i8* by GEP with the byte count in the first index.
5047 C = ConstantExpr::getBitCast(C,Type::getInt8PtrTy(C->getContext()));
5050 // Don't bother trying to sum two pointers. We probably can't
5051 // statically compute a load that results from it anyway.
5052 if (C2->getType()->isPointerTy())
5055 if (C->getType()->isPointerTy()) {
5056 if (cast<PointerType>(C->getType())->getElementType()->isStructTy())
5057 C2 = ConstantExpr::getIntegerCast(
5058 C2, Type::getInt32Ty(C->getContext()), true);
5059 C = ConstantExpr::getGetElementPtr(C, C2);
5061 C = ConstantExpr::getAdd(C, C2);
5068 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5069 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5070 // Don't bother with pointers at all.
5071 if (C->getType()->isPointerTy()) return 0;
5072 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5073 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5074 if (!C2 || C2->getType()->isPointerTy()) return 0;
5075 C = ConstantExpr::getMul(C, C2);
5082 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5083 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5084 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5085 if (LHS->getType() == RHS->getType())
5086 return ConstantExpr::getUDiv(LHS, RHS);
5093 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5094 if (isa<SCEVConstant>(V)) return V;
5096 // If this instruction is evolved from a constant-evolving PHI, compute the
5097 // exit value from the loop without using SCEVs.
5098 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5099 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5100 const Loop *LI = (*this->LI)[I->getParent()];
5101 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5102 if (PHINode *PN = dyn_cast<PHINode>(I))
5103 if (PN->getParent() == LI->getHeader()) {
5104 // Okay, there is no closed form solution for the PHI node. Check
5105 // to see if the loop that contains it has a known backedge-taken
5106 // count. If so, we may be able to force computation of the exit
5108 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5109 if (const SCEVConstant *BTCC =
5110 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5111 // Okay, we know how many times the containing loop executes. If
5112 // this is a constant evolving PHI node, get the final value at
5113 // the specified iteration number.
5114 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5115 BTCC->getValue()->getValue(),
5117 if (RV) return getSCEV(RV);
5121 // Okay, this is an expression that we cannot symbolically evaluate
5122 // into a SCEV. Check to see if it's possible to symbolically evaluate
5123 // the arguments into constants, and if so, try to constant propagate the
5124 // result. This is particularly useful for computing loop exit values.
5125 if (CanConstantFold(I)) {
5126 SmallVector<Constant *, 4> Operands;
5127 bool MadeImprovement = false;
5128 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5129 Value *Op = I->getOperand(i);
5130 if (Constant *C = dyn_cast<Constant>(Op)) {
5131 Operands.push_back(C);
5135 // If any of the operands is non-constant and if they are
5136 // non-integer and non-pointer, don't even try to analyze them
5137 // with scev techniques.
5138 if (!isSCEVable(Op->getType()))
5141 const SCEV *OrigV = getSCEV(Op);
5142 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5143 MadeImprovement |= OrigV != OpV;
5145 Constant *C = BuildConstantFromSCEV(OpV);
5147 if (C->getType() != Op->getType())
5148 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5152 Operands.push_back(C);
5155 // Check to see if getSCEVAtScope actually made an improvement.
5156 if (MadeImprovement) {
5158 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5159 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5160 Operands[0], Operands[1], TD,
5162 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5163 if (!LI->isVolatile())
5164 C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
5166 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5174 // This is some other type of SCEVUnknown, just return it.
5178 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5179 // Avoid performing the look-up in the common case where the specified
5180 // expression has no loop-variant portions.
5181 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5182 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5183 if (OpAtScope != Comm->getOperand(i)) {
5184 // Okay, at least one of these operands is loop variant but might be
5185 // foldable. Build a new instance of the folded commutative expression.
5186 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5187 Comm->op_begin()+i);
5188 NewOps.push_back(OpAtScope);
5190 for (++i; i != e; ++i) {
5191 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5192 NewOps.push_back(OpAtScope);
5194 if (isa<SCEVAddExpr>(Comm))
5195 return getAddExpr(NewOps);
5196 if (isa<SCEVMulExpr>(Comm))
5197 return getMulExpr(NewOps);
5198 if (isa<SCEVSMaxExpr>(Comm))
5199 return getSMaxExpr(NewOps);
5200 if (isa<SCEVUMaxExpr>(Comm))
5201 return getUMaxExpr(NewOps);
5202 llvm_unreachable("Unknown commutative SCEV type!");
5205 // If we got here, all operands are loop invariant.
5209 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5210 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5211 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5212 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5213 return Div; // must be loop invariant
5214 return getUDivExpr(LHS, RHS);
5217 // If this is a loop recurrence for a loop that does not contain L, then we
5218 // are dealing with the final value computed by the loop.
5219 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5220 // First, attempt to evaluate each operand.
5221 // Avoid performing the look-up in the common case where the specified
5222 // expression has no loop-variant portions.
5223 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5224 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5225 if (OpAtScope == AddRec->getOperand(i))
5228 // Okay, at least one of these operands is loop variant but might be
5229 // foldable. Build a new instance of the folded commutative expression.
5230 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5231 AddRec->op_begin()+i);
5232 NewOps.push_back(OpAtScope);
5233 for (++i; i != e; ++i)
5234 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5236 const SCEV *FoldedRec =
5237 getAddRecExpr(NewOps, AddRec->getLoop(),
5238 AddRec->getNoWrapFlags(SCEV::FlagNW));
5239 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5240 // The addrec may be folded to a nonrecurrence, for example, if the
5241 // induction variable is multiplied by zero after constant folding. Go
5242 // ahead and return the folded value.
5248 // If the scope is outside the addrec's loop, evaluate it by using the
5249 // loop exit value of the addrec.
5250 if (!AddRec->getLoop()->contains(L)) {
5251 // To evaluate this recurrence, we need to know how many times the AddRec
5252 // loop iterates. Compute this now.
5253 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5254 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5256 // Then, evaluate the AddRec.
5257 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5263 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5264 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5265 if (Op == Cast->getOperand())
5266 return Cast; // must be loop invariant
5267 return getZeroExtendExpr(Op, Cast->getType());
5270 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5271 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5272 if (Op == Cast->getOperand())
5273 return Cast; // must be loop invariant
5274 return getSignExtendExpr(Op, Cast->getType());
5277 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5278 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5279 if (Op == Cast->getOperand())
5280 return Cast; // must be loop invariant
5281 return getTruncateExpr(Op, Cast->getType());
5284 llvm_unreachable("Unknown SCEV type!");
5287 /// getSCEVAtScope - This is a convenience function which does
5288 /// getSCEVAtScope(getSCEV(V), L).
5289 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5290 return getSCEVAtScope(getSCEV(V), L);
5293 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5294 /// following equation:
5296 /// A * X = B (mod N)
5298 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5299 /// A and B isn't important.
5301 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5302 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5303 ScalarEvolution &SE) {
5304 uint32_t BW = A.getBitWidth();
5305 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5306 assert(A != 0 && "A must be non-zero.");
5310 // The gcd of A and N may have only one prime factor: 2. The number of
5311 // trailing zeros in A is its multiplicity
5312 uint32_t Mult2 = A.countTrailingZeros();
5315 // 2. Check if B is divisible by D.
5317 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5318 // is not less than multiplicity of this prime factor for D.
5319 if (B.countTrailingZeros() < Mult2)
5320 return SE.getCouldNotCompute();
5322 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5325 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5326 // bit width during computations.
5327 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5328 APInt Mod(BW + 1, 0);
5329 Mod.setBit(BW - Mult2); // Mod = N / D
5330 APInt I = AD.multiplicativeInverse(Mod);
5332 // 4. Compute the minimum unsigned root of the equation:
5333 // I * (B / D) mod (N / D)
5334 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5336 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5338 return SE.getConstant(Result.trunc(BW));
5341 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5342 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5343 /// might be the same) or two SCEVCouldNotCompute objects.
5345 static std::pair<const SCEV *,const SCEV *>
5346 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5347 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5348 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5349 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5350 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5352 // We currently can only solve this if the coefficients are constants.
5353 if (!LC || !MC || !NC) {
5354 const SCEV *CNC = SE.getCouldNotCompute();
5355 return std::make_pair(CNC, CNC);
5358 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5359 const APInt &L = LC->getValue()->getValue();
5360 const APInt &M = MC->getValue()->getValue();
5361 const APInt &N = NC->getValue()->getValue();
5362 APInt Two(BitWidth, 2);
5363 APInt Four(BitWidth, 4);
5366 using namespace APIntOps;
5368 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5369 // The B coefficient is M-N/2
5373 // The A coefficient is N/2
5374 APInt A(N.sdiv(Two));
5376 // Compute the B^2-4ac term.
5379 SqrtTerm -= Four * (A * C);
5381 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5382 // integer value or else APInt::sqrt() will assert.
5383 APInt SqrtVal(SqrtTerm.sqrt());
5385 // Compute the two solutions for the quadratic formula.
5386 // The divisions must be performed as signed divisions.
5389 if (TwoA.isMinValue()) {
5390 const SCEV *CNC = SE.getCouldNotCompute();
5391 return std::make_pair(CNC, CNC);
5394 LLVMContext &Context = SE.getContext();
5396 ConstantInt *Solution1 =
5397 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5398 ConstantInt *Solution2 =
5399 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5401 return std::make_pair(SE.getConstant(Solution1),
5402 SE.getConstant(Solution2));
5403 } // end APIntOps namespace
5406 /// HowFarToZero - Return the number of times a backedge comparing the specified
5407 /// value to zero will execute. If not computable, return CouldNotCompute.
5409 /// This is only used for loops with a "x != y" exit test. The exit condition is
5410 /// now expressed as a single expression, V = x-y. So the exit test is
5411 /// effectively V != 0. We know and take advantage of the fact that this
5412 /// expression only being used in a comparison by zero context.
5413 ScalarEvolution::ExitLimit
5414 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
5415 // If the value is a constant
5416 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5417 // If the value is already zero, the branch will execute zero times.
5418 if (C->getValue()->isZero()) return C;
5419 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5422 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5423 if (!AddRec || AddRec->getLoop() != L)
5424 return getCouldNotCompute();
5426 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5427 // the quadratic equation to solve it.
5428 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5429 std::pair<const SCEV *,const SCEV *> Roots =
5430 SolveQuadraticEquation(AddRec, *this);
5431 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5432 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5435 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5436 << " sol#2: " << *R2 << "\n";
5438 // Pick the smallest positive root value.
5439 if (ConstantInt *CB =
5440 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5443 if (CB->getZExtValue() == false)
5444 std::swap(R1, R2); // R1 is the minimum root now.
5446 // We can only use this value if the chrec ends up with an exact zero
5447 // value at this index. When solving for "X*X != 5", for example, we
5448 // should not accept a root of 2.
5449 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5451 return R1; // We found a quadratic root!
5454 return getCouldNotCompute();
5457 // Otherwise we can only handle this if it is affine.
5458 if (!AddRec->isAffine())
5459 return getCouldNotCompute();
5461 // If this is an affine expression, the execution count of this branch is
5462 // the minimum unsigned root of the following equation:
5464 // Start + Step*N = 0 (mod 2^BW)
5468 // Step*N = -Start (mod 2^BW)
5470 // where BW is the common bit width of Start and Step.
5472 // Get the initial value for the loop.
5473 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5474 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5476 // For now we handle only constant steps.
5478 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5479 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5480 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5481 // We have not yet seen any such cases.
5482 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5484 return getCouldNotCompute();
5486 // For positive steps (counting up until unsigned overflow):
5487 // N = -Start/Step (as unsigned)
5488 // For negative steps (counting down to zero):
5490 // First compute the unsigned distance from zero in the direction of Step.
5491 bool CountDown = StepC->getValue()->getValue().isNegative();
5492 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5494 // Handle unitary steps, which cannot wraparound.
5495 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5496 // N = Distance (as unsigned)
5497 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5498 ConstantRange CR = getUnsignedRange(Start);
5499 const SCEV *MaxBECount;
5500 if (!CountDown && CR.getUnsignedMin().isMinValue())
5501 // When counting up, the worst starting value is 1, not 0.
5502 MaxBECount = CR.getUnsignedMax().isMinValue()
5503 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5504 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5506 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5507 : -CR.getUnsignedMin());
5508 return ExitLimit(Distance, MaxBECount);
5511 // If the recurrence is known not to wraparound, unsigned divide computes the
5512 // back edge count. We know that the value will either become zero (and thus
5513 // the loop terminates), that the loop will terminate through some other exit
5514 // condition first, or that the loop has undefined behavior. This means
5515 // we can't "miss" the exit value, even with nonunit stride.
5517 // FIXME: Prove that loops always exhibits *acceptable* undefined
5518 // behavior. Loops must exhibit defined behavior until a wrapped value is
5519 // actually used. So the trip count computed by udiv could be smaller than the
5520 // number of well-defined iterations.
5521 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5522 // FIXME: We really want an "isexact" bit for udiv.
5523 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5525 // Then, try to solve the above equation provided that Start is constant.
5526 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5527 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5528 -StartC->getValue()->getValue(),
5530 return getCouldNotCompute();
5533 /// HowFarToNonZero - Return the number of times a backedge checking the
5534 /// specified value for nonzero will execute. If not computable, return
5536 ScalarEvolution::ExitLimit
5537 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5538 // Loops that look like: while (X == 0) are very strange indeed. We don't
5539 // handle them yet except for the trivial case. This could be expanded in the
5540 // future as needed.
5542 // If the value is a constant, check to see if it is known to be non-zero
5543 // already. If so, the backedge will execute zero times.
5544 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5545 if (!C->getValue()->isNullValue())
5546 return getConstant(C->getType(), 0);
5547 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5550 // We could implement others, but I really doubt anyone writes loops like
5551 // this, and if they did, they would already be constant folded.
5552 return getCouldNotCompute();
5555 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5556 /// (which may not be an immediate predecessor) which has exactly one
5557 /// successor from which BB is reachable, or null if no such block is
5560 std::pair<BasicBlock *, BasicBlock *>
5561 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5562 // If the block has a unique predecessor, then there is no path from the
5563 // predecessor to the block that does not go through the direct edge
5564 // from the predecessor to the block.
5565 if (BasicBlock *Pred = BB->getSinglePredecessor())
5566 return std::make_pair(Pred, BB);
5568 // A loop's header is defined to be a block that dominates the loop.
5569 // If the header has a unique predecessor outside the loop, it must be
5570 // a block that has exactly one successor that can reach the loop.
5571 if (Loop *L = LI->getLoopFor(BB))
5572 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5574 return std::pair<BasicBlock *, BasicBlock *>();
5577 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5578 /// testing whether two expressions are equal, however for the purposes of
5579 /// looking for a condition guarding a loop, it can be useful to be a little
5580 /// more general, since a front-end may have replicated the controlling
5583 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5584 // Quick check to see if they are the same SCEV.
5585 if (A == B) return true;
5587 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5588 // two different instructions with the same value. Check for this case.
5589 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5590 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5591 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5592 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5593 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5596 // Otherwise assume they may have a different value.
5600 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5601 /// predicate Pred. Return true iff any changes were made.
5603 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5604 const SCEV *&LHS, const SCEV *&RHS) {
5605 bool Changed = false;
5607 // Canonicalize a constant to the right side.
5608 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5609 // Check for both operands constant.
5610 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5611 if (ConstantExpr::getICmp(Pred,
5613 RHSC->getValue())->isNullValue())
5614 goto trivially_false;
5616 goto trivially_true;
5618 // Otherwise swap the operands to put the constant on the right.
5619 std::swap(LHS, RHS);
5620 Pred = ICmpInst::getSwappedPredicate(Pred);
5624 // If we're comparing an addrec with a value which is loop-invariant in the
5625 // addrec's loop, put the addrec on the left. Also make a dominance check,
5626 // as both operands could be addrecs loop-invariant in each other's loop.
5627 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5628 const Loop *L = AR->getLoop();
5629 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5630 std::swap(LHS, RHS);
5631 Pred = ICmpInst::getSwappedPredicate(Pred);
5636 // If there's a constant operand, canonicalize comparisons with boundary
5637 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5638 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5639 const APInt &RA = RC->getValue()->getValue();
5641 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5642 case ICmpInst::ICMP_EQ:
5643 case ICmpInst::ICMP_NE:
5645 case ICmpInst::ICMP_UGE:
5646 if ((RA - 1).isMinValue()) {
5647 Pred = ICmpInst::ICMP_NE;
5648 RHS = getConstant(RA - 1);
5652 if (RA.isMaxValue()) {
5653 Pred = ICmpInst::ICMP_EQ;
5657 if (RA.isMinValue()) goto trivially_true;
5659 Pred = ICmpInst::ICMP_UGT;
5660 RHS = getConstant(RA - 1);
5663 case ICmpInst::ICMP_ULE:
5664 if ((RA + 1).isMaxValue()) {
5665 Pred = ICmpInst::ICMP_NE;
5666 RHS = getConstant(RA + 1);
5670 if (RA.isMinValue()) {
5671 Pred = ICmpInst::ICMP_EQ;
5675 if (RA.isMaxValue()) goto trivially_true;
5677 Pred = ICmpInst::ICMP_ULT;
5678 RHS = getConstant(RA + 1);
5681 case ICmpInst::ICMP_SGE:
5682 if ((RA - 1).isMinSignedValue()) {
5683 Pred = ICmpInst::ICMP_NE;
5684 RHS = getConstant(RA - 1);
5688 if (RA.isMaxSignedValue()) {
5689 Pred = ICmpInst::ICMP_EQ;
5693 if (RA.isMinSignedValue()) goto trivially_true;
5695 Pred = ICmpInst::ICMP_SGT;
5696 RHS = getConstant(RA - 1);
5699 case ICmpInst::ICMP_SLE:
5700 if ((RA + 1).isMaxSignedValue()) {
5701 Pred = ICmpInst::ICMP_NE;
5702 RHS = getConstant(RA + 1);
5706 if (RA.isMinSignedValue()) {
5707 Pred = ICmpInst::ICMP_EQ;
5711 if (RA.isMaxSignedValue()) goto trivially_true;
5713 Pred = ICmpInst::ICMP_SLT;
5714 RHS = getConstant(RA + 1);
5717 case ICmpInst::ICMP_UGT:
5718 if (RA.isMinValue()) {
5719 Pred = ICmpInst::ICMP_NE;
5723 if ((RA + 1).isMaxValue()) {
5724 Pred = ICmpInst::ICMP_EQ;
5725 RHS = getConstant(RA + 1);
5729 if (RA.isMaxValue()) goto trivially_false;
5731 case ICmpInst::ICMP_ULT:
5732 if (RA.isMaxValue()) {
5733 Pred = ICmpInst::ICMP_NE;
5737 if ((RA - 1).isMinValue()) {
5738 Pred = ICmpInst::ICMP_EQ;
5739 RHS = getConstant(RA - 1);
5743 if (RA.isMinValue()) goto trivially_false;
5745 case ICmpInst::ICMP_SGT:
5746 if (RA.isMinSignedValue()) {
5747 Pred = ICmpInst::ICMP_NE;
5751 if ((RA + 1).isMaxSignedValue()) {
5752 Pred = ICmpInst::ICMP_EQ;
5753 RHS = getConstant(RA + 1);
5757 if (RA.isMaxSignedValue()) goto trivially_false;
5759 case ICmpInst::ICMP_SLT:
5760 if (RA.isMaxSignedValue()) {
5761 Pred = ICmpInst::ICMP_NE;
5765 if ((RA - 1).isMinSignedValue()) {
5766 Pred = ICmpInst::ICMP_EQ;
5767 RHS = getConstant(RA - 1);
5771 if (RA.isMinSignedValue()) goto trivially_false;
5776 // Check for obvious equality.
5777 if (HasSameValue(LHS, RHS)) {
5778 if (ICmpInst::isTrueWhenEqual(Pred))
5779 goto trivially_true;
5780 if (ICmpInst::isFalseWhenEqual(Pred))
5781 goto trivially_false;
5784 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5785 // adding or subtracting 1 from one of the operands.
5787 case ICmpInst::ICMP_SLE:
5788 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5789 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5791 Pred = ICmpInst::ICMP_SLT;
5793 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5794 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5796 Pred = ICmpInst::ICMP_SLT;
5800 case ICmpInst::ICMP_SGE:
5801 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5802 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5804 Pred = ICmpInst::ICMP_SGT;
5806 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5807 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5809 Pred = ICmpInst::ICMP_SGT;
5813 case ICmpInst::ICMP_ULE:
5814 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5815 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5817 Pred = ICmpInst::ICMP_ULT;
5819 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5820 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5822 Pred = ICmpInst::ICMP_ULT;
5826 case ICmpInst::ICMP_UGE:
5827 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5828 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5830 Pred = ICmpInst::ICMP_UGT;
5832 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5833 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5835 Pred = ICmpInst::ICMP_UGT;
5843 // TODO: More simplifications are possible here.
5849 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5850 Pred = ICmpInst::ICMP_EQ;
5855 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5856 Pred = ICmpInst::ICMP_NE;
5860 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5861 return getSignedRange(S).getSignedMax().isNegative();
5864 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5865 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5868 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5869 return !getSignedRange(S).getSignedMin().isNegative();
5872 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5873 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5876 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5877 return isKnownNegative(S) || isKnownPositive(S);
5880 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5881 const SCEV *LHS, const SCEV *RHS) {
5882 // Canonicalize the inputs first.
5883 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5885 // If LHS or RHS is an addrec, check to see if the condition is true in
5886 // every iteration of the loop.
5887 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5888 if (isLoopEntryGuardedByCond(
5889 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5890 isLoopBackedgeGuardedByCond(
5891 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5893 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5894 if (isLoopEntryGuardedByCond(
5895 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5896 isLoopBackedgeGuardedByCond(
5897 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5900 // Otherwise see what can be done with known constant ranges.
5901 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5905 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5906 const SCEV *LHS, const SCEV *RHS) {
5907 if (HasSameValue(LHS, RHS))
5908 return ICmpInst::isTrueWhenEqual(Pred);
5910 // This code is split out from isKnownPredicate because it is called from
5911 // within isLoopEntryGuardedByCond.
5914 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5915 case ICmpInst::ICMP_SGT:
5916 Pred = ICmpInst::ICMP_SLT;
5917 std::swap(LHS, RHS);
5918 case ICmpInst::ICMP_SLT: {
5919 ConstantRange LHSRange = getSignedRange(LHS);
5920 ConstantRange RHSRange = getSignedRange(RHS);
5921 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5923 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5927 case ICmpInst::ICMP_SGE:
5928 Pred = ICmpInst::ICMP_SLE;
5929 std::swap(LHS, RHS);
5930 case ICmpInst::ICMP_SLE: {
5931 ConstantRange LHSRange = getSignedRange(LHS);
5932 ConstantRange RHSRange = getSignedRange(RHS);
5933 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5935 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5939 case ICmpInst::ICMP_UGT:
5940 Pred = ICmpInst::ICMP_ULT;
5941 std::swap(LHS, RHS);
5942 case ICmpInst::ICMP_ULT: {
5943 ConstantRange LHSRange = getUnsignedRange(LHS);
5944 ConstantRange RHSRange = getUnsignedRange(RHS);
5945 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5947 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5951 case ICmpInst::ICMP_UGE:
5952 Pred = ICmpInst::ICMP_ULE;
5953 std::swap(LHS, RHS);
5954 case ICmpInst::ICMP_ULE: {
5955 ConstantRange LHSRange = getUnsignedRange(LHS);
5956 ConstantRange RHSRange = getUnsignedRange(RHS);
5957 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5959 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5963 case ICmpInst::ICMP_NE: {
5964 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5966 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5969 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5970 if (isKnownNonZero(Diff))
5974 case ICmpInst::ICMP_EQ:
5975 // The check at the top of the function catches the case where
5976 // the values are known to be equal.
5982 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5983 /// protected by a conditional between LHS and RHS. This is used to
5984 /// to eliminate casts.
5986 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5987 ICmpInst::Predicate Pred,
5988 const SCEV *LHS, const SCEV *RHS) {
5989 // Interpret a null as meaning no loop, where there is obviously no guard
5990 // (interprocedural conditions notwithstanding).
5991 if (!L) return true;
5993 BasicBlock *Latch = L->getLoopLatch();
5997 BranchInst *LoopContinuePredicate =
5998 dyn_cast<BranchInst>(Latch->getTerminator());
5999 if (!LoopContinuePredicate ||
6000 LoopContinuePredicate->isUnconditional())
6003 return isImpliedCond(Pred, LHS, RHS,
6004 LoopContinuePredicate->getCondition(),
6005 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6008 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6009 /// by a conditional between LHS and RHS. This is used to help avoid max
6010 /// expressions in loop trip counts, and to eliminate casts.
6012 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6013 ICmpInst::Predicate Pred,
6014 const SCEV *LHS, const SCEV *RHS) {
6015 // Interpret a null as meaning no loop, where there is obviously no guard
6016 // (interprocedural conditions notwithstanding).
6017 if (!L) return false;
6019 // Starting at the loop predecessor, climb up the predecessor chain, as long
6020 // as there are predecessors that can be found that have unique successors
6021 // leading to the original header.
6022 for (std::pair<BasicBlock *, BasicBlock *>
6023 Pair(L->getLoopPredecessor(), L->getHeader());
6025 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6027 BranchInst *LoopEntryPredicate =
6028 dyn_cast<BranchInst>(Pair.first->getTerminator());
6029 if (!LoopEntryPredicate ||
6030 LoopEntryPredicate->isUnconditional())
6033 if (isImpliedCond(Pred, LHS, RHS,
6034 LoopEntryPredicate->getCondition(),
6035 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6042 /// RAII wrapper to prevent recursive application of isImpliedCond.
6043 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6044 /// currently evaluating isImpliedCond.
6045 struct MarkPendingLoopPredicate {
6047 DenseSet<Value*> &LoopPreds;
6050 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6051 : Cond(C), LoopPreds(LP) {
6052 Pending = !LoopPreds.insert(Cond).second;
6054 ~MarkPendingLoopPredicate() {
6056 LoopPreds.erase(Cond);
6060 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6061 /// and RHS is true whenever the given Cond value evaluates to true.
6062 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6063 const SCEV *LHS, const SCEV *RHS,
6064 Value *FoundCondValue,
6066 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6070 // Recursively handle And and Or conditions.
6071 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6072 if (BO->getOpcode() == Instruction::And) {
6074 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6075 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6076 } else if (BO->getOpcode() == Instruction::Or) {
6078 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6079 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6083 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6084 if (!ICI) return false;
6086 // Bail if the ICmp's operands' types are wider than the needed type
6087 // before attempting to call getSCEV on them. This avoids infinite
6088 // recursion, since the analysis of widening casts can require loop
6089 // exit condition information for overflow checking, which would
6091 if (getTypeSizeInBits(LHS->getType()) <
6092 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6095 // Now that we found a conditional branch that dominates the loop, check to
6096 // see if it is the comparison we are looking for.
6097 ICmpInst::Predicate FoundPred;
6099 FoundPred = ICI->getInversePredicate();
6101 FoundPred = ICI->getPredicate();
6103 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6104 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6106 // Balance the types. The case where FoundLHS' type is wider than
6107 // LHS' type is checked for above.
6108 if (getTypeSizeInBits(LHS->getType()) >
6109 getTypeSizeInBits(FoundLHS->getType())) {
6110 if (CmpInst::isSigned(Pred)) {
6111 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6112 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6114 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6115 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6119 // Canonicalize the query to match the way instcombine will have
6120 // canonicalized the comparison.
6121 if (SimplifyICmpOperands(Pred, LHS, RHS))
6123 return CmpInst::isTrueWhenEqual(Pred);
6124 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6125 if (FoundLHS == FoundRHS)
6126 return CmpInst::isFalseWhenEqual(Pred);
6128 // Check to see if we can make the LHS or RHS match.
6129 if (LHS == FoundRHS || RHS == FoundLHS) {
6130 if (isa<SCEVConstant>(RHS)) {
6131 std::swap(FoundLHS, FoundRHS);
6132 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6134 std::swap(LHS, RHS);
6135 Pred = ICmpInst::getSwappedPredicate(Pred);
6139 // Check whether the found predicate is the same as the desired predicate.
6140 if (FoundPred == Pred)
6141 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6143 // Check whether swapping the found predicate makes it the same as the
6144 // desired predicate.
6145 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6146 if (isa<SCEVConstant>(RHS))
6147 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6149 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6150 RHS, LHS, FoundLHS, FoundRHS);
6153 // Check whether the actual condition is beyond sufficient.
6154 if (FoundPred == ICmpInst::ICMP_EQ)
6155 if (ICmpInst::isTrueWhenEqual(Pred))
6156 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6158 if (Pred == ICmpInst::ICMP_NE)
6159 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6160 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6163 // Otherwise assume the worst.
6167 /// isImpliedCondOperands - Test whether the condition described by Pred,
6168 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6169 /// and FoundRHS is true.
6170 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6171 const SCEV *LHS, const SCEV *RHS,
6172 const SCEV *FoundLHS,
6173 const SCEV *FoundRHS) {
6174 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6175 FoundLHS, FoundRHS) ||
6176 // ~x < ~y --> x > y
6177 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6178 getNotSCEV(FoundRHS),
6179 getNotSCEV(FoundLHS));
6182 /// isImpliedCondOperandsHelper - Test whether the condition described by
6183 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6184 /// FoundLHS, and FoundRHS is true.
6186 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6187 const SCEV *LHS, const SCEV *RHS,
6188 const SCEV *FoundLHS,
6189 const SCEV *FoundRHS) {
6191 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6192 case ICmpInst::ICMP_EQ:
6193 case ICmpInst::ICMP_NE:
6194 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6197 case ICmpInst::ICMP_SLT:
6198 case ICmpInst::ICMP_SLE:
6199 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6200 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6203 case ICmpInst::ICMP_SGT:
6204 case ICmpInst::ICMP_SGE:
6205 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6206 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6209 case ICmpInst::ICMP_ULT:
6210 case ICmpInst::ICMP_ULE:
6211 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6212 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6215 case ICmpInst::ICMP_UGT:
6216 case ICmpInst::ICMP_UGE:
6217 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6218 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6226 /// getBECount - Subtract the end and start values and divide by the step,
6227 /// rounding up, to get the number of times the backedge is executed. Return
6228 /// CouldNotCompute if an intermediate computation overflows.
6229 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
6233 assert(!isKnownNegative(Step) &&
6234 "This code doesn't handle negative strides yet!");
6236 Type *Ty = Start->getType();
6238 // When Start == End, we have an exact BECount == 0. Short-circuit this case
6239 // here because SCEV may not be able to determine that the unsigned division
6240 // after rounding is zero.
6242 return getConstant(Ty, 0);
6244 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
6245 const SCEV *Diff = getMinusSCEV(End, Start);
6246 const SCEV *RoundUp = getAddExpr(Step, NegOne);
6248 // Add an adjustment to the difference between End and Start so that
6249 // the division will effectively round up.
6250 const SCEV *Add = getAddExpr(Diff, RoundUp);
6253 // Check Add for unsigned overflow.
6254 // TODO: More sophisticated things could be done here.
6255 Type *WideTy = IntegerType::get(getContext(),
6256 getTypeSizeInBits(Ty) + 1);
6257 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
6258 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
6259 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
6260 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
6261 return getCouldNotCompute();
6264 return getUDivExpr(Add, Step);
6267 /// HowManyLessThans - Return the number of times a backedge containing the
6268 /// specified less-than comparison will execute. If not computable, return
6269 /// CouldNotCompute.
6270 ScalarEvolution::ExitLimit
6271 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6272 const Loop *L, bool isSigned) {
6273 // Only handle: "ADDREC < LoopInvariant".
6274 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
6276 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
6277 if (!AddRec || AddRec->getLoop() != L)
6278 return getCouldNotCompute();
6280 // Check to see if we have a flag which makes analysis easy.
6281 bool NoWrap = isSigned ?
6282 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNW)) :
6283 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNW));
6285 if (AddRec->isAffine()) {
6286 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
6287 const SCEV *Step = AddRec->getStepRecurrence(*this);
6290 return getCouldNotCompute();
6291 if (Step->isOne()) {
6292 // With unit stride, the iteration never steps past the limit value.
6293 } else if (isKnownPositive(Step)) {
6294 // Test whether a positive iteration can step past the limit
6295 // value and past the maximum value for its type in a single step.
6296 // Note that it's not sufficient to check NoWrap here, because even
6297 // though the value after a wrap is undefined, it's not undefined
6298 // behavior, so if wrap does occur, the loop could either terminate or
6299 // loop infinitely, but in either case, the loop is guaranteed to
6300 // iterate at least until the iteration where the wrapping occurs.
6301 const SCEV *One = getConstant(Step->getType(), 1);
6303 APInt Max = APInt::getSignedMaxValue(BitWidth);
6304 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
6305 .slt(getSignedRange(RHS).getSignedMax()))
6306 return getCouldNotCompute();
6308 APInt Max = APInt::getMaxValue(BitWidth);
6309 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
6310 .ult(getUnsignedRange(RHS).getUnsignedMax()))
6311 return getCouldNotCompute();
6314 // TODO: Handle negative strides here and below.
6315 return getCouldNotCompute();
6317 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6318 // m. So, we count the number of iterations in which {n,+,s} < m is true.
6319 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6320 // treat m-n as signed nor unsigned due to overflow possibility.
6322 // First, we get the value of the LHS in the first iteration: n
6323 const SCEV *Start = AddRec->getOperand(0);
6325 // Determine the minimum constant start value.
6326 const SCEV *MinStart = getConstant(isSigned ?
6327 getSignedRange(Start).getSignedMin() :
6328 getUnsignedRange(Start).getUnsignedMin());
6330 // If we know that the condition is true in order to enter the loop,
6331 // then we know that it will run exactly (m-n)/s times. Otherwise, we
6332 // only know that it will execute (max(m,n)-n)/s times. In both cases,
6333 // the division must round up.
6334 const SCEV *End = RHS;
6335 if (!isLoopEntryGuardedByCond(L,
6336 isSigned ? ICmpInst::ICMP_SLT :
6338 getMinusSCEV(Start, Step), RHS))
6339 End = isSigned ? getSMaxExpr(RHS, Start)
6340 : getUMaxExpr(RHS, Start);
6342 // Determine the maximum constant end value.
6343 const SCEV *MaxEnd = getConstant(isSigned ?
6344 getSignedRange(End).getSignedMax() :
6345 getUnsignedRange(End).getUnsignedMax());
6347 // If MaxEnd is within a step of the maximum integer value in its type,
6348 // adjust it down to the minimum value which would produce the same effect.
6349 // This allows the subsequent ceiling division of (N+(step-1))/step to
6350 // compute the correct value.
6351 const SCEV *StepMinusOne = getMinusSCEV(Step,
6352 getConstant(Step->getType(), 1));
6355 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6358 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6361 // Finally, we subtract these two values and divide, rounding up, to get
6362 // the number of times the backedge is executed.
6363 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6365 // The maximum backedge count is similar, except using the minimum start
6366 // value and the maximum end value.
6367 // If we already have an exact constant BECount, use it instead.
6368 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6369 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6371 // If the stride is nonconstant, and NoWrap == true, then
6372 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6373 // exact BECount and invalid MaxBECount, which should be avoided to catch
6374 // more optimization opportunities.
6375 if (isa<SCEVCouldNotCompute>(MaxBECount))
6376 MaxBECount = BECount;
6378 return ExitLimit(BECount, MaxBECount);
6381 return getCouldNotCompute();
6384 /// getNumIterationsInRange - Return the number of iterations of this loop that
6385 /// produce values in the specified constant range. Another way of looking at
6386 /// this is that it returns the first iteration number where the value is not in
6387 /// the condition, thus computing the exit count. If the iteration count can't
6388 /// be computed, an instance of SCEVCouldNotCompute is returned.
6389 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6390 ScalarEvolution &SE) const {
6391 if (Range.isFullSet()) // Infinite loop.
6392 return SE.getCouldNotCompute();
6394 // If the start is a non-zero constant, shift the range to simplify things.
6395 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6396 if (!SC->getValue()->isZero()) {
6397 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6398 Operands[0] = SE.getConstant(SC->getType(), 0);
6399 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6400 getNoWrapFlags(FlagNW));
6401 if (const SCEVAddRecExpr *ShiftedAddRec =
6402 dyn_cast<SCEVAddRecExpr>(Shifted))
6403 return ShiftedAddRec->getNumIterationsInRange(
6404 Range.subtract(SC->getValue()->getValue()), SE);
6405 // This is strange and shouldn't happen.
6406 return SE.getCouldNotCompute();
6409 // The only time we can solve this is when we have all constant indices.
6410 // Otherwise, we cannot determine the overflow conditions.
6411 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6412 if (!isa<SCEVConstant>(getOperand(i)))
6413 return SE.getCouldNotCompute();
6416 // Okay at this point we know that all elements of the chrec are constants and
6417 // that the start element is zero.
6419 // First check to see if the range contains zero. If not, the first
6421 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6422 if (!Range.contains(APInt(BitWidth, 0)))
6423 return SE.getConstant(getType(), 0);
6426 // If this is an affine expression then we have this situation:
6427 // Solve {0,+,A} in Range === Ax in Range
6429 // We know that zero is in the range. If A is positive then we know that
6430 // the upper value of the range must be the first possible exit value.
6431 // If A is negative then the lower of the range is the last possible loop
6432 // value. Also note that we already checked for a full range.
6433 APInt One(BitWidth,1);
6434 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6435 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6437 // The exit value should be (End+A)/A.
6438 APInt ExitVal = (End + A).udiv(A);
6439 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6441 // Evaluate at the exit value. If we really did fall out of the valid
6442 // range, then we computed our trip count, otherwise wrap around or other
6443 // things must have happened.
6444 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6445 if (Range.contains(Val->getValue()))
6446 return SE.getCouldNotCompute(); // Something strange happened
6448 // Ensure that the previous value is in the range. This is a sanity check.
6449 assert(Range.contains(
6450 EvaluateConstantChrecAtConstant(this,
6451 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6452 "Linear scev computation is off in a bad way!");
6453 return SE.getConstant(ExitValue);
6454 } else if (isQuadratic()) {
6455 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6456 // quadratic equation to solve it. To do this, we must frame our problem in
6457 // terms of figuring out when zero is crossed, instead of when
6458 // Range.getUpper() is crossed.
6459 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6460 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6461 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6462 // getNoWrapFlags(FlagNW)
6465 // Next, solve the constructed addrec
6466 std::pair<const SCEV *,const SCEV *> Roots =
6467 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6468 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6469 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6471 // Pick the smallest positive root value.
6472 if (ConstantInt *CB =
6473 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6474 R1->getValue(), R2->getValue()))) {
6475 if (CB->getZExtValue() == false)
6476 std::swap(R1, R2); // R1 is the minimum root now.
6478 // Make sure the root is not off by one. The returned iteration should
6479 // not be in the range, but the previous one should be. When solving
6480 // for "X*X < 5", for example, we should not return a root of 2.
6481 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6484 if (Range.contains(R1Val->getValue())) {
6485 // The next iteration must be out of the range...
6486 ConstantInt *NextVal =
6487 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6489 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6490 if (!Range.contains(R1Val->getValue()))
6491 return SE.getConstant(NextVal);
6492 return SE.getCouldNotCompute(); // Something strange happened
6495 // If R1 was not in the range, then it is a good return value. Make
6496 // sure that R1-1 WAS in the range though, just in case.
6497 ConstantInt *NextVal =
6498 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6499 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6500 if (Range.contains(R1Val->getValue()))
6502 return SE.getCouldNotCompute(); // Something strange happened
6507 return SE.getCouldNotCompute();
6512 //===----------------------------------------------------------------------===//
6513 // SCEVCallbackVH Class Implementation
6514 //===----------------------------------------------------------------------===//
6516 void ScalarEvolution::SCEVCallbackVH::deleted() {
6517 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6518 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6519 SE->ConstantEvolutionLoopExitValue.erase(PN);
6520 SE->ValueExprMap.erase(getValPtr());
6521 // this now dangles!
6524 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6525 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6527 // Forget all the expressions associated with users of the old value,
6528 // so that future queries will recompute the expressions using the new
6530 Value *Old = getValPtr();
6531 SmallVector<User *, 16> Worklist;
6532 SmallPtrSet<User *, 8> Visited;
6533 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6535 Worklist.push_back(*UI);
6536 while (!Worklist.empty()) {
6537 User *U = Worklist.pop_back_val();
6538 // Deleting the Old value will cause this to dangle. Postpone
6539 // that until everything else is done.
6542 if (!Visited.insert(U))
6544 if (PHINode *PN = dyn_cast<PHINode>(U))
6545 SE->ConstantEvolutionLoopExitValue.erase(PN);
6546 SE->ValueExprMap.erase(U);
6547 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6549 Worklist.push_back(*UI);
6551 // Delete the Old value.
6552 if (PHINode *PN = dyn_cast<PHINode>(Old))
6553 SE->ConstantEvolutionLoopExitValue.erase(PN);
6554 SE->ValueExprMap.erase(Old);
6555 // this now dangles!
6558 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6559 : CallbackVH(V), SE(se) {}
6561 //===----------------------------------------------------------------------===//
6562 // ScalarEvolution Class Implementation
6563 //===----------------------------------------------------------------------===//
6565 ScalarEvolution::ScalarEvolution()
6566 : FunctionPass(ID), FirstUnknown(0) {
6567 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6570 bool ScalarEvolution::runOnFunction(Function &F) {
6572 LI = &getAnalysis<LoopInfo>();
6573 TD = getAnalysisIfAvailable<TargetData>();
6574 TLI = &getAnalysis<TargetLibraryInfo>();
6575 DT = &getAnalysis<DominatorTree>();
6579 void ScalarEvolution::releaseMemory() {
6580 // Iterate through all the SCEVUnknown instances and call their
6581 // destructors, so that they release their references to their values.
6582 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6586 ValueExprMap.clear();
6588 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6589 // that a loop had multiple computable exits.
6590 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6591 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6596 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
6598 BackedgeTakenCounts.clear();
6599 ConstantEvolutionLoopExitValue.clear();
6600 ValuesAtScopes.clear();
6601 LoopDispositions.clear();
6602 BlockDispositions.clear();
6603 UnsignedRanges.clear();
6604 SignedRanges.clear();
6605 UniqueSCEVs.clear();
6606 SCEVAllocator.Reset();
6609 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6610 AU.setPreservesAll();
6611 AU.addRequiredTransitive<LoopInfo>();
6612 AU.addRequiredTransitive<DominatorTree>();
6613 AU.addRequired<TargetLibraryInfo>();
6616 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6617 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6620 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6622 // Print all inner loops first
6623 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6624 PrintLoopInfo(OS, SE, *I);
6627 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6630 SmallVector<BasicBlock *, 8> ExitBlocks;
6631 L->getExitBlocks(ExitBlocks);
6632 if (ExitBlocks.size() != 1)
6633 OS << "<multiple exits> ";
6635 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6636 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6638 OS << "Unpredictable backedge-taken count. ";
6643 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6646 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6647 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6649 OS << "Unpredictable max backedge-taken count. ";
6655 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6656 // ScalarEvolution's implementation of the print method is to print
6657 // out SCEV values of all instructions that are interesting. Doing
6658 // this potentially causes it to create new SCEV objects though,
6659 // which technically conflicts with the const qualifier. This isn't
6660 // observable from outside the class though, so casting away the
6661 // const isn't dangerous.
6662 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6664 OS << "Classifying expressions for: ";
6665 WriteAsOperand(OS, F, /*PrintType=*/false);
6667 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6668 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6671 const SCEV *SV = SE.getSCEV(&*I);
6674 const Loop *L = LI->getLoopFor((*I).getParent());
6676 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6683 OS << "\t\t" "Exits: ";
6684 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6685 if (!SE.isLoopInvariant(ExitValue, L)) {
6686 OS << "<<Unknown>>";
6695 OS << "Determining loop execution counts for: ";
6696 WriteAsOperand(OS, F, /*PrintType=*/false);
6698 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6699 PrintLoopInfo(OS, &SE, *I);
6702 ScalarEvolution::LoopDisposition
6703 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6704 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6705 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6706 Values.insert(std::make_pair(L, LoopVariant));
6708 return Pair.first->second;
6710 LoopDisposition D = computeLoopDisposition(S, L);
6711 return LoopDispositions[S][L] = D;
6714 ScalarEvolution::LoopDisposition
6715 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6716 switch (S->getSCEVType()) {
6718 return LoopInvariant;
6722 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6723 case scAddRecExpr: {
6724 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6726 // If L is the addrec's loop, it's computable.
6727 if (AR->getLoop() == L)
6728 return LoopComputable;
6730 // Add recurrences are never invariant in the function-body (null loop).
6734 // This recurrence is variant w.r.t. L if L contains AR's loop.
6735 if (L->contains(AR->getLoop()))
6738 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6739 if (AR->getLoop()->contains(L))
6740 return LoopInvariant;
6742 // This recurrence is variant w.r.t. L if any of its operands
6744 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6746 if (!isLoopInvariant(*I, L))
6749 // Otherwise it's loop-invariant.
6750 return LoopInvariant;
6756 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6757 bool HasVarying = false;
6758 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6760 LoopDisposition D = getLoopDisposition(*I, L);
6761 if (D == LoopVariant)
6763 if (D == LoopComputable)
6766 return HasVarying ? LoopComputable : LoopInvariant;
6769 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6770 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6771 if (LD == LoopVariant)
6773 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6774 if (RD == LoopVariant)
6776 return (LD == LoopInvariant && RD == LoopInvariant) ?
6777 LoopInvariant : LoopComputable;
6780 // All non-instruction values are loop invariant. All instructions are loop
6781 // invariant if they are not contained in the specified loop.
6782 // Instructions are never considered invariant in the function body
6783 // (null loop) because they are defined within the "loop".
6784 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6785 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6786 return LoopInvariant;
6787 case scCouldNotCompute:
6788 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6789 default: llvm_unreachable("Unknown SCEV kind!");
6793 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6794 return getLoopDisposition(S, L) == LoopInvariant;
6797 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6798 return getLoopDisposition(S, L) == LoopComputable;
6801 ScalarEvolution::BlockDisposition
6802 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6803 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6804 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6805 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6807 return Pair.first->second;
6809 BlockDisposition D = computeBlockDisposition(S, BB);
6810 return BlockDispositions[S][BB] = D;
6813 ScalarEvolution::BlockDisposition
6814 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6815 switch (S->getSCEVType()) {
6817 return ProperlyDominatesBlock;
6821 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6822 case scAddRecExpr: {
6823 // This uses a "dominates" query instead of "properly dominates" query
6824 // to test for proper dominance too, because the instruction which
6825 // produces the addrec's value is a PHI, and a PHI effectively properly
6826 // dominates its entire containing block.
6827 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6828 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6829 return DoesNotDominateBlock;
6831 // FALL THROUGH into SCEVNAryExpr handling.
6836 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6838 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6840 BlockDisposition D = getBlockDisposition(*I, BB);
6841 if (D == DoesNotDominateBlock)
6842 return DoesNotDominateBlock;
6843 if (D == DominatesBlock)
6846 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6849 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6850 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6851 BlockDisposition LD = getBlockDisposition(LHS, BB);
6852 if (LD == DoesNotDominateBlock)
6853 return DoesNotDominateBlock;
6854 BlockDisposition RD = getBlockDisposition(RHS, BB);
6855 if (RD == DoesNotDominateBlock)
6856 return DoesNotDominateBlock;
6857 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6858 ProperlyDominatesBlock : DominatesBlock;
6861 if (Instruction *I =
6862 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6863 if (I->getParent() == BB)
6864 return DominatesBlock;
6865 if (DT->properlyDominates(I->getParent(), BB))
6866 return ProperlyDominatesBlock;
6867 return DoesNotDominateBlock;
6869 return ProperlyDominatesBlock;
6870 case scCouldNotCompute:
6871 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6873 llvm_unreachable("Unknown SCEV kind!");
6877 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6878 return getBlockDisposition(S, BB) >= DominatesBlock;
6881 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6882 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6885 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6886 SmallVector<const SCEV *, 8> Worklist;
6887 Worklist.push_back(S);
6889 S = Worklist.pop_back_val();
6891 switch (S->getSCEVType()) {
6896 case scSignExtend: {
6897 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
6898 const SCEV *CastOp = Cast->getOperand();
6901 Worklist.push_back(CastOp);
6909 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6910 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6912 const SCEV *NAryOp = *I;
6915 Worklist.push_back(NAryOp);
6920 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6921 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6922 if (LHS == Op || RHS == Op)
6924 Worklist.push_back(LHS);
6925 Worklist.push_back(RHS);
6930 case scCouldNotCompute:
6931 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6933 llvm_unreachable("Unknown SCEV kind!");
6935 } while (!Worklist.empty());
6940 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6941 ValuesAtScopes.erase(S);
6942 LoopDispositions.erase(S);
6943 BlockDispositions.erase(S);
6944 UnsignedRanges.erase(S);
6945 SignedRanges.erase(S);