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 absence 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())
2043 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2044 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2045 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2046 // ]]],+,...up to x=2n}.
2047 // Note that the arguments to choose() are always integers with values
2048 // known at compile time, never SCEV objects.
2050 // The implementation avoids pointless extra computations when the two
2051 // addrec's are of different length (mathematically, it's equivalent to
2052 // an infinite stream of zeros on the right).
2053 bool OpsModified = false;
2054 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2056 const SCEVAddRecExpr *OtherAddRec =
2057 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2058 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2061 bool Overflow = false;
2062 Type *Ty = AddRec->getType();
2063 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2064 SmallVector<const SCEV*, 7> AddRecOps;
2065 for (int x = 0, xe = AddRec->getNumOperands() +
2066 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2067 const SCEV *Term = getConstant(Ty, 0);
2068 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2069 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2070 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2071 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2072 z < ze && !Overflow; ++z) {
2073 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2075 if (LargerThan64Bits)
2076 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2078 Coeff = Coeff1*Coeff2;
2079 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2080 const SCEV *Term1 = AddRec->getOperand(y-z);
2081 const SCEV *Term2 = OtherAddRec->getOperand(z);
2082 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2085 AddRecOps.push_back(Term);
2088 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2090 if (Ops.size() == 2) return NewAddRec;
2091 Ops[Idx] = NewAddRec;
2092 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2094 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2100 return getMulExpr(Ops);
2103 // Otherwise couldn't fold anything into this recurrence. Move onto the
2107 // Okay, it looks like we really DO need an mul expr. Check to see if we
2108 // already have one, otherwise create a new one.
2109 FoldingSetNodeID ID;
2110 ID.AddInteger(scMulExpr);
2111 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2112 ID.AddPointer(Ops[i]);
2115 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2117 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2118 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2119 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2121 UniqueSCEVs.InsertNode(S, IP);
2123 S->setNoWrapFlags(Flags);
2127 /// getUDivExpr - Get a canonical unsigned division expression, or something
2128 /// simpler if possible.
2129 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2131 assert(getEffectiveSCEVType(LHS->getType()) ==
2132 getEffectiveSCEVType(RHS->getType()) &&
2133 "SCEVUDivExpr operand types don't match!");
2135 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2136 if (RHSC->getValue()->equalsInt(1))
2137 return LHS; // X udiv 1 --> x
2138 // If the denominator is zero, the result of the udiv is undefined. Don't
2139 // try to analyze it, because the resolution chosen here may differ from
2140 // the resolution chosen in other parts of the compiler.
2141 if (!RHSC->getValue()->isZero()) {
2142 // Determine if the division can be folded into the operands of
2144 // TODO: Generalize this to non-constants by using known-bits information.
2145 Type *Ty = LHS->getType();
2146 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2147 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2148 // For non-power-of-two values, effectively round the value up to the
2149 // nearest power of two.
2150 if (!RHSC->getValue()->getValue().isPowerOf2())
2152 IntegerType *ExtTy =
2153 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2154 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2155 if (const SCEVConstant *Step =
2156 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2157 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2158 const APInt &StepInt = Step->getValue()->getValue();
2159 const APInt &DivInt = RHSC->getValue()->getValue();
2160 if (!StepInt.urem(DivInt) &&
2161 getZeroExtendExpr(AR, ExtTy) ==
2162 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2163 getZeroExtendExpr(Step, ExtTy),
2164 AR->getLoop(), SCEV::FlagAnyWrap)) {
2165 SmallVector<const SCEV *, 4> Operands;
2166 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2167 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2168 return getAddRecExpr(Operands, AR->getLoop(),
2171 /// Get a canonical UDivExpr for a recurrence.
2172 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2173 // We can currently only fold X%N if X is constant.
2174 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2175 if (StartC && !DivInt.urem(StepInt) &&
2176 getZeroExtendExpr(AR, ExtTy) ==
2177 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2178 getZeroExtendExpr(Step, ExtTy),
2179 AR->getLoop(), SCEV::FlagAnyWrap)) {
2180 const APInt &StartInt = StartC->getValue()->getValue();
2181 const APInt &StartRem = StartInt.urem(StepInt);
2183 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2184 AR->getLoop(), SCEV::FlagNW);
2187 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2188 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2189 SmallVector<const SCEV *, 4> Operands;
2190 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2191 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2192 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2193 // Find an operand that's safely divisible.
2194 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2195 const SCEV *Op = M->getOperand(i);
2196 const SCEV *Div = getUDivExpr(Op, RHSC);
2197 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2198 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2201 return getMulExpr(Operands);
2205 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2206 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2207 SmallVector<const SCEV *, 4> Operands;
2208 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2209 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2210 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2212 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2213 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2214 if (isa<SCEVUDivExpr>(Op) ||
2215 getMulExpr(Op, RHS) != A->getOperand(i))
2217 Operands.push_back(Op);
2219 if (Operands.size() == A->getNumOperands())
2220 return getAddExpr(Operands);
2224 // Fold if both operands are constant.
2225 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2226 Constant *LHSCV = LHSC->getValue();
2227 Constant *RHSCV = RHSC->getValue();
2228 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2234 FoldingSetNodeID ID;
2235 ID.AddInteger(scUDivExpr);
2239 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2240 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2242 UniqueSCEVs.InsertNode(S, IP);
2247 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2248 /// Simplify the expression as much as possible.
2249 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2251 SCEV::NoWrapFlags Flags) {
2252 SmallVector<const SCEV *, 4> Operands;
2253 Operands.push_back(Start);
2254 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2255 if (StepChrec->getLoop() == L) {
2256 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2257 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2260 Operands.push_back(Step);
2261 return getAddRecExpr(Operands, L, Flags);
2264 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2265 /// Simplify the expression as much as possible.
2267 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2268 const Loop *L, SCEV::NoWrapFlags Flags) {
2269 if (Operands.size() == 1) return Operands[0];
2271 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2272 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2273 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2274 "SCEVAddRecExpr operand types don't match!");
2275 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2276 assert(isLoopInvariant(Operands[i], L) &&
2277 "SCEVAddRecExpr operand is not loop-invariant!");
2280 if (Operands.back()->isZero()) {
2281 Operands.pop_back();
2282 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2285 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2286 // use that information to infer NUW and NSW flags. However, computing a
2287 // BE count requires calling getAddRecExpr, so we may not yet have a
2288 // meaningful BE count at this point (and if we don't, we'd be stuck
2289 // with a SCEVCouldNotCompute as the cached BE count).
2291 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2293 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2294 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2295 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2297 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2298 E = Operands.end(); I != E; ++I)
2299 if (!isKnownNonNegative(*I)) {
2303 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2306 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2307 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2308 const Loop *NestedLoop = NestedAR->getLoop();
2309 if (L->contains(NestedLoop) ?
2310 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2311 (!NestedLoop->contains(L) &&
2312 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2313 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2314 NestedAR->op_end());
2315 Operands[0] = NestedAR->getStart();
2316 // AddRecs require their operands be loop-invariant with respect to their
2317 // loops. Don't perform this transformation if it would break this
2319 bool AllInvariant = true;
2320 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2321 if (!isLoopInvariant(Operands[i], L)) {
2322 AllInvariant = false;
2326 // Create a recurrence for the outer loop with the same step size.
2328 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2329 // inner recurrence has the same property.
2330 SCEV::NoWrapFlags OuterFlags =
2331 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2333 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2334 AllInvariant = true;
2335 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2336 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2337 AllInvariant = false;
2341 // Ok, both add recurrences are valid after the transformation.
2343 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2344 // the outer recurrence has the same property.
2345 SCEV::NoWrapFlags InnerFlags =
2346 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2347 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2350 // Reset Operands to its original state.
2351 Operands[0] = NestedAR;
2355 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2356 // already have one, otherwise create a new one.
2357 FoldingSetNodeID ID;
2358 ID.AddInteger(scAddRecExpr);
2359 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2360 ID.AddPointer(Operands[i]);
2364 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2366 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2367 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2368 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2369 O, Operands.size(), L);
2370 UniqueSCEVs.InsertNode(S, IP);
2372 S->setNoWrapFlags(Flags);
2376 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2378 SmallVector<const SCEV *, 2> Ops;
2381 return getSMaxExpr(Ops);
2385 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2386 assert(!Ops.empty() && "Cannot get empty smax!");
2387 if (Ops.size() == 1) return Ops[0];
2389 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2390 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2391 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2392 "SCEVSMaxExpr operand types don't match!");
2395 // Sort by complexity, this groups all similar expression types together.
2396 GroupByComplexity(Ops, LI);
2398 // If there are any constants, fold them together.
2400 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2402 assert(Idx < Ops.size());
2403 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2404 // We found two constants, fold them together!
2405 ConstantInt *Fold = ConstantInt::get(getContext(),
2406 APIntOps::smax(LHSC->getValue()->getValue(),
2407 RHSC->getValue()->getValue()));
2408 Ops[0] = getConstant(Fold);
2409 Ops.erase(Ops.begin()+1); // Erase the folded element
2410 if (Ops.size() == 1) return Ops[0];
2411 LHSC = cast<SCEVConstant>(Ops[0]);
2414 // If we are left with a constant minimum-int, strip it off.
2415 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2416 Ops.erase(Ops.begin());
2418 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2419 // If we have an smax with a constant maximum-int, it will always be
2424 if (Ops.size() == 1) return Ops[0];
2427 // Find the first SMax
2428 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2431 // Check to see if one of the operands is an SMax. If so, expand its operands
2432 // onto our operand list, and recurse to simplify.
2433 if (Idx < Ops.size()) {
2434 bool DeletedSMax = false;
2435 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2436 Ops.erase(Ops.begin()+Idx);
2437 Ops.append(SMax->op_begin(), SMax->op_end());
2442 return getSMaxExpr(Ops);
2445 // Okay, check to see if the same value occurs in the operand list twice. If
2446 // so, delete one. Since we sorted the list, these values are required to
2448 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2449 // X smax Y smax Y --> X smax Y
2450 // X smax Y --> X, if X is always greater than Y
2451 if (Ops[i] == Ops[i+1] ||
2452 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2453 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2455 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2456 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2460 if (Ops.size() == 1) return Ops[0];
2462 assert(!Ops.empty() && "Reduced smax down to nothing!");
2464 // Okay, it looks like we really DO need an smax expr. Check to see if we
2465 // already have one, otherwise create a new one.
2466 FoldingSetNodeID ID;
2467 ID.AddInteger(scSMaxExpr);
2468 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2469 ID.AddPointer(Ops[i]);
2471 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2472 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2473 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2474 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2476 UniqueSCEVs.InsertNode(S, IP);
2480 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2482 SmallVector<const SCEV *, 2> Ops;
2485 return getUMaxExpr(Ops);
2489 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2490 assert(!Ops.empty() && "Cannot get empty umax!");
2491 if (Ops.size() == 1) return Ops[0];
2493 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2494 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2495 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2496 "SCEVUMaxExpr operand types don't match!");
2499 // Sort by complexity, this groups all similar expression types together.
2500 GroupByComplexity(Ops, LI);
2502 // If there are any constants, fold them together.
2504 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2506 assert(Idx < Ops.size());
2507 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2508 // We found two constants, fold them together!
2509 ConstantInt *Fold = ConstantInt::get(getContext(),
2510 APIntOps::umax(LHSC->getValue()->getValue(),
2511 RHSC->getValue()->getValue()));
2512 Ops[0] = getConstant(Fold);
2513 Ops.erase(Ops.begin()+1); // Erase the folded element
2514 if (Ops.size() == 1) return Ops[0];
2515 LHSC = cast<SCEVConstant>(Ops[0]);
2518 // If we are left with a constant minimum-int, strip it off.
2519 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2520 Ops.erase(Ops.begin());
2522 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2523 // If we have an umax with a constant maximum-int, it will always be
2528 if (Ops.size() == 1) return Ops[0];
2531 // Find the first UMax
2532 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2535 // Check to see if one of the operands is a UMax. If so, expand its operands
2536 // onto our operand list, and recurse to simplify.
2537 if (Idx < Ops.size()) {
2538 bool DeletedUMax = false;
2539 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2540 Ops.erase(Ops.begin()+Idx);
2541 Ops.append(UMax->op_begin(), UMax->op_end());
2546 return getUMaxExpr(Ops);
2549 // Okay, check to see if the same value occurs in the operand list twice. If
2550 // so, delete one. Since we sorted the list, these values are required to
2552 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2553 // X umax Y umax Y --> X umax Y
2554 // X umax Y --> X, if X is always greater than Y
2555 if (Ops[i] == Ops[i+1] ||
2556 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2557 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2559 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2560 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2564 if (Ops.size() == 1) return Ops[0];
2566 assert(!Ops.empty() && "Reduced umax down to nothing!");
2568 // Okay, it looks like we really DO need a umax expr. Check to see if we
2569 // already have one, otherwise create a new one.
2570 FoldingSetNodeID ID;
2571 ID.AddInteger(scUMaxExpr);
2572 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2573 ID.AddPointer(Ops[i]);
2575 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2576 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2577 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2578 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2580 UniqueSCEVs.InsertNode(S, IP);
2584 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2586 // ~smax(~x, ~y) == smin(x, y).
2587 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2590 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2592 // ~umax(~x, ~y) == umin(x, y)
2593 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2596 const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) {
2597 // If we have TargetData, we can bypass creating a target-independent
2598 // constant expression and then folding it back into a ConstantInt.
2599 // This is just a compile-time optimization.
2601 return getConstant(TD->getIntPtrType(getContext()),
2602 TD->getTypeAllocSize(AllocTy));
2604 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2605 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2606 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2608 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2609 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2612 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2613 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2614 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2615 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2617 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2618 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2621 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy,
2623 // If we have TargetData, we can bypass creating a target-independent
2624 // constant expression and then folding it back into a ConstantInt.
2625 // This is just a compile-time optimization.
2627 return getConstant(TD->getIntPtrType(getContext()),
2628 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2630 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2631 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2632 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2634 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2635 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2638 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2639 Constant *FieldNo) {
2640 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2641 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2642 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2644 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2645 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2648 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2649 // Don't attempt to do anything other than create a SCEVUnknown object
2650 // here. createSCEV only calls getUnknown after checking for all other
2651 // interesting possibilities, and any other code that calls getUnknown
2652 // is doing so in order to hide a value from SCEV canonicalization.
2654 FoldingSetNodeID ID;
2655 ID.AddInteger(scUnknown);
2658 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2659 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2660 "Stale SCEVUnknown in uniquing map!");
2663 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2665 FirstUnknown = cast<SCEVUnknown>(S);
2666 UniqueSCEVs.InsertNode(S, IP);
2670 //===----------------------------------------------------------------------===//
2671 // Basic SCEV Analysis and PHI Idiom Recognition Code
2674 /// isSCEVable - Test if values of the given type are analyzable within
2675 /// the SCEV framework. This primarily includes integer types, and it
2676 /// can optionally include pointer types if the ScalarEvolution class
2677 /// has access to target-specific information.
2678 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2679 // Integers and pointers are always SCEVable.
2680 return Ty->isIntegerTy() || Ty->isPointerTy();
2683 /// getTypeSizeInBits - Return the size in bits of the specified type,
2684 /// for which isSCEVable must return true.
2685 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2686 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2688 // If we have a TargetData, use it!
2690 return TD->getTypeSizeInBits(Ty);
2692 // Integer types have fixed sizes.
2693 if (Ty->isIntegerTy())
2694 return Ty->getPrimitiveSizeInBits();
2696 // The only other support type is pointer. Without TargetData, conservatively
2697 // assume pointers are 64-bit.
2698 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2702 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2703 /// the given type and which represents how SCEV will treat the given
2704 /// type, for which isSCEVable must return true. For pointer types,
2705 /// this is the pointer-sized integer type.
2706 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2707 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2709 if (Ty->isIntegerTy())
2712 // The only other support type is pointer.
2713 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2714 if (TD) return TD->getIntPtrType(getContext());
2716 // Without TargetData, conservatively assume pointers are 64-bit.
2717 return Type::getInt64Ty(getContext());
2720 const SCEV *ScalarEvolution::getCouldNotCompute() {
2721 return &CouldNotCompute;
2724 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2725 /// expression and create a new one.
2726 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2727 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2729 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2730 if (I != ValueExprMap.end()) return I->second;
2731 const SCEV *S = createSCEV(V);
2733 // The process of creating a SCEV for V may have caused other SCEVs
2734 // to have been created, so it's necessary to insert the new entry
2735 // from scratch, rather than trying to remember the insert position
2737 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2741 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2743 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2744 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2746 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2748 Type *Ty = V->getType();
2749 Ty = getEffectiveSCEVType(Ty);
2750 return getMulExpr(V,
2751 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2754 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2755 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2756 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2758 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2760 Type *Ty = V->getType();
2761 Ty = getEffectiveSCEVType(Ty);
2762 const SCEV *AllOnes =
2763 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2764 return getMinusSCEV(AllOnes, V);
2767 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2768 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2769 SCEV::NoWrapFlags Flags) {
2770 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2772 // Fast path: X - X --> 0.
2774 return getConstant(LHS->getType(), 0);
2777 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2780 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2781 /// input value to the specified type. If the type must be extended, it is zero
2784 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2785 Type *SrcTy = V->getType();
2786 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2787 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2788 "Cannot truncate or zero extend with non-integer arguments!");
2789 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2790 return V; // No conversion
2791 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2792 return getTruncateExpr(V, Ty);
2793 return getZeroExtendExpr(V, Ty);
2796 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2797 /// input value to the specified type. If the type must be extended, it is sign
2800 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2802 Type *SrcTy = V->getType();
2803 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2804 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2805 "Cannot truncate or zero extend with non-integer arguments!");
2806 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2807 return V; // No conversion
2808 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2809 return getTruncateExpr(V, Ty);
2810 return getSignExtendExpr(V, Ty);
2813 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2814 /// input value to the specified type. If the type must be extended, it is zero
2815 /// extended. The conversion must not be narrowing.
2817 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2818 Type *SrcTy = V->getType();
2819 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2820 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2821 "Cannot noop or zero extend with non-integer arguments!");
2822 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2823 "getNoopOrZeroExtend cannot truncate!");
2824 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2825 return V; // No conversion
2826 return getZeroExtendExpr(V, Ty);
2829 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2830 /// input value to the specified type. If the type must be extended, it is sign
2831 /// extended. The conversion must not be narrowing.
2833 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2834 Type *SrcTy = V->getType();
2835 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2836 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2837 "Cannot noop or sign extend with non-integer arguments!");
2838 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2839 "getNoopOrSignExtend cannot truncate!");
2840 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2841 return V; // No conversion
2842 return getSignExtendExpr(V, Ty);
2845 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2846 /// the input value to the specified type. If the type must be extended,
2847 /// it is extended with unspecified bits. The conversion must not be
2850 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2851 Type *SrcTy = V->getType();
2852 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2853 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2854 "Cannot noop or any extend with non-integer arguments!");
2855 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2856 "getNoopOrAnyExtend cannot truncate!");
2857 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2858 return V; // No conversion
2859 return getAnyExtendExpr(V, Ty);
2862 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2863 /// input value to the specified type. The conversion must not be widening.
2865 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2866 Type *SrcTy = V->getType();
2867 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2868 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2869 "Cannot truncate or noop with non-integer arguments!");
2870 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2871 "getTruncateOrNoop cannot extend!");
2872 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2873 return V; // No conversion
2874 return getTruncateExpr(V, Ty);
2877 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2878 /// the types using zero-extension, and then perform a umax operation
2880 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2882 const SCEV *PromotedLHS = LHS;
2883 const SCEV *PromotedRHS = RHS;
2885 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2886 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2888 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2890 return getUMaxExpr(PromotedLHS, PromotedRHS);
2893 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2894 /// the types using zero-extension, and then perform a umin operation
2896 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2898 const SCEV *PromotedLHS = LHS;
2899 const SCEV *PromotedRHS = RHS;
2901 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2902 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2904 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2906 return getUMinExpr(PromotedLHS, PromotedRHS);
2909 /// getPointerBase - Transitively follow the chain of pointer-type operands
2910 /// until reaching a SCEV that does not have a single pointer operand. This
2911 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2912 /// but corner cases do exist.
2913 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2914 // A pointer operand may evaluate to a nonpointer expression, such as null.
2915 if (!V->getType()->isPointerTy())
2918 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2919 return getPointerBase(Cast->getOperand());
2921 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2922 const SCEV *PtrOp = 0;
2923 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2925 if ((*I)->getType()->isPointerTy()) {
2926 // Cannot find the base of an expression with multiple pointer operands.
2934 return getPointerBase(PtrOp);
2939 /// PushDefUseChildren - Push users of the given Instruction
2940 /// onto the given Worklist.
2942 PushDefUseChildren(Instruction *I,
2943 SmallVectorImpl<Instruction *> &Worklist) {
2944 // Push the def-use children onto the Worklist stack.
2945 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2947 Worklist.push_back(cast<Instruction>(*UI));
2950 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2951 /// instructions that depend on the given instruction and removes them from
2952 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2955 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2956 SmallVector<Instruction *, 16> Worklist;
2957 PushDefUseChildren(PN, Worklist);
2959 SmallPtrSet<Instruction *, 8> Visited;
2961 while (!Worklist.empty()) {
2962 Instruction *I = Worklist.pop_back_val();
2963 if (!Visited.insert(I)) continue;
2965 ValueExprMapType::iterator It =
2966 ValueExprMap.find(static_cast<Value *>(I));
2967 if (It != ValueExprMap.end()) {
2968 const SCEV *Old = It->second;
2970 // Short-circuit the def-use traversal if the symbolic name
2971 // ceases to appear in expressions.
2972 if (Old != SymName && !hasOperand(Old, SymName))
2975 // SCEVUnknown for a PHI either means that it has an unrecognized
2976 // structure, it's a PHI that's in the progress of being computed
2977 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2978 // additional loop trip count information isn't going to change anything.
2979 // In the second case, createNodeForPHI will perform the necessary
2980 // updates on its own when it gets to that point. In the third, we do
2981 // want to forget the SCEVUnknown.
2982 if (!isa<PHINode>(I) ||
2983 !isa<SCEVUnknown>(Old) ||
2984 (I != PN && Old == SymName)) {
2985 forgetMemoizedResults(Old);
2986 ValueExprMap.erase(It);
2990 PushDefUseChildren(I, Worklist);
2994 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2995 /// a loop header, making it a potential recurrence, or it doesn't.
2997 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2998 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2999 if (L->getHeader() == PN->getParent()) {
3000 // The loop may have multiple entrances or multiple exits; we can analyze
3001 // this phi as an addrec if it has a unique entry value and a unique
3003 Value *BEValueV = 0, *StartValueV = 0;
3004 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3005 Value *V = PN->getIncomingValue(i);
3006 if (L->contains(PN->getIncomingBlock(i))) {
3009 } else if (BEValueV != V) {
3013 } else if (!StartValueV) {
3015 } else if (StartValueV != V) {
3020 if (BEValueV && StartValueV) {
3021 // While we are analyzing this PHI node, handle its value symbolically.
3022 const SCEV *SymbolicName = getUnknown(PN);
3023 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
3024 "PHI node already processed?");
3025 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3027 // Using this symbolic name for the PHI, analyze the value coming around
3029 const SCEV *BEValue = getSCEV(BEValueV);
3031 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3032 // has a special value for the first iteration of the loop.
3034 // If the value coming around the backedge is an add with the symbolic
3035 // value we just inserted, then we found a simple induction variable!
3036 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3037 // If there is a single occurrence of the symbolic value, replace it
3038 // with a recurrence.
3039 unsigned FoundIndex = Add->getNumOperands();
3040 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3041 if (Add->getOperand(i) == SymbolicName)
3042 if (FoundIndex == e) {
3047 if (FoundIndex != Add->getNumOperands()) {
3048 // Create an add with everything but the specified operand.
3049 SmallVector<const SCEV *, 8> Ops;
3050 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3051 if (i != FoundIndex)
3052 Ops.push_back(Add->getOperand(i));
3053 const SCEV *Accum = getAddExpr(Ops);
3055 // This is not a valid addrec if the step amount is varying each
3056 // loop iteration, but is not itself an addrec in this loop.
3057 if (isLoopInvariant(Accum, L) ||
3058 (isa<SCEVAddRecExpr>(Accum) &&
3059 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3060 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3062 // If the increment doesn't overflow, then neither the addrec nor
3063 // the post-increment will overflow.
3064 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3065 if (OBO->hasNoUnsignedWrap())
3066 Flags = setFlags(Flags, SCEV::FlagNUW);
3067 if (OBO->hasNoSignedWrap())
3068 Flags = setFlags(Flags, SCEV::FlagNSW);
3069 } else if (const GEPOperator *GEP =
3070 dyn_cast<GEPOperator>(BEValueV)) {
3071 // If the increment is an inbounds GEP, then we know the address
3072 // space cannot be wrapped around. We cannot make any guarantee
3073 // about signed or unsigned overflow because pointers are
3074 // unsigned but we may have a negative index from the base
3076 if (GEP->isInBounds())
3077 Flags = setFlags(Flags, SCEV::FlagNW);
3080 const SCEV *StartVal = getSCEV(StartValueV);
3081 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3083 // Since the no-wrap flags are on the increment, they apply to the
3084 // post-incremented value as well.
3085 if (isLoopInvariant(Accum, L))
3086 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3089 // Okay, for the entire analysis of this edge we assumed the PHI
3090 // to be symbolic. We now need to go back and purge all of the
3091 // entries for the scalars that use the symbolic expression.
3092 ForgetSymbolicName(PN, SymbolicName);
3093 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3097 } else if (const SCEVAddRecExpr *AddRec =
3098 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3099 // Otherwise, this could be a loop like this:
3100 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3101 // In this case, j = {1,+,1} and BEValue is j.
3102 // Because the other in-value of i (0) fits the evolution of BEValue
3103 // i really is an addrec evolution.
3104 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3105 const SCEV *StartVal = getSCEV(StartValueV);
3107 // If StartVal = j.start - j.stride, we can use StartVal as the
3108 // initial step of the addrec evolution.
3109 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3110 AddRec->getOperand(1))) {
3111 // FIXME: For constant StartVal, we should be able to infer
3113 const SCEV *PHISCEV =
3114 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3117 // Okay, for the entire analysis of this edge we assumed the PHI
3118 // to be symbolic. We now need to go back and purge all of the
3119 // entries for the scalars that use the symbolic expression.
3120 ForgetSymbolicName(PN, SymbolicName);
3121 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3129 // If the PHI has a single incoming value, follow that value, unless the
3130 // PHI's incoming blocks are in a different loop, in which case doing so
3131 // risks breaking LCSSA form. Instcombine would normally zap these, but
3132 // it doesn't have DominatorTree information, so it may miss cases.
3133 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
3134 if (LI->replacementPreservesLCSSAForm(PN, V))
3137 // If it's not a loop phi, we can't handle it yet.
3138 return getUnknown(PN);
3141 /// createNodeForGEP - Expand GEP instructions into add and multiply
3142 /// operations. This allows them to be analyzed by regular SCEV code.
3144 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3146 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3147 // Add expression, because the Instruction may be guarded by control flow
3148 // and the no-overflow bits may not be valid for the expression in any
3150 bool isInBounds = GEP->isInBounds();
3152 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3153 Value *Base = GEP->getOperand(0);
3154 // Don't attempt to analyze GEPs over unsized objects.
3155 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3156 return getUnknown(GEP);
3157 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3158 gep_type_iterator GTI = gep_type_begin(GEP);
3159 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3163 // Compute the (potentially symbolic) offset in bytes for this index.
3164 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3165 // For a struct, add the member offset.
3166 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3167 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
3169 // Add the field offset to the running total offset.
3170 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3172 // For an array, add the element offset, explicitly scaled.
3173 const SCEV *ElementSize = getSizeOfExpr(*GTI);
3174 const SCEV *IndexS = getSCEV(Index);
3175 // Getelementptr indices are signed.
3176 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3178 // Multiply the index by the element size to compute the element offset.
3179 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3180 isInBounds ? SCEV::FlagNSW :
3183 // Add the element offset to the running total offset.
3184 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3188 // Get the SCEV for the GEP base.
3189 const SCEV *BaseS = getSCEV(Base);
3191 // Add the total offset from all the GEP indices to the base.
3192 return getAddExpr(BaseS, TotalOffset,
3193 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3196 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3197 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3198 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3199 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3201 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3202 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3203 return C->getValue()->getValue().countTrailingZeros();
3205 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3206 return std::min(GetMinTrailingZeros(T->getOperand()),
3207 (uint32_t)getTypeSizeInBits(T->getType()));
3209 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3210 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3211 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3212 getTypeSizeInBits(E->getType()) : OpRes;
3215 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3216 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3217 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3218 getTypeSizeInBits(E->getType()) : OpRes;
3221 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3222 // The result is the min of all operands results.
3223 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3224 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3225 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3229 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3230 // The result is the sum of all operands results.
3231 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3232 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3233 for (unsigned i = 1, e = M->getNumOperands();
3234 SumOpRes != BitWidth && i != e; ++i)
3235 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3240 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3241 // The result is the min of all operands results.
3242 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3243 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3244 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3248 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3249 // The result is the min of all operands results.
3250 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3251 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3252 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3256 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3257 // The result is the min of all operands results.
3258 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3259 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3260 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3264 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3265 // For a SCEVUnknown, ask ValueTracking.
3266 unsigned BitWidth = getTypeSizeInBits(U->getType());
3267 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3268 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3269 return Zeros.countTrailingOnes();
3276 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3279 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3280 // See if we've computed this range already.
3281 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3282 if (I != UnsignedRanges.end())
3285 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3286 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3288 unsigned BitWidth = getTypeSizeInBits(S->getType());
3289 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3291 // If the value has known zeros, the maximum unsigned value will have those
3292 // known zeros as well.
3293 uint32_t TZ = GetMinTrailingZeros(S);
3295 ConservativeResult =
3296 ConstantRange(APInt::getMinValue(BitWidth),
3297 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3299 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3300 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3301 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3302 X = X.add(getUnsignedRange(Add->getOperand(i)));
3303 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3306 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3307 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3308 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3309 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3310 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3313 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3314 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3315 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3316 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3317 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3320 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3321 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3322 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3323 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3324 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3327 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3328 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3329 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3330 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3333 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3334 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3335 return setUnsignedRange(ZExt,
3336 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3339 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3340 ConstantRange X = getUnsignedRange(SExt->getOperand());
3341 return setUnsignedRange(SExt,
3342 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3345 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3346 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3347 return setUnsignedRange(Trunc,
3348 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3351 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3352 // If there's no unsigned wrap, the value will never be less than its
3354 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3355 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3356 if (!C->getValue()->isZero())
3357 ConservativeResult =
3358 ConservativeResult.intersectWith(
3359 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3361 // TODO: non-affine addrec
3362 if (AddRec->isAffine()) {
3363 Type *Ty = AddRec->getType();
3364 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3365 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3366 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3367 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3369 const SCEV *Start = AddRec->getStart();
3370 const SCEV *Step = AddRec->getStepRecurrence(*this);
3372 ConstantRange StartRange = getUnsignedRange(Start);
3373 ConstantRange StepRange = getSignedRange(Step);
3374 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3375 ConstantRange EndRange =
3376 StartRange.add(MaxBECountRange.multiply(StepRange));
3378 // Check for overflow. This must be done with ConstantRange arithmetic
3379 // because we could be called from within the ScalarEvolution overflow
3381 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3382 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3383 ConstantRange ExtMaxBECountRange =
3384 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3385 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3386 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3388 return setUnsignedRange(AddRec, ConservativeResult);
3390 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3391 EndRange.getUnsignedMin());
3392 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3393 EndRange.getUnsignedMax());
3394 if (Min.isMinValue() && Max.isMaxValue())
3395 return setUnsignedRange(AddRec, ConservativeResult);
3396 return setUnsignedRange(AddRec,
3397 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3401 return setUnsignedRange(AddRec, ConservativeResult);
3404 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3405 // For a SCEVUnknown, ask ValueTracking.
3406 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3407 ComputeMaskedBits(U->getValue(), Zeros, Ones, TD);
3408 if (Ones == ~Zeros + 1)
3409 return setUnsignedRange(U, ConservativeResult);
3410 return setUnsignedRange(U,
3411 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3414 return setUnsignedRange(S, ConservativeResult);
3417 /// getSignedRange - Determine the signed range for a particular SCEV.
3420 ScalarEvolution::getSignedRange(const SCEV *S) {
3421 // See if we've computed this range already.
3422 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3423 if (I != SignedRanges.end())
3426 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3427 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3429 unsigned BitWidth = getTypeSizeInBits(S->getType());
3430 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3432 // If the value has known zeros, the maximum signed value will have those
3433 // known zeros as well.
3434 uint32_t TZ = GetMinTrailingZeros(S);
3436 ConservativeResult =
3437 ConstantRange(APInt::getSignedMinValue(BitWidth),
3438 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3440 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3441 ConstantRange X = getSignedRange(Add->getOperand(0));
3442 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3443 X = X.add(getSignedRange(Add->getOperand(i)));
3444 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3447 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3448 ConstantRange X = getSignedRange(Mul->getOperand(0));
3449 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3450 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3451 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3454 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3455 ConstantRange X = getSignedRange(SMax->getOperand(0));
3456 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3457 X = X.smax(getSignedRange(SMax->getOperand(i)));
3458 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3461 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3462 ConstantRange X = getSignedRange(UMax->getOperand(0));
3463 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3464 X = X.umax(getSignedRange(UMax->getOperand(i)));
3465 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3468 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3469 ConstantRange X = getSignedRange(UDiv->getLHS());
3470 ConstantRange Y = getSignedRange(UDiv->getRHS());
3471 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3474 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3475 ConstantRange X = getSignedRange(ZExt->getOperand());
3476 return setSignedRange(ZExt,
3477 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3480 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3481 ConstantRange X = getSignedRange(SExt->getOperand());
3482 return setSignedRange(SExt,
3483 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3486 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3487 ConstantRange X = getSignedRange(Trunc->getOperand());
3488 return setSignedRange(Trunc,
3489 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3492 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3493 // If there's no signed wrap, and all the operands have the same sign or
3494 // zero, the value won't ever change sign.
3495 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3496 bool AllNonNeg = true;
3497 bool AllNonPos = true;
3498 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3499 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3500 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3503 ConservativeResult = ConservativeResult.intersectWith(
3504 ConstantRange(APInt(BitWidth, 0),
3505 APInt::getSignedMinValue(BitWidth)));
3507 ConservativeResult = ConservativeResult.intersectWith(
3508 ConstantRange(APInt::getSignedMinValue(BitWidth),
3509 APInt(BitWidth, 1)));
3512 // TODO: non-affine addrec
3513 if (AddRec->isAffine()) {
3514 Type *Ty = AddRec->getType();
3515 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3516 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3517 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3518 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3520 const SCEV *Start = AddRec->getStart();
3521 const SCEV *Step = AddRec->getStepRecurrence(*this);
3523 ConstantRange StartRange = getSignedRange(Start);
3524 ConstantRange StepRange = getSignedRange(Step);
3525 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3526 ConstantRange EndRange =
3527 StartRange.add(MaxBECountRange.multiply(StepRange));
3529 // Check for overflow. This must be done with ConstantRange arithmetic
3530 // because we could be called from within the ScalarEvolution overflow
3532 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3533 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3534 ConstantRange ExtMaxBECountRange =
3535 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3536 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3537 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3539 return setSignedRange(AddRec, ConservativeResult);
3541 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3542 EndRange.getSignedMin());
3543 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3544 EndRange.getSignedMax());
3545 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3546 return setSignedRange(AddRec, ConservativeResult);
3547 return setSignedRange(AddRec,
3548 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3552 return setSignedRange(AddRec, ConservativeResult);
3555 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3556 // For a SCEVUnknown, ask ValueTracking.
3557 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3558 return setSignedRange(U, ConservativeResult);
3559 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3561 return setSignedRange(U, ConservativeResult);
3562 return setSignedRange(U, ConservativeResult.intersectWith(
3563 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3564 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3567 return setSignedRange(S, ConservativeResult);
3570 /// createSCEV - We know that there is no SCEV for the specified value.
3571 /// Analyze the expression.
3573 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3574 if (!isSCEVable(V->getType()))
3575 return getUnknown(V);
3577 unsigned Opcode = Instruction::UserOp1;
3578 if (Instruction *I = dyn_cast<Instruction>(V)) {
3579 Opcode = I->getOpcode();
3581 // Don't attempt to analyze instructions in blocks that aren't
3582 // reachable. Such instructions don't matter, and they aren't required
3583 // to obey basic rules for definitions dominating uses which this
3584 // analysis depends on.
3585 if (!DT->isReachableFromEntry(I->getParent()))
3586 return getUnknown(V);
3587 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3588 Opcode = CE->getOpcode();
3589 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3590 return getConstant(CI);
3591 else if (isa<ConstantPointerNull>(V))
3592 return getConstant(V->getType(), 0);
3593 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3594 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3596 return getUnknown(V);
3598 Operator *U = cast<Operator>(V);
3600 case Instruction::Add: {
3601 // The simple thing to do would be to just call getSCEV on both operands
3602 // and call getAddExpr with the result. However if we're looking at a
3603 // bunch of things all added together, this can be quite inefficient,
3604 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3605 // Instead, gather up all the operands and make a single getAddExpr call.
3606 // LLVM IR canonical form means we need only traverse the left operands.
3608 // Don't apply this instruction's NSW or NUW flags to the new
3609 // expression. The instruction may be guarded by control flow that the
3610 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3611 // mapped to the same SCEV expression, and it would be incorrect to transfer
3612 // NSW/NUW semantics to those operations.
3613 SmallVector<const SCEV *, 4> AddOps;
3614 AddOps.push_back(getSCEV(U->getOperand(1)));
3615 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3616 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3617 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3619 U = cast<Operator>(Op);
3620 const SCEV *Op1 = getSCEV(U->getOperand(1));
3621 if (Opcode == Instruction::Sub)
3622 AddOps.push_back(getNegativeSCEV(Op1));
3624 AddOps.push_back(Op1);
3626 AddOps.push_back(getSCEV(U->getOperand(0)));
3627 return getAddExpr(AddOps);
3629 case Instruction::Mul: {
3630 // Don't transfer NSW/NUW for the same reason as AddExpr.
3631 SmallVector<const SCEV *, 4> MulOps;
3632 MulOps.push_back(getSCEV(U->getOperand(1)));
3633 for (Value *Op = U->getOperand(0);
3634 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3635 Op = U->getOperand(0)) {
3636 U = cast<Operator>(Op);
3637 MulOps.push_back(getSCEV(U->getOperand(1)));
3639 MulOps.push_back(getSCEV(U->getOperand(0)));
3640 return getMulExpr(MulOps);
3642 case Instruction::UDiv:
3643 return getUDivExpr(getSCEV(U->getOperand(0)),
3644 getSCEV(U->getOperand(1)));
3645 case Instruction::Sub:
3646 return getMinusSCEV(getSCEV(U->getOperand(0)),
3647 getSCEV(U->getOperand(1)));
3648 case Instruction::And:
3649 // For an expression like x&255 that merely masks off the high bits,
3650 // use zext(trunc(x)) as the SCEV expression.
3651 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3652 if (CI->isNullValue())
3653 return getSCEV(U->getOperand(1));
3654 if (CI->isAllOnesValue())
3655 return getSCEV(U->getOperand(0));
3656 const APInt &A = CI->getValue();
3658 // Instcombine's ShrinkDemandedConstant may strip bits out of
3659 // constants, obscuring what would otherwise be a low-bits mask.
3660 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3661 // knew about to reconstruct a low-bits mask value.
3662 unsigned LZ = A.countLeadingZeros();
3663 unsigned BitWidth = A.getBitWidth();
3664 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3665 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD);
3667 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3669 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3671 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3672 IntegerType::get(getContext(), BitWidth - LZ)),
3677 case Instruction::Or:
3678 // If the RHS of the Or is a constant, we may have something like:
3679 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3680 // optimizations will transparently handle this case.
3682 // In order for this transformation to be safe, the LHS must be of the
3683 // form X*(2^n) and the Or constant must be less than 2^n.
3684 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3685 const SCEV *LHS = getSCEV(U->getOperand(0));
3686 const APInt &CIVal = CI->getValue();
3687 if (GetMinTrailingZeros(LHS) >=
3688 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3689 // Build a plain add SCEV.
3690 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3691 // If the LHS of the add was an addrec and it has no-wrap flags,
3692 // transfer the no-wrap flags, since an or won't introduce a wrap.
3693 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3694 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3695 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3696 OldAR->getNoWrapFlags());
3702 case Instruction::Xor:
3703 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3704 // If the RHS of the xor is a signbit, then this is just an add.
3705 // Instcombine turns add of signbit into xor as a strength reduction step.
3706 if (CI->getValue().isSignBit())
3707 return getAddExpr(getSCEV(U->getOperand(0)),
3708 getSCEV(U->getOperand(1)));
3710 // If the RHS of xor is -1, then this is a not operation.
3711 if (CI->isAllOnesValue())
3712 return getNotSCEV(getSCEV(U->getOperand(0)));
3714 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3715 // This is a variant of the check for xor with -1, and it handles
3716 // the case where instcombine has trimmed non-demanded bits out
3717 // of an xor with -1.
3718 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3719 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3720 if (BO->getOpcode() == Instruction::And &&
3721 LCI->getValue() == CI->getValue())
3722 if (const SCEVZeroExtendExpr *Z =
3723 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3724 Type *UTy = U->getType();
3725 const SCEV *Z0 = Z->getOperand();
3726 Type *Z0Ty = Z0->getType();
3727 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3729 // If C is a low-bits mask, the zero extend is serving to
3730 // mask off the high bits. Complement the operand and
3731 // re-apply the zext.
3732 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3733 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3735 // If C is a single bit, it may be in the sign-bit position
3736 // before the zero-extend. In this case, represent the xor
3737 // using an add, which is equivalent, and re-apply the zext.
3738 APInt Trunc = CI->getValue().trunc(Z0TySize);
3739 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3741 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3747 case Instruction::Shl:
3748 // Turn shift left of a constant amount into a multiply.
3749 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3750 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3752 // If the shift count is not less than the bitwidth, the result of
3753 // the shift is undefined. Don't try to analyze it, because the
3754 // resolution chosen here may differ from the resolution chosen in
3755 // other parts of the compiler.
3756 if (SA->getValue().uge(BitWidth))
3759 Constant *X = ConstantInt::get(getContext(),
3760 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3761 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3765 case Instruction::LShr:
3766 // Turn logical shift right of a constant into a unsigned divide.
3767 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3768 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3770 // If the shift count is not less than the bitwidth, the result of
3771 // the shift is undefined. Don't try to analyze it, because the
3772 // resolution chosen here may differ from the resolution chosen in
3773 // other parts of the compiler.
3774 if (SA->getValue().uge(BitWidth))
3777 Constant *X = ConstantInt::get(getContext(),
3778 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3779 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3783 case Instruction::AShr:
3784 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3785 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3786 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3787 if (L->getOpcode() == Instruction::Shl &&
3788 L->getOperand(1) == U->getOperand(1)) {
3789 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3791 // If the shift count is not less than the bitwidth, the result of
3792 // the shift is undefined. Don't try to analyze it, because the
3793 // resolution chosen here may differ from the resolution chosen in
3794 // other parts of the compiler.
3795 if (CI->getValue().uge(BitWidth))
3798 uint64_t Amt = BitWidth - CI->getZExtValue();
3799 if (Amt == BitWidth)
3800 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3802 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3803 IntegerType::get(getContext(),
3809 case Instruction::Trunc:
3810 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3812 case Instruction::ZExt:
3813 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3815 case Instruction::SExt:
3816 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3818 case Instruction::BitCast:
3819 // BitCasts are no-op casts so we just eliminate the cast.
3820 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3821 return getSCEV(U->getOperand(0));
3824 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3825 // lead to pointer expressions which cannot safely be expanded to GEPs,
3826 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3827 // simplifying integer expressions.
3829 case Instruction::GetElementPtr:
3830 return createNodeForGEP(cast<GEPOperator>(U));
3832 case Instruction::PHI:
3833 return createNodeForPHI(cast<PHINode>(U));
3835 case Instruction::Select:
3836 // This could be a smax or umax that was lowered earlier.
3837 // Try to recover it.
3838 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3839 Value *LHS = ICI->getOperand(0);
3840 Value *RHS = ICI->getOperand(1);
3841 switch (ICI->getPredicate()) {
3842 case ICmpInst::ICMP_SLT:
3843 case ICmpInst::ICMP_SLE:
3844 std::swap(LHS, RHS);
3846 case ICmpInst::ICMP_SGT:
3847 case ICmpInst::ICMP_SGE:
3848 // a >s b ? a+x : b+x -> smax(a, b)+x
3849 // a >s b ? b+x : a+x -> smin(a, b)+x
3850 if (LHS->getType() == U->getType()) {
3851 const SCEV *LS = getSCEV(LHS);
3852 const SCEV *RS = getSCEV(RHS);
3853 const SCEV *LA = getSCEV(U->getOperand(1));
3854 const SCEV *RA = getSCEV(U->getOperand(2));
3855 const SCEV *LDiff = getMinusSCEV(LA, LS);
3856 const SCEV *RDiff = getMinusSCEV(RA, RS);
3858 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3859 LDiff = getMinusSCEV(LA, RS);
3860 RDiff = getMinusSCEV(RA, LS);
3862 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3865 case ICmpInst::ICMP_ULT:
3866 case ICmpInst::ICMP_ULE:
3867 std::swap(LHS, RHS);
3869 case ICmpInst::ICMP_UGT:
3870 case ICmpInst::ICMP_UGE:
3871 // a >u b ? a+x : b+x -> umax(a, b)+x
3872 // a >u b ? b+x : a+x -> umin(a, b)+x
3873 if (LHS->getType() == U->getType()) {
3874 const SCEV *LS = getSCEV(LHS);
3875 const SCEV *RS = getSCEV(RHS);
3876 const SCEV *LA = getSCEV(U->getOperand(1));
3877 const SCEV *RA = getSCEV(U->getOperand(2));
3878 const SCEV *LDiff = getMinusSCEV(LA, LS);
3879 const SCEV *RDiff = getMinusSCEV(RA, RS);
3881 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3882 LDiff = getMinusSCEV(LA, RS);
3883 RDiff = getMinusSCEV(RA, LS);
3885 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3888 case ICmpInst::ICMP_NE:
3889 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3890 if (LHS->getType() == U->getType() &&
3891 isa<ConstantInt>(RHS) &&
3892 cast<ConstantInt>(RHS)->isZero()) {
3893 const SCEV *One = getConstant(LHS->getType(), 1);
3894 const SCEV *LS = getSCEV(LHS);
3895 const SCEV *LA = getSCEV(U->getOperand(1));
3896 const SCEV *RA = getSCEV(U->getOperand(2));
3897 const SCEV *LDiff = getMinusSCEV(LA, LS);
3898 const SCEV *RDiff = getMinusSCEV(RA, One);
3900 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3903 case ICmpInst::ICMP_EQ:
3904 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3905 if (LHS->getType() == U->getType() &&
3906 isa<ConstantInt>(RHS) &&
3907 cast<ConstantInt>(RHS)->isZero()) {
3908 const SCEV *One = getConstant(LHS->getType(), 1);
3909 const SCEV *LS = getSCEV(LHS);
3910 const SCEV *LA = getSCEV(U->getOperand(1));
3911 const SCEV *RA = getSCEV(U->getOperand(2));
3912 const SCEV *LDiff = getMinusSCEV(LA, One);
3913 const SCEV *RDiff = getMinusSCEV(RA, LS);
3915 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3923 default: // We cannot analyze this expression.
3927 return getUnknown(V);
3932 //===----------------------------------------------------------------------===//
3933 // Iteration Count Computation Code
3936 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3937 /// normal unsigned value. Returns 0 if the trip count is unknown or not
3938 /// constant. Will also return 0 if the maximum trip count is very large (>=
3941 /// This "trip count" assumes that control exits via ExitingBlock. More
3942 /// precisely, it is the number of times that control may reach ExitingBlock
3943 /// before taking the branch. For loops with multiple exits, it may not be the
3944 /// number times that the loop header executes because the loop may exit
3945 /// prematurely via another branch.
3946 unsigned ScalarEvolution::
3947 getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock) {
3948 const SCEVConstant *ExitCount =
3949 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
3953 ConstantInt *ExitConst = ExitCount->getValue();
3955 // Guard against huge trip counts.
3956 if (ExitConst->getValue().getActiveBits() > 32)
3959 // In case of integer overflow, this returns 0, which is correct.
3960 return ((unsigned)ExitConst->getZExtValue()) + 1;
3963 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3964 /// trip count of this loop as a normal unsigned value, if possible. This
3965 /// means that the actual trip count is always a multiple of the returned
3966 /// value (don't forget the trip count could very well be zero as well!).
3968 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3969 /// multiple of a constant (which is also the case if the trip count is simply
3970 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3971 /// if the trip count is very large (>= 2^32).
3973 /// As explained in the comments for getSmallConstantTripCount, this assumes
3974 /// that control exits the loop via ExitingBlock.
3975 unsigned ScalarEvolution::
3976 getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock) {
3977 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
3978 if (ExitCount == getCouldNotCompute())
3981 // Get the trip count from the BE count by adding 1.
3982 const SCEV *TCMul = getAddExpr(ExitCount,
3983 getConstant(ExitCount->getType(), 1));
3984 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
3985 // to factor simple cases.
3986 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
3987 TCMul = Mul->getOperand(0);
3989 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
3993 ConstantInt *Result = MulC->getValue();
3995 // Guard against huge trip counts.
3996 if (!Result || Result->getValue().getActiveBits() > 32)
3999 return (unsigned)Result->getZExtValue();
4002 // getExitCount - Get the expression for the number of loop iterations for which
4003 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return
4004 // SCEVCouldNotCompute.
4005 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4006 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4009 /// getBackedgeTakenCount - If the specified loop has a predictable
4010 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4011 /// object. The backedge-taken count is the number of times the loop header
4012 /// will be branched to from within the loop. This is one less than the
4013 /// trip count of the loop, since it doesn't count the first iteration,
4014 /// when the header is branched to from outside the loop.
4016 /// Note that it is not valid to call this method on a loop without a
4017 /// loop-invariant backedge-taken count (see
4018 /// hasLoopInvariantBackedgeTakenCount).
4020 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4021 return getBackedgeTakenInfo(L).getExact(this);
4024 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4025 /// return the least SCEV value that is known never to be less than the
4026 /// actual backedge taken count.
4027 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4028 return getBackedgeTakenInfo(L).getMax(this);
4031 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4032 /// onto the given Worklist.
4034 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4035 BasicBlock *Header = L->getHeader();
4037 // Push all Loop-header PHIs onto the Worklist stack.
4038 for (BasicBlock::iterator I = Header->begin();
4039 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4040 Worklist.push_back(PN);
4043 const ScalarEvolution::BackedgeTakenInfo &
4044 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4045 // Initially insert an invalid entry for this loop. If the insertion
4046 // succeeds, proceed to actually compute a backedge-taken count and
4047 // update the value. The temporary CouldNotCompute value tells SCEV
4048 // code elsewhere that it shouldn't attempt to request a new
4049 // backedge-taken count, which could result in infinite recursion.
4050 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4051 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4053 return Pair.first->second;
4055 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4056 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4057 // must be cleared in this scope.
4058 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4060 if (Result.getExact(this) != getCouldNotCompute()) {
4061 assert(isLoopInvariant(Result.getExact(this), L) &&
4062 isLoopInvariant(Result.getMax(this), L) &&
4063 "Computed backedge-taken count isn't loop invariant for loop!");
4064 ++NumTripCountsComputed;
4066 else if (Result.getMax(this) == getCouldNotCompute() &&
4067 isa<PHINode>(L->getHeader()->begin())) {
4068 // Only count loops that have phi nodes as not being computable.
4069 ++NumTripCountsNotComputed;
4072 // Now that we know more about the trip count for this loop, forget any
4073 // existing SCEV values for PHI nodes in this loop since they are only
4074 // conservative estimates made without the benefit of trip count
4075 // information. This is similar to the code in forgetLoop, except that
4076 // it handles SCEVUnknown PHI nodes specially.
4077 if (Result.hasAnyInfo()) {
4078 SmallVector<Instruction *, 16> Worklist;
4079 PushLoopPHIs(L, Worklist);
4081 SmallPtrSet<Instruction *, 8> Visited;
4082 while (!Worklist.empty()) {
4083 Instruction *I = Worklist.pop_back_val();
4084 if (!Visited.insert(I)) continue;
4086 ValueExprMapType::iterator It =
4087 ValueExprMap.find(static_cast<Value *>(I));
4088 if (It != ValueExprMap.end()) {
4089 const SCEV *Old = It->second;
4091 // SCEVUnknown for a PHI either means that it has an unrecognized
4092 // structure, or it's a PHI that's in the progress of being computed
4093 // by createNodeForPHI. In the former case, additional loop trip
4094 // count information isn't going to change anything. In the later
4095 // case, createNodeForPHI will perform the necessary updates on its
4096 // own when it gets to that point.
4097 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4098 forgetMemoizedResults(Old);
4099 ValueExprMap.erase(It);
4101 if (PHINode *PN = dyn_cast<PHINode>(I))
4102 ConstantEvolutionLoopExitValue.erase(PN);
4105 PushDefUseChildren(I, Worklist);
4109 // Re-lookup the insert position, since the call to
4110 // ComputeBackedgeTakenCount above could result in a
4111 // recusive call to getBackedgeTakenInfo (on a different
4112 // loop), which would invalidate the iterator computed
4114 return BackedgeTakenCounts.find(L)->second = Result;
4117 /// forgetLoop - This method should be called by the client when it has
4118 /// changed a loop in a way that may effect ScalarEvolution's ability to
4119 /// compute a trip count, or if the loop is deleted.
4120 void ScalarEvolution::forgetLoop(const Loop *L) {
4121 // Drop any stored trip count value.
4122 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4123 BackedgeTakenCounts.find(L);
4124 if (BTCPos != BackedgeTakenCounts.end()) {
4125 BTCPos->second.clear();
4126 BackedgeTakenCounts.erase(BTCPos);
4129 // Drop information about expressions based on loop-header PHIs.
4130 SmallVector<Instruction *, 16> Worklist;
4131 PushLoopPHIs(L, Worklist);
4133 SmallPtrSet<Instruction *, 8> Visited;
4134 while (!Worklist.empty()) {
4135 Instruction *I = Worklist.pop_back_val();
4136 if (!Visited.insert(I)) continue;
4138 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4139 if (It != ValueExprMap.end()) {
4140 forgetMemoizedResults(It->second);
4141 ValueExprMap.erase(It);
4142 if (PHINode *PN = dyn_cast<PHINode>(I))
4143 ConstantEvolutionLoopExitValue.erase(PN);
4146 PushDefUseChildren(I, Worklist);
4149 // Forget all contained loops too, to avoid dangling entries in the
4150 // ValuesAtScopes map.
4151 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4155 /// forgetValue - This method should be called by the client when it has
4156 /// changed a value in a way that may effect its value, or which may
4157 /// disconnect it from a def-use chain linking it to a loop.
4158 void ScalarEvolution::forgetValue(Value *V) {
4159 Instruction *I = dyn_cast<Instruction>(V);
4162 // Drop information about expressions based on loop-header PHIs.
4163 SmallVector<Instruction *, 16> Worklist;
4164 Worklist.push_back(I);
4166 SmallPtrSet<Instruction *, 8> Visited;
4167 while (!Worklist.empty()) {
4168 I = Worklist.pop_back_val();
4169 if (!Visited.insert(I)) continue;
4171 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4172 if (It != ValueExprMap.end()) {
4173 forgetMemoizedResults(It->second);
4174 ValueExprMap.erase(It);
4175 if (PHINode *PN = dyn_cast<PHINode>(I))
4176 ConstantEvolutionLoopExitValue.erase(PN);
4179 PushDefUseChildren(I, Worklist);
4183 /// getExact - Get the exact loop backedge taken count considering all loop
4184 /// exits. A computable result can only be return for loops with a single exit.
4185 /// Returning the minimum taken count among all exits is incorrect because one
4186 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4187 /// the limit of each loop test is never skipped. This is a valid assumption as
4188 /// long as the loop exits via that test. For precise results, it is the
4189 /// caller's responsibility to specify the relevant loop exit using
4190 /// getExact(ExitingBlock, SE).
4192 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4193 // If any exits were not computable, the loop is not computable.
4194 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4196 // We need exactly one computable exit.
4197 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4198 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4200 const SCEV *BECount = 0;
4201 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4202 ENT != 0; ENT = ENT->getNextExit()) {
4204 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4207 BECount = ENT->ExactNotTaken;
4208 else if (BECount != ENT->ExactNotTaken)
4209 return SE->getCouldNotCompute();
4211 assert(BECount && "Invalid not taken count for loop exit");
4215 /// getExact - Get the exact not taken count for this loop exit.
4217 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4218 ScalarEvolution *SE) const {
4219 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4220 ENT != 0; ENT = ENT->getNextExit()) {
4222 if (ENT->ExitingBlock == ExitingBlock)
4223 return ENT->ExactNotTaken;
4225 return SE->getCouldNotCompute();
4228 /// getMax - Get the max backedge taken count for the loop.
4230 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4231 return Max ? Max : SE->getCouldNotCompute();
4234 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4235 /// computable exit into a persistent ExitNotTakenInfo array.
4236 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4237 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4238 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4241 ExitNotTaken.setIncomplete();
4243 unsigned NumExits = ExitCounts.size();
4244 if (NumExits == 0) return;
4246 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4247 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4248 if (NumExits == 1) return;
4250 // Handle the rare case of multiple computable exits.
4251 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4253 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4254 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4255 PrevENT->setNextExit(ENT);
4256 ENT->ExitingBlock = ExitCounts[i].first;
4257 ENT->ExactNotTaken = ExitCounts[i].second;
4261 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4262 void ScalarEvolution::BackedgeTakenInfo::clear() {
4263 ExitNotTaken.ExitingBlock = 0;
4264 ExitNotTaken.ExactNotTaken = 0;
4265 delete[] ExitNotTaken.getNextExit();
4268 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4269 /// of the specified loop will execute.
4270 ScalarEvolution::BackedgeTakenInfo
4271 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4272 SmallVector<BasicBlock *, 8> ExitingBlocks;
4273 L->getExitingBlocks(ExitingBlocks);
4275 // Examine all exits and pick the most conservative values.
4276 const SCEV *MaxBECount = getCouldNotCompute();
4277 bool CouldComputeBECount = true;
4278 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4279 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4280 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4281 if (EL.Exact == getCouldNotCompute())
4282 // We couldn't compute an exact value for this exit, so
4283 // we won't be able to compute an exact value for the loop.
4284 CouldComputeBECount = false;
4286 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4288 if (MaxBECount == getCouldNotCompute())
4289 MaxBECount = EL.Max;
4290 else if (EL.Max != getCouldNotCompute()) {
4291 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4292 // skip some loop tests. Taking the max over the exits is sufficiently
4293 // conservative. TODO: We could do better taking into consideration
4294 // that (1) the loop has unit stride (2) the last loop test is
4295 // less-than/greater-than (3) any loop test is less-than/greater-than AND
4296 // falls-through some constant times less then the other tests.
4297 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4301 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4304 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4305 /// loop will execute if it exits via the specified block.
4306 ScalarEvolution::ExitLimit
4307 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4309 // Okay, we've chosen an exiting block. See what condition causes us to
4310 // exit at this block.
4312 // FIXME: we should be able to handle switch instructions (with a single exit)
4313 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4314 if (ExitBr == 0) return getCouldNotCompute();
4315 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4317 // At this point, we know we have a conditional branch that determines whether
4318 // the loop is exited. However, we don't know if the branch is executed each
4319 // time through the loop. If not, then the execution count of the branch will
4320 // not be equal to the trip count of the loop.
4322 // Currently we check for this by checking to see if the Exit branch goes to
4323 // the loop header. If so, we know it will always execute the same number of
4324 // times as the loop. We also handle the case where the exit block *is* the
4325 // loop header. This is common for un-rotated loops.
4327 // If both of those tests fail, walk up the unique predecessor chain to the
4328 // header, stopping if there is an edge that doesn't exit the loop. If the
4329 // header is reached, the execution count of the branch will be equal to the
4330 // trip count of the loop.
4332 // More extensive analysis could be done to handle more cases here.
4334 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4335 ExitBr->getSuccessor(1) != L->getHeader() &&
4336 ExitBr->getParent() != L->getHeader()) {
4337 // The simple checks failed, try climbing the unique predecessor chain
4338 // up to the header.
4340 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4341 BasicBlock *Pred = BB->getUniquePredecessor();
4343 return getCouldNotCompute();
4344 TerminatorInst *PredTerm = Pred->getTerminator();
4345 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4346 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4349 // If the predecessor has a successor that isn't BB and isn't
4350 // outside the loop, assume the worst.
4351 if (L->contains(PredSucc))
4352 return getCouldNotCompute();
4354 if (Pred == L->getHeader()) {
4361 return getCouldNotCompute();
4364 // Proceed to the next level to examine the exit condition expression.
4365 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4366 ExitBr->getSuccessor(0),
4367 ExitBr->getSuccessor(1));
4370 /// ComputeExitLimitFromCond - Compute the number of times the
4371 /// backedge of the specified loop will execute if its exit condition
4372 /// were a conditional branch of ExitCond, TBB, and FBB.
4373 ScalarEvolution::ExitLimit
4374 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4378 // Check if the controlling expression for this loop is an And or Or.
4379 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4380 if (BO->getOpcode() == Instruction::And) {
4381 // Recurse on the operands of the and.
4382 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4383 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4384 const SCEV *BECount = getCouldNotCompute();
4385 const SCEV *MaxBECount = getCouldNotCompute();
4386 if (L->contains(TBB)) {
4387 // Both conditions must be true for the loop to continue executing.
4388 // Choose the less conservative count.
4389 if (EL0.Exact == getCouldNotCompute() ||
4390 EL1.Exact == getCouldNotCompute())
4391 BECount = getCouldNotCompute();
4393 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4394 if (EL0.Max == getCouldNotCompute())
4395 MaxBECount = EL1.Max;
4396 else if (EL1.Max == getCouldNotCompute())
4397 MaxBECount = EL0.Max;
4399 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4401 // Both conditions must be true at the same time for the loop to exit.
4402 // For now, be conservative.
4403 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4404 if (EL0.Max == EL1.Max)
4405 MaxBECount = EL0.Max;
4406 if (EL0.Exact == EL1.Exact)
4407 BECount = EL0.Exact;
4410 return ExitLimit(BECount, MaxBECount);
4412 if (BO->getOpcode() == Instruction::Or) {
4413 // Recurse on the operands of the or.
4414 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4415 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4416 const SCEV *BECount = getCouldNotCompute();
4417 const SCEV *MaxBECount = getCouldNotCompute();
4418 if (L->contains(FBB)) {
4419 // Both conditions must be false for the loop to continue executing.
4420 // Choose the less conservative count.
4421 if (EL0.Exact == getCouldNotCompute() ||
4422 EL1.Exact == getCouldNotCompute())
4423 BECount = getCouldNotCompute();
4425 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4426 if (EL0.Max == getCouldNotCompute())
4427 MaxBECount = EL1.Max;
4428 else if (EL1.Max == getCouldNotCompute())
4429 MaxBECount = EL0.Max;
4431 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4433 // Both conditions must be false at the same time for the loop to exit.
4434 // For now, be conservative.
4435 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4436 if (EL0.Max == EL1.Max)
4437 MaxBECount = EL0.Max;
4438 if (EL0.Exact == EL1.Exact)
4439 BECount = EL0.Exact;
4442 return ExitLimit(BECount, MaxBECount);
4446 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4447 // Proceed to the next level to examine the icmp.
4448 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4449 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB);
4451 // Check for a constant condition. These are normally stripped out by
4452 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4453 // preserve the CFG and is temporarily leaving constant conditions
4455 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4456 if (L->contains(FBB) == !CI->getZExtValue())
4457 // The backedge is always taken.
4458 return getCouldNotCompute();
4460 // The backedge is never taken.
4461 return getConstant(CI->getType(), 0);
4464 // If it's not an integer or pointer comparison then compute it the hard way.
4465 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4468 /// ComputeExitLimitFromICmp - Compute the number of times the
4469 /// backedge of the specified loop will execute if its exit condition
4470 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4471 ScalarEvolution::ExitLimit
4472 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4477 // If the condition was exit on true, convert the condition to exit on false
4478 ICmpInst::Predicate Cond;
4479 if (!L->contains(FBB))
4480 Cond = ExitCond->getPredicate();
4482 Cond = ExitCond->getInversePredicate();
4484 // Handle common loops like: for (X = "string"; *X; ++X)
4485 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4486 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4488 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4489 if (ItCnt.hasAnyInfo())
4493 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4494 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4496 // Try to evaluate any dependencies out of the loop.
4497 LHS = getSCEVAtScope(LHS, L);
4498 RHS = getSCEVAtScope(RHS, L);
4500 // At this point, we would like to compute how many iterations of the
4501 // loop the predicate will return true for these inputs.
4502 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4503 // If there is a loop-invariant, force it into the RHS.
4504 std::swap(LHS, RHS);
4505 Cond = ICmpInst::getSwappedPredicate(Cond);
4508 // Simplify the operands before analyzing them.
4509 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4511 // If we have a comparison of a chrec against a constant, try to use value
4512 // ranges to answer this query.
4513 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4514 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4515 if (AddRec->getLoop() == L) {
4516 // Form the constant range.
4517 ConstantRange CompRange(
4518 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4520 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4521 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4525 case ICmpInst::ICMP_NE: { // while (X != Y)
4526 // Convert to: while (X-Y != 0)
4527 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4528 if (EL.hasAnyInfo()) return EL;
4531 case ICmpInst::ICMP_EQ: { // while (X == Y)
4532 // Convert to: while (X-Y == 0)
4533 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4534 if (EL.hasAnyInfo()) return EL;
4537 case ICmpInst::ICMP_SLT: {
4538 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true);
4539 if (EL.hasAnyInfo()) return EL;
4542 case ICmpInst::ICMP_SGT: {
4543 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4544 getNotSCEV(RHS), L, true);
4545 if (EL.hasAnyInfo()) return EL;
4548 case ICmpInst::ICMP_ULT: {
4549 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false);
4550 if (EL.hasAnyInfo()) return EL;
4553 case ICmpInst::ICMP_UGT: {
4554 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4555 getNotSCEV(RHS), L, false);
4556 if (EL.hasAnyInfo()) return EL;
4561 dbgs() << "ComputeBackedgeTakenCount ";
4562 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4563 dbgs() << "[unsigned] ";
4564 dbgs() << *LHS << " "
4565 << Instruction::getOpcodeName(Instruction::ICmp)
4566 << " " << *RHS << "\n";
4570 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4573 static ConstantInt *
4574 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4575 ScalarEvolution &SE) {
4576 const SCEV *InVal = SE.getConstant(C);
4577 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4578 assert(isa<SCEVConstant>(Val) &&
4579 "Evaluation of SCEV at constant didn't fold correctly?");
4580 return cast<SCEVConstant>(Val)->getValue();
4583 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4584 /// 'icmp op load X, cst', try to see if we can compute the backedge
4585 /// execution count.
4586 ScalarEvolution::ExitLimit
4587 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4591 ICmpInst::Predicate predicate) {
4593 if (LI->isVolatile()) return getCouldNotCompute();
4595 // Check to see if the loaded pointer is a getelementptr of a global.
4596 // TODO: Use SCEV instead of manually grubbing with GEPs.
4597 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4598 if (!GEP) return getCouldNotCompute();
4600 // Make sure that it is really a constant global we are gepping, with an
4601 // initializer, and make sure the first IDX is really 0.
4602 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4603 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4604 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4605 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4606 return getCouldNotCompute();
4608 // Okay, we allow one non-constant index into the GEP instruction.
4610 std::vector<Constant*> Indexes;
4611 unsigned VarIdxNum = 0;
4612 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4613 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4614 Indexes.push_back(CI);
4615 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4616 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4617 VarIdx = GEP->getOperand(i);
4619 Indexes.push_back(0);
4622 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4624 return getCouldNotCompute();
4626 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4627 // Check to see if X is a loop variant variable value now.
4628 const SCEV *Idx = getSCEV(VarIdx);
4629 Idx = getSCEVAtScope(Idx, L);
4631 // We can only recognize very limited forms of loop index expressions, in
4632 // particular, only affine AddRec's like {C1,+,C2}.
4633 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4634 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4635 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4636 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4637 return getCouldNotCompute();
4639 unsigned MaxSteps = MaxBruteForceIterations;
4640 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4641 ConstantInt *ItCst = ConstantInt::get(
4642 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4643 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4645 // Form the GEP offset.
4646 Indexes[VarIdxNum] = Val;
4648 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4650 if (Result == 0) break; // Cannot compute!
4652 // Evaluate the condition for this iteration.
4653 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4654 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4655 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4657 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4658 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4661 ++NumArrayLenItCounts;
4662 return getConstant(ItCst); // Found terminating iteration!
4665 return getCouldNotCompute();
4669 /// CanConstantFold - Return true if we can constant fold an instruction of the
4670 /// specified type, assuming that all operands were constants.
4671 static bool CanConstantFold(const Instruction *I) {
4672 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4673 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4677 if (const CallInst *CI = dyn_cast<CallInst>(I))
4678 if (const Function *F = CI->getCalledFunction())
4679 return canConstantFoldCallTo(F);
4683 /// Determine whether this instruction can constant evolve within this loop
4684 /// assuming its operands can all constant evolve.
4685 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4686 // An instruction outside of the loop can't be derived from a loop PHI.
4687 if (!L->contains(I)) return false;
4689 if (isa<PHINode>(I)) {
4690 if (L->getHeader() == I->getParent())
4693 // We don't currently keep track of the control flow needed to evaluate
4694 // PHIs, so we cannot handle PHIs inside of loops.
4698 // If we won't be able to constant fold this expression even if the operands
4699 // are constants, bail early.
4700 return CanConstantFold(I);
4703 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4704 /// recursing through each instruction operand until reaching a loop header phi.
4706 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4707 DenseMap<Instruction *, PHINode *> &PHIMap) {
4709 // Otherwise, we can evaluate this instruction if all of its operands are
4710 // constant or derived from a PHI node themselves.
4712 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4713 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4715 if (isa<Constant>(*OpI)) continue;
4717 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4718 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4720 PHINode *P = dyn_cast<PHINode>(OpInst);
4722 // If this operand is already visited, reuse the prior result.
4723 // We may have P != PHI if this is the deepest point at which the
4724 // inconsistent paths meet.
4725 P = PHIMap.lookup(OpInst);
4727 // Recurse and memoize the results, whether a phi is found or not.
4728 // This recursive call invalidates pointers into PHIMap.
4729 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4732 if (P == 0) return 0; // Not evolving from PHI
4733 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4736 // This is a expression evolving from a constant PHI!
4740 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4741 /// in the loop that V is derived from. We allow arbitrary operations along the
4742 /// way, but the operands of an operation must either be constants or a value
4743 /// derived from a constant PHI. If this expression does not fit with these
4744 /// constraints, return null.
4745 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4746 Instruction *I = dyn_cast<Instruction>(V);
4747 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4749 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4753 // Record non-constant instructions contained by the loop.
4754 DenseMap<Instruction *, PHINode *> PHIMap;
4755 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4758 /// EvaluateExpression - Given an expression that passes the
4759 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4760 /// in the loop has the value PHIVal. If we can't fold this expression for some
4761 /// reason, return null.
4762 static Constant *EvaluateExpression(Value *V, const Loop *L,
4763 DenseMap<Instruction *, Constant *> &Vals,
4764 const TargetData *TD,
4765 const TargetLibraryInfo *TLI) {
4766 // Convenient constant check, but redundant for recursive calls.
4767 if (Constant *C = dyn_cast<Constant>(V)) return C;
4768 Instruction *I = dyn_cast<Instruction>(V);
4771 if (Constant *C = Vals.lookup(I)) return C;
4773 // An instruction inside the loop depends on a value outside the loop that we
4774 // weren't given a mapping for, or a value such as a call inside the loop.
4775 if (!canConstantEvolve(I, L)) return 0;
4777 // An unmapped PHI can be due to a branch or another loop inside this loop,
4778 // or due to this not being the initial iteration through a loop where we
4779 // couldn't compute the evolution of this particular PHI last time.
4780 if (isa<PHINode>(I)) return 0;
4782 std::vector<Constant*> Operands(I->getNumOperands());
4784 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4785 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4787 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4788 if (!Operands[i]) return 0;
4791 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
4797 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4798 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4799 Operands[1], TD, TLI);
4800 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4801 if (!LI->isVolatile())
4802 return ConstantFoldLoadFromConstPtr(Operands[0], TD);
4804 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
4808 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4809 /// in the header of its containing loop, we know the loop executes a
4810 /// constant number of times, and the PHI node is just a recurrence
4811 /// involving constants, fold it.
4813 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4816 DenseMap<PHINode*, Constant*>::const_iterator I =
4817 ConstantEvolutionLoopExitValue.find(PN);
4818 if (I != ConstantEvolutionLoopExitValue.end())
4821 if (BEs.ugt(MaxBruteForceIterations))
4822 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4824 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4826 DenseMap<Instruction *, Constant *> CurrentIterVals;
4827 BasicBlock *Header = L->getHeader();
4828 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4830 // Since the loop is canonicalized, the PHI node must have two entries. One
4831 // entry must be a constant (coming in from outside of the loop), and the
4832 // second must be derived from the same PHI.
4833 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4835 for (BasicBlock::iterator I = Header->begin();
4836 (PHI = dyn_cast<PHINode>(I)); ++I) {
4837 Constant *StartCST =
4838 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4839 if (StartCST == 0) continue;
4840 CurrentIterVals[PHI] = StartCST;
4842 if (!CurrentIterVals.count(PN))
4845 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4847 // Execute the loop symbolically to determine the exit value.
4848 if (BEs.getActiveBits() >= 32)
4849 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4851 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4852 unsigned IterationNum = 0;
4853 for (; ; ++IterationNum) {
4854 if (IterationNum == NumIterations)
4855 return RetVal = CurrentIterVals[PN]; // Got exit value!
4857 // Compute the value of the PHIs for the next iteration.
4858 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
4859 DenseMap<Instruction *, Constant *> NextIterVals;
4860 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
4863 return 0; // Couldn't evaluate!
4864 NextIterVals[PN] = NextPHI;
4866 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
4868 // Also evaluate the other PHI nodes. However, we don't get to stop if we
4869 // cease to be able to evaluate one of them or if they stop evolving,
4870 // because that doesn't necessarily prevent us from computing PN.
4871 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
4872 for (DenseMap<Instruction *, Constant *>::const_iterator
4873 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4874 PHINode *PHI = dyn_cast<PHINode>(I->first);
4875 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
4876 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
4878 // We use two distinct loops because EvaluateExpression may invalidate any
4879 // iterators into CurrentIterVals.
4880 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
4881 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
4882 PHINode *PHI = I->first;
4883 Constant *&NextPHI = NextIterVals[PHI];
4884 if (!NextPHI) { // Not already computed.
4885 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4886 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4888 if (NextPHI != I->second)
4889 StoppedEvolving = false;
4892 // If all entries in CurrentIterVals == NextIterVals then we can stop
4893 // iterating, the loop can't continue to change.
4894 if (StoppedEvolving)
4895 return RetVal = CurrentIterVals[PN];
4897 CurrentIterVals.swap(NextIterVals);
4901 /// ComputeExitCountExhaustively - If the loop is known to execute a
4902 /// constant number of times (the condition evolves only from constants),
4903 /// try to evaluate a few iterations of the loop until we get the exit
4904 /// condition gets a value of ExitWhen (true or false). If we cannot
4905 /// evaluate the trip count of the loop, return getCouldNotCompute().
4906 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4909 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4910 if (PN == 0) return getCouldNotCompute();
4912 // If the loop is canonicalized, the PHI will have exactly two entries.
4913 // That's the only form we support here.
4914 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4916 DenseMap<Instruction *, Constant *> CurrentIterVals;
4917 BasicBlock *Header = L->getHeader();
4918 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4920 // One entry must be a constant (coming in from outside of the loop), and the
4921 // second must be derived from the same PHI.
4922 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4924 for (BasicBlock::iterator I = Header->begin();
4925 (PHI = dyn_cast<PHINode>(I)); ++I) {
4926 Constant *StartCST =
4927 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4928 if (StartCST == 0) continue;
4929 CurrentIterVals[PHI] = StartCST;
4931 if (!CurrentIterVals.count(PN))
4932 return getCouldNotCompute();
4934 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4935 // the loop symbolically to determine when the condition gets a value of
4938 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4939 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
4940 ConstantInt *CondVal =
4941 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
4944 // Couldn't symbolically evaluate.
4945 if (!CondVal) return getCouldNotCompute();
4947 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4948 ++NumBruteForceTripCountsComputed;
4949 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4952 // Update all the PHI nodes for the next iteration.
4953 DenseMap<Instruction *, Constant *> NextIterVals;
4955 // Create a list of which PHIs we need to compute. We want to do this before
4956 // calling EvaluateExpression on them because that may invalidate iterators
4957 // into CurrentIterVals.
4958 SmallVector<PHINode *, 8> PHIsToCompute;
4959 for (DenseMap<Instruction *, Constant *>::const_iterator
4960 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4961 PHINode *PHI = dyn_cast<PHINode>(I->first);
4962 if (!PHI || PHI->getParent() != Header) continue;
4963 PHIsToCompute.push_back(PHI);
4965 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
4966 E = PHIsToCompute.end(); I != E; ++I) {
4968 Constant *&NextPHI = NextIterVals[PHI];
4969 if (NextPHI) continue; // Already computed!
4971 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4972 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4974 CurrentIterVals.swap(NextIterVals);
4977 // Too many iterations were needed to evaluate.
4978 return getCouldNotCompute();
4981 /// getSCEVAtScope - Return a SCEV expression for the specified value
4982 /// at the specified scope in the program. The L value specifies a loop
4983 /// nest to evaluate the expression at, where null is the top-level or a
4984 /// specified loop is immediately inside of the loop.
4986 /// This method can be used to compute the exit value for a variable defined
4987 /// in a loop by querying what the value will hold in the parent loop.
4989 /// In the case that a relevant loop exit value cannot be computed, the
4990 /// original value V is returned.
4991 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4992 // Check to see if we've folded this expression at this loop before.
4993 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4994 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4995 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4997 return Pair.first->second ? Pair.first->second : V;
4999 // Otherwise compute it.
5000 const SCEV *C = computeSCEVAtScope(V, L);
5001 ValuesAtScopes[V][L] = C;
5005 /// This builds up a Constant using the ConstantExpr interface. That way, we
5006 /// will return Constants for objects which aren't represented by a
5007 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5008 /// Returns NULL if the SCEV isn't representable as a Constant.
5009 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5010 switch (V->getSCEVType()) {
5011 default: // TODO: smax, umax.
5012 case scCouldNotCompute:
5016 return cast<SCEVConstant>(V)->getValue();
5018 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5019 case scSignExtend: {
5020 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5021 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5022 return ConstantExpr::getSExt(CastOp, SS->getType());
5025 case scZeroExtend: {
5026 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5027 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5028 return ConstantExpr::getZExt(CastOp, SZ->getType());
5032 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5033 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5034 return ConstantExpr::getTrunc(CastOp, ST->getType());
5038 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5039 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5040 if (C->getType()->isPointerTy())
5041 C = ConstantExpr::getBitCast(C, Type::getInt8PtrTy(C->getContext()));
5042 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5043 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5047 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5049 // The offsets have been converted to bytes. We can add bytes to an
5050 // i8* by GEP with the byte count in the first index.
5051 C = ConstantExpr::getBitCast(C,Type::getInt8PtrTy(C->getContext()));
5054 // Don't bother trying to sum two pointers. We probably can't
5055 // statically compute a load that results from it anyway.
5056 if (C2->getType()->isPointerTy())
5059 if (C->getType()->isPointerTy()) {
5060 if (cast<PointerType>(C->getType())->getElementType()->isStructTy())
5061 C2 = ConstantExpr::getIntegerCast(
5062 C2, Type::getInt32Ty(C->getContext()), true);
5063 C = ConstantExpr::getGetElementPtr(C, C2);
5065 C = ConstantExpr::getAdd(C, C2);
5072 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5073 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5074 // Don't bother with pointers at all.
5075 if (C->getType()->isPointerTy()) return 0;
5076 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5077 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5078 if (!C2 || C2->getType()->isPointerTy()) return 0;
5079 C = ConstantExpr::getMul(C, C2);
5086 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5087 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5088 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5089 if (LHS->getType() == RHS->getType())
5090 return ConstantExpr::getUDiv(LHS, RHS);
5097 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5098 if (isa<SCEVConstant>(V)) return V;
5100 // If this instruction is evolved from a constant-evolving PHI, compute the
5101 // exit value from the loop without using SCEVs.
5102 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5103 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5104 const Loop *LI = (*this->LI)[I->getParent()];
5105 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5106 if (PHINode *PN = dyn_cast<PHINode>(I))
5107 if (PN->getParent() == LI->getHeader()) {
5108 // Okay, there is no closed form solution for the PHI node. Check
5109 // to see if the loop that contains it has a known backedge-taken
5110 // count. If so, we may be able to force computation of the exit
5112 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5113 if (const SCEVConstant *BTCC =
5114 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5115 // Okay, we know how many times the containing loop executes. If
5116 // this is a constant evolving PHI node, get the final value at
5117 // the specified iteration number.
5118 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5119 BTCC->getValue()->getValue(),
5121 if (RV) return getSCEV(RV);
5125 // Okay, this is an expression that we cannot symbolically evaluate
5126 // into a SCEV. Check to see if it's possible to symbolically evaluate
5127 // the arguments into constants, and if so, try to constant propagate the
5128 // result. This is particularly useful for computing loop exit values.
5129 if (CanConstantFold(I)) {
5130 SmallVector<Constant *, 4> Operands;
5131 bool MadeImprovement = false;
5132 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5133 Value *Op = I->getOperand(i);
5134 if (Constant *C = dyn_cast<Constant>(Op)) {
5135 Operands.push_back(C);
5139 // If any of the operands is non-constant and if they are
5140 // non-integer and non-pointer, don't even try to analyze them
5141 // with scev techniques.
5142 if (!isSCEVable(Op->getType()))
5145 const SCEV *OrigV = getSCEV(Op);
5146 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5147 MadeImprovement |= OrigV != OpV;
5149 Constant *C = BuildConstantFromSCEV(OpV);
5151 if (C->getType() != Op->getType())
5152 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5156 Operands.push_back(C);
5159 // Check to see if getSCEVAtScope actually made an improvement.
5160 if (MadeImprovement) {
5162 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5163 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5164 Operands[0], Operands[1], TD,
5166 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5167 if (!LI->isVolatile())
5168 C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
5170 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5178 // This is some other type of SCEVUnknown, just return it.
5182 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5183 // Avoid performing the look-up in the common case where the specified
5184 // expression has no loop-variant portions.
5185 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5186 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5187 if (OpAtScope != Comm->getOperand(i)) {
5188 // Okay, at least one of these operands is loop variant but might be
5189 // foldable. Build a new instance of the folded commutative expression.
5190 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5191 Comm->op_begin()+i);
5192 NewOps.push_back(OpAtScope);
5194 for (++i; i != e; ++i) {
5195 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5196 NewOps.push_back(OpAtScope);
5198 if (isa<SCEVAddExpr>(Comm))
5199 return getAddExpr(NewOps);
5200 if (isa<SCEVMulExpr>(Comm))
5201 return getMulExpr(NewOps);
5202 if (isa<SCEVSMaxExpr>(Comm))
5203 return getSMaxExpr(NewOps);
5204 if (isa<SCEVUMaxExpr>(Comm))
5205 return getUMaxExpr(NewOps);
5206 llvm_unreachable("Unknown commutative SCEV type!");
5209 // If we got here, all operands are loop invariant.
5213 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5214 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5215 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5216 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5217 return Div; // must be loop invariant
5218 return getUDivExpr(LHS, RHS);
5221 // If this is a loop recurrence for a loop that does not contain L, then we
5222 // are dealing with the final value computed by the loop.
5223 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5224 // First, attempt to evaluate each operand.
5225 // Avoid performing the look-up in the common case where the specified
5226 // expression has no loop-variant portions.
5227 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5228 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5229 if (OpAtScope == AddRec->getOperand(i))
5232 // Okay, at least one of these operands is loop variant but might be
5233 // foldable. Build a new instance of the folded commutative expression.
5234 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5235 AddRec->op_begin()+i);
5236 NewOps.push_back(OpAtScope);
5237 for (++i; i != e; ++i)
5238 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5240 const SCEV *FoldedRec =
5241 getAddRecExpr(NewOps, AddRec->getLoop(),
5242 AddRec->getNoWrapFlags(SCEV::FlagNW));
5243 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5244 // The addrec may be folded to a nonrecurrence, for example, if the
5245 // induction variable is multiplied by zero after constant folding. Go
5246 // ahead and return the folded value.
5252 // If the scope is outside the addrec's loop, evaluate it by using the
5253 // loop exit value of the addrec.
5254 if (!AddRec->getLoop()->contains(L)) {
5255 // To evaluate this recurrence, we need to know how many times the AddRec
5256 // loop iterates. Compute this now.
5257 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5258 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5260 // Then, evaluate the AddRec.
5261 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5267 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5268 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5269 if (Op == Cast->getOperand())
5270 return Cast; // must be loop invariant
5271 return getZeroExtendExpr(Op, Cast->getType());
5274 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5275 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5276 if (Op == Cast->getOperand())
5277 return Cast; // must be loop invariant
5278 return getSignExtendExpr(Op, Cast->getType());
5281 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5282 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5283 if (Op == Cast->getOperand())
5284 return Cast; // must be loop invariant
5285 return getTruncateExpr(Op, Cast->getType());
5288 llvm_unreachable("Unknown SCEV type!");
5291 /// getSCEVAtScope - This is a convenience function which does
5292 /// getSCEVAtScope(getSCEV(V), L).
5293 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5294 return getSCEVAtScope(getSCEV(V), L);
5297 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5298 /// following equation:
5300 /// A * X = B (mod N)
5302 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5303 /// A and B isn't important.
5305 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5306 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5307 ScalarEvolution &SE) {
5308 uint32_t BW = A.getBitWidth();
5309 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5310 assert(A != 0 && "A must be non-zero.");
5314 // The gcd of A and N may have only one prime factor: 2. The number of
5315 // trailing zeros in A is its multiplicity
5316 uint32_t Mult2 = A.countTrailingZeros();
5319 // 2. Check if B is divisible by D.
5321 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5322 // is not less than multiplicity of this prime factor for D.
5323 if (B.countTrailingZeros() < Mult2)
5324 return SE.getCouldNotCompute();
5326 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5329 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5330 // bit width during computations.
5331 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5332 APInt Mod(BW + 1, 0);
5333 Mod.setBit(BW - Mult2); // Mod = N / D
5334 APInt I = AD.multiplicativeInverse(Mod);
5336 // 4. Compute the minimum unsigned root of the equation:
5337 // I * (B / D) mod (N / D)
5338 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5340 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5342 return SE.getConstant(Result.trunc(BW));
5345 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5346 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5347 /// might be the same) or two SCEVCouldNotCompute objects.
5349 static std::pair<const SCEV *,const SCEV *>
5350 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5351 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5352 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5353 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5354 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5356 // We currently can only solve this if the coefficients are constants.
5357 if (!LC || !MC || !NC) {
5358 const SCEV *CNC = SE.getCouldNotCompute();
5359 return std::make_pair(CNC, CNC);
5362 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5363 const APInt &L = LC->getValue()->getValue();
5364 const APInt &M = MC->getValue()->getValue();
5365 const APInt &N = NC->getValue()->getValue();
5366 APInt Two(BitWidth, 2);
5367 APInt Four(BitWidth, 4);
5370 using namespace APIntOps;
5372 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5373 // The B coefficient is M-N/2
5377 // The A coefficient is N/2
5378 APInt A(N.sdiv(Two));
5380 // Compute the B^2-4ac term.
5383 SqrtTerm -= Four * (A * C);
5385 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5386 // integer value or else APInt::sqrt() will assert.
5387 APInt SqrtVal(SqrtTerm.sqrt());
5389 // Compute the two solutions for the quadratic formula.
5390 // The divisions must be performed as signed divisions.
5393 if (TwoA.isMinValue()) {
5394 const SCEV *CNC = SE.getCouldNotCompute();
5395 return std::make_pair(CNC, CNC);
5398 LLVMContext &Context = SE.getContext();
5400 ConstantInt *Solution1 =
5401 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5402 ConstantInt *Solution2 =
5403 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5405 return std::make_pair(SE.getConstant(Solution1),
5406 SE.getConstant(Solution2));
5407 } // end APIntOps namespace
5410 /// HowFarToZero - Return the number of times a backedge comparing the specified
5411 /// value to zero will execute. If not computable, return CouldNotCompute.
5413 /// This is only used for loops with a "x != y" exit test. The exit condition is
5414 /// now expressed as a single expression, V = x-y. So the exit test is
5415 /// effectively V != 0. We know and take advantage of the fact that this
5416 /// expression only being used in a comparison by zero context.
5417 ScalarEvolution::ExitLimit
5418 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
5419 // If the value is a constant
5420 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5421 // If the value is already zero, the branch will execute zero times.
5422 if (C->getValue()->isZero()) return C;
5423 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5426 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5427 if (!AddRec || AddRec->getLoop() != L)
5428 return getCouldNotCompute();
5430 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5431 // the quadratic equation to solve it.
5432 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5433 std::pair<const SCEV *,const SCEV *> Roots =
5434 SolveQuadraticEquation(AddRec, *this);
5435 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5436 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5439 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5440 << " sol#2: " << *R2 << "\n";
5442 // Pick the smallest positive root value.
5443 if (ConstantInt *CB =
5444 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5447 if (CB->getZExtValue() == false)
5448 std::swap(R1, R2); // R1 is the minimum root now.
5450 // We can only use this value if the chrec ends up with an exact zero
5451 // value at this index. When solving for "X*X != 5", for example, we
5452 // should not accept a root of 2.
5453 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5455 return R1; // We found a quadratic root!
5458 return getCouldNotCompute();
5461 // Otherwise we can only handle this if it is affine.
5462 if (!AddRec->isAffine())
5463 return getCouldNotCompute();
5465 // If this is an affine expression, the execution count of this branch is
5466 // the minimum unsigned root of the following equation:
5468 // Start + Step*N = 0 (mod 2^BW)
5472 // Step*N = -Start (mod 2^BW)
5474 // where BW is the common bit width of Start and Step.
5476 // Get the initial value for the loop.
5477 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5478 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5480 // For now we handle only constant steps.
5482 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5483 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5484 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5485 // We have not yet seen any such cases.
5486 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5488 return getCouldNotCompute();
5490 // For positive steps (counting up until unsigned overflow):
5491 // N = -Start/Step (as unsigned)
5492 // For negative steps (counting down to zero):
5494 // First compute the unsigned distance from zero in the direction of Step.
5495 bool CountDown = StepC->getValue()->getValue().isNegative();
5496 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5498 // Handle unitary steps, which cannot wraparound.
5499 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5500 // N = Distance (as unsigned)
5501 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5502 ConstantRange CR = getUnsignedRange(Start);
5503 const SCEV *MaxBECount;
5504 if (!CountDown && CR.getUnsignedMin().isMinValue())
5505 // When counting up, the worst starting value is 1, not 0.
5506 MaxBECount = CR.getUnsignedMax().isMinValue()
5507 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5508 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5510 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5511 : -CR.getUnsignedMin());
5512 return ExitLimit(Distance, MaxBECount);
5515 // If the recurrence is known not to wraparound, unsigned divide computes the
5516 // back edge count. We know that the value will either become zero (and thus
5517 // the loop terminates), that the loop will terminate through some other exit
5518 // condition first, or that the loop has undefined behavior. This means
5519 // we can't "miss" the exit value, even with nonunit stride.
5521 // FIXME: Prove that loops always exhibits *acceptable* undefined
5522 // behavior. Loops must exhibit defined behavior until a wrapped value is
5523 // actually used. So the trip count computed by udiv could be smaller than the
5524 // number of well-defined iterations.
5525 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5526 // FIXME: We really want an "isexact" bit for udiv.
5527 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5529 // Then, try to solve the above equation provided that Start is constant.
5530 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5531 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5532 -StartC->getValue()->getValue(),
5534 return getCouldNotCompute();
5537 /// HowFarToNonZero - Return the number of times a backedge checking the
5538 /// specified value for nonzero will execute. If not computable, return
5540 ScalarEvolution::ExitLimit
5541 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5542 // Loops that look like: while (X == 0) are very strange indeed. We don't
5543 // handle them yet except for the trivial case. This could be expanded in the
5544 // future as needed.
5546 // If the value is a constant, check to see if it is known to be non-zero
5547 // already. If so, the backedge will execute zero times.
5548 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5549 if (!C->getValue()->isNullValue())
5550 return getConstant(C->getType(), 0);
5551 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5554 // We could implement others, but I really doubt anyone writes loops like
5555 // this, and if they did, they would already be constant folded.
5556 return getCouldNotCompute();
5559 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5560 /// (which may not be an immediate predecessor) which has exactly one
5561 /// successor from which BB is reachable, or null if no such block is
5564 std::pair<BasicBlock *, BasicBlock *>
5565 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5566 // If the block has a unique predecessor, then there is no path from the
5567 // predecessor to the block that does not go through the direct edge
5568 // from the predecessor to the block.
5569 if (BasicBlock *Pred = BB->getSinglePredecessor())
5570 return std::make_pair(Pred, BB);
5572 // A loop's header is defined to be a block that dominates the loop.
5573 // If the header has a unique predecessor outside the loop, it must be
5574 // a block that has exactly one successor that can reach the loop.
5575 if (Loop *L = LI->getLoopFor(BB))
5576 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5578 return std::pair<BasicBlock *, BasicBlock *>();
5581 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5582 /// testing whether two expressions are equal, however for the purposes of
5583 /// looking for a condition guarding a loop, it can be useful to be a little
5584 /// more general, since a front-end may have replicated the controlling
5587 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5588 // Quick check to see if they are the same SCEV.
5589 if (A == B) return true;
5591 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5592 // two different instructions with the same value. Check for this case.
5593 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5594 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5595 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5596 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5597 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5600 // Otherwise assume they may have a different value.
5604 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5605 /// predicate Pred. Return true iff any changes were made.
5607 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5608 const SCEV *&LHS, const SCEV *&RHS,
5610 bool Changed = false;
5612 // If we hit the max recursion limit bail out.
5616 // Canonicalize a constant to the right side.
5617 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5618 // Check for both operands constant.
5619 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5620 if (ConstantExpr::getICmp(Pred,
5622 RHSC->getValue())->isNullValue())
5623 goto trivially_false;
5625 goto trivially_true;
5627 // Otherwise swap the operands to put the constant on the right.
5628 std::swap(LHS, RHS);
5629 Pred = ICmpInst::getSwappedPredicate(Pred);
5633 // If we're comparing an addrec with a value which is loop-invariant in the
5634 // addrec's loop, put the addrec on the left. Also make a dominance check,
5635 // as both operands could be addrecs loop-invariant in each other's loop.
5636 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5637 const Loop *L = AR->getLoop();
5638 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5639 std::swap(LHS, RHS);
5640 Pred = ICmpInst::getSwappedPredicate(Pred);
5645 // If there's a constant operand, canonicalize comparisons with boundary
5646 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5647 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5648 const APInt &RA = RC->getValue()->getValue();
5650 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5651 case ICmpInst::ICMP_EQ:
5652 case ICmpInst::ICMP_NE:
5653 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5655 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5656 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5657 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5658 ME->getOperand(0)->isAllOnesValue()) {
5659 RHS = AE->getOperand(1);
5660 LHS = ME->getOperand(1);
5664 case ICmpInst::ICMP_UGE:
5665 if ((RA - 1).isMinValue()) {
5666 Pred = ICmpInst::ICMP_NE;
5667 RHS = getConstant(RA - 1);
5671 if (RA.isMaxValue()) {
5672 Pred = ICmpInst::ICMP_EQ;
5676 if (RA.isMinValue()) goto trivially_true;
5678 Pred = ICmpInst::ICMP_UGT;
5679 RHS = getConstant(RA - 1);
5682 case ICmpInst::ICMP_ULE:
5683 if ((RA + 1).isMaxValue()) {
5684 Pred = ICmpInst::ICMP_NE;
5685 RHS = getConstant(RA + 1);
5689 if (RA.isMinValue()) {
5690 Pred = ICmpInst::ICMP_EQ;
5694 if (RA.isMaxValue()) goto trivially_true;
5696 Pred = ICmpInst::ICMP_ULT;
5697 RHS = getConstant(RA + 1);
5700 case ICmpInst::ICMP_SGE:
5701 if ((RA - 1).isMinSignedValue()) {
5702 Pred = ICmpInst::ICMP_NE;
5703 RHS = getConstant(RA - 1);
5707 if (RA.isMaxSignedValue()) {
5708 Pred = ICmpInst::ICMP_EQ;
5712 if (RA.isMinSignedValue()) goto trivially_true;
5714 Pred = ICmpInst::ICMP_SGT;
5715 RHS = getConstant(RA - 1);
5718 case ICmpInst::ICMP_SLE:
5719 if ((RA + 1).isMaxSignedValue()) {
5720 Pred = ICmpInst::ICMP_NE;
5721 RHS = getConstant(RA + 1);
5725 if (RA.isMinSignedValue()) {
5726 Pred = ICmpInst::ICMP_EQ;
5730 if (RA.isMaxSignedValue()) goto trivially_true;
5732 Pred = ICmpInst::ICMP_SLT;
5733 RHS = getConstant(RA + 1);
5736 case ICmpInst::ICMP_UGT:
5737 if (RA.isMinValue()) {
5738 Pred = ICmpInst::ICMP_NE;
5742 if ((RA + 1).isMaxValue()) {
5743 Pred = ICmpInst::ICMP_EQ;
5744 RHS = getConstant(RA + 1);
5748 if (RA.isMaxValue()) goto trivially_false;
5750 case ICmpInst::ICMP_ULT:
5751 if (RA.isMaxValue()) {
5752 Pred = ICmpInst::ICMP_NE;
5756 if ((RA - 1).isMinValue()) {
5757 Pred = ICmpInst::ICMP_EQ;
5758 RHS = getConstant(RA - 1);
5762 if (RA.isMinValue()) goto trivially_false;
5764 case ICmpInst::ICMP_SGT:
5765 if (RA.isMinSignedValue()) {
5766 Pred = ICmpInst::ICMP_NE;
5770 if ((RA + 1).isMaxSignedValue()) {
5771 Pred = ICmpInst::ICMP_EQ;
5772 RHS = getConstant(RA + 1);
5776 if (RA.isMaxSignedValue()) goto trivially_false;
5778 case ICmpInst::ICMP_SLT:
5779 if (RA.isMaxSignedValue()) {
5780 Pred = ICmpInst::ICMP_NE;
5784 if ((RA - 1).isMinSignedValue()) {
5785 Pred = ICmpInst::ICMP_EQ;
5786 RHS = getConstant(RA - 1);
5790 if (RA.isMinSignedValue()) goto trivially_false;
5795 // Check for obvious equality.
5796 if (HasSameValue(LHS, RHS)) {
5797 if (ICmpInst::isTrueWhenEqual(Pred))
5798 goto trivially_true;
5799 if (ICmpInst::isFalseWhenEqual(Pred))
5800 goto trivially_false;
5803 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5804 // adding or subtracting 1 from one of the operands.
5806 case ICmpInst::ICMP_SLE:
5807 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5808 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5810 Pred = ICmpInst::ICMP_SLT;
5812 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5813 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5815 Pred = ICmpInst::ICMP_SLT;
5819 case ICmpInst::ICMP_SGE:
5820 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5821 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5823 Pred = ICmpInst::ICMP_SGT;
5825 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5826 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5828 Pred = ICmpInst::ICMP_SGT;
5832 case ICmpInst::ICMP_ULE:
5833 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5834 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5836 Pred = ICmpInst::ICMP_ULT;
5838 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5839 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5841 Pred = ICmpInst::ICMP_ULT;
5845 case ICmpInst::ICMP_UGE:
5846 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5847 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5849 Pred = ICmpInst::ICMP_UGT;
5851 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5852 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5854 Pred = ICmpInst::ICMP_UGT;
5862 // TODO: More simplifications are possible here.
5864 // Recursively simplify until we either hit a recursion limit or nothing
5867 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
5873 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5874 Pred = ICmpInst::ICMP_EQ;
5879 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5880 Pred = ICmpInst::ICMP_NE;
5884 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5885 return getSignedRange(S).getSignedMax().isNegative();
5888 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5889 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5892 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5893 return !getSignedRange(S).getSignedMin().isNegative();
5896 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5897 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5900 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5901 return isKnownNegative(S) || isKnownPositive(S);
5904 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5905 const SCEV *LHS, const SCEV *RHS) {
5906 // Canonicalize the inputs first.
5907 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5909 // If LHS or RHS is an addrec, check to see if the condition is true in
5910 // every iteration of the loop.
5911 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5912 if (isLoopEntryGuardedByCond(
5913 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5914 isLoopBackedgeGuardedByCond(
5915 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5917 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5918 if (isLoopEntryGuardedByCond(
5919 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5920 isLoopBackedgeGuardedByCond(
5921 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5924 // Otherwise see what can be done with known constant ranges.
5925 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5929 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5930 const SCEV *LHS, const SCEV *RHS) {
5931 if (HasSameValue(LHS, RHS))
5932 return ICmpInst::isTrueWhenEqual(Pred);
5934 // This code is split out from isKnownPredicate because it is called from
5935 // within isLoopEntryGuardedByCond.
5938 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5939 case ICmpInst::ICMP_SGT:
5940 Pred = ICmpInst::ICMP_SLT;
5941 std::swap(LHS, RHS);
5942 case ICmpInst::ICMP_SLT: {
5943 ConstantRange LHSRange = getSignedRange(LHS);
5944 ConstantRange RHSRange = getSignedRange(RHS);
5945 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5947 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5951 case ICmpInst::ICMP_SGE:
5952 Pred = ICmpInst::ICMP_SLE;
5953 std::swap(LHS, RHS);
5954 case ICmpInst::ICMP_SLE: {
5955 ConstantRange LHSRange = getSignedRange(LHS);
5956 ConstantRange RHSRange = getSignedRange(RHS);
5957 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5959 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5963 case ICmpInst::ICMP_UGT:
5964 Pred = ICmpInst::ICMP_ULT;
5965 std::swap(LHS, RHS);
5966 case ICmpInst::ICMP_ULT: {
5967 ConstantRange LHSRange = getUnsignedRange(LHS);
5968 ConstantRange RHSRange = getUnsignedRange(RHS);
5969 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5971 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5975 case ICmpInst::ICMP_UGE:
5976 Pred = ICmpInst::ICMP_ULE;
5977 std::swap(LHS, RHS);
5978 case ICmpInst::ICMP_ULE: {
5979 ConstantRange LHSRange = getUnsignedRange(LHS);
5980 ConstantRange RHSRange = getUnsignedRange(RHS);
5981 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5983 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5987 case ICmpInst::ICMP_NE: {
5988 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5990 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5993 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5994 if (isKnownNonZero(Diff))
5998 case ICmpInst::ICMP_EQ:
5999 // The check at the top of the function catches the case where
6000 // the values are known to be equal.
6006 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6007 /// protected by a conditional between LHS and RHS. This is used to
6008 /// to eliminate casts.
6010 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6011 ICmpInst::Predicate Pred,
6012 const SCEV *LHS, const SCEV *RHS) {
6013 // Interpret a null as meaning no loop, where there is obviously no guard
6014 // (interprocedural conditions notwithstanding).
6015 if (!L) return true;
6017 BasicBlock *Latch = L->getLoopLatch();
6021 BranchInst *LoopContinuePredicate =
6022 dyn_cast<BranchInst>(Latch->getTerminator());
6023 if (!LoopContinuePredicate ||
6024 LoopContinuePredicate->isUnconditional())
6027 return isImpliedCond(Pred, LHS, RHS,
6028 LoopContinuePredicate->getCondition(),
6029 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6032 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6033 /// by a conditional between LHS and RHS. This is used to help avoid max
6034 /// expressions in loop trip counts, and to eliminate casts.
6036 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6037 ICmpInst::Predicate Pred,
6038 const SCEV *LHS, const SCEV *RHS) {
6039 // Interpret a null as meaning no loop, where there is obviously no guard
6040 // (interprocedural conditions notwithstanding).
6041 if (!L) return false;
6043 // Starting at the loop predecessor, climb up the predecessor chain, as long
6044 // as there are predecessors that can be found that have unique successors
6045 // leading to the original header.
6046 for (std::pair<BasicBlock *, BasicBlock *>
6047 Pair(L->getLoopPredecessor(), L->getHeader());
6049 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6051 BranchInst *LoopEntryPredicate =
6052 dyn_cast<BranchInst>(Pair.first->getTerminator());
6053 if (!LoopEntryPredicate ||
6054 LoopEntryPredicate->isUnconditional())
6057 if (isImpliedCond(Pred, LHS, RHS,
6058 LoopEntryPredicate->getCondition(),
6059 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6066 /// RAII wrapper to prevent recursive application of isImpliedCond.
6067 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6068 /// currently evaluating isImpliedCond.
6069 struct MarkPendingLoopPredicate {
6071 DenseSet<Value*> &LoopPreds;
6074 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6075 : Cond(C), LoopPreds(LP) {
6076 Pending = !LoopPreds.insert(Cond).second;
6078 ~MarkPendingLoopPredicate() {
6080 LoopPreds.erase(Cond);
6084 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6085 /// and RHS is true whenever the given Cond value evaluates to true.
6086 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6087 const SCEV *LHS, const SCEV *RHS,
6088 Value *FoundCondValue,
6090 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6094 // Recursively handle And and Or conditions.
6095 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6096 if (BO->getOpcode() == Instruction::And) {
6098 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6099 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6100 } else if (BO->getOpcode() == Instruction::Or) {
6102 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6103 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6107 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6108 if (!ICI) return false;
6110 // Bail if the ICmp's operands' types are wider than the needed type
6111 // before attempting to call getSCEV on them. This avoids infinite
6112 // recursion, since the analysis of widening casts can require loop
6113 // exit condition information for overflow checking, which would
6115 if (getTypeSizeInBits(LHS->getType()) <
6116 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6119 // Now that we found a conditional branch that dominates the loop, check to
6120 // see if it is the comparison we are looking for.
6121 ICmpInst::Predicate FoundPred;
6123 FoundPred = ICI->getInversePredicate();
6125 FoundPred = ICI->getPredicate();
6127 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6128 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6130 // Balance the types. The case where FoundLHS' type is wider than
6131 // LHS' type is checked for above.
6132 if (getTypeSizeInBits(LHS->getType()) >
6133 getTypeSizeInBits(FoundLHS->getType())) {
6134 if (CmpInst::isSigned(Pred)) {
6135 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6136 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6138 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6139 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6143 // Canonicalize the query to match the way instcombine will have
6144 // canonicalized the comparison.
6145 if (SimplifyICmpOperands(Pred, LHS, RHS))
6147 return CmpInst::isTrueWhenEqual(Pred);
6148 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6149 if (FoundLHS == FoundRHS)
6150 return CmpInst::isFalseWhenEqual(Pred);
6152 // Check to see if we can make the LHS or RHS match.
6153 if (LHS == FoundRHS || RHS == FoundLHS) {
6154 if (isa<SCEVConstant>(RHS)) {
6155 std::swap(FoundLHS, FoundRHS);
6156 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6158 std::swap(LHS, RHS);
6159 Pred = ICmpInst::getSwappedPredicate(Pred);
6163 // Check whether the found predicate is the same as the desired predicate.
6164 if (FoundPred == Pred)
6165 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6167 // Check whether swapping the found predicate makes it the same as the
6168 // desired predicate.
6169 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6170 if (isa<SCEVConstant>(RHS))
6171 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6173 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6174 RHS, LHS, FoundLHS, FoundRHS);
6177 // Check whether the actual condition is beyond sufficient.
6178 if (FoundPred == ICmpInst::ICMP_EQ)
6179 if (ICmpInst::isTrueWhenEqual(Pred))
6180 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6182 if (Pred == ICmpInst::ICMP_NE)
6183 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6184 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6187 // Otherwise assume the worst.
6191 /// isImpliedCondOperands - Test whether the condition described by Pred,
6192 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6193 /// and FoundRHS is true.
6194 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6195 const SCEV *LHS, const SCEV *RHS,
6196 const SCEV *FoundLHS,
6197 const SCEV *FoundRHS) {
6198 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6199 FoundLHS, FoundRHS) ||
6200 // ~x < ~y --> x > y
6201 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6202 getNotSCEV(FoundRHS),
6203 getNotSCEV(FoundLHS));
6206 /// isImpliedCondOperandsHelper - Test whether the condition described by
6207 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6208 /// FoundLHS, and FoundRHS is true.
6210 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6211 const SCEV *LHS, const SCEV *RHS,
6212 const SCEV *FoundLHS,
6213 const SCEV *FoundRHS) {
6215 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6216 case ICmpInst::ICMP_EQ:
6217 case ICmpInst::ICMP_NE:
6218 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6221 case ICmpInst::ICMP_SLT:
6222 case ICmpInst::ICMP_SLE:
6223 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6224 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6227 case ICmpInst::ICMP_SGT:
6228 case ICmpInst::ICMP_SGE:
6229 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6230 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6233 case ICmpInst::ICMP_ULT:
6234 case ICmpInst::ICMP_ULE:
6235 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6236 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6239 case ICmpInst::ICMP_UGT:
6240 case ICmpInst::ICMP_UGE:
6241 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6242 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6250 /// getBECount - Subtract the end and start values and divide by the step,
6251 /// rounding up, to get the number of times the backedge is executed. Return
6252 /// CouldNotCompute if an intermediate computation overflows.
6253 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
6257 assert(!isKnownNegative(Step) &&
6258 "This code doesn't handle negative strides yet!");
6260 Type *Ty = Start->getType();
6262 // When Start == End, we have an exact BECount == 0. Short-circuit this case
6263 // here because SCEV may not be able to determine that the unsigned division
6264 // after rounding is zero.
6266 return getConstant(Ty, 0);
6268 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
6269 const SCEV *Diff = getMinusSCEV(End, Start);
6270 const SCEV *RoundUp = getAddExpr(Step, NegOne);
6272 // Add an adjustment to the difference between End and Start so that
6273 // the division will effectively round up.
6274 const SCEV *Add = getAddExpr(Diff, RoundUp);
6277 // Check Add for unsigned overflow.
6278 // TODO: More sophisticated things could be done here.
6279 Type *WideTy = IntegerType::get(getContext(),
6280 getTypeSizeInBits(Ty) + 1);
6281 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
6282 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
6283 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
6284 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
6285 return getCouldNotCompute();
6288 return getUDivExpr(Add, Step);
6291 /// HowManyLessThans - Return the number of times a backedge containing the
6292 /// specified less-than comparison will execute. If not computable, return
6293 /// CouldNotCompute.
6294 ScalarEvolution::ExitLimit
6295 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6296 const Loop *L, bool isSigned) {
6297 // Only handle: "ADDREC < LoopInvariant".
6298 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
6300 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
6301 if (!AddRec || AddRec->getLoop() != L)
6302 return getCouldNotCompute();
6304 // Check to see if we have a flag which makes analysis easy.
6305 bool NoWrap = isSigned ?
6306 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNW)) :
6307 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNW));
6309 if (AddRec->isAffine()) {
6310 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
6311 const SCEV *Step = AddRec->getStepRecurrence(*this);
6314 return getCouldNotCompute();
6315 if (Step->isOne()) {
6316 // With unit stride, the iteration never steps past the limit value.
6317 } else if (isKnownPositive(Step)) {
6318 // Test whether a positive iteration can step past the limit
6319 // value and past the maximum value for its type in a single step.
6320 // Note that it's not sufficient to check NoWrap here, because even
6321 // though the value after a wrap is undefined, it's not undefined
6322 // behavior, so if wrap does occur, the loop could either terminate or
6323 // loop infinitely, but in either case, the loop is guaranteed to
6324 // iterate at least until the iteration where the wrapping occurs.
6325 const SCEV *One = getConstant(Step->getType(), 1);
6327 APInt Max = APInt::getSignedMaxValue(BitWidth);
6328 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
6329 .slt(getSignedRange(RHS).getSignedMax()))
6330 return getCouldNotCompute();
6332 APInt Max = APInt::getMaxValue(BitWidth);
6333 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
6334 .ult(getUnsignedRange(RHS).getUnsignedMax()))
6335 return getCouldNotCompute();
6338 // TODO: Handle negative strides here and below.
6339 return getCouldNotCompute();
6341 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6342 // m. So, we count the number of iterations in which {n,+,s} < m is true.
6343 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6344 // treat m-n as signed nor unsigned due to overflow possibility.
6346 // First, we get the value of the LHS in the first iteration: n
6347 const SCEV *Start = AddRec->getOperand(0);
6349 // Determine the minimum constant start value.
6350 const SCEV *MinStart = getConstant(isSigned ?
6351 getSignedRange(Start).getSignedMin() :
6352 getUnsignedRange(Start).getUnsignedMin());
6354 // If we know that the condition is true in order to enter the loop,
6355 // then we know that it will run exactly (m-n)/s times. Otherwise, we
6356 // only know that it will execute (max(m,n)-n)/s times. In both cases,
6357 // the division must round up.
6358 const SCEV *End = RHS;
6359 if (!isLoopEntryGuardedByCond(L,
6360 isSigned ? ICmpInst::ICMP_SLT :
6362 getMinusSCEV(Start, Step), RHS))
6363 End = isSigned ? getSMaxExpr(RHS, Start)
6364 : getUMaxExpr(RHS, Start);
6366 // Determine the maximum constant end value.
6367 const SCEV *MaxEnd = getConstant(isSigned ?
6368 getSignedRange(End).getSignedMax() :
6369 getUnsignedRange(End).getUnsignedMax());
6371 // If MaxEnd is within a step of the maximum integer value in its type,
6372 // adjust it down to the minimum value which would produce the same effect.
6373 // This allows the subsequent ceiling division of (N+(step-1))/step to
6374 // compute the correct value.
6375 const SCEV *StepMinusOne = getMinusSCEV(Step,
6376 getConstant(Step->getType(), 1));
6379 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6382 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6385 // Finally, we subtract these two values and divide, rounding up, to get
6386 // the number of times the backedge is executed.
6387 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6389 // The maximum backedge count is similar, except using the minimum start
6390 // value and the maximum end value.
6391 // If we already have an exact constant BECount, use it instead.
6392 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6393 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6395 // If the stride is nonconstant, and NoWrap == true, then
6396 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6397 // exact BECount and invalid MaxBECount, which should be avoided to catch
6398 // more optimization opportunities.
6399 if (isa<SCEVCouldNotCompute>(MaxBECount))
6400 MaxBECount = BECount;
6402 return ExitLimit(BECount, MaxBECount);
6405 return getCouldNotCompute();
6408 /// getNumIterationsInRange - Return the number of iterations of this loop that
6409 /// produce values in the specified constant range. Another way of looking at
6410 /// this is that it returns the first iteration number where the value is not in
6411 /// the condition, thus computing the exit count. If the iteration count can't
6412 /// be computed, an instance of SCEVCouldNotCompute is returned.
6413 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6414 ScalarEvolution &SE) const {
6415 if (Range.isFullSet()) // Infinite loop.
6416 return SE.getCouldNotCompute();
6418 // If the start is a non-zero constant, shift the range to simplify things.
6419 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6420 if (!SC->getValue()->isZero()) {
6421 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6422 Operands[0] = SE.getConstant(SC->getType(), 0);
6423 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6424 getNoWrapFlags(FlagNW));
6425 if (const SCEVAddRecExpr *ShiftedAddRec =
6426 dyn_cast<SCEVAddRecExpr>(Shifted))
6427 return ShiftedAddRec->getNumIterationsInRange(
6428 Range.subtract(SC->getValue()->getValue()), SE);
6429 // This is strange and shouldn't happen.
6430 return SE.getCouldNotCompute();
6433 // The only time we can solve this is when we have all constant indices.
6434 // Otherwise, we cannot determine the overflow conditions.
6435 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6436 if (!isa<SCEVConstant>(getOperand(i)))
6437 return SE.getCouldNotCompute();
6440 // Okay at this point we know that all elements of the chrec are constants and
6441 // that the start element is zero.
6443 // First check to see if the range contains zero. If not, the first
6445 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6446 if (!Range.contains(APInt(BitWidth, 0)))
6447 return SE.getConstant(getType(), 0);
6450 // If this is an affine expression then we have this situation:
6451 // Solve {0,+,A} in Range === Ax in Range
6453 // We know that zero is in the range. If A is positive then we know that
6454 // the upper value of the range must be the first possible exit value.
6455 // If A is negative then the lower of the range is the last possible loop
6456 // value. Also note that we already checked for a full range.
6457 APInt One(BitWidth,1);
6458 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6459 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6461 // The exit value should be (End+A)/A.
6462 APInt ExitVal = (End + A).udiv(A);
6463 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6465 // Evaluate at the exit value. If we really did fall out of the valid
6466 // range, then we computed our trip count, otherwise wrap around or other
6467 // things must have happened.
6468 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6469 if (Range.contains(Val->getValue()))
6470 return SE.getCouldNotCompute(); // Something strange happened
6472 // Ensure that the previous value is in the range. This is a sanity check.
6473 assert(Range.contains(
6474 EvaluateConstantChrecAtConstant(this,
6475 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6476 "Linear scev computation is off in a bad way!");
6477 return SE.getConstant(ExitValue);
6478 } else if (isQuadratic()) {
6479 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6480 // quadratic equation to solve it. To do this, we must frame our problem in
6481 // terms of figuring out when zero is crossed, instead of when
6482 // Range.getUpper() is crossed.
6483 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6484 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6485 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6486 // getNoWrapFlags(FlagNW)
6489 // Next, solve the constructed addrec
6490 std::pair<const SCEV *,const SCEV *> Roots =
6491 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6492 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6493 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6495 // Pick the smallest positive root value.
6496 if (ConstantInt *CB =
6497 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6498 R1->getValue(), R2->getValue()))) {
6499 if (CB->getZExtValue() == false)
6500 std::swap(R1, R2); // R1 is the minimum root now.
6502 // Make sure the root is not off by one. The returned iteration should
6503 // not be in the range, but the previous one should be. When solving
6504 // for "X*X < 5", for example, we should not return a root of 2.
6505 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6508 if (Range.contains(R1Val->getValue())) {
6509 // The next iteration must be out of the range...
6510 ConstantInt *NextVal =
6511 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6513 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6514 if (!Range.contains(R1Val->getValue()))
6515 return SE.getConstant(NextVal);
6516 return SE.getCouldNotCompute(); // Something strange happened
6519 // If R1 was not in the range, then it is a good return value. Make
6520 // sure that R1-1 WAS in the range though, just in case.
6521 ConstantInt *NextVal =
6522 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6523 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6524 if (Range.contains(R1Val->getValue()))
6526 return SE.getCouldNotCompute(); // Something strange happened
6531 return SE.getCouldNotCompute();
6536 //===----------------------------------------------------------------------===//
6537 // SCEVCallbackVH Class Implementation
6538 //===----------------------------------------------------------------------===//
6540 void ScalarEvolution::SCEVCallbackVH::deleted() {
6541 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6542 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6543 SE->ConstantEvolutionLoopExitValue.erase(PN);
6544 SE->ValueExprMap.erase(getValPtr());
6545 // this now dangles!
6548 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6549 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6551 // Forget all the expressions associated with users of the old value,
6552 // so that future queries will recompute the expressions using the new
6554 Value *Old = getValPtr();
6555 SmallVector<User *, 16> Worklist;
6556 SmallPtrSet<User *, 8> Visited;
6557 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6559 Worklist.push_back(*UI);
6560 while (!Worklist.empty()) {
6561 User *U = Worklist.pop_back_val();
6562 // Deleting the Old value will cause this to dangle. Postpone
6563 // that until everything else is done.
6566 if (!Visited.insert(U))
6568 if (PHINode *PN = dyn_cast<PHINode>(U))
6569 SE->ConstantEvolutionLoopExitValue.erase(PN);
6570 SE->ValueExprMap.erase(U);
6571 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6573 Worklist.push_back(*UI);
6575 // Delete the Old value.
6576 if (PHINode *PN = dyn_cast<PHINode>(Old))
6577 SE->ConstantEvolutionLoopExitValue.erase(PN);
6578 SE->ValueExprMap.erase(Old);
6579 // this now dangles!
6582 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6583 : CallbackVH(V), SE(se) {}
6585 //===----------------------------------------------------------------------===//
6586 // ScalarEvolution Class Implementation
6587 //===----------------------------------------------------------------------===//
6589 ScalarEvolution::ScalarEvolution()
6590 : FunctionPass(ID), FirstUnknown(0) {
6591 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6594 bool ScalarEvolution::runOnFunction(Function &F) {
6596 LI = &getAnalysis<LoopInfo>();
6597 TD = getAnalysisIfAvailable<TargetData>();
6598 TLI = &getAnalysis<TargetLibraryInfo>();
6599 DT = &getAnalysis<DominatorTree>();
6603 void ScalarEvolution::releaseMemory() {
6604 // Iterate through all the SCEVUnknown instances and call their
6605 // destructors, so that they release their references to their values.
6606 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6610 ValueExprMap.clear();
6612 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6613 // that a loop had multiple computable exits.
6614 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6615 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6620 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
6622 BackedgeTakenCounts.clear();
6623 ConstantEvolutionLoopExitValue.clear();
6624 ValuesAtScopes.clear();
6625 LoopDispositions.clear();
6626 BlockDispositions.clear();
6627 UnsignedRanges.clear();
6628 SignedRanges.clear();
6629 UniqueSCEVs.clear();
6630 SCEVAllocator.Reset();
6633 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6634 AU.setPreservesAll();
6635 AU.addRequiredTransitive<LoopInfo>();
6636 AU.addRequiredTransitive<DominatorTree>();
6637 AU.addRequired<TargetLibraryInfo>();
6640 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6641 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6644 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6646 // Print all inner loops first
6647 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6648 PrintLoopInfo(OS, SE, *I);
6651 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6654 SmallVector<BasicBlock *, 8> ExitBlocks;
6655 L->getExitBlocks(ExitBlocks);
6656 if (ExitBlocks.size() != 1)
6657 OS << "<multiple exits> ";
6659 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6660 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6662 OS << "Unpredictable backedge-taken count. ";
6667 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6670 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6671 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6673 OS << "Unpredictable max backedge-taken count. ";
6679 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6680 // ScalarEvolution's implementation of the print method is to print
6681 // out SCEV values of all instructions that are interesting. Doing
6682 // this potentially causes it to create new SCEV objects though,
6683 // which technically conflicts with the const qualifier. This isn't
6684 // observable from outside the class though, so casting away the
6685 // const isn't dangerous.
6686 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6688 OS << "Classifying expressions for: ";
6689 WriteAsOperand(OS, F, /*PrintType=*/false);
6691 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6692 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6695 const SCEV *SV = SE.getSCEV(&*I);
6698 const Loop *L = LI->getLoopFor((*I).getParent());
6700 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6707 OS << "\t\t" "Exits: ";
6708 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6709 if (!SE.isLoopInvariant(ExitValue, L)) {
6710 OS << "<<Unknown>>";
6719 OS << "Determining loop execution counts for: ";
6720 WriteAsOperand(OS, F, /*PrintType=*/false);
6722 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6723 PrintLoopInfo(OS, &SE, *I);
6726 ScalarEvolution::LoopDisposition
6727 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6728 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6729 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6730 Values.insert(std::make_pair(L, LoopVariant));
6732 return Pair.first->second;
6734 LoopDisposition D = computeLoopDisposition(S, L);
6735 return LoopDispositions[S][L] = D;
6738 ScalarEvolution::LoopDisposition
6739 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6740 switch (S->getSCEVType()) {
6742 return LoopInvariant;
6746 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6747 case scAddRecExpr: {
6748 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6750 // If L is the addrec's loop, it's computable.
6751 if (AR->getLoop() == L)
6752 return LoopComputable;
6754 // Add recurrences are never invariant in the function-body (null loop).
6758 // This recurrence is variant w.r.t. L if L contains AR's loop.
6759 if (L->contains(AR->getLoop()))
6762 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6763 if (AR->getLoop()->contains(L))
6764 return LoopInvariant;
6766 // This recurrence is variant w.r.t. L if any of its operands
6768 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6770 if (!isLoopInvariant(*I, L))
6773 // Otherwise it's loop-invariant.
6774 return LoopInvariant;
6780 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6781 bool HasVarying = false;
6782 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6784 LoopDisposition D = getLoopDisposition(*I, L);
6785 if (D == LoopVariant)
6787 if (D == LoopComputable)
6790 return HasVarying ? LoopComputable : LoopInvariant;
6793 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6794 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6795 if (LD == LoopVariant)
6797 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6798 if (RD == LoopVariant)
6800 return (LD == LoopInvariant && RD == LoopInvariant) ?
6801 LoopInvariant : LoopComputable;
6804 // All non-instruction values are loop invariant. All instructions are loop
6805 // invariant if they are not contained in the specified loop.
6806 // Instructions are never considered invariant in the function body
6807 // (null loop) because they are defined within the "loop".
6808 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6809 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6810 return LoopInvariant;
6811 case scCouldNotCompute:
6812 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6813 default: llvm_unreachable("Unknown SCEV kind!");
6817 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6818 return getLoopDisposition(S, L) == LoopInvariant;
6821 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6822 return getLoopDisposition(S, L) == LoopComputable;
6825 ScalarEvolution::BlockDisposition
6826 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6827 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6828 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6829 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6831 return Pair.first->second;
6833 BlockDisposition D = computeBlockDisposition(S, BB);
6834 return BlockDispositions[S][BB] = D;
6837 ScalarEvolution::BlockDisposition
6838 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6839 switch (S->getSCEVType()) {
6841 return ProperlyDominatesBlock;
6845 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6846 case scAddRecExpr: {
6847 // This uses a "dominates" query instead of "properly dominates" query
6848 // to test for proper dominance too, because the instruction which
6849 // produces the addrec's value is a PHI, and a PHI effectively properly
6850 // dominates its entire containing block.
6851 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6852 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6853 return DoesNotDominateBlock;
6855 // FALL THROUGH into SCEVNAryExpr handling.
6860 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6862 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6864 BlockDisposition D = getBlockDisposition(*I, BB);
6865 if (D == DoesNotDominateBlock)
6866 return DoesNotDominateBlock;
6867 if (D == DominatesBlock)
6870 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6873 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6874 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6875 BlockDisposition LD = getBlockDisposition(LHS, BB);
6876 if (LD == DoesNotDominateBlock)
6877 return DoesNotDominateBlock;
6878 BlockDisposition RD = getBlockDisposition(RHS, BB);
6879 if (RD == DoesNotDominateBlock)
6880 return DoesNotDominateBlock;
6881 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6882 ProperlyDominatesBlock : DominatesBlock;
6885 if (Instruction *I =
6886 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6887 if (I->getParent() == BB)
6888 return DominatesBlock;
6889 if (DT->properlyDominates(I->getParent(), BB))
6890 return ProperlyDominatesBlock;
6891 return DoesNotDominateBlock;
6893 return ProperlyDominatesBlock;
6894 case scCouldNotCompute:
6895 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6897 llvm_unreachable("Unknown SCEV kind!");
6901 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6902 return getBlockDisposition(S, BB) >= DominatesBlock;
6905 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6906 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6909 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6910 SmallVector<const SCEV *, 8> Worklist;
6911 Worklist.push_back(S);
6913 S = Worklist.pop_back_val();
6915 switch (S->getSCEVType()) {
6920 case scSignExtend: {
6921 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
6922 const SCEV *CastOp = Cast->getOperand();
6925 Worklist.push_back(CastOp);
6933 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6934 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6936 const SCEV *NAryOp = *I;
6939 Worklist.push_back(NAryOp);
6944 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6945 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6946 if (LHS == Op || RHS == Op)
6948 Worklist.push_back(LHS);
6949 Worklist.push_back(RHS);
6954 case scCouldNotCompute:
6955 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6957 llvm_unreachable("Unknown SCEV kind!");
6959 } while (!Worklist.empty());
6964 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6965 ValuesAtScopes.erase(S);
6966 LoopDispositions.erase(S);
6967 BlockDispositions.erase(S);
6968 UnsignedRanges.erase(S);
6969 SignedRanges.erase(S);